fof(t95_enumset1,theorem,(
    ! [A,B] : k6_enumset1(A,A,A,A,A,A,A,B) = k2_tarski(A,B) ),
    inference(mizar_proof,[status(thm)],[t93_enumset1,t70_enumset1]),
    [file(enumset1,t95_enumset1),interesting(1.00)]).

fof(t93_enumset1,theorem,(
    ! [A,B,C] : k6_enumset1(A,A,A,A,A,A,B,C) = k1_enumset1(A,B,C) ),
    inference(mizar_proof,[status(thm)],[t90_enumset1,t71_enumset1]),
    [file(enumset1,t93_enumset1),interesting(0.98)]).

fof(t96_enumset1,theorem,(
    ! [A] : k6_enumset1(A,A,A,A,A,A,A,A) = k1_tarski(A) ),
    inference(mizar_proof,[status(thm)],[t95_enumset1,t69_enumset1]),
    [file(enumset1,t96_enumset1),interesting(0.98)]).

fof(t90_enumset1,theorem,(
    ! [A,B,C,D] : k6_enumset1(A,A,A,A,A,B,C,D) = k2_enumset1(A,B,C,D) ),
    inference(mizar_proof,[status(thm)],[t86_enumset1,t72_enumset1]),
    [file(enumset1,t90_enumset1),interesting(0.97)]).

fof(t86_enumset1,theorem,(
    ! [A,B,C,D,E] : k6_enumset1(A,A,A,A,B,C,D,E) = k3_enumset1(A,B,C,D,E) ),
    inference(mizar_proof,[status(thm)],[t81_enumset1,t73_enumset1]),
    [file(enumset1,t86_enumset1),interesting(0.94)]).

fof(t92_enumset1,theorem,(
    ! [A,B] : k5_enumset1(A,A,A,A,A,A,B) = k2_tarski(A,B) ),
    inference(mizar_proof,[status(thm)],[t89_enumset1,t70_enumset1]),
    [file(enumset1,t92_enumset1),interesting(0.93)]).

fof(t89_enumset1,theorem,(
    ! [A,B,C] : k5_enumset1(A,A,A,A,A,B,C) = k1_enumset1(A,B,C) ),
    inference(mizar_proof,[status(thm)],[t85_enumset1,t71_enumset1]),
    [file(enumset1,t89_enumset1),interesting(0.92)]).

fof(t81_enumset1,theorem,(
    ! [A,B,C,D,E,F] : k6_enumset1(A,A,A,B,C,D,E,F) = k4_enumset1(A,B,C,D,E,F) ),
    inference(mizar_proof,[status(thm)],[t75_enumset1,t74_enumset1]),
    [file(enumset1,t81_enumset1),interesting(0.91)]).

fof(t85_enumset1,theorem,(
    ! [A,B,C,D] : k5_enumset1(A,A,A,A,B,C,D) = k2_enumset1(A,B,C,D) ),
    inference(mizar_proof,[status(thm)],[t80_enumset1,t72_enumset1]),
    [file(enumset1,t85_enumset1),interesting(0.90)]).

fof(t94_enumset1,theorem,(
    ! [A] : k5_enumset1(A,A,A,A,A,A,A) = k1_tarski(A) ),
    inference(mizar_proof,[status(thm)],[t92_enumset1,t69_enumset1]),
    [file(enumset1,t94_enumset1),interesting(0.90)]).

fof(t80_enumset1,theorem,(
    ! [A,B,C,D,E] : k5_enumset1(A,A,A,B,C,D,E) = k3_enumset1(A,B,C,D,E) ),
    inference(mizar_proof,[status(thm)],[t74_enumset1,t73_enumset1]),
    [file(enumset1,t80_enumset1),interesting(0.88)]).

fof(t125_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_enumset1(D,C,B,A) ),
    inference(mizar_proof,[status(thm)],[t119_enumset1,t108_enumset1]),
    [file(enumset1,t125_enumset1),interesting(0.87)]).

fof(t88_enumset1,theorem,(
    ! [A,B] : k4_enumset1(A,A,A,A,A,B) = k2_tarski(A,B) ),
    inference(mizar_proof,[status(thm)],[t84_enumset1,t70_enumset1]),
    [file(enumset1,t88_enumset1),interesting(0.87)]).

fof(t119_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_enumset1(C,D,B,A) ),
    inference(mizar_proof,[status(thm)],[l127_enumset1,t105_enumset1]),
    [file(enumset1,t119_enumset1),interesting(0.86)]).

fof(t123_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_enumset1(D,B,C,A) ),
    inference(mizar_proof,[status(thm)],[t119_enumset1,l121_enumset1]),
    [file(enumset1,t123_enumset1),interesting(0.86)]).

fof(t84_enumset1,theorem,(
    ! [A,B,C] : k4_enumset1(A,A,A,A,B,C) = k1_enumset1(A,B,C) ),
    inference(mizar_proof,[status(thm)],[t79_enumset1,t71_enumset1]),
    [file(enumset1,t84_enumset1),interesting(0.85)]).

fof(t75_enumset1,theorem,(
    ! [A,B,C,D,E,F,G] : k6_enumset1(A,A,B,C,D,E,F,G) = k5_enumset1(A,B,C,D,E,F,G) ),
    inference(mizar_proof,[status(thm)],[t63_enumset1,t69_enumset1,t56_enumset1]),
    [file(enumset1,t75_enumset1),interesting(0.85)]).

fof(t79_enumset1,theorem,(
    ! [A,B,C,D] : k4_enumset1(A,A,A,B,C,D) = k2_enumset1(A,B,C,D) ),
    inference(mizar_proof,[status(thm)],[t73_enumset1,t72_enumset1]),
    [file(enumset1,t79_enumset1),interesting(0.84)]).

fof(t74_enumset1,theorem,(
    ! [A,B,C,D,E,F] : k5_enumset1(A,A,B,C,D,E,F) = k4_enumset1(A,B,C,D,E,F) ),
    inference(mizar_proof,[status(thm)],[t57_enumset1,t69_enumset1,t51_enumset1]),
    [file(enumset1,t74_enumset1),interesting(0.84)]).

fof(l121_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_enumset1(B,C,A,D) ),
    inference(mizar_proof,[status(thm)],[t46_enumset1,t100_enumset1,t46_enumset1]),
    [file(enumset1,l121_enumset1),interesting(0.82)]).

fof(l127_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_enumset1(C,B,A,D) ),
    inference(mizar_proof,[status(thm)],[t46_enumset1,t102_enumset1,t46_enumset1]),
    [file(enumset1,l127_enumset1),interesting(0.82)]).

fof(t118_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_enumset1(C,D,A,B) ),
    inference(mizar_proof,[status(thm)],[l127_enumset1,t107_enumset1]),
    [file(enumset1,t118_enumset1),interesting(0.82)]).

fof(t108_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_enumset1(B,A,C,D) ),
    inference(mizar_proof,[status(thm)],[t46_enumset1,t99_enumset1,t46_enumset1]),
    [file(enumset1,t108_enumset1),interesting(0.82)]).

fof(t91_enumset1,theorem,(
    ! [A] : k4_enumset1(A,A,A,A,A,A) = k1_tarski(A) ),
    inference(mizar_proof,[status(thm)],[t88_enumset1,t69_enumset1]),
    [file(enumset1,t91_enumset1),interesting(0.82)]).

fof(t107_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_enumset1(A,D,C,B) ),
    inference(mizar_proof,[status(thm)],[t44_enumset1,t102_enumset1,t44_enumset1]),
    [file(enumset1,t107_enumset1),interesting(0.81)]).

fof(t112_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_enumset1(B,D,A,C) ),
    inference(mizar_proof,[status(thm)],[l121_enumset1,t107_enumset1]),
    [file(enumset1,t112_enumset1),interesting(0.81)]).

fof(t83_enumset1,theorem,(
    ! [A,B] : k3_enumset1(A,A,A,A,B) = k2_tarski(A,B) ),
    inference(mizar_proof,[status(thm)],[t78_enumset1,t70_enumset1]),
    [file(enumset1,t83_enumset1),interesting(0.81)]).

fof(t73_enumset1,theorem,(
    ! [A,B,C,D,E] : k4_enumset1(A,A,B,C,D,E) = k3_enumset1(A,B,C,D,E) ),
    inference(mizar_proof,[status(thm)],[t52_enumset1,t69_enumset1,t47_enumset1]),
    [file(enumset1,t73_enumset1),interesting(0.81)]).

fof(t105_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_enumset1(A,C,D,B) ),
    inference(mizar_proof,[status(thm)],[t44_enumset1,t100_enumset1,t44_enumset1]),
    [file(enumset1,t105_enumset1),interesting(0.80)]).

fof(t109_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_enumset1(B,A,D,C) ),
    inference(mizar_proof,[status(thm)],[l121_enumset1,t105_enumset1]),
    [file(enumset1,t109_enumset1),interesting(0.80)]).

fof(t103_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_enumset1(A,B,D,C) ),
    inference(mizar_proof,[status(thm)],[t44_enumset1,t98_enumset1,t44_enumset1]),
    [file(enumset1,t103_enumset1),interesting(0.80)]).

fof(t113_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_enumset1(B,D,C,A) ),
    inference(mizar_proof,[status(thm)],[l121_enumset1,t105_enumset1]),
    [file(enumset1,t113_enumset1),interesting(0.80)]).

fof(t117_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_enumset1(C,B,D,A) ),
    inference(mizar_proof,[status(thm)],[l127_enumset1,t103_enumset1]),
    [file(enumset1,t117_enumset1),interesting(0.80)]).

fof(t78_enumset1,theorem,(
    ! [A,B,C] : k3_enumset1(A,A,A,B,C) = k1_enumset1(A,B,C) ),
    inference(mizar_proof,[status(thm)],[t72_enumset1,t71_enumset1]),
    [file(enumset1,t78_enumset1),interesting(0.80)]).

fof(t111_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_enumset1(B,C,D,A) ),
    inference(mizar_proof,[status(thm)],[l121_enumset1,t103_enumset1]),
    [file(enumset1,t111_enumset1),interesting(0.79)]).

fof(t99_enumset1,theorem,(
    ! [A,B,C] : k1_enumset1(A,B,C) = k1_enumset1(B,A,C) ),
    inference(mizar_proof,[status(thm)],[t43_enumset1,t43_enumset1]),
    [file(enumset1,t99_enumset1),interesting(0.78)]).

fof(t100_enumset1,theorem,(
    ! [A,B,C] : k1_enumset1(A,B,C) = k1_enumset1(B,C,A) ),
    inference(mizar_proof,[status(thm)],[t42_enumset1,t43_enumset1]),
    [file(enumset1,t100_enumset1),interesting(0.78)]).

fof(t102_enumset1,theorem,(
    ! [A,B,C] : k1_enumset1(A,B,C) = k1_enumset1(C,B,A) ),
    inference(mizar_proof,[status(thm)],[t100_enumset1,t98_enumset1]),
    [file(enumset1,t102_enumset1),interesting(0.78)]).

fof(t72_enumset1,theorem,(
    ! [A,B,C,D] : k3_enumset1(A,A,B,C,D) = k2_enumset1(A,B,C,D) ),
    inference(mizar_proof,[status(thm)],[t48_enumset1,t69_enumset1,t44_enumset1]),
    [file(enumset1,t72_enumset1),interesting(0.78)]).

fof(t116_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_enumset1(C,B,A,D) ),
    inference(mizar_proof,[status(thm)],[l127_enumset1]),
    [file(enumset1,t116_enumset1),interesting(0.77)]).

fof(t77_enumset1,theorem,(
    ! [A,B] : k2_enumset1(A,A,A,B) = k2_tarski(A,B) ),
    inference(mizar_proof,[status(thm)],[t71_enumset1,t70_enumset1]),
    [file(enumset1,t77_enumset1),interesting(0.77)]).

fof(t110_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_enumset1(B,C,A,D) ),
    inference(mizar_proof,[status(thm)],[l121_enumset1]),
    [file(enumset1,t110_enumset1),interesting(0.76)]).

fof(t87_enumset1,theorem,(
    ! [A] : k3_enumset1(A,A,A,A,A) = k1_tarski(A) ),
    inference(mizar_proof,[status(thm)],[t83_enumset1,t69_enumset1]),
    [file(enumset1,t87_enumset1),interesting(0.76)]).

fof(t104_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_enumset1(A,C,B,D) ),
    inference(mizar_proof,[status(thm)],[t44_enumset1,t99_enumset1,t44_enumset1]),
    [file(enumset1,t104_enumset1),interesting(0.75)]).

fof(t98_enumset1,theorem,(
    ! [A,B,C] : k1_enumset1(A,B,C) = k1_enumset1(A,C,B) ),
    inference(mizar_proof,[status(thm)],[t42_enumset1,t42_enumset1]),
    [file(enumset1,t98_enumset1),interesting(0.74)]).

fof(t70_enumset1,theorem,(
    ! [A,B] : k1_enumset1(A,A,B) = k2_tarski(A,B) ),
    inference(mizar_proof,[status(thm)],[t43_enumset1,t69_enumset1,t41_enumset1]),
    [file(enumset1,t70_enumset1),interesting(0.74)]).

fof(t71_enumset1,theorem,(
    ! [A,B,C] : k2_enumset1(A,A,B,C) = k1_enumset1(A,B,C) ),
    inference(mizar_proof,[status(thm)],[l51_enumset1,t69_enumset1,t42_enumset1]),
    [file(enumset1,t71_enumset1),interesting(0.72)]).

fof(t82_enumset1,theorem,(
    ! [A] : k2_enumset1(A,A,A,A) = k1_tarski(A) ),
    inference(mizar_proof,[status(thm)],[t77_enumset1,t69_enumset1]),
    [file(enumset1,t82_enumset1),interesting(0.70)]).

fof(t76_enumset1,theorem,(
    ! [A] : k1_enumset1(A,A,A) = k1_tarski(A) ),
    inference(mizar_proof,[status(thm)],[t70_enumset1,t69_enumset1]),
    [file(enumset1,t76_enumset1),interesting(0.67)]).

fof(t69_enumset1,theorem,(
    ! [A] : k2_tarski(A,A) = k1_tarski(A) ),
    inference(mizar_proof,[status(thm)],[d2_tarski,d1_tarski,t2_tarski]),
    [file(enumset1,t69_enumset1),interesting(0.66)]).

fof(l73_enumset1,theorem,(
    ! [A,B,C,D,E,F,G,H] : k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k2_enumset1(A,B,C,D),k2_enumset1(E,F,G,H)) ),
    inference(mizar_proof,[status(thm)],[d2_enumset1,d2_enumset1,d6_enumset1,d2_xboole_0,t2_tarski]),
    [file(enumset1,l73_enumset1),interesting(0.45)]).

fof(l60_enumset1,theorem,(
    ! [A,B,C,D,E,F] : k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k1_enumset1(A,B,C),k1_enumset1(D,E,F)) ),
    inference(mizar_proof,[status(thm)],[d4_enumset1,d1_enumset1,d2_xboole_0,t2_tarski]),
    [file(enumset1,l60_enumset1),interesting(0.43)]).

fof(t63_enumset1,theorem,(
    ! [A,B,C,D,E,F,G,H] : k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k2_tarski(A,B),k4_enumset1(C,D,E,F,G,H)) ),
    inference(mizar_proof,[status(thm)],[l73_enumset1,l51_enumset1,t4_xboole_1,t52_enumset1]),
    [file(enumset1,t63_enumset1),interesting(0.42)]).

fof(l51_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_xboole_0(k2_tarski(A,B),k2_tarski(C,D)) ),
    inference(mizar_proof,[status(thm)],[d2_enumset1,d2_tarski,d2_xboole_0,t2_tarski]),
    [file(enumset1,l51_enumset1),interesting(0.41)]).

fof(t58_enumset1,theorem,(
    ! [A,B,C,D,E,F,G] : k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k1_enumset1(A,B,C),k2_enumset1(D,E,F,G)) ),
    inference(mizar_proof,[status(thm)],[l66_enumset1,t46_enumset1,t4_xboole_1,t44_enumset1]),
    [file(enumset1,t58_enumset1),interesting(0.40)]).

fof(t57_enumset1,theorem,(
    ! [A,B,C,D,E,F,G] : k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k2_tarski(A,B),k3_enumset1(C,D,E,F,G)) ),
    inference(mizar_proof,[status(thm)],[l66_enumset1,l51_enumset1,t4_xboole_1,t48_enumset1]),
    [file(enumset1,t57_enumset1),interesting(0.40)]).

fof(t56_enumset1,theorem,(
    ! [A,B,C,D,E,F,G] : k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k1_tarski(A),k4_enumset1(B,C,D,E,F,G)) ),
    inference(mizar_proof,[status(thm)],[l66_enumset1,t44_enumset1,t4_xboole_1,l60_enumset1]),
    [file(enumset1,t56_enumset1),interesting(0.40)]).

fof(t41_enumset1,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_xboole_0(k1_tarski(A),k1_tarski(B)) ),
    inference(mizar_proof,[status(thm)],[d2_tarski,d1_tarski,d2_xboole_0,t2_tarski]),
    [file(enumset1,t41_enumset1),interesting(0.39)]).

fof(t51_enumset1,theorem,(
    ! [A,B,C,D,E,F] : k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k1_tarski(A),k3_enumset1(B,C,D,E,F)) ),
    inference(mizar_proof,[status(thm)],[l60_enumset1,t42_enumset1,t4_xboole_1,t48_enumset1]),
    [file(enumset1,t51_enumset1),interesting(0.39)]).

fof(t50_enumset1,theorem,(
    ! [A,B,C,D,E] : k3_enumset1(A,B,C,D,E) = k2_xboole_0(k2_enumset1(A,B,C,D),k1_tarski(E)) ),
    inference(mizar_proof,[status(thm)],[l55_enumset1,t41_enumset1,t4_xboole_1,t46_enumset1]),
    [file(enumset1,t50_enumset1),interesting(0.38)]).

fof(t54_enumset1,theorem,(
    ! [A,B,C,D,E,F] : k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k2_enumset1(A,B,C,D),k2_tarski(E,F)) ),
    inference(mizar_proof,[status(thm)],[l60_enumset1,t42_enumset1,t4_xboole_1,t46_enumset1]),
    [file(enumset1,t54_enumset1),interesting(0.38)]).

fof(t52_enumset1,theorem,(
    ! [A,B,C,D,E,F] : k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k2_tarski(A,B),k2_enumset1(C,D,E,F)) ),
    inference(mizar_proof,[status(thm)],[l60_enumset1,t43_enumset1,t4_xboole_1,t44_enumset1]),
    [file(enumset1,t52_enumset1),interesting(0.38)]).

fof(t47_enumset1,theorem,(
    ! [A,B,C,D,E] : k3_enumset1(A,B,C,D,E) = k2_xboole_0(k1_tarski(A),k2_enumset1(B,C,D,E)) ),
    inference(mizar_proof,[status(thm)],[l55_enumset1,t42_enumset1,t4_xboole_1,l51_enumset1]),
    [file(enumset1,t47_enumset1),interesting(0.37)]).

fof(t46_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_xboole_0(k1_enumset1(A,B,C),k1_tarski(D)) ),
    inference(mizar_proof,[status(thm)],[l51_enumset1,t41_enumset1,t4_xboole_1,t43_enumset1]),
    [file(enumset1,t46_enumset1),interesting(0.36)]).

fof(t48_enumset1,theorem,(
    ! [A,B,C,D,E] : k3_enumset1(A,B,C,D,E) = k2_xboole_0(k2_tarski(A,B),k1_enumset1(C,D,E)) ),
    inference(mizar_proof,[status(thm)],[l55_enumset1,t43_enumset1,t4_xboole_1,t42_enumset1]),
    [file(enumset1,t48_enumset1),interesting(0.36)]).

fof(t44_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_xboole_0(k1_tarski(A),k1_enumset1(B,C,D)) ),
    inference(mizar_proof,[status(thm)],[l51_enumset1,t41_enumset1,t4_xboole_1,t42_enumset1]),
    [file(enumset1,t44_enumset1),interesting(0.35)]).

fof(l66_enumset1,theorem,(
    ! [A,B,C,D,E,F,G] : k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k2_enumset1(A,B,C,D),k1_enumset1(E,F,G)) ),
    inference(mizar_proof,[status(thm)],[d2_enumset1,d1_enumset1,d5_enumset1,d2_xboole_0,t2_tarski]),
    [file(enumset1,l66_enumset1),interesting(0.35)]).

fof(t43_enumset1,theorem,(
    ! [A,B,C] : k1_enumset1(A,B,C) = k2_xboole_0(k2_tarski(A,B),k1_tarski(C)) ),
    inference(mizar_proof,[status(thm)],[t42_enumset1,t41_enumset1,t4_xboole_1,t41_enumset1]),
    [file(enumset1,t43_enumset1),interesting(0.33)]).

fof(t65_enumset1,theorem,(
    ! [A,B,C,D,E,F,G,H] : k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k2_enumset1(A,B,C,D),k2_enumset1(E,F,G,H)) ),
    inference(mizar_proof,[status(thm)],[l73_enumset1]),
    [file(enumset1,t65_enumset1),interesting(0.33)]).

fof(l55_enumset1,theorem,(
    ! [A,B,C,D,E] : k3_enumset1(A,B,C,D,E) = k2_xboole_0(k1_enumset1(A,B,C),k2_tarski(D,E)) ),
    inference(mizar_proof,[status(thm)],[d3_enumset1,d1_enumset1,d2_tarski,d2_xboole_0,t2_tarski]),
    [file(enumset1,l55_enumset1),interesting(0.32)]).

fof(t53_enumset1,theorem,(
    ! [A,B,C,D,E,F] : k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k1_enumset1(A,B,C),k1_enumset1(D,E,F)) ),
    inference(mizar_proof,[status(thm)],[l60_enumset1]),
    [file(enumset1,t53_enumset1),interesting(0.30)]).

fof(t62_enumset1,theorem,(
    ! [A,B,C,D,E,F,G,H] : k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k1_tarski(A),k5_enumset1(B,C,D,E,F,G,H)) ),
    inference(mizar_proof,[status(thm)],[l73_enumset1,t44_enumset1,t4_xboole_1,t58_enumset1]),
    [file(enumset1,t62_enumset1),interesting(0.30)]).

fof(t42_enumset1,theorem,(
    ! [A,B,C] : k1_enumset1(A,B,C) = k2_xboole_0(k1_tarski(A),k2_tarski(B,C)) ),
    inference(mizar_proof,[status(thm)],[d1_enumset1,d1_tarski,d2_tarski,d2_xboole_0,t2_tarski]),
    [file(enumset1,t42_enumset1),interesting(0.29)]).

fof(t45_enumset1,theorem,(
    ! [A,B,C,D] : k2_enumset1(A,B,C,D) = k2_xboole_0(k2_tarski(A,B),k2_tarski(C,D)) ),
    inference(mizar_proof,[status(thm)],[l51_enumset1]),
    [file(enumset1,t45_enumset1),interesting(0.28)]).

fof(t61_enumset1,theorem,(
    ! [A,B,C,D,E,F,G] : k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k1_tarski(G)) ),
    inference(mizar_proof,[status(thm)],[l66_enumset1,t43_enumset1,t4_xboole_1,t54_enumset1]),
    [file(enumset1,t61_enumset1),interesting(0.28)]).

fof(t66_enumset1,theorem,(
    ! [A,B,C,D,E,F,G,H] : k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k3_enumset1(A,B,C,D,E),k1_enumset1(F,G,H)) ),
    inference(mizar_proof,[status(thm)],[l73_enumset1,t44_enumset1,t4_xboole_1,t50_enumset1]),
    [file(enumset1,t66_enumset1),interesting(0.28)]).

fof(t67_enumset1,theorem,(
    ! [A,B,C,D,E,F,G,H] : k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k2_tarski(G,H)) ),
    inference(mizar_proof,[status(thm)],[l73_enumset1,l51_enumset1,t4_xboole_1,t54_enumset1]),
    [file(enumset1,t67_enumset1),interesting(0.28)]).

fof(t68_enumset1,theorem,(
    ! [A,B,C,D,E,F,G,H] : k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k5_enumset1(A,B,C,D,E,F,G),k1_tarski(H)) ),
    inference(mizar_proof,[status(thm)],[l73_enumset1,t46_enumset1,t4_xboole_1,l66_enumset1]),
    [file(enumset1,t68_enumset1),interesting(0.28)]).

fof(t60_enumset1,theorem,(
    ! [A,B,C,D,E,F,G] : k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k3_enumset1(A,B,C,D,E),k2_tarski(F,G)) ),
    inference(mizar_proof,[status(thm)],[l66_enumset1,t42_enumset1,t4_xboole_1,t50_enumset1]),
    [file(enumset1,t60_enumset1),interesting(0.27)]).

fof(t64_enumset1,theorem,(
    ! [A,B,C,D,E,F,G,H] : k6_enumset1(A,B,C,D,E,F,G,H) = k2_xboole_0(k1_enumset1(A,B,C),k3_enumset1(D,E,F,G,H)) ),
    inference(mizar_proof,[status(thm)],[l73_enumset1,t46_enumset1,t4_xboole_1,t47_enumset1]),
    [file(enumset1,t64_enumset1),interesting(0.27)]).

fof(t55_enumset1,theorem,(
    ! [A,B,C,D,E,F] : k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k3_enumset1(A,B,C,D,E),k1_tarski(F)) ),
    inference(mizar_proof,[status(thm)],[l60_enumset1,t43_enumset1,t4_xboole_1,l55_enumset1]),
    [file(enumset1,t55_enumset1),interesting(0.24)]).

fof(t59_enumset1,theorem,(
    ! [A,B,C,D,E,F,G] : k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k2_enumset1(A,B,C,D),k1_enumset1(E,F,G)) ),
    inference(mizar_proof,[status(thm)],[l66_enumset1]),
    [file(enumset1,t59_enumset1),interesting(0.20)]).

fof(t49_enumset1,theorem,(
    ! [A,B,C,D,E] : k3_enumset1(A,B,C,D,E) = k2_xboole_0(k1_enumset1(A,B,C),k2_tarski(D,E)) ),
    inference(mizar_proof,[status(thm)],[l55_enumset1]),
    [file(enumset1,t49_enumset1),interesting(0.17)]).

fof(d4_tarski,definition,(
    ! [A,B] : 
      ( B = k3_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ? [D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,A) ) ) ) ),
    file(tarski,d4_tarski),
    [interesting(0.00)]).

fof(d2_tarski,definition,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    [interesting(0.00)]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.00)]).

fof(l1_enumset1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(A,k3_tarski(k2_tarski(B,k1_tarski(C))))
    <=> ( r2_hidden(A,B)
        | A = C ) ) ),
    inference(mizar_proof,[status(thm)],[d4_tarski,d2_tarski,d2_tarski,d1_tarski,d4_tarski]),
    [file(enumset1,l1_enumset1),interesting(0.00)]).

fof(t101_enumset1,theorem,(
    $true ),
    file(enumset1,t101_enumset1),
    [interesting(0.00)]).

fof(d2_enumset1,definition,(
    ! [A,B,C,D,E] : 
      ( E = k2_enumset1(A,B,C,D)
    <=> ! [F] : 
          ( r2_hidden(F,E)
        <=> ~ ( F != A
              & F != B
              & F != C
              & F != D ) ) ) ),
    file(enumset1,d2_enumset1),
    [interesting(0.00)]).

fof(d2_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    [interesting(0.00)]).

fof(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.00)]).

fof(t4_xboole_1,theorem,(
    ! [A,B,C] : k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C)) ),
    file(xboole_1,t4_xboole_1),
    [interesting(0.00)]).

fof(d1_enumset1,definition,(
    ! [A,B,C,D] : 
      ( D = k1_enumset1(A,B,C)
    <=> ! [E] : 
          ( r2_hidden(E,D)
        <=> ~ ( E != A
              & E != B
              & E != C ) ) ) ),
    file(enumset1,d1_enumset1),
    [interesting(0.00)]).

fof(t106_enumset1,theorem,(
    $true ),
    file(enumset1,t106_enumset1),
    [interesting(0.00)]).

fof(t10_enumset1,theorem,(
    $true ),
    file(enumset1,t10_enumset1),
    [interesting(0.00)]).

fof(t114_enumset1,theorem,(
    $true ),
    file(enumset1,t114_enumset1),
    [interesting(0.00)]).

fof(t115_enumset1,theorem,(
    $true ),
    file(enumset1,t115_enumset1),
    [interesting(0.00)]).

fof(t11_enumset1,theorem,(
    $true ),
    file(enumset1,t11_enumset1),
    [interesting(0.00)]).

fof(t120_enumset1,theorem,(
    $true ),
    file(enumset1,t120_enumset1),
    [interesting(0.00)]).

fof(t121_enumset1,theorem,(
    $true ),
    file(enumset1,t121_enumset1),
    [interesting(0.00)]).

fof(t122_enumset1,theorem,(
    $true ),
    file(enumset1,t122_enumset1),
    [interesting(0.00)]).

fof(t124_enumset1,theorem,(
    $true ),
    file(enumset1,t124_enumset1),
    [interesting(0.00)]).

fof(t12_enumset1,theorem,(
    $true ),
    file(enumset1,t12_enumset1),
    [interesting(0.00)]).

fof(t13_enumset1,theorem,(
    $true ),
    file(enumset1,t13_enumset1),
    [interesting(0.00)]).

fof(t14_enumset1,theorem,(
    $true ),
    file(enumset1,t14_enumset1),
    [interesting(0.00)]).

fof(t15_enumset1,theorem,(
    $true ),
    file(enumset1,t15_enumset1),
    [interesting(0.00)]).

fof(t16_enumset1,theorem,(
    $true ),
    file(enumset1,t16_enumset1),
    [interesting(0.00)]).

fof(t17_enumset1,theorem,(
    $true ),
    file(enumset1,t17_enumset1),
    [interesting(0.00)]).

fof(t18_enumset1,theorem,(
    $true ),
    file(enumset1,t18_enumset1),
    [interesting(0.00)]).

fof(t19_enumset1,theorem,(
    $true ),
    file(enumset1,t19_enumset1),
    [interesting(0.00)]).

fof(t1_enumset1,theorem,(
    $true ),
    file(enumset1,t1_enumset1),
    [interesting(0.00)]).

fof(t20_enumset1,theorem,(
    $true ),
    file(enumset1,t20_enumset1),
    [interesting(0.00)]).

fof(t21_enumset1,theorem,(
    $true ),
    file(enumset1,t21_enumset1),
    [interesting(0.00)]).

fof(t22_enumset1,theorem,(
    $true ),
    file(enumset1,t22_enumset1),
    [interesting(0.00)]).

fof(t23_enumset1,theorem,(
    $true ),
    file(enumset1,t23_enumset1),
    [interesting(0.00)]).

fof(t24_enumset1,theorem,(
    $true ),
    file(enumset1,t24_enumset1),
    [interesting(0.00)]).

fof(t25_enumset1,theorem,(
    $true ),
    file(enumset1,t25_enumset1),
    [interesting(0.00)]).

fof(t26_enumset1,theorem,(
    $true ),
    file(enumset1,t26_enumset1),
    [interesting(0.00)]).

fof(t27_enumset1,theorem,(
    $true ),
    file(enumset1,t27_enumset1),
    [interesting(0.00)]).

fof(t28_enumset1,theorem,(
    $true ),
    file(enumset1,t28_enumset1),
    [interesting(0.00)]).

fof(t29_enumset1,theorem,(
    $true ),
    file(enumset1,t29_enumset1),
    [interesting(0.00)]).

fof(t2_enumset1,theorem,(
    $true ),
    file(enumset1,t2_enumset1),
    [interesting(0.00)]).

fof(t30_enumset1,theorem,(
    $true ),
    file(enumset1,t30_enumset1),
    [interesting(0.00)]).

fof(t31_enumset1,theorem,(
    $true ),
    file(enumset1,t31_enumset1),
    [interesting(0.00)]).

fof(t32_enumset1,theorem,(
    $true ),
    file(enumset1,t32_enumset1),
    [interesting(0.00)]).

fof(t33_enumset1,theorem,(
    $true ),
    file(enumset1,t33_enumset1),
    [interesting(0.00)]).

fof(t34_enumset1,theorem,(
    $true ),
    file(enumset1,t34_enumset1),
    [interesting(0.00)]).

fof(t35_enumset1,theorem,(
    $true ),
    file(enumset1,t35_enumset1),
    [interesting(0.00)]).

fof(t36_enumset1,theorem,(
    $true ),
    file(enumset1,t36_enumset1),
    [interesting(0.00)]).

fof(t37_enumset1,theorem,(
    $true ),
    file(enumset1,t37_enumset1),
    [interesting(0.00)]).

fof(t38_enumset1,theorem,(
    $true ),
    file(enumset1,t38_enumset1),
    [interesting(0.00)]).

fof(t39_enumset1,theorem,(
    $true ),
    file(enumset1,t39_enumset1),
    [interesting(0.00)]).

fof(t3_enumset1,theorem,(
    $true ),
    file(enumset1,t3_enumset1),
    [interesting(0.00)]).

fof(t40_enumset1,theorem,(
    $true ),
    file(enumset1,t40_enumset1),
    [interesting(0.00)]).

fof(d3_enumset1,definition,(
    ! [A,B,C,D,E,F] : 
      ( F = k3_enumset1(A,B,C,D,E)
    <=> ! [G] : 
          ( r2_hidden(G,F)
        <=> ~ ( G != A
              & G != B
              & G != C
              & G != D
              & G != E ) ) ) ),
    file(enumset1,d3_enumset1),
    [interesting(0.00)]).

fof(t4_enumset1,theorem,(
    $true ),
    file(enumset1,t4_enumset1),
    [interesting(0.00)]).

fof(d4_enumset1,definition,(
    ! [A,B,C,D,E,F,G] : 
      ( G = k4_enumset1(A,B,C,D,E,F)
    <=> ! [H] : 
          ( r2_hidden(H,G)
        <=> ~ ( H != A
              & H != B
              & H != C
              & H != D
              & H != E
              & H != F ) ) ) ),
    file(enumset1,d4_enumset1),
    [interesting(0.00)]).

fof(d5_enumset1,definition,(
    ! [A,B,C,D,E,F,G,H] : 
      ( H = k5_enumset1(A,B,C,D,E,F,G)
    <=> ! [I] : 
          ( r2_hidden(I,H)
        <=> ~ ( I != A
              & I != B
              & I != C
              & I != D
              & I != E
              & I != F
              & I != G ) ) ) ),
    file(enumset1,d5_enumset1),
    [interesting(0.00)]).

fof(t5_enumset1,theorem,(
    $true ),
    file(enumset1,t5_enumset1),
    [interesting(0.00)]).

fof(d6_enumset1,definition,(
    ! [A,B,C,D,E,F,G,H,I] : 
      ( I = k6_enumset1(A,B,C,D,E,F,G,H)
    <=> ! [J] : 
          ( r2_hidden(J,I)
        <=> ~ ( J != A
              & J != B
              & J != C
              & J != D
              & J != E
              & J != F
              & J != G
              & J != H ) ) ) ),
    file(enumset1,d6_enumset1),
    [interesting(0.00)]).

fof(t6_enumset1,theorem,(
    $true ),
    file(enumset1,t6_enumset1),
    [interesting(0.00)]).

fof(t7_enumset1,theorem,(
    $true ),
    file(enumset1,t7_enumset1),
    [interesting(0.00)]).

fof(t8_enumset1,theorem,(
    $true ),
    file(enumset1,t8_enumset1),
    [interesting(0.00)]).

fof(t97_enumset1,theorem,(
    $true ),
    file(enumset1,t97_enumset1),
    [interesting(0.00)]).

fof(t9_enumset1,theorem,(
    $true ),
    file(enumset1,t9_enumset1),
    [interesting(0.00)]).