%------------------------------------------------------------------------------ % File : SYO071^4.004 : TPTP v7.0.0. Released v4.0.0. % Domain : Logic Calculi (Intuitionistic logic) % Problem : ILTP Problem SYJ207+1.004 % Version : [Goe33] axioms. % English : % Refs : [Goe33] Goedel (1933), An Interpretation of the Intuitionistic % : [Gol06] Goldblatt (2006), Mathematical Modal Logic: A View of % : [ROK06] Raths et al. (2006), The ILTP Problem Library for Intu % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe % : [BP10] Benzmueller & Paulson (2009), Exploring Properties of % Source : [Ben09] % Names : SYJ207+1.004 [ROK06] % Status : CounterSatisfiable % Rating : 0.67 v5.4.0, 1.00 v4.0.0 % Syntax : Number of formulae : 59 ( 0 unit; 29 type; 19 defn) % Number of atoms : 382 ( 19 equality; 48 variable) % Maximal formula depth : 14 ( 6 average) % Number of connectives : 317 ( 3 ~; 1 |; 2 &; 309 @) % ( 0 <=>; 2 =>; 0 <=; 0 <~>) % ( 0 ~|; 0 ~&) % Number of type conns : 104 ( 104 >; 0 *; 0 +; 0 <<) % Number of symbols : 32 ( 29 :; 0 =) % Number of variables : 40 ( 1 sgn; 7 !; 2 ?; 31 ^) % ( 40 :; 0 !>; 0 ?*) % ( 0 @-; 0 @+) % SPC : TH0_CSA_EQU_NAR % Comments : This is an ILTP problem embedded in TH0 % : In classical logic this is a Theorem. %------------------------------------------------------------------------------ include('Axioms/LCL010^0.ax'). %------------------------------------------------------------------------------ thf(p0_type,type,( p0: $i > $o )). thf(p1_type,type,( p1: $i > $o )). thf(p2_type,type,( p2: $i > $o )). thf(p3_type,type,( p3: $i > $o )). thf(p4_type,type,( p4: $i > $o )). thf(p5_type,type,( p5: $i > $o )). thf(p6_type,type,( p6: $i > $o )). thf(p7_type,type,( p7: $i > $o )). thf(p8_type,type,( p8: $i > $o )). thf(axiom1,axiom, ( ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p1 ) @ ( iatom @ p2 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iand @ ( iatom @ p7 ) @ ( iatom @ p8 ) ) ) ) ) ) ) ) ) )). thf(axiom2,axiom, ( ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p2 ) @ ( iatom @ p3 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iand @ ( iatom @ p7 ) @ ( iatom @ p8 ) ) ) ) ) ) ) ) ) )). thf(axiom3,axiom, ( ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p3 ) @ ( iatom @ p4 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iand @ ( iatom @ p7 ) @ ( iatom @ p8 ) ) ) ) ) ) ) ) ) )). thf(axiom4,axiom, ( ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p4 ) @ ( iatom @ p5 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iand @ ( iatom @ p7 ) @ ( iatom @ p8 ) ) ) ) ) ) ) ) ) )). thf(axiom5,axiom, ( ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p5 ) @ ( iatom @ p6 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iand @ ( iatom @ p7 ) @ ( iatom @ p8 ) ) ) ) ) ) ) ) ) )). thf(axiom6,axiom, ( ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p6 ) @ ( iatom @ p7 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iand @ ( iatom @ p7 ) @ ( iatom @ p8 ) ) ) ) ) ) ) ) ) )). thf(axiom7,axiom, ( ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p7 ) @ ( iatom @ p8 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iand @ ( iatom @ p7 ) @ ( iatom @ p8 ) ) ) ) ) ) ) ) ) )). thf(axiom8,axiom, ( ivalid @ ( iimplies @ ( iequiv @ ( iatom @ p8 ) @ ( iatom @ p1 ) ) @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iand @ ( iatom @ p7 ) @ ( iatom @ p8 ) ) ) ) ) ) ) ) ) )). thf(con,conjecture, ( ivalid @ ( ior @ ( iatom @ p0 ) @ ( ior @ ( iand @ ( iatom @ p1 ) @ ( iand @ ( iatom @ p2 ) @ ( iand @ ( iatom @ p3 ) @ ( iand @ ( iatom @ p4 ) @ ( iand @ ( iatom @ p5 ) @ ( iand @ ( iatom @ p6 ) @ ( iand @ ( iatom @ p7 ) @ ( iatom @ p8 ) ) ) ) ) ) ) ) @ ( inot @ ( iatom @ p0 ) ) ) ) )). %------------------------------------------------------------------------------