%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL548+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:07:58 PM UTC 2026
% Result : Theorem 7.95s 1.54s
% Output : CNFRefutation 7.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 90
% Syntax : Number of formulae : 334 ( 62 unt; 48 def)
% Number of atoms : 948 ( 49 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 1086 ( 472 ~; 492 |; 46 &)
% ( 68 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 73 ( 71 usr; 71 prp; 0-2 aty)
% Number of functors : 38 ( 38 usr; 30 con; 0-2 aty)
% Number of variables : 304 ( 272 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
( or_2
<=> ! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
( or_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
( equivalence_3
<=> ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
or_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
or_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
or_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,axiom,
( axiom_M
<=> ! [X] : is_a_theorem(implies(necessarily(X),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
( axiom_4
<=> ! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f71,axiom,
( axiom_m9
<=> ! [X] : is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,axiom,
( op_possibly
=> ! [X] : possibly(X) = not(necessarily(not(X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f75,axiom,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f77,axiom,
op_possibly,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f81,axiom,
axiom_4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f89,conjecture,
axiom_m9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f90,negated_conjecture,
~ axiom_m9,
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f91,plain,
( modus_ponens
<=> ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f92,plain,
( ( ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
| modus_ponens )
& ( ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) )
| ~ modus_ponens ) ),
inference(NNF_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
( ( ? [Y] :
( ~ is_a_theorem(Y)
& ? [X] :
( is_a_theorem(implies(X,Y))
& is_a_theorem(X) ) )
| modus_ponens )
& ( ! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) ) )
| ~ modus_ponens ) ),
inference(miniscoping,[status(thm)],[f92]) ).
fof(f94,plain,
( ( ( ~ is_a_theorem(sK0_skl)
& is_a_theorem(implies(sK1_skl,sK0_skl))
& is_a_theorem(sK1_skl) )
| modus_ponens )
& ( ! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) ) )
| ~ modus_ponens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f99,plain,
( substitution_of_equivalents
<=> ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f100,plain,
( ( ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) )
| substitution_of_equivalents )
& ( ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) )
| ~ substitution_of_equivalents ) ),
inference(NNF_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
( ( ( sK2_skl != sK3_skl
& is_a_theorem(equiv(sK2_skl,sK3_skl)) )
| substitution_of_equivalents )
& ( ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) )
| ~ substitution_of_equivalents ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f100]) ).
fof(f102,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f105,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| modus_tollens )
& ( ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| ~ modus_tollens ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f106,plain,
( ( ~ is_a_theorem(implies(implies(not(sK5_skl),not(sK4_skl)),implies(sK4_skl,sK5_skl)))
| modus_tollens )
& ( ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| ~ modus_tollens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(X,sK4_skl),skolemize(Y,sK5_skl)],[f105]) ).
fof(f107,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0)))
| ~ modus_tollens ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f109,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,X)))
| implies_1 )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,X)))
| ~ implies_1 ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f110,plain,
( ( ~ is_a_theorem(implies(sK6_skl,implies(sK7_skl,sK6_skl)))
| implies_1 )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,X)))
| ~ implies_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(X,sK6_skl),skolemize(Y,sK7_skl)],[f109]) ).
fof(f111,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f113,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| implies_2 )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| ~ implies_2 ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f114,plain,
( ( ~ is_a_theorem(implies(implies(sK8_skl,implies(sK8_skl,sK9_skl)),implies(sK8_skl,sK9_skl)))
| implies_2 )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| ~ implies_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(X,sK8_skl),skolemize(Y,sK9_skl)],[f113]) ).
fof(f115,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f121,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),X))
| and_1 )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),X))
| ~ and_1 ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f122,plain,
( ( ~ is_a_theorem(implies(and(sK13_skl,sK14_skl),sK13_skl))
| and_1 )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),X))
| ~ and_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(X,sK13_skl),skolemize(Y,sK14_skl)],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f129,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y))))
| and_3 )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y))))
| ~ and_3 ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f130,plain,
( ( ~ is_a_theorem(implies(sK17_skl,implies(sK18_skl,and(sK17_skl,sK18_skl))))
| and_3 )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y))))
| ~ and_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(X,sK17_skl),skolemize(Y,sK18_skl)],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f133,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,or(X,Y)))
| or_1 )
& ( ! [X,Y] : is_a_theorem(implies(X,or(X,Y)))
| ~ or_1 ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f134,plain,
( ( ~ is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl)))
| or_1 )
& ( ! [X,Y] : is_a_theorem(implies(X,or(X,Y)))
| ~ or_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl]),skolemize(X,sK19_skl),skolemize(Y,sK20_skl)],[f133]) ).
fof(f135,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(cnf_transformation,[status(thm)],[f134]) ).
fof(f137,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(Y,or(X,Y)))
| or_2 )
& ( ! [X,Y] : is_a_theorem(implies(Y,or(X,Y)))
| ~ or_2 ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f138,plain,
( ( ~ is_a_theorem(implies(sK22_skl,or(sK21_skl,sK22_skl)))
| or_2 )
& ( ! [X,Y] : is_a_theorem(implies(Y,or(X,Y)))
| ~ or_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl]),skolemize(X,sK21_skl),skolemize(Y,sK22_skl)],[f137]) ).
fof(f139,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X1,X0)))
| ~ or_2 ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f141,plain,
( ( ? [X,Y,Z] : ~ is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))
| or_3 )
& ( ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))
| ~ or_3 ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f142,plain,
( ( ~ is_a_theorem(implies(implies(sK23_skl,sK25_skl),implies(implies(sK24_skl,sK25_skl),implies(or(sK23_skl,sK24_skl),sK25_skl))))
| or_3 )
& ( ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))
| ~ or_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl,sK25_skl]),skolemize(X,sK23_skl),skolemize(Y,sK24_skl),skolemize(Z,sK25_skl)],[f141]) ).
fof(f143,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1))))
| ~ or_3 ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f153,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))
| equivalence_3 )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))
| ~ equivalence_3 ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f154,plain,
( ( ~ is_a_theorem(implies(implies(sK30_skl,sK31_skl),implies(implies(sK31_skl,sK30_skl),equiv(sK30_skl,sK31_skl))))
| equivalence_3 )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))
| ~ equivalence_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30_skl,sK31_skl]),skolemize(X,sK30_skl),skolemize(Y,sK31_skl)],[f153]) ).
fof(f155,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f157,plain,
( ( ? [P] : ~ is_a_theorem(implies(P,and(P,P)))
| kn1 )
& ( ! [P] : is_a_theorem(implies(P,and(P,P)))
| ~ kn1 ) ),
inference(NNF_transformation,[status(thm)],[f16]) ).
fof(f158,plain,
( ( ~ is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl)))
| kn1 )
& ( ! [P] : is_a_theorem(implies(P,and(P,P)))
| ~ kn1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32_skl]),skolemize(P,sK32_skl)],[f157]) ).
fof(f159,plain,
! [X0] :
( is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(cnf_transformation,[status(thm)],[f158]) ).
fof(f160,plain,
( ~ is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl)))
| kn1 ),
inference(cnf_transformation,[status(thm)],[f158]) ).
fof(f189,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P)))
| r3 )
& ( ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ r3 ) ),
inference(NNF_transformation,[status(thm)],[f24]) ).
fof(f190,plain,
( ( ~ is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl)))
| r3 )
& ( ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ r3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl]),skolemize(P,sK47_skl),skolemize(Q,sK48_skl)],[f189]) ).
fof(f191,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f192,plain,
( ~ is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl)))
| r3 ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f201,plain,
( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f202,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f205,plain,
( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f206,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f209,plain,
( ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X))
| ~ op_equiv ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f210,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f211,plain,
op_or,
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f212,plain,
op_implies_and,
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f213,plain,
op_equiv,
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f214,plain,
modus_ponens,
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f215,plain,
modus_tollens,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f216,plain,
implies_1,
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f217,plain,
implies_2,
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f219,plain,
and_1,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f221,plain,
and_3,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f222,plain,
or_1,
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f223,plain,
or_2,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f224,plain,
or_3,
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f227,plain,
equivalence_3,
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f228,plain,
substitution_of_equivalents,
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f229,plain,
( necessitation
<=> ! [X] :
( is_a_theorem(necessarily(X))
| ~ is_a_theorem(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f230,plain,
( ( ? [X] :
( ~ is_a_theorem(necessarily(X))
& is_a_theorem(X) )
| necessitation )
& ( ! [X] :
( is_a_theorem(necessarily(X))
| ~ is_a_theorem(X) )
| ~ necessitation ) ),
inference(NNF_transformation,[status(thm)],[f229]) ).
fof(f231,plain,
( ( ( ~ is_a_theorem(necessarily(sK55_skl))
& is_a_theorem(sK55_skl) )
| necessitation )
& ( ! [X] :
( is_a_theorem(necessarily(X))
| ~ is_a_theorem(X) )
| ~ necessitation ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl]),skolemize(X,sK55_skl)],[f230]) ).
fof(f232,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f260,plain,
( ( ? [X] : ~ is_a_theorem(implies(necessarily(X),X))
| axiom_M )
& ( ! [X] : is_a_theorem(implies(necessarily(X),X))
| ~ axiom_M ) ),
inference(NNF_transformation,[status(thm)],[f55]) ).
fof(f261,plain,
( ( ~ is_a_theorem(implies(necessarily(sK64_skl),sK64_skl))
| axiom_M )
& ( ! [X] : is_a_theorem(implies(necessarily(X),X))
| ~ axiom_M ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64_skl]),skolemize(X,sK64_skl)],[f260]) ).
fof(f262,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[status(thm)],[f261]) ).
fof(f264,plain,
( ( ? [X] : ~ is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))
| axiom_4 )
& ( ! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))
| ~ axiom_4 ) ),
inference(NNF_transformation,[status(thm)],[f56]) ).
fof(f265,plain,
( ( ~ is_a_theorem(implies(necessarily(sK65_skl),necessarily(necessarily(sK65_skl))))
| axiom_4 )
& ( ! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))
| ~ axiom_4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65_skl]),skolemize(X,sK65_skl)],[f264]) ).
fof(f266,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0))))
| ~ axiom_4 ),
inference(cnf_transformation,[status(thm)],[f265]) ).
fof(f324,plain,
( ( ? [X] : ~ is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))
| axiom_m9 )
& ( ! [X] : is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))
| ~ axiom_m9 ) ),
inference(NNF_transformation,[status(thm)],[f71]) ).
fof(f325,plain,
( ( ~ is_a_theorem(strict_implies(possibly(possibly(sK92_skl)),possibly(sK92_skl)))
| axiom_m9 )
& ( ! [X] : is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))
| ~ axiom_m9 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92_skl]),skolemize(X,sK92_skl)],[f324]) ).
fof(f327,plain,
( ~ is_a_theorem(strict_implies(possibly(possibly(sK92_skl)),possibly(sK92_skl)))
| axiom_m9 ),
inference(cnf_transformation,[status(thm)],[f325]) ).
fof(f332,plain,
( ! [X] : possibly(X) = not(necessarily(not(X)))
| ~ op_possibly ),
inference(pre_NNF_transformation,[status(thm)],[f73]) ).
fof(f333,plain,
! [X0] :
( possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(cnf_transformation,[status(thm)],[f332]) ).
fof(f336,plain,
( ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y))
| ~ op_strict_implies ),
inference(pre_NNF_transformation,[status(thm)],[f75]) ).
fof(f337,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[status(thm)],[f336]) ).
fof(f340,plain,
op_possibly,
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f341,plain,
necessitation,
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f343,plain,
axiom_M,
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f344,plain,
axiom_4,
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f349,plain,
op_strict_implies,
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f352,plain,
~ axiom_m9,
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f353,definition,
( sQ0_spl
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f355,plain,
( sQ0_spl
| ~ modus_ponens ),
inference(component_clause,[status(thm)],[f353]) ).
fof(f356,definition,
! [X0,X1] :
( sQ1_spl
<=> ( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f357,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f356]) ).
fof(f359,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f95,f353,f356]) ).
fof(f372,definition,
( sQ5_spl
<=> substitution_of_equivalents ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f374,plain,
( sQ5_spl
| ~ substitution_of_equivalents ),
inference(component_clause,[status(thm)],[f372]) ).
fof(f375,definition,
! [X0,X1] :
( sQ6_spl
<=> ( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f376,plain,
! [X0,X1] :
( ~ sQ6_spl
| X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f378,plain,
( sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f102,f372,f375]) ).
fof(f387,definition,
( sQ9_spl
<=> modus_tollens ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f389,plain,
( sQ9_spl
| ~ modus_tollens ),
inference(component_clause,[status(thm)],[f387]) ).
fof(f390,definition,
! [X0,X1] :
( sQ10_spl
<=> is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f391,plain,
! [X0,X1] :
( ~ sQ10_spl
| is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f390]) ).
fof(f393,plain,
( sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f107,f387,f390]) ).
fof(f398,definition,
( sQ12_spl
<=> implies_1 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f400,plain,
( sQ12_spl
| ~ implies_1 ),
inference(component_clause,[status(thm)],[f398]) ).
fof(f401,definition,
! [X0,X1] :
( sQ13_spl
<=> is_a_theorem(implies(X0,implies(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f402,plain,
! [X0,X1] :
( ~ sQ13_spl
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f401]) ).
fof(f404,plain,
( sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f111,f398,f401]) ).
fof(f409,definition,
( sQ15_spl
<=> implies_2 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f411,plain,
( sQ15_spl
| ~ implies_2 ),
inference(component_clause,[status(thm)],[f409]) ).
fof(f412,definition,
! [X0,X1] :
( sQ16_spl
<=> is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f413,plain,
! [X0,X1] :
( ~ sQ16_spl
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(component_clause,[status(thm)],[f412]) ).
fof(f415,plain,
( sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f115,f409,f412]) ).
fof(f431,definition,
( sQ21_spl
<=> and_1 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f433,plain,
( sQ21_spl
| ~ and_1 ),
inference(component_clause,[status(thm)],[f431]) ).
fof(f434,definition,
! [X0,X1] :
( sQ22_spl
<=> is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f435,plain,
! [X0,X1] :
( ~ sQ22_spl
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,plain,
( sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f123,f431,f434]) ).
fof(f453,definition,
( sQ27_spl
<=> and_3 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( sQ27_spl
| ~ and_3 ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,definition,
! [X0,X1] :
( sQ28_spl
<=> is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f457,plain,
! [X0,X1] :
( ~ sQ28_spl
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(component_clause,[status(thm)],[f456]) ).
fof(f459,plain,
( sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f131,f453,f456]) ).
fof(f464,definition,
( sQ30_spl
<=> or_1 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( sQ30_spl
| ~ or_1 ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f467,definition,
! [X0,X1] :
( sQ31_spl
<=> is_a_theorem(implies(X0,or(X0,X1))) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f468,plain,
! [X0,X1] :
( ~ sQ31_spl
| is_a_theorem(implies(X0,or(X0,X1))) ),
inference(component_clause,[status(thm)],[f467]) ).
fof(f470,plain,
( sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f135,f464,f467]) ).
fof(f475,definition,
( sQ33_spl
<=> or_2 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f477,plain,
( sQ33_spl
| ~ or_2 ),
inference(component_clause,[status(thm)],[f475]) ).
fof(f478,definition,
! [X0,X1] :
( sQ34_spl
<=> is_a_theorem(implies(X0,or(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f479,plain,
! [X0,X1] :
( ~ sQ34_spl
| is_a_theorem(implies(X0,or(X1,X0))) ),
inference(component_clause,[status(thm)],[f478]) ).
fof(f481,plain,
( sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f139,f475,f478]) ).
fof(f486,definition,
( sQ36_spl
<=> or_3 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f488,plain,
( sQ36_spl
| ~ or_3 ),
inference(component_clause,[status(thm)],[f486]) ).
fof(f489,definition,
! [X0,X1,X2] :
( sQ37_spl
<=> is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f490,plain,
! [X0,X1,X2] :
( ~ sQ37_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))) ),
inference(component_clause,[status(thm)],[f489]) ).
fof(f492,plain,
( sQ37_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f143,f486,f489]) ).
fof(f519,definition,
( sQ45_spl
<=> equivalence_3 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f521,plain,
( sQ45_spl
| ~ equivalence_3 ),
inference(component_clause,[status(thm)],[f519]) ).
fof(f522,definition,
! [X0,X1] :
( sQ46_spl
<=> is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f523,plain,
! [X0,X1] :
( ~ sQ46_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(component_clause,[status(thm)],[f522]) ).
fof(f525,plain,
( sQ46_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f155,f519,f522]) ).
fof(f530,definition,
( sQ48_spl
<=> kn1 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f533,definition,
! [X0] :
( sQ49_spl
<=> is_a_theorem(implies(X0,and(X0,X0))) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f534,plain,
! [X0] :
( ~ sQ49_spl
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(component_clause,[status(thm)],[f533]) ).
fof(f536,plain,
( sQ49_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f159,f530,f533]) ).
fof(f537,definition,
( sQ50_spl
<=> is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl))) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f539,plain,
( sQ50_spl
| ~ is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl))) ),
inference(component_clause,[status(thm)],[f537]) ).
fof(f540,plain,
( ~ sQ50_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f160,f530,f537]) ).
fof(f609,definition,
( sQ69_spl
<=> r3 ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f612,definition,
! [X0,X1] :
( sQ70_spl
<=> is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f613,plain,
! [X0,X1] :
( ~ sQ70_spl
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(component_clause,[status(thm)],[f612]) ).
fof(f615,plain,
( sQ70_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f191,f609,f612]) ).
fof(f616,definition,
( sQ71_spl
<=> is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f618,plain,
( sQ71_spl
| ~ is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl))) ),
inference(component_clause,[status(thm)],[f616]) ).
fof(f619,plain,
( ~ sQ71_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f192,f609,f616]) ).
fof(f642,definition,
( sQ78_spl
<=> op_or ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f644,plain,
( sQ78_spl
| ~ op_or ),
inference(component_clause,[status(thm)],[f642]) ).
fof(f645,definition,
! [X0,X1] :
( sQ79_spl
<=> or(X0,X1) = not(and(not(X0),not(X1))) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f646,plain,
! [X0,X1] :
( ~ sQ79_spl
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(component_clause,[status(thm)],[f645]) ).
fof(f648,plain,
( sQ79_spl
| ~ sQ78_spl ),
inference(split_clause,[status(thm)],[f202,f642,f645]) ).
fof(f656,definition,
( sQ82_spl
<=> op_implies_and ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f658,plain,
( sQ82_spl
| ~ op_implies_and ),
inference(component_clause,[status(thm)],[f656]) ).
fof(f659,definition,
! [X0,X1] :
( sQ83_spl
<=> implies(X0,X1) = not(and(X0,not(X1))) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f660,plain,
! [X0,X1] :
( ~ sQ83_spl
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(component_clause,[status(thm)],[f659]) ).
fof(f662,plain,
( sQ83_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f206,f656,f659]) ).
fof(f670,definition,
( sQ86_spl
<=> op_equiv ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f672,plain,
( sQ86_spl
| ~ op_equiv ),
inference(component_clause,[status(thm)],[f670]) ).
fof(f673,definition,
! [X0,X1] :
( sQ87_spl
<=> equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f674,plain,
! [X0,X1] :
( ~ sQ87_spl
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(component_clause,[status(thm)],[f673]) ).
fof(f676,plain,
( sQ87_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f210,f670,f673]) ).
fof(f677,definition,
( sQ88_spl
<=> necessitation ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f679,plain,
( sQ88_spl
| ~ necessitation ),
inference(component_clause,[status(thm)],[f677]) ).
fof(f680,definition,
! [X0] :
( sQ89_spl
<=> ( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f681,plain,
! [X0] :
( ~ sQ89_spl
| is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f680]) ).
fof(f683,plain,
( sQ89_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f232,f677,f680]) ).
fof(f756,definition,
( sQ109_spl
<=> axiom_M ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f758,plain,
( sQ109_spl
| ~ axiom_M ),
inference(component_clause,[status(thm)],[f756]) ).
fof(f759,definition,
! [X0] :
( sQ110_spl
<=> is_a_theorem(implies(necessarily(X0),X0)) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f760,plain,
! [X0] :
( ~ sQ110_spl
| is_a_theorem(implies(necessarily(X0),X0)) ),
inference(component_clause,[status(thm)],[f759]) ).
fof(f762,plain,
( sQ110_spl
| ~ sQ109_spl ),
inference(split_clause,[status(thm)],[f262,f756,f759]) ).
fof(f767,definition,
( sQ112_spl
<=> axiom_4 ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f769,plain,
( sQ112_spl
| ~ axiom_4 ),
inference(component_clause,[status(thm)],[f767]) ).
fof(f770,definition,
! [X0] :
( sQ113_spl
<=> is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f771,plain,
! [X0] :
( ~ sQ113_spl
| is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
inference(component_clause,[status(thm)],[f770]) ).
fof(f773,plain,
( sQ113_spl
| ~ sQ112_spl ),
inference(split_clause,[status(thm)],[f266,f767,f770]) ).
fof(f932,definition,
( sQ157_spl
<=> axiom_m9 ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f933,plain,
( ~ sQ157_spl
| axiom_m9 ),
inference(component_clause,[status(thm)],[f932]) ).
fof(f939,definition,
( sQ159_spl
<=> is_a_theorem(strict_implies(possibly(possibly(sK92_skl)),possibly(sK92_skl))) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f941,plain,
( sQ159_spl
| ~ is_a_theorem(strict_implies(possibly(possibly(sK92_skl)),possibly(sK92_skl))) ),
inference(component_clause,[status(thm)],[f939]) ).
fof(f942,plain,
( ~ sQ159_spl
| sQ157_spl ),
inference(split_clause,[status(thm)],[f327,f932,f939]) ).
fof(f954,definition,
( sQ163_spl
<=> op_possibly ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f956,plain,
( sQ163_spl
| ~ op_possibly ),
inference(component_clause,[status(thm)],[f954]) ).
fof(f957,definition,
! [X0] :
( sQ164_spl
<=> possibly(X0) = not(necessarily(not(X0))) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f958,plain,
! [X0] :
( ~ sQ164_spl
| possibly(X0) = not(necessarily(not(X0))) ),
inference(component_clause,[status(thm)],[f957]) ).
fof(f960,plain,
( sQ164_spl
| ~ sQ163_spl ),
inference(split_clause,[status(thm)],[f333,f954,f957]) ).
fof(f968,definition,
( sQ167_spl
<=> op_strict_implies ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f970,plain,
( sQ167_spl
| ~ op_strict_implies ),
inference(component_clause,[status(thm)],[f968]) ).
fof(f971,definition,
! [X0,X1] :
( sQ168_spl
<=> strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f972,plain,
! [X0,X1] :
( ~ sQ168_spl
| strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(component_clause,[status(thm)],[f971]) ).
fof(f974,plain,
( sQ168_spl
| ~ sQ167_spl ),
inference(split_clause,[status(thm)],[f337,f968,f971]) ).
fof(f984,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f355,f214]) ).
fof(f985,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f984]) ).
fof(f986,plain,
( sQ88_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f679,f341]) ).
fof(f987,plain,
sQ88_spl,
inference(contradiction_clause,[status(thm)],[f986]) ).
fof(f988,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f374,f228]) ).
fof(f989,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f988]) ).
fof(f990,plain,
( sQ167_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f970,f349]) ).
fof(f991,plain,
sQ167_spl,
inference(contradiction_clause,[status(thm)],[f990]) ).
fof(f992,plain,
( sQ163_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f956,f340]) ).
fof(f993,plain,
sQ163_spl,
inference(contradiction_clause,[status(thm)],[f992]) ).
fof(f994,plain,
( sQ86_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f672,f213]) ).
fof(f995,plain,
sQ86_spl,
inference(contradiction_clause,[status(thm)],[f994]) ).
fof(f996,plain,
( sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f658,f212]) ).
fof(f997,plain,
sQ82_spl,
inference(contradiction_clause,[status(thm)],[f996]) ).
fof(f998,plain,
( sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f644,f211]) ).
fof(f999,plain,
sQ78_spl,
inference(contradiction_clause,[status(thm)],[f998]) ).
fof(f1010,plain,
( sQ109_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f758,f343]) ).
fof(f1011,plain,
sQ109_spl,
inference(contradiction_clause,[status(thm)],[f1010]) ).
fof(f1013,plain,
! [X0,X1] :
( ~ sQ168_spl
| ~ sQ89_spl
| is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f972,f681]) ).
fof(f1039,plain,
( sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f477,f223]) ).
fof(f1040,plain,
sQ33_spl,
inference(contradiction_clause,[status(thm)],[f1039]) ).
fof(f1049,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f433,f219]) ).
fof(f1050,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f1049]) ).
fof(f1059,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f466,f222]) ).
fof(f1060,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f1059]) ).
fof(f1067,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f400,f216]) ).
fof(f1068,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f1067]) ).
fof(f1071,plain,
! [X0,X1,X2] :
( ~ sQ6_spl
| ~ sQ1_spl
| X1 = X2
| ~ is_a_theorem(implies(X0,equiv(X1,X2)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f357,f376]) ).
fof(f1113,plain,
( sQ112_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f769,f344]) ).
fof(f1114,plain,
sQ112_spl,
inference(contradiction_clause,[status(thm)],[f1113]) ).
fof(f1118,plain,
! [X0] :
( ~ sQ1_spl
| sQ50_spl
| ~ is_a_theorem(implies(X0,implies(sK32_skl,and(sK32_skl,sK32_skl))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f539,f357]) ).
fof(f1185,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| or(X0,X1) = implies(not(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f660,f646]) ).
fof(f1236,plain,
( sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f521,f227]) ).
fof(f1237,plain,
sQ45_spl,
inference(contradiction_clause,[status(thm)],[f1236]) ).
fof(f1315,plain,
( sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f488,f224]) ).
fof(f1316,plain,
sQ36_spl,
inference(contradiction_clause,[status(thm)],[f1315]) ).
fof(f1319,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f455,f221]) ).
fof(f1320,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f1319]) ).
fof(f1333,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f411,f217]) ).
fof(f1334,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f1333]) ).
fof(f1386,plain,
! [X0,X1] :
( ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f1185,f391]) ).
fof(f1393,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f389,f215]) ).
fof(f1394,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f1393]) ).
fof(f1526,plain,
! [X0] :
( ~ sQ1_spl
| sQ71_spl
| ~ is_a_theorem(implies(X0,implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f618,f357]) ).
fof(f1951,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(resolution,[status(thm)],[f1386,f357]) ).
fof(f1984,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ16_spl
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[f413,f357]) ).
fof(f1994,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ46_spl
| is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f523,f357]) ).
fof(f1997,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ37_spl
| is_a_theorem(implies(implies(X2,X1),implies(or(X0,X2),X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f490,f357]) ).
fof(f2367,plain,
( ~ sQ16_spl
| ~ sQ1_spl
| sQ50_spl
| ~ is_a_theorem(implies(sK32_skl,implies(sK32_skl,and(sK32_skl,sK32_skl)))) ),
inference(resolution,[status(thm)],[f1118,f413]) ).
fof(f2373,plain,
( ~ sQ16_spl
| ~ sQ1_spl
| sQ50_spl
| ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2367,f457]) ).
fof(f2374,plain,
( ~ sQ16_spl
| ~ sQ1_spl
| sQ50_spl
| ~ sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f2373]) ).
fof(f2376,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ49_spl
| is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f534,f357]) ).
fof(f2411,plain,
! [X0] :
( ~ sQ87_spl
| ~ sQ1_spl
| ~ sQ49_spl
| is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(paramodulation,[status(thm)],[f674,f2376]) ).
fof(f4145,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ16_spl
| is_a_theorem(implies(X0,X0)) ),
inference(resolution,[status(thm)],[f1984,f402]) ).
fof(f4158,plain,
! [X0] :
( ~ sQ87_spl
| ~ sQ1_spl
| ~ sQ49_spl
| ~ sQ13_spl
| ~ sQ16_spl
| is_a_theorem(equiv(X0,X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f2411,f4145]) ).
fof(f4194,plain,
! [X0] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ16_spl
| is_a_theorem(or(X0,not(X0))) ),
inference(paramodulation,[status(thm)],[f1185,f4145]) ).
fof(f4379,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ46_spl
| X0 = X1
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f1994,f1071]) ).
fof(f5186,plain,
( ~ sQ1_spl
| sQ71_spl
| ~ sQ37_spl
| ~ is_a_theorem(implies(sK48_skl,or(sK48_skl,sK47_skl)))
| ~ is_a_theorem(implies(sK47_skl,or(sK48_skl,sK47_skl))) ),
inference(resolution,[status(thm)],[f1997,f1526]) ).
fof(f5199,definition,
( sQ213_spl
<=> is_a_theorem(implies(sK47_skl,or(sK48_skl,sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f5201,plain,
( sQ213_spl
| ~ is_a_theorem(implies(sK47_skl,or(sK48_skl,sK47_skl))) ),
inference(component_clause,[status(thm)],[f5199]) ).
fof(f5202,definition,
( sQ214_spl
<=> is_a_theorem(implies(sK48_skl,or(sK48_skl,sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition]) ).
fof(f5204,plain,
( sQ214_spl
| ~ is_a_theorem(implies(sK48_skl,or(sK48_skl,sK47_skl))) ),
inference(component_clause,[status(thm)],[f5202]) ).
fof(f5205,plain,
( ~ sQ1_spl
| sQ71_spl
| ~ sQ37_spl
| ~ sQ214_spl
| ~ sQ213_spl ),
inference(split_clause,[status(thm)],[f5186,f5199,f5202,f489,f616,f356]) ).
fof(f5235,plain,
( sQ213_spl
| ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5201,f479]) ).
fof(f5236,plain,
( sQ213_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f5235]) ).
fof(f5239,plain,
( sQ214_spl
| ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5204,f468]) ).
fof(f5240,plain,
( sQ214_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f5239]) ).
fof(f5344,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ70_spl
| is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f613,f357]) ).
fof(f5405,plain,
! [X0] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ70_spl
| is_a_theorem(or(not(X0),X0)) ),
inference(resolution,[status(thm)],[f5344,f4194]) ).
fof(f5427,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ70_spl
| is_a_theorem(implies(X0,not(not(X0)))) ),
inference(resolution,[status(thm)],[f5405,f1951]) ).
fof(f6477,plain,
! [X0] :
( ~ sQ113_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ46_spl
| necessarily(necessarily(X0)) = necessarily(X0)
| ~ is_a_theorem(implies(necessarily(necessarily(X0)),necessarily(X0))) ),
inference(resolution,[status(thm)],[f4379,f771]) ).
fof(f6504,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ70_spl
| ~ sQ6_spl
| ~ sQ46_spl
| not(not(X0)) = X0
| ~ is_a_theorem(implies(not(not(X0)),X0)) ),
inference(resolution,[status(thm)],[f4379,f5427]) ).
fof(f6506,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ46_spl
| and(X0,X0) = X0
| ~ is_a_theorem(implies(and(X0,X0),X0)) ),
inference(resolution,[status(thm)],[f4379,f534]) ).
fof(f6540,plain,
! [X0] :
( ~ sQ113_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ46_spl
| ~ sQ110_spl
| necessarily(necessarily(X0)) = necessarily(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f6477,f760]) ).
fof(f6549,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ70_spl
| ~ sQ6_spl
| ~ sQ46_spl
| not(not(X0)) = X0
| ~ is_a_theorem(or(not(X0),X0)) ),
inference(forward_demodulation,[status(thm)],[f1185,f6504]) ).
fof(f6550,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ70_spl
| ~ sQ6_spl
| ~ sQ46_spl
| not(not(X0)) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[f6549,f5405]) ).
fof(f6552,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ46_spl
| ~ sQ22_spl
| and(X0,X0) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[f6506,f435]) ).
fof(f6691,plain,
! [X0] :
( ~ sQ87_spl
| ~ sQ49_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ46_spl
| ~ sQ22_spl
| equiv(X0,X0) = implies(X0,X0) ),
inference(paramodulation,[status(thm)],[f674,f6552]) ).
fof(f6810,plain,
! [X0] :
( ~ sQ164_spl
| ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ70_spl
| ~ sQ6_spl
| ~ sQ46_spl
| not(possibly(X0)) = necessarily(not(X0)) ),
inference(paramodulation,[status(thm)],[f958,f6550]) ).
fof(f14453,plain,
! [X0] :
( ~ sQ164_spl
| ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ70_spl
| ~ sQ6_spl
| ~ sQ46_spl
| possibly(possibly(X0)) = not(necessarily(necessarily(not(X0)))) ),
inference(paramodulation,[status(thm)],[f6810,f958]) ).
fof(f14472,plain,
! [X0] :
( ~ sQ164_spl
| ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ70_spl
| ~ sQ6_spl
| ~ sQ46_spl
| ~ sQ113_spl
| ~ sQ110_spl
| possibly(possibly(X0)) = not(necessarily(not(X0))) ),
inference(forward_demodulation,[status(thm)],[f6540,f14453]) ).
fof(f14473,plain,
! [X0] :
( ~ sQ164_spl
| ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ70_spl
| ~ sQ6_spl
| ~ sQ46_spl
| ~ sQ113_spl
| ~ sQ110_spl
| possibly(possibly(X0)) = possibly(X0) ),
inference(forward_demodulation,[status(thm)],[f958,f14472]) ).
fof(f14475,plain,
( sQ159_spl
| ~ sQ164_spl
| ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ70_spl
| ~ sQ6_spl
| ~ sQ46_spl
| ~ sQ113_spl
| ~ sQ110_spl
| ~ is_a_theorem(strict_implies(possibly(sK92_skl),possibly(sK92_skl))) ),
inference(backward_demodulation,[status(thm)],[f14473,f941]) ).
fof(f15467,plain,
( ~ sQ168_spl
| ~ sQ89_spl
| sQ159_spl
| ~ sQ164_spl
| ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ70_spl
| ~ sQ6_spl
| ~ sQ46_spl
| ~ sQ113_spl
| ~ sQ110_spl
| ~ is_a_theorem(implies(possibly(sK92_skl),possibly(sK92_skl))) ),
inference(resolution,[status(thm)],[f14475,f1013]) ).
fof(f15468,plain,
( ~ sQ168_spl
| ~ sQ89_spl
| sQ159_spl
| ~ sQ164_spl
| ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ70_spl
| ~ sQ6_spl
| ~ sQ46_spl
| ~ sQ113_spl
| ~ sQ110_spl
| ~ sQ87_spl
| ~ sQ49_spl
| ~ sQ22_spl
| ~ is_a_theorem(equiv(possibly(sK92_skl),possibly(sK92_skl))) ),
inference(forward_demodulation,[status(thm)],[f6691,f15467]) ).
fof(f15469,plain,
( ~ sQ168_spl
| ~ sQ89_spl
| sQ159_spl
| ~ sQ164_spl
| ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ70_spl
| ~ sQ6_spl
| ~ sQ46_spl
| ~ sQ113_spl
| ~ sQ110_spl
| ~ sQ87_spl
| ~ sQ49_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f15468,f4158]) ).
fof(f15470,plain,
( ~ sQ168_spl
| ~ sQ89_spl
| sQ159_spl
| ~ sQ164_spl
| ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ70_spl
| ~ sQ6_spl
| ~ sQ46_spl
| ~ sQ113_spl
| ~ sQ110_spl
| ~ sQ87_spl
| ~ sQ49_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f15469]) ).
fof(f15505,plain,
( ~ sQ157_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f933,f352]) ).
fof(f15506,plain,
~ sQ157_spl,
inference(contradiction_clause,[status(thm)],[f15505]) ).
fof(f15507,plain,
$false,
inference(sat_refutation,[status(thm)],[f359,f378,f393,f404,f415,f437,f459,f470,f481,f492,f525,f536,f540,f615,f619,f648,f662,f676,f683,f762,f773,f942,f960,f974,f985,f987,f989,f991,f993,f995,f997,f999,f1011,f1040,f1050,f1060,f1068,f1114,f1237,f1316,f1320,f1334,f1394,f2374,f5205,f5236,f5240,f15470,f15506]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL548+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 00:38:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 7.95/1.54 % Refutation found
% 7.95/1.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.95/1.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.85/1.60 % Elapsed time: 1.220439 seconds
% 0.85/1.60 % CPU time: 9.286256 seconds
% 0.85/1.60 % Total memory used: 228.547 MB
% 0.85/1.60 % Net memory used: 219.259 MB
%------------------------------------------------------------------------------