%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL568+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 : n018.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 01:08:00 PM UTC 2026
% Result : Theorem 73.16s 9.66s
% Output : CNFRefutation 35.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 60
% Syntax : Number of formulae : 264 ( 47 unt; 30 def)
% Number of atoms : 1064 ( 75 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1502 ( 702 ~; 714 |; 35 &)
% ( 43 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 48 ( 46 usr; 46 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 17 con; 0-2 aty)
% Number of variables : 273 ( 254 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
( modus_ponens_strict_implies
<=> ! [X,Y] :
( ( is_a_theorem(strict_implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
( adjunction
<=> ! [X,Y] :
( ( is_a_theorem(Y)
& is_a_theorem(X) )
=> is_a_theorem(and(X,Y)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
( substitution_strict_equiv
<=> ! [X,Y] :
( is_a_theorem(strict_equiv(X,Y))
=> X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
( axiom_4
<=> ! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
( axiom_m1
<=> ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),and(Y,X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
( axiom_m2
<=> ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
( axiom_m4
<=> ! [X] : is_a_theorem(strict_implies(X,and(X,X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
( axiom_m5
<=> ! [X,Y,Z] : is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
( axiom_m6
<=> ! [X] : is_a_theorem(strict_implies(X,possibly(X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
( axiom_m9
<=> ! [X] : is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
( op_possibly
=> ! [X] : possibly(X) = not(necessarily(not(X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
( op_strict_equiv
=> ! [X,Y] : strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
op_possibly,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
op_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
adjunction,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
axiom_m1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
axiom_m2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
axiom_m4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
axiom_m5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
axiom_m6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
axiom_m9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,conjecture,
axiom_4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
~ axiom_4,
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f57,plain,
( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f58,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f61,plain,
( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f62,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f73,plain,
( modus_ponens_strict_implies
<=> ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(strict_implies(X,Y))
| ~ is_a_theorem(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f74,plain,
( ( ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(strict_implies(X,Y))
& is_a_theorem(X) )
| modus_ponens_strict_implies )
& ( ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(strict_implies(X,Y))
| ~ is_a_theorem(X) )
| ~ modus_ponens_strict_implies ) ),
inference(NNF_transformation,[status(thm)],[f73]) ).
fof(f75,plain,
( ( ? [Y] :
( ~ is_a_theorem(Y)
& ? [X] :
( is_a_theorem(strict_implies(X,Y))
& is_a_theorem(X) ) )
| modus_ponens_strict_implies )
& ( ! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(strict_implies(X,Y))
| ~ is_a_theorem(X) ) )
| ~ modus_ponens_strict_implies ) ),
inference(miniscoping,[status(thm)],[f74]) ).
fof(f76,plain,
( ( ( ~ is_a_theorem(sK1_skl)
& is_a_theorem(strict_implies(sK2_skl,sK1_skl))
& is_a_theorem(sK2_skl) )
| modus_ponens_strict_implies )
& ( ! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(strict_implies(X,Y))
| ~ is_a_theorem(X) ) )
| ~ modus_ponens_strict_implies ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(Y,sK1_skl),skolemize(X,sK2_skl)],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens_strict_implies ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f81,plain,
( adjunction
<=> ! [X,Y] :
( is_a_theorem(and(X,Y))
| ~ is_a_theorem(Y)
| ~ is_a_theorem(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f82,plain,
( ( ? [X,Y] :
( ~ is_a_theorem(and(X,Y))
& is_a_theorem(Y)
& is_a_theorem(X) )
| adjunction )
& ( ! [X,Y] :
( is_a_theorem(and(X,Y))
| ~ is_a_theorem(Y)
| ~ is_a_theorem(X) )
| ~ adjunction ) ),
inference(NNF_transformation,[status(thm)],[f81]) ).
fof(f83,plain,
( ( ( ~ is_a_theorem(and(sK3_skl,sK4_skl))
& is_a_theorem(sK4_skl)
& is_a_theorem(sK3_skl) )
| adjunction )
& ( ! [X,Y] :
( is_a_theorem(and(X,Y))
| ~ is_a_theorem(Y)
| ~ is_a_theorem(X) )
| ~ adjunction ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(X,sK3_skl),skolemize(Y,sK4_skl)],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ adjunction ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f88,plain,
( substitution_strict_equiv
<=> ! [X,Y] :
( X = Y
| ~ is_a_theorem(strict_equiv(X,Y)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f89,plain,
( ( ? [X,Y] :
( X != Y
& is_a_theorem(strict_equiv(X,Y)) )
| substitution_strict_equiv )
& ( ! [X,Y] :
( X = Y
| ~ is_a_theorem(strict_equiv(X,Y)) )
| ~ substitution_strict_equiv ) ),
inference(NNF_transformation,[status(thm)],[f88]) ).
fof(f90,plain,
( ( ( sK5_skl != sK6_skl
& is_a_theorem(strict_equiv(sK5_skl,sK6_skl)) )
| substitution_strict_equiv )
& ( ! [X,Y] :
( X = Y
| ~ is_a_theorem(strict_equiv(X,Y)) )
| ~ substitution_strict_equiv ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(X,sK5_skl),skolemize(Y,sK6_skl)],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1))
| ~ substitution_strict_equiv ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f102,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)],[f12]) ).
fof(f103,plain,
( ( ~ is_a_theorem(implies(necessarily(sK10_skl),necessarily(necessarily(sK10_skl))))
| axiom_4 )
& ( ! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))
| ~ axiom_4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(X,sK10_skl)],[f102]) ).
fof(f105,plain,
( ~ is_a_theorem(implies(necessarily(sK10_skl),necessarily(necessarily(sK10_skl))))
| axiom_4 ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f130,plain,
( ( ? [X,Y] : ~ is_a_theorem(strict_implies(and(X,Y),and(Y,X)))
| axiom_m1 )
& ( ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),and(Y,X)))
| ~ axiom_m1 ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f131,plain,
( ( ~ is_a_theorem(strict_implies(and(sK21_skl,sK22_skl),and(sK22_skl,sK21_skl)))
| axiom_m1 )
& ( ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),and(Y,X)))
| ~ axiom_m1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl]),skolemize(X,sK21_skl),skolemize(Y,sK22_skl)],[f130]) ).
fof(f132,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
| ~ axiom_m1 ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f134,plain,
( ( ? [X,Y] : ~ is_a_theorem(strict_implies(and(X,Y),X))
| axiom_m2 )
& ( ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X))
| ~ axiom_m2 ) ),
inference(NNF_transformation,[status(thm)],[f20]) ).
fof(f135,plain,
( ( ~ is_a_theorem(strict_implies(and(sK23_skl,sK24_skl),sK23_skl))
| axiom_m2 )
& ( ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X))
| ~ axiom_m2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl]),skolemize(X,sK23_skl),skolemize(Y,sK24_skl)],[f134]) ).
fof(f136,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ axiom_m2 ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f142,plain,
( ( ? [X] : ~ is_a_theorem(strict_implies(X,and(X,X)))
| axiom_m4 )
& ( ! [X] : is_a_theorem(strict_implies(X,and(X,X)))
| ~ axiom_m4 ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f143,plain,
( ( ~ is_a_theorem(strict_implies(sK28_skl,and(sK28_skl,sK28_skl)))
| axiom_m4 )
& ( ! [X] : is_a_theorem(strict_implies(X,and(X,X)))
| ~ axiom_m4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28_skl]),skolemize(X,sK28_skl)],[f142]) ).
fof(f144,plain,
! [X0] :
( is_a_theorem(strict_implies(X0,and(X0,X0)))
| ~ axiom_m4 ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f146,plain,
( ( ? [X,Y,Z] : ~ is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z)))
| axiom_m5 )
& ( ! [X,Y,Z] : is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z)))
| ~ axiom_m5 ) ),
inference(NNF_transformation,[status(thm)],[f23]) ).
fof(f147,plain,
( ( ~ is_a_theorem(strict_implies(and(strict_implies(sK29_skl,sK30_skl),strict_implies(sK30_skl,sK31_skl)),strict_implies(sK29_skl,sK31_skl)))
| axiom_m5 )
& ( ! [X,Y,Z] : is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z)))
| ~ axiom_m5 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29_skl,sK30_skl,sK31_skl]),skolemize(X,sK29_skl),skolemize(Y,sK30_skl),skolemize(Z,sK31_skl)],[f146]) ).
fof(f148,plain,
! [X0,X1,X2] :
( is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))
| ~ axiom_m5 ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f150,plain,
( ( ? [X] : ~ is_a_theorem(strict_implies(X,possibly(X)))
| axiom_m6 )
& ( ! [X] : is_a_theorem(strict_implies(X,possibly(X)))
| ~ axiom_m6 ) ),
inference(NNF_transformation,[status(thm)],[f24]) ).
fof(f151,plain,
( ( ~ is_a_theorem(strict_implies(sK32_skl,possibly(sK32_skl)))
| axiom_m6 )
& ( ! [X] : is_a_theorem(strict_implies(X,possibly(X)))
| ~ axiom_m6 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32_skl]),skolemize(X,sK32_skl)],[f150]) ).
fof(f152,plain,
! [X0] :
( is_a_theorem(strict_implies(X0,possibly(X0)))
| ~ axiom_m6 ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f162,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)],[f27]) ).
fof(f163,plain,
( ( ~ is_a_theorem(strict_implies(possibly(possibly(sK37_skl)),possibly(sK37_skl)))
| axiom_m9 )
& ( ! [X] : is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))
| ~ axiom_m9 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37_skl]),skolemize(X,sK37_skl)],[f162]) ).
fof(f164,plain,
! [X0] :
( is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0)))
| ~ axiom_m9 ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f170,plain,
( ! [X] : possibly(X) = not(necessarily(not(X)))
| ~ op_possibly ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f171,plain,
! [X0] :
( possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f174,plain,
( ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y))
| ~ op_strict_implies ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f175,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f176,plain,
( ! [X,Y] : strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X))
| ~ op_strict_equiv ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f177,plain,
! [X0,X1] :
( strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f178,plain,
op_possibly,
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f179,plain,
op_or,
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f181,plain,
op_strict_implies,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f183,plain,
op_strict_equiv,
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f184,plain,
modus_ponens_strict_implies,
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f185,plain,
substitution_strict_equiv,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f186,plain,
adjunction,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f187,plain,
axiom_m1,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f188,plain,
axiom_m2,
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f190,plain,
axiom_m4,
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f191,plain,
axiom_m5,
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f192,plain,
axiom_m6,
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f194,plain,
axiom_m9,
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f197,plain,
op_implies_and,
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f200,plain,
~ axiom_4,
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f201,definition,
( sQ0_spl
<=> op_or ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( sQ0_spl
| ~ op_or ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f204,definition,
! [X0,X1] :
( sQ1_spl
<=> or(X0,X1) = not(and(not(X0),not(X1))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f205,plain,
! [X0,X1] :
( ~ sQ1_spl
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f58,f201,f204]) ).
fof(f215,definition,
( sQ4_spl
<=> op_implies_and ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f217,plain,
( sQ4_spl
| ~ op_implies_and ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,definition,
! [X0,X1] :
( sQ5_spl
<=> implies(X0,X1) = not(and(X0,not(X1))) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f219,plain,
! [X0,X1] :
( ~ sQ5_spl
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f221,plain,
( sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f62,f215,f218]) ).
fof(f251,definition,
( sQ14_spl
<=> modus_ponens_strict_implies ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f253,plain,
( sQ14_spl
| ~ modus_ponens_strict_implies ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f254,definition,
! [X0,X1] :
( sQ15_spl
<=> ( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f255,plain,
! [X0,X1] :
( ~ sQ15_spl
| is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f257,plain,
( sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f77,f251,f254]) ).
fof(f270,definition,
( sQ19_spl
<=> adjunction ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f272,plain,
( sQ19_spl
| ~ adjunction ),
inference(component_clause,[status(thm)],[f270]) ).
fof(f273,definition,
! [X0,X1] :
( sQ20_spl
<=> ( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f274,plain,
! [X0,X1] :
( ~ sQ20_spl
| is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f276,plain,
( sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f84,f270,f273]) ).
fof(f289,definition,
( sQ24_spl
<=> substitution_strict_equiv ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f291,plain,
( sQ24_spl
| ~ substitution_strict_equiv ),
inference(component_clause,[status(thm)],[f289]) ).
fof(f292,definition,
! [X0,X1] :
( sQ25_spl
<=> ( X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f293,plain,
! [X0,X1] :
( ~ sQ25_spl
| X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f295,plain,
( sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f91,f289,f292]) ).
fof(f326,definition,
( sQ34_spl
<=> axiom_4 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f327,plain,
( ~ sQ34_spl
| axiom_4 ),
inference(component_clause,[status(thm)],[f326]) ).
fof(f333,definition,
( sQ36_spl
<=> is_a_theorem(implies(necessarily(sK10_skl),necessarily(necessarily(sK10_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f335,plain,
( sQ36_spl
| ~ is_a_theorem(implies(necessarily(sK10_skl),necessarily(necessarily(sK10_skl)))) ),
inference(component_clause,[status(thm)],[f333]) ).
fof(f336,plain,
( ~ sQ36_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f105,f326,f333]) ).
fof(f403,definition,
( sQ55_spl
<=> axiom_m1 ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f405,plain,
( sQ55_spl
| ~ axiom_m1 ),
inference(component_clause,[status(thm)],[f403]) ).
fof(f406,definition,
! [X0,X1] :
( sQ56_spl
<=> is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f407,plain,
! [X0,X1] :
( ~ sQ56_spl
| is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
inference(component_clause,[status(thm)],[f406]) ).
fof(f409,plain,
( sQ56_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f132,f403,f406]) ).
fof(f414,definition,
( sQ58_spl
<=> axiom_m2 ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f416,plain,
( sQ58_spl
| ~ axiom_m2 ),
inference(component_clause,[status(thm)],[f414]) ).
fof(f417,definition,
! [X0,X1] :
( sQ59_spl
<=> is_a_theorem(strict_implies(and(X0,X1),X0)) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f418,plain,
! [X0,X1] :
( ~ sQ59_spl
| is_a_theorem(strict_implies(and(X0,X1),X0)) ),
inference(component_clause,[status(thm)],[f417]) ).
fof(f420,plain,
( sQ59_spl
| ~ sQ58_spl ),
inference(split_clause,[status(thm)],[f136,f414,f417]) ).
fof(f436,definition,
( sQ64_spl
<=> axiom_m4 ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f438,plain,
( sQ64_spl
| ~ axiom_m4 ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f439,definition,
! [X0] :
( sQ65_spl
<=> is_a_theorem(strict_implies(X0,and(X0,X0))) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f440,plain,
! [X0] :
( ~ sQ65_spl
| is_a_theorem(strict_implies(X0,and(X0,X0))) ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,plain,
( sQ65_spl
| ~ sQ64_spl ),
inference(split_clause,[status(thm)],[f144,f436,f439]) ).
fof(f447,definition,
( sQ67_spl
<=> axiom_m5 ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( sQ67_spl
| ~ axiom_m5 ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,definition,
! [X0,X1,X2] :
( sQ68_spl
<=> is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f451,plain,
! [X0,X1,X2] :
( ~ sQ68_spl
| is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))) ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f453,plain,
( sQ68_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f148,f447,f450]) ).
fof(f458,definition,
( sQ70_spl
<=> axiom_m6 ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f460,plain,
( sQ70_spl
| ~ axiom_m6 ),
inference(component_clause,[status(thm)],[f458]) ).
fof(f461,definition,
! [X0] :
( sQ71_spl
<=> is_a_theorem(strict_implies(X0,possibly(X0))) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f462,plain,
! [X0] :
( ~ sQ71_spl
| is_a_theorem(strict_implies(X0,possibly(X0))) ),
inference(component_clause,[status(thm)],[f461]) ).
fof(f464,plain,
( sQ71_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f152,f458,f461]) ).
fof(f491,definition,
( sQ79_spl
<=> axiom_m9 ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f493,plain,
( sQ79_spl
| ~ axiom_m9 ),
inference(component_clause,[status(thm)],[f491]) ).
fof(f494,definition,
! [X0] :
( sQ80_spl
<=> is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f495,plain,
! [X0] :
( ~ sQ80_spl
| is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))) ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f497,plain,
( sQ80_spl
| ~ sQ79_spl ),
inference(split_clause,[status(thm)],[f164,f491,f494]) ).
fof(f513,definition,
( sQ85_spl
<=> op_possibly ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f515,plain,
( sQ85_spl
| ~ op_possibly ),
inference(component_clause,[status(thm)],[f513]) ).
fof(f516,definition,
! [X0] :
( sQ86_spl
<=> possibly(X0) = not(necessarily(not(X0))) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f517,plain,
! [X0] :
( ~ sQ86_spl
| possibly(X0) = not(necessarily(not(X0))) ),
inference(component_clause,[status(thm)],[f516]) ).
fof(f519,plain,
( sQ86_spl
| ~ sQ85_spl ),
inference(split_clause,[status(thm)],[f171,f513,f516]) ).
fof(f527,definition,
( sQ89_spl
<=> op_strict_implies ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f529,plain,
( sQ89_spl
| ~ op_strict_implies ),
inference(component_clause,[status(thm)],[f527]) ).
fof(f530,definition,
! [X0,X1] :
( sQ90_spl
<=> strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f531,plain,
! [X0,X1] :
( ~ sQ90_spl
| strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(component_clause,[status(thm)],[f530]) ).
fof(f533,plain,
( sQ90_spl
| ~ sQ89_spl ),
inference(split_clause,[status(thm)],[f175,f527,f530]) ).
fof(f534,definition,
( sQ91_spl
<=> op_strict_equiv ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f536,plain,
( sQ91_spl
| ~ op_strict_equiv ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f537,definition,
! [X0,X1] :
( sQ92_spl
<=> strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f538,plain,
! [X0,X1] :
( ~ sQ92_spl
| strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
inference(component_clause,[status(thm)],[f537]) ).
fof(f540,plain,
( sQ92_spl
| ~ sQ91_spl ),
inference(split_clause,[status(thm)],[f177,f534,f537]) ).
fof(f541,plain,
( sQ91_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f536,f183]) ).
fof(f542,plain,
sQ91_spl,
inference(contradiction_clause,[status(thm)],[f541]) ).
fof(f543,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f272,f186]) ).
fof(f544,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f543]) ).
fof(f545,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f184]) ).
fof(f546,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f545]) ).
fof(f547,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f291,f185]) ).
fof(f548,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f547]) ).
fof(f549,plain,
( sQ89_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f529,f181]) ).
fof(f550,plain,
sQ89_spl,
inference(contradiction_clause,[status(thm)],[f549]) ).
fof(f551,plain,
( sQ85_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f515,f178]) ).
fof(f552,plain,
sQ85_spl,
inference(contradiction_clause,[status(thm)],[f551]) ).
fof(f555,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f217,f197]) ).
fof(f556,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f555]) ).
fof(f557,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f203,f179]) ).
fof(f558,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f557]) ).
fof(f570,plain,
( sQ70_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f460,f192]) ).
fof(f571,plain,
sQ70_spl,
inference(contradiction_clause,[status(thm)],[f570]) ).
fof(f578,plain,
( sQ64_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f438,f190]) ).
fof(f579,plain,
sQ64_spl,
inference(contradiction_clause,[status(thm)],[f578]) ).
fof(f583,plain,
( sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f416,f188]) ).
fof(f584,plain,
sQ58_spl,
inference(contradiction_clause,[status(thm)],[f583]) ).
fof(f596,plain,
( sQ79_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f493,f194]) ).
fof(f597,plain,
sQ79_spl,
inference(contradiction_clause,[status(thm)],[f596]) ).
fof(f605,plain,
( sQ67_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f449,f191]) ).
fof(f606,plain,
sQ67_spl,
inference(contradiction_clause,[status(thm)],[f605]) ).
fof(f615,plain,
! [X0,X1] :
( ~ sQ92_spl
| ~ sQ20_spl
| is_a_theorem(strict_equiv(X0,X1))
| ~ is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f538,f274]) ).
fof(f633,plain,
! [X0,X1] :
( ~ sQ86_spl
| ~ sQ5_spl
| implies(X0,necessarily(not(X1))) = not(and(X0,possibly(X1))) ),
inference(paramodulation,[status(thm)],[f517,f219]) ).
fof(f664,plain,
( sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f405,f187]) ).
fof(f665,plain,
sQ55_spl,
inference(contradiction_clause,[status(thm)],[f664]) ).
fof(f722,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ5_spl
| or(X0,X1) = implies(not(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f219,f205]) ).
fof(f723,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| ~ sQ1_spl
| or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f219,f722]) ).
fof(f724,plain,
! [X0,X1] :
( ~ sQ86_spl
| ~ sQ1_spl
| ~ sQ5_spl
| or(necessarily(not(X0)),X1) = implies(possibly(X0),X1) ),
inference(paramodulation,[status(thm)],[f517,f722]) ).
fof(f727,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ90_spl
| strict_implies(not(X0),X1) = necessarily(or(X0,X1)) ),
inference(paramodulation,[status(thm)],[f722,f531]) ).
fof(f744,plain,
! [X0,X1,X2] :
( ~ sQ15_spl
| ~ sQ68_spl
| is_a_theorem(strict_implies(X0,X2))
| ~ is_a_theorem(and(strict_implies(X0,X1),strict_implies(X1,X2))) ),
inference(resolution,[status(thm)],[f451,f255]) ).
fof(f853,plain,
! [X0] :
( ~ sQ80_spl
| ~ sQ92_spl
| ~ sQ20_spl
| is_a_theorem(strict_equiv(possibly(X0),possibly(possibly(X0))))
| ~ is_a_theorem(strict_implies(possibly(X0),possibly(possibly(X0)))) ),
inference(resolution,[status(thm)],[f615,f495]) ).
fof(f861,plain,
! [X0,X1] :
( ~ sQ56_spl
| ~ sQ92_spl
| ~ sQ20_spl
| is_a_theorem(strict_equiv(and(X0,X1),and(X1,X0)))
| ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
inference(resolution,[status(thm)],[f615,f407]) ).
fof(f863,plain,
! [X0] :
( ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| is_a_theorem(strict_equiv(and(X0,X0),X0))
| ~ is_a_theorem(strict_implies(and(X0,X0),X0)) ),
inference(resolution,[status(thm)],[f615,f440]) ).
fof(f869,plain,
! [X0,X1] :
( ~ sQ25_spl
| ~ sQ92_spl
| ~ sQ20_spl
| X0 = X1
| ~ is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[status(thm)],[f615,f293]) ).
fof(f872,plain,
! [X0] :
( ~ sQ80_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ71_spl
| is_a_theorem(strict_equiv(possibly(X0),possibly(possibly(X0)))) ),
inference(forward_subsumption_resolution,[status(thm)],[f853,f462]) ).
fof(f875,plain,
! [X0,X1] :
( ~ sQ56_spl
| ~ sQ92_spl
| ~ sQ20_spl
| is_a_theorem(strict_equiv(and(X0,X1),and(X1,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f861,f407]) ).
fof(f876,plain,
! [X0] :
( ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| is_a_theorem(strict_equiv(and(X0,X0),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f863,f418]) ).
fof(f881,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| and(X0,X0) = X0 ),
inference(resolution,[status(thm)],[f876,f293]) ).
fof(f886,plain,
! [X0] :
( ~ sQ65_spl
| ~ sQ25_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| is_a_theorem(strict_implies(X0,X0)) ),
inference(backward_demodulation,[status(thm)],[f881,f440]) ).
fof(f893,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ86_spl
| ~ sQ5_spl
| implies(possibly(X0),necessarily(not(X0))) = not(possibly(X0)) ),
inference(paramodulation,[status(thm)],[f881,f633]) ).
fof(f896,plain,
! [X0,X1] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| or(not(X0),X1) = implies(implies(not(X0),X0),X1) ),
inference(paramodulation,[status(thm)],[f881,f723]) ).
fof(f898,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| implies(not(X0),X0) = not(not(X0)) ),
inference(paramodulation,[status(thm)],[f881,f219]) ).
fof(f908,plain,
! [X0,X1] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| or(not(X0),X1) = implies(or(X0,X0),X1) ),
inference(forward_demodulation,[status(thm)],[f722,f896]) ).
fof(f909,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| or(X0,X0) = not(not(X0)) ),
inference(forward_demodulation,[status(thm)],[f722,f898]) ).
fof(f981,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ90_spl
| strict_implies(not(X0),X0) = necessarily(not(not(X0))) ),
inference(paramodulation,[status(thm)],[f909,f727]) ).
fof(f992,plain,
! [X0,X1] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| implies(X0,not(X1)) = not(and(X0,or(X1,X1))) ),
inference(paramodulation,[status(thm)],[f909,f219]) ).
fof(f1048,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ80_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ71_spl
| possibly(X0) = possibly(possibly(X0)) ),
inference(resolution,[status(thm)],[f872,f293]) ).
fof(f1128,plain,
! [X0,X1] :
( ~ sQ25_spl
| ~ sQ56_spl
| ~ sQ92_spl
| ~ sQ20_spl
| and(X0,X1) = and(X1,X0) ),
inference(resolution,[status(thm)],[f875,f293]) ).
fof(f1170,plain,
! [X0,X1] :
( ~ sQ25_spl
| ~ sQ56_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ5_spl
| implies(X0,X1) = not(and(not(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1128,f219]) ).
fof(f1363,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ68_spl
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(strict_implies(X0,X2))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[status(thm)],[f744,f274]) ).
fof(f1422,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ25_spl
| ~ sQ56_spl
| ~ sQ92_spl
| ~ sQ20_spl
| implies(not(X0),X1) = implies(not(X1),X0) ),
inference(paramodulation,[status(thm)],[f219,f1170]) ).
fof(f1451,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ25_spl
| ~ sQ56_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ1_spl
| or(X0,X1) = implies(not(X1),X0) ),
inference(forward_demodulation,[status(thm)],[f722,f1422]) ).
fof(f1452,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ25_spl
| ~ sQ56_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ1_spl
| or(X0,X1) = or(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f722,f1451]) ).
fof(f1478,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ25_spl
| ~ sQ56_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ1_spl
| ~ sQ90_spl
| strict_implies(not(X0),X1) = necessarily(or(X1,X0)) ),
inference(paramodulation,[status(thm)],[f1452,f727]) ).
fof(f1485,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ25_spl
| ~ sQ56_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ1_spl
| ~ sQ90_spl
| strict_implies(not(X0),X1) = strict_implies(not(X1),X0) ),
inference(forward_demodulation,[status(thm)],[f727,f1478]) ).
fof(f1507,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ25_spl
| ~ sQ56_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ1_spl
| ~ sQ90_spl
| ~ sQ71_spl
| is_a_theorem(strict_implies(not(possibly(not(X0))),X0)) ),
inference(paramodulation,[status(thm)],[f1485,f462]) ).
fof(f1516,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ25_spl
| ~ sQ56_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ1_spl
| ~ sQ90_spl
| ~ sQ65_spl
| ~ sQ59_spl
| is_a_theorem(strict_implies(not(not(X0)),X0)) ),
inference(paramodulation,[status(thm)],[f1485,f886]) ).
fof(f1557,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ56_spl
| ~ sQ90_spl
| is_a_theorem(strict_implies(or(X0,X0),X0)) ),
inference(paramodulation,[status(thm)],[f909,f1516]) ).
fof(f1592,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ5_spl
| ~ sQ25_spl
| ~ sQ56_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ1_spl
| ~ sQ90_spl
| ~ sQ71_spl
| is_a_theorem(X0)
| ~ is_a_theorem(not(possibly(not(X0)))) ),
inference(resolution,[status(thm)],[f1507,f255]) ).
fof(f1809,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ56_spl
| ~ sQ90_spl
| X0 = or(X0,X0)
| ~ is_a_theorem(strict_implies(X0,or(X0,X0))) ),
inference(resolution,[status(thm)],[f869,f1557]) ).
fof(f5779,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| implies(or(X0,X0),not(X0)) = not(or(X0,X0)) ),
inference(paramodulation,[status(thm)],[f881,f992]) ).
fof(f5850,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| or(not(X0),not(X0)) = not(or(X0,X0)) ),
inference(forward_demodulation,[status(thm)],[f908,f5779]) ).
fof(f9999,plain,
! [X0,X1,X2] :
( ~ sQ59_spl
| ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ68_spl
| ~ is_a_theorem(strict_implies(X0,and(X1,X2)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[status(thm)],[f1363,f418]) ).
fof(f10001,plain,
! [X0,X1] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ56_spl
| ~ sQ90_spl
| ~ sQ15_spl
| ~ sQ68_spl
| ~ is_a_theorem(strict_implies(X0,or(X1,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[status(thm)],[f1363,f1557]) ).
fof(f14954,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ25_spl
| ~ sQ56_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ1_spl
| ~ sQ90_spl
| ~ sQ65_spl
| ~ sQ59_spl
| ~ sQ15_spl
| ~ sQ68_spl
| is_a_theorem(strict_implies(not(not(and(X0,X1))),X0)) ),
inference(resolution,[status(thm)],[f9999,f1516]) ).
fof(f15375,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ25_spl
| ~ sQ56_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ1_spl
| ~ sQ90_spl
| ~ sQ65_spl
| ~ sQ59_spl
| ~ sQ15_spl
| ~ sQ68_spl
| is_a_theorem(strict_implies(not(implies(X0,X1)),X0)) ),
inference(paramodulation,[status(thm)],[f219,f14954]) ).
fof(f17894,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ25_spl
| ~ sQ56_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ1_spl
| ~ sQ90_spl
| ~ sQ65_spl
| ~ sQ59_spl
| ~ sQ15_spl
| ~ sQ68_spl
| is_a_theorem(strict_implies(not(implies(or(X0,X0),X1)),X0)) ),
inference(resolution,[status(thm)],[f10001,f15375]) ).
fof(f17931,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ25_spl
| ~ sQ56_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ1_spl
| ~ sQ90_spl
| ~ sQ65_spl
| ~ sQ59_spl
| ~ sQ15_spl
| ~ sQ68_spl
| is_a_theorem(strict_implies(not(or(not(X0),X1)),X0)) ),
inference(forward_demodulation,[status(thm)],[f908,f17894]) ).
fof(f18161,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ25_spl
| ~ sQ56_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ1_spl
| ~ sQ90_spl
| ~ sQ65_spl
| ~ sQ59_spl
| ~ sQ15_spl
| ~ sQ68_spl
| is_a_theorem(strict_implies(not(X0),or(not(X0),X1))) ),
inference(paramodulation,[status(thm)],[f1485,f17931]) ).
fof(f18781,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ56_spl
| ~ sQ90_spl
| ~ sQ15_spl
| ~ sQ68_spl
| not(X0) = or(not(X0),not(X0)) ),
inference(resolution,[status(thm)],[f18161,f1809]) ).
fof(f18827,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ56_spl
| ~ sQ90_spl
| ~ sQ15_spl
| ~ sQ68_spl
| not(X0) = not(or(X0,X0)) ),
inference(forward_demodulation,[status(thm)],[f5850,f18781]) ).
fof(f18989,plain,
! [X0,X1] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ56_spl
| ~ sQ90_spl
| ~ sQ15_spl
| ~ sQ68_spl
| implies(X0,or(X1,X1)) = not(and(not(X1),X0)) ),
inference(paramodulation,[status(thm)],[f18827,f1170]) ).
fof(f19062,plain,
! [X0,X1] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ56_spl
| ~ sQ90_spl
| ~ sQ15_spl
| ~ sQ68_spl
| implies(X0,or(X1,X1)) = implies(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f1170,f18989]) ).
fof(f21648,plain,
! [X0,X1] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ56_spl
| ~ sQ90_spl
| ~ sQ15_spl
| ~ sQ68_spl
| strict_implies(X0,or(X1,X1)) = necessarily(implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f19062,f531]) ).
fof(f21727,plain,
! [X0,X1] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ56_spl
| ~ sQ90_spl
| ~ sQ15_spl
| ~ sQ68_spl
| strict_implies(X0,or(X1,X1)) = strict_implies(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f531,f21648]) ).
fof(f21729,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ56_spl
| ~ sQ90_spl
| ~ sQ15_spl
| ~ sQ68_spl
| X0 = or(X0,X0)
| ~ is_a_theorem(strict_implies(X0,X0)) ),
inference(backward_demodulation,[status(thm)],[f21727,f1809]) ).
fof(f21863,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ56_spl
| ~ sQ90_spl
| ~ sQ15_spl
| ~ sQ68_spl
| X0 = or(X0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f21729,f886]) ).
fof(f22001,plain,
! [X0] :
( ~ sQ86_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ56_spl
| ~ sQ90_spl
| ~ sQ15_spl
| ~ sQ68_spl
| necessarily(not(X0)) = implies(possibly(X0),necessarily(not(X0))) ),
inference(paramodulation,[status(thm)],[f724,f21863]) ).
fof(f22043,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ56_spl
| ~ sQ90_spl
| ~ sQ15_spl
| ~ sQ68_spl
| strict_implies(not(X0),X0) = necessarily(X0) ),
inference(paramodulation,[status(thm)],[f21863,f727]) ).
fof(f22044,plain,
! [X0] :
( ~ sQ86_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ56_spl
| ~ sQ90_spl
| ~ sQ15_spl
| ~ sQ68_spl
| necessarily(not(X0)) = not(possibly(X0)) ),
inference(forward_demodulation,[status(thm)],[f893,f22001]) ).
fof(f22052,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ90_spl
| ~ sQ56_spl
| ~ sQ15_spl
| ~ sQ68_spl
| necessarily(X0) = necessarily(not(not(X0))) ),
inference(backward_demodulation,[status(thm)],[f22043,f981]) ).
fof(f23823,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ5_spl
| ~ sQ25_spl
| ~ sQ56_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ1_spl
| ~ sQ90_spl
| ~ sQ71_spl
| ~ sQ65_spl
| ~ sQ59_spl
| ~ sQ68_spl
| ~ sQ86_spl
| is_a_theorem(X0)
| ~ is_a_theorem(necessarily(X0)) ),
inference(backward_demodulation,[status(thm)],[f23824,f1592]) ).
fof(f23824,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ90_spl
| ~ sQ56_spl
| ~ sQ15_spl
| ~ sQ68_spl
| ~ sQ86_spl
| necessarily(X0) = not(possibly(not(X0))) ),
inference(forward_demodulation,[status(thm)],[f22044,f22052]) ).
fof(f23849,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ90_spl
| ~ sQ56_spl
| ~ sQ15_spl
| ~ sQ68_spl
| ~ sQ86_spl
| necessarily(necessarily(X0)) = not(possibly(possibly(not(X0)))) ),
inference(paramodulation,[status(thm)],[f23824,f22044]) ).
fof(f23940,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ90_spl
| ~ sQ56_spl
| ~ sQ15_spl
| ~ sQ68_spl
| ~ sQ86_spl
| ~ sQ80_spl
| ~ sQ71_spl
| necessarily(necessarily(X0)) = not(possibly(not(X0))) ),
inference(forward_demodulation,[status(thm)],[f1048,f23849]) ).
fof(f23941,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ90_spl
| ~ sQ56_spl
| ~ sQ15_spl
| ~ sQ68_spl
| ~ sQ86_spl
| ~ sQ80_spl
| ~ sQ71_spl
| necessarily(necessarily(X0)) = necessarily(X0) ),
inference(forward_demodulation,[status(thm)],[f23824,f23940]) ).
fof(f23982,plain,
! [X0,X1] :
( ~ sQ90_spl
| ~ sQ15_spl
| ~ sQ5_spl
| ~ sQ25_spl
| ~ sQ56_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ1_spl
| ~ sQ71_spl
| ~ sQ65_spl
| ~ sQ59_spl
| ~ sQ68_spl
| ~ sQ86_spl
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f531,f23823]) ).
fof(f23984,plain,
( sQ36_spl
| ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ90_spl
| ~ sQ56_spl
| ~ sQ15_spl
| ~ sQ68_spl
| ~ sQ86_spl
| ~ sQ80_spl
| ~ sQ71_spl
| ~ is_a_theorem(implies(necessarily(sK10_skl),necessarily(sK10_skl))) ),
inference(backward_demodulation,[status(thm)],[f23941,f335]) ).
fof(f30739,plain,
! [X0] :
( ~ sQ65_spl
| ~ sQ25_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ90_spl
| ~ sQ15_spl
| ~ sQ5_spl
| ~ sQ56_spl
| ~ sQ1_spl
| ~ sQ71_spl
| ~ sQ68_spl
| ~ sQ86_spl
| is_a_theorem(implies(X0,X0)) ),
inference(resolution,[status(thm)],[f23982,f886]) ).
fof(f31110,plain,
( sQ36_spl
| ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ90_spl
| ~ sQ56_spl
| ~ sQ15_spl
| ~ sQ68_spl
| ~ sQ86_spl
| ~ sQ80_spl
| ~ sQ71_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f23984,f30739]) ).
fof(f31124,plain,
( sQ36_spl
| ~ sQ25_spl
| ~ sQ65_spl
| ~ sQ92_spl
| ~ sQ20_spl
| ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ90_spl
| ~ sQ56_spl
| ~ sQ15_spl
| ~ sQ68_spl
| ~ sQ86_spl
| ~ sQ80_spl
| ~ sQ71_spl ),
inference(contradiction_clause,[status(thm)],[f31110]) ).
fof(f31133,plain,
( ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f327,f200]) ).
fof(f31134,plain,
~ sQ34_spl,
inference(contradiction_clause,[status(thm)],[f31133]) ).
fof(f31135,plain,
$false,
inference(sat_refutation,[status(thm)],[f207,f221,f257,f276,f295,f336,f409,f420,f442,f453,f464,f497,f519,f533,f540,f542,f544,f546,f548,f550,f552,f556,f558,f571,f579,f584,f597,f606,f665,f31124,f31134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL568+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 00:40:58 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 73.16/9.66 % Refutation found
% 73.16/9.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 73.16/9.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 35.85/10.24 % Elapsed time: 9.853268 seconds
% 35.85/10.24 % CPU time: 74.676363 seconds
% 35.85/10.24 % Total memory used: 797.350 MB
% 35.85/10.24 % Net memory used: 755.294 MB
%------------------------------------------------------------------------------