%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL550+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 : n005.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 51.43s 6.95s
% Output : CNFRefutation 32.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 60
% Syntax : Number of formulae : 260 ( 44 unt; 32 def)
% Number of atoms : 987 ( 75 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1339 ( 612 ~; 628 |; 43 &)
% ( 46 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 49 ( 47 usr; 47 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 18 con; 0-2 aty)
% Number of variables : 281 ( 259 !; 22 ?)
% 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(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(f33,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(f34,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(f35,axiom,
( substitution_strict_equiv
<=> ! [X,Y] :
( is_a_theorem(strict_equiv(X,Y))
=> X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
( axiom_m1
<=> ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),and(Y,X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
( axiom_m2
<=> ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
( axiom_m4
<=> ! [X] : is_a_theorem(strict_implies(X,and(X,X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,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(f57,axiom,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,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(f60,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,axiom,
op_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,axiom,
adjunction,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,axiom,
axiom_m1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,axiom,
axiom_m2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f71,axiom,
axiom_m4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f72,axiom,
axiom_m5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f76,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f77,conjecture,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f78,negated_conjecture,
~ modus_ponens,
inference(negated_conjecture,[status(cth)],[f77]) ).
fof(f79,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(f80,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)],[f79]) ).
fof(f81,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)],[f80]) ).
fof(f82,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)],[f81]) ).
fof(f84,plain,
( is_a_theorem(sK1_skl)
| modus_ponens ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f85,plain,
( is_a_theorem(implies(sK1_skl,sK0_skl))
| modus_ponens ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f86,plain,
( ~ is_a_theorem(sK0_skl)
| modus_ponens ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f87,plain,
( substitution_of_equivalents
<=> ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f88,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)],[f87]) ).
fof(f89,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)],[f88]) ).
fof(f90,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f189,plain,
( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f190,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f193,plain,
( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f194,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f197,plain,
( ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X))
| ~ op_equiv ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f198,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f205,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)],[f33]) ).
fof(f206,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)],[f205]) ).
fof(f207,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)],[f206]) ).
fof(f208,plain,
( ( ( ~ is_a_theorem(sK56_skl)
& is_a_theorem(strict_implies(sK57_skl,sK56_skl))
& is_a_theorem(sK57_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,[sK56_skl,sK57_skl]),skolemize(Y,sK56_skl),skolemize(X,sK57_skl)],[f207]) ).
fof(f209,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)],[f208]) ).
fof(f213,plain,
( adjunction
<=> ! [X,Y] :
( is_a_theorem(and(X,Y))
| ~ is_a_theorem(Y)
| ~ is_a_theorem(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f214,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)],[f213]) ).
fof(f215,plain,
( ( ( ~ is_a_theorem(and(sK58_skl,sK59_skl))
& is_a_theorem(sK59_skl)
& is_a_theorem(sK58_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,[sK58_skl,sK59_skl]),skolemize(X,sK58_skl),skolemize(Y,sK59_skl)],[f214]) ).
fof(f216,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ adjunction ),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f220,plain,
( substitution_strict_equiv
<=> ! [X,Y] :
( X = Y
| ~ is_a_theorem(strict_equiv(X,Y)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f221,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)],[f220]) ).
fof(f222,plain,
( ( ( sK60_skl != sK61_skl
& is_a_theorem(strict_equiv(sK60_skl,sK61_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,[sK60_skl,sK61_skl]),skolemize(X,sK60_skl),skolemize(Y,sK61_skl)],[f221]) ).
fof(f223,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1))
| ~ substitution_strict_equiv ),
inference(cnf_transformation,[status(thm)],[f222]) ).
fof(f262,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)],[f45]) ).
fof(f263,plain,
( ( ~ is_a_theorem(strict_implies(and(sK76_skl,sK77_skl),and(sK77_skl,sK76_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,[sK76_skl,sK77_skl]),skolemize(X,sK76_skl),skolemize(Y,sK77_skl)],[f262]) ).
fof(f264,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
| ~ axiom_m1 ),
inference(cnf_transformation,[status(thm)],[f263]) ).
fof(f266,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)],[f46]) ).
fof(f267,plain,
( ( ~ is_a_theorem(strict_implies(and(sK78_skl,sK79_skl),sK78_skl))
| axiom_m2 )
& ( ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X))
| ~ axiom_m2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78_skl,sK79_skl]),skolemize(X,sK78_skl),skolemize(Y,sK79_skl)],[f266]) ).
fof(f268,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ axiom_m2 ),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f274,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)],[f48]) ).
fof(f275,plain,
( ( ~ is_a_theorem(strict_implies(sK83_skl,and(sK83_skl,sK83_skl)))
| axiom_m4 )
& ( ! [X] : is_a_theorem(strict_implies(X,and(X,X)))
| ~ axiom_m4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83_skl]),skolemize(X,sK83_skl)],[f274]) ).
fof(f276,plain,
! [X0] :
( is_a_theorem(strict_implies(X0,and(X0,X0)))
| ~ axiom_m4 ),
inference(cnf_transformation,[status(thm)],[f275]) ).
fof(f278,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)],[f49]) ).
fof(f279,plain,
( ( ~ is_a_theorem(strict_implies(and(strict_implies(sK84_skl,sK85_skl),strict_implies(sK85_skl,sK86_skl)),strict_implies(sK84_skl,sK86_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,[sK84_skl,sK85_skl,sK86_skl]),skolemize(X,sK84_skl),skolemize(Y,sK85_skl),skolemize(Z,sK86_skl)],[f278]) ).
fof(f280,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)],[f279]) ).
fof(f306,plain,
( ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y))
| ~ op_strict_implies ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f307,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[status(thm)],[f306]) ).
fof(f308,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)],[f58]) ).
fof(f309,plain,
! [X0,X1] :
( strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(cnf_transformation,[status(thm)],[f308]) ).
fof(f311,plain,
op_or,
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f313,plain,
op_strict_implies,
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f314,plain,
op_equiv,
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f315,plain,
op_strict_equiv,
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f316,plain,
modus_ponens_strict_implies,
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f317,plain,
substitution_strict_equiv,
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f318,plain,
adjunction,
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f319,plain,
axiom_m1,
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f320,plain,
axiom_m2,
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f322,plain,
axiom_m4,
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f323,plain,
axiom_m5,
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f325,plain,
op_implies_and,
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f327,plain,
substitution_of_equivalents,
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f328,plain,
~ modus_ponens,
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f329,definition,
( sQ0_spl
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( ~ sQ0_spl
| modus_ponens ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f336,definition,
( sQ2_spl
<=> is_a_theorem(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f337,plain,
( ~ sQ2_spl
| is_a_theorem(sK1_skl) ),
inference(component_clause,[status(thm)],[f336]) ).
fof(f339,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f84,f329,f336]) ).
fof(f340,definition,
( sQ3_spl
<=> is_a_theorem(implies(sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f341,plain,
( ~ sQ3_spl
| is_a_theorem(implies(sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f343,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f85,f329,f340]) ).
fof(f344,definition,
( sQ4_spl
<=> is_a_theorem(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f346,plain,
( sQ4_spl
| ~ is_a_theorem(sK0_skl) ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f347,plain,
( ~ sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f86,f329,f344]) ).
fof(f348,definition,
( sQ5_spl
<=> substitution_of_equivalents ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f350,plain,
( sQ5_spl
| ~ substitution_of_equivalents ),
inference(component_clause,[status(thm)],[f348]) ).
fof(f351,definition,
! [X0,X1] :
( sQ6_spl
<=> ( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f352,plain,
! [X0,X1] :
( ~ sQ6_spl
| X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(component_clause,[status(thm)],[f351]) ).
fof(f354,plain,
( sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f90,f348,f351]) ).
fof(f618,definition,
( sQ78_spl
<=> op_or ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f620,plain,
( sQ78_spl
| ~ op_or ),
inference(component_clause,[status(thm)],[f618]) ).
fof(f621,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(f622,plain,
! [X0,X1] :
( ~ sQ79_spl
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(component_clause,[status(thm)],[f621]) ).
fof(f624,plain,
( sQ79_spl
| ~ sQ78_spl ),
inference(split_clause,[status(thm)],[f190,f618,f621]) ).
fof(f632,definition,
( sQ82_spl
<=> op_implies_and ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f634,plain,
( sQ82_spl
| ~ op_implies_and ),
inference(component_clause,[status(thm)],[f632]) ).
fof(f635,definition,
! [X0,X1] :
( sQ83_spl
<=> implies(X0,X1) = not(and(X0,not(X1))) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f636,plain,
! [X0,X1] :
( ~ sQ83_spl
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(component_clause,[status(thm)],[f635]) ).
fof(f638,plain,
( sQ83_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f194,f632,f635]) ).
fof(f646,definition,
( sQ86_spl
<=> op_equiv ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f648,plain,
( sQ86_spl
| ~ op_equiv ),
inference(component_clause,[status(thm)],[f646]) ).
fof(f649,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(f650,plain,
! [X0,X1] :
( ~ sQ87_spl
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(component_clause,[status(thm)],[f649]) ).
fof(f652,plain,
( sQ87_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f198,f646,f649]) ).
fof(f668,definition,
( sQ92_spl
<=> modus_ponens_strict_implies ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f670,plain,
( sQ92_spl
| ~ modus_ponens_strict_implies ),
inference(component_clause,[status(thm)],[f668]) ).
fof(f671,definition,
! [X0,X1] :
( sQ93_spl
<=> ( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f672,plain,
! [X0,X1] :
( ~ sQ93_spl
| is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f671]) ).
fof(f674,plain,
( sQ93_spl
| ~ sQ92_spl ),
inference(split_clause,[status(thm)],[f209,f668,f671]) ).
fof(f687,definition,
( sQ97_spl
<=> adjunction ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f689,plain,
( sQ97_spl
| ~ adjunction ),
inference(component_clause,[status(thm)],[f687]) ).
fof(f690,definition,
! [X0,X1] :
( sQ98_spl
<=> ( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f691,plain,
! [X0,X1] :
( ~ sQ98_spl
| is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f690]) ).
fof(f693,plain,
( sQ98_spl
| ~ sQ97_spl ),
inference(split_clause,[status(thm)],[f216,f687,f690]) ).
fof(f706,definition,
( sQ102_spl
<=> substitution_strict_equiv ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f708,plain,
( sQ102_spl
| ~ substitution_strict_equiv ),
inference(component_clause,[status(thm)],[f706]) ).
fof(f709,definition,
! [X0,X1] :
( sQ103_spl
<=> ( X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f710,plain,
! [X0,X1] :
( ~ sQ103_spl
| X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(component_clause,[status(thm)],[f709]) ).
fof(f712,plain,
( sQ103_spl
| ~ sQ102_spl ),
inference(split_clause,[status(thm)],[f223,f706,f709]) ).
fof(f820,definition,
( sQ133_spl
<=> axiom_m1 ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f822,plain,
( sQ133_spl
| ~ axiom_m1 ),
inference(component_clause,[status(thm)],[f820]) ).
fof(f823,definition,
! [X0,X1] :
( sQ134_spl
<=> is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f824,plain,
! [X0,X1] :
( ~ sQ134_spl
| is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
inference(component_clause,[status(thm)],[f823]) ).
fof(f826,plain,
( sQ134_spl
| ~ sQ133_spl ),
inference(split_clause,[status(thm)],[f264,f820,f823]) ).
fof(f831,definition,
( sQ136_spl
<=> axiom_m2 ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f833,plain,
( sQ136_spl
| ~ axiom_m2 ),
inference(component_clause,[status(thm)],[f831]) ).
fof(f834,definition,
! [X0,X1] :
( sQ137_spl
<=> is_a_theorem(strict_implies(and(X0,X1),X0)) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f835,plain,
! [X0,X1] :
( ~ sQ137_spl
| is_a_theorem(strict_implies(and(X0,X1),X0)) ),
inference(component_clause,[status(thm)],[f834]) ).
fof(f837,plain,
( sQ137_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f268,f831,f834]) ).
fof(f853,definition,
( sQ142_spl
<=> axiom_m4 ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f855,plain,
( sQ142_spl
| ~ axiom_m4 ),
inference(component_clause,[status(thm)],[f853]) ).
fof(f856,definition,
! [X0] :
( sQ143_spl
<=> is_a_theorem(strict_implies(X0,and(X0,X0))) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f857,plain,
! [X0] :
( ~ sQ143_spl
| is_a_theorem(strict_implies(X0,and(X0,X0))) ),
inference(component_clause,[status(thm)],[f856]) ).
fof(f859,plain,
( sQ143_spl
| ~ sQ142_spl ),
inference(split_clause,[status(thm)],[f276,f853,f856]) ).
fof(f864,definition,
( sQ145_spl
<=> axiom_m5 ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f866,plain,
( sQ145_spl
| ~ axiom_m5 ),
inference(component_clause,[status(thm)],[f864]) ).
fof(f867,definition,
! [X0,X1,X2] :
( sQ146_spl
<=> is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f868,plain,
! [X0,X1,X2] :
( ~ sQ146_spl
| is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))) ),
inference(component_clause,[status(thm)],[f867]) ).
fof(f870,plain,
( sQ146_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f280,f864,f867]) ).
fof(f944,definition,
( sQ167_spl
<=> op_strict_implies ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f946,plain,
( sQ167_spl
| ~ op_strict_implies ),
inference(component_clause,[status(thm)],[f944]) ).
fof(f947,definition,
! [X0,X1] :
( sQ168_spl
<=> strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f948,plain,
! [X0,X1] :
( ~ sQ168_spl
| strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(component_clause,[status(thm)],[f947]) ).
fof(f950,plain,
( sQ168_spl
| ~ sQ167_spl ),
inference(split_clause,[status(thm)],[f307,f944,f947]) ).
fof(f951,definition,
( sQ169_spl
<=> op_strict_equiv ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f953,plain,
( sQ169_spl
| ~ op_strict_equiv ),
inference(component_clause,[status(thm)],[f951]) ).
fof(f954,definition,
! [X0,X1] :
( sQ170_spl
<=> strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f955,plain,
! [X0,X1] :
( ~ sQ170_spl
| strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
inference(component_clause,[status(thm)],[f954]) ).
fof(f957,plain,
( sQ170_spl
| ~ sQ169_spl ),
inference(split_clause,[status(thm)],[f309,f951,f954]) ).
fof(f958,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f330,f328]) ).
fof(f959,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f958]) ).
fof(f960,plain,
( sQ169_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f953,f315]) ).
fof(f961,plain,
sQ169_spl,
inference(contradiction_clause,[status(thm)],[f960]) ).
fof(f962,plain,
( sQ167_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f946,f313]) ).
fof(f963,plain,
sQ167_spl,
inference(contradiction_clause,[status(thm)],[f962]) ).
fof(f966,plain,
( sQ86_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f648,f314]) ).
fof(f967,plain,
sQ86_spl,
inference(contradiction_clause,[status(thm)],[f966]) ).
fof(f968,plain,
( sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f634,f325]) ).
fof(f969,plain,
sQ82_spl,
inference(contradiction_clause,[status(thm)],[f968]) ).
fof(f970,plain,
( sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f620,f311]) ).
fof(f971,plain,
sQ78_spl,
inference(contradiction_clause,[status(thm)],[f970]) ).
fof(f972,plain,
( sQ97_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f689,f318]) ).
fof(f973,plain,
sQ97_spl,
inference(contradiction_clause,[status(thm)],[f972]) ).
fof(f974,plain,
( sQ92_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f670,f316]) ).
fof(f975,plain,
sQ92_spl,
inference(contradiction_clause,[status(thm)],[f974]) ).
fof(f976,plain,
( sQ102_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f708,f317]) ).
fof(f977,plain,
sQ102_spl,
inference(contradiction_clause,[status(thm)],[f976]) ).
fof(f982,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f350,f327]) ).
fof(f983,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f982]) ).
fof(f997,plain,
! [X0,X1] :
( ~ sQ170_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(strict_equiv(X0,X1),strict_implies(X0,X0))) ),
inference(paramodulation,[status(thm)],[f955,f868]) ).
fof(f999,plain,
( sQ145_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f866,f323]) ).
fof(f1000,plain,
sQ145_spl,
inference(contradiction_clause,[status(thm)],[f999]) ).
fof(f1003,plain,
( sQ142_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f855,f322]) ).
fof(f1004,plain,
sQ142_spl,
inference(contradiction_clause,[status(thm)],[f1003]) ).
fof(f1013,plain,
( sQ136_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f833,f320]) ).
fof(f1014,plain,
sQ136_spl,
inference(contradiction_clause,[status(thm)],[f1013]) ).
fof(f1016,plain,
! [X0,X1] :
( ~ sQ170_spl
| ~ sQ134_spl
| is_a_theorem(strict_implies(strict_equiv(X0,X1),and(strict_implies(X1,X0),strict_implies(X0,X1)))) ),
inference(paramodulation,[status(thm)],[f955,f824]) ).
fof(f1018,plain,
! [X0,X1] :
( ~ sQ170_spl
| ~ sQ134_spl
| is_a_theorem(strict_implies(strict_equiv(X0,X1),strict_equiv(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f955,f1016]) ).
fof(f1047,plain,
( sQ133_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f822,f319]) ).
fof(f1048,plain,
sQ133_spl,
inference(contradiction_clause,[status(thm)],[f1047]) ).
fof(f1098,plain,
! [X0,X1] :
( ~ sQ170_spl
| ~ sQ98_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)],[f955,f691]) ).
fof(f1112,plain,
! [X0,X1] :
( ~ sQ93_spl
| ~ sQ170_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(X0,X0))
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(resolution,[status(thm)],[f997,f672]) ).
fof(f1126,plain,
! [X0,X1] :
( ~ sQ93_spl
| ~ sQ170_spl
| ~ sQ134_spl
| is_a_theorem(strict_equiv(X1,X0))
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(resolution,[status(thm)],[f1018,f672]) ).
fof(f1154,plain,
! [X0,X1] :
( ~ sQ93_spl
| ~ sQ170_spl
| ~ sQ146_spl
| ~ sQ134_spl
| is_a_theorem(strict_implies(X1,X1))
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(resolution,[status(thm)],[f1126,f1112]) ).
fof(f1167,plain,
! [X0,X1] :
( ~ sQ87_spl
| ~ sQ98_spl
| is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f650,f691]) ).
fof(f1182,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| or(X0,X1) = implies(not(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f636,f622]) ).
fof(f1189,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ168_spl
| strict_implies(not(X0),X1) = necessarily(or(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1182,f948]) ).
fof(f1206,plain,
! [X0,X1,X2] :
( ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(X0,X2))
| ~ is_a_theorem(and(strict_implies(X0,X1),strict_implies(X1,X2))) ),
inference(resolution,[status(thm)],[f868,f672]) ).
fof(f1296,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_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)],[f1098,f824]) ).
fof(f1298,plain,
! [X0] :
( ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| is_a_theorem(strict_equiv(and(X0,X0),X0))
| ~ is_a_theorem(strict_implies(and(X0,X0),X0)) ),
inference(resolution,[status(thm)],[f1098,f857]) ).
fof(f1303,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| X0 = X1
| ~ is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[status(thm)],[f1098,f710]) ).
fof(f1308,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| is_a_theorem(strict_equiv(and(X0,X1),and(X1,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1296,f824]) ).
fof(f1309,plain,
! [X0] :
( ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| is_a_theorem(strict_equiv(and(X0,X0),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1298,f835]) ).
fof(f1310,plain,
! [X0] :
( ~ sQ93_spl
| ~ sQ170_spl
| ~ sQ146_spl
| ~ sQ134_spl
| ~ sQ143_spl
| ~ sQ98_spl
| ~ sQ137_spl
| is_a_theorem(strict_implies(X0,X0)) ),
inference(resolution,[status(thm)],[f1309,f1154]) ).
fof(f1314,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| and(X0,X0) = X0 ),
inference(resolution,[status(thm)],[f1309,f710]) ).
fof(f1332,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| implies(not(X0),X0) = not(not(X0)) ),
inference(paramodulation,[status(thm)],[f1314,f636]) ).
fof(f1343,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| or(X0,X0) = not(not(X0)) ),
inference(forward_demodulation,[status(thm)],[f1182,f1332]) ).
fof(f1513,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| and(X0,X1) = and(X1,X0) ),
inference(resolution,[status(thm)],[f1308,f710]) ).
fof(f1551,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| implies(X0,X1) = not(and(not(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1513,f636]) ).
fof(f1641,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ sQ87_spl
| ~ sQ98_spl
| X0 = X1
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f1167,f352]) ).
fof(f1647,definition,
( sQ173_spl
<=> is_a_theorem(implies(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f1649,plain,
( sQ173_spl
| ~ is_a_theorem(implies(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f1647]) ).
fof(f1733,plain,
! [X0,X1,X2] :
( ~ sQ98_spl
| ~ sQ93_spl
| ~ sQ146_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)],[f1206,f691]) ).
fof(f1757,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| implies(not(X0),X1) = implies(not(X1),X0) ),
inference(paramodulation,[status(thm)],[f636,f1551]) ).
fof(f1761,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| implies(X0,not(X1)) = not(and(or(X1,X1),X0)) ),
inference(paramodulation,[status(thm)],[f1343,f1551]) ).
fof(f1784,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| or(X0,X1) = implies(not(X1),X0) ),
inference(forward_demodulation,[status(thm)],[f1182,f1757]) ).
fof(f1785,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| or(X0,X1) = or(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f1182,f1784]) ).
fof(f1814,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| ~ sQ168_spl
| strict_implies(not(X0),X1) = necessarily(or(X1,X0)) ),
inference(paramodulation,[status(thm)],[f1785,f1189]) ).
fof(f1825,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| ~ sQ168_spl
| strict_implies(not(X0),X1) = strict_implies(not(X1),X0) ),
inference(forward_demodulation,[status(thm)],[f1189,f1814]) ).
fof(f1829,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| strict_implies(or(X0,X0),X1) = strict_implies(not(X1),not(X0)) ),
inference(paramodulation,[status(thm)],[f1343,f1825]) ).
fof(f1852,plain,
! [X0] :
( ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ143_spl
| ~ sQ137_spl
| is_a_theorem(strict_implies(not(not(X0)),X0)) ),
inference(paramodulation,[status(thm)],[f1825,f1310]) ).
fof(f1885,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(or(X0,X0),X0)) ),
inference(paramodulation,[status(thm)],[f1343,f1852]) ).
fof(f1886,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(not(or(X0,X0)),not(X0))) ),
inference(paramodulation,[status(thm)],[f1343,f1852]) ).
fof(f1996,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| X0 = or(X0,X0)
| ~ is_a_theorem(strict_implies(X0,or(X0,X0))) ),
inference(resolution,[status(thm)],[f1303,f1885]) ).
fof(f2366,plain,
( ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ87_spl
| ~ sQ98_spl
| sK0_skl = sK1_skl
| ~ is_a_theorem(implies(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f1641,f341]) ).
fof(f2369,definition,
( sQ175_spl
<=> sK0_skl = sK1_skl ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f2370,plain,
( ~ sQ175_spl
| sK0_skl = sK1_skl ),
inference(component_clause,[status(thm)],[f2369]) ).
fof(f2372,plain,
( ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ87_spl
| ~ sQ98_spl
| sQ175_spl
| ~ sQ173_spl ),
inference(split_clause,[status(thm)],[f2366,f1647,f2369,f690,f649,f351,f340]) ).
fof(f7917,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ is_a_theorem(strict_implies(X0,or(X1,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[status(thm)],[f1733,f1885]) ).
fof(f13242,plain,
! [X0] :
( ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ143_spl
| ~ sQ137_spl
| is_a_theorem(strict_implies(not(not(or(X0,X0))),X0)) ),
inference(resolution,[status(thm)],[f7917,f1852]) ).
fof(f13489,plain,
! [X0] :
( ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ143_spl
| ~ sQ137_spl
| is_a_theorem(strict_implies(not(X0),not(or(X0,X0)))) ),
inference(paramodulation,[status(thm)],[f1825,f13242]) ).
fof(f13639,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ143_spl
| ~ sQ137_spl
| not(or(X0,X0)) = not(X0)
| ~ is_a_theorem(strict_implies(not(or(X0,X0)),not(X0))) ),
inference(resolution,[status(thm)],[f13489,f1303]) ).
fof(f13672,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ143_spl
| ~ sQ137_spl
| not(or(X0,X0)) = not(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f13639,f1886]) ).
fof(f13791,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ143_spl
| ~ sQ137_spl
| implies(X0,or(X1,X1)) = not(and(not(X1),X0)) ),
inference(paramodulation,[status(thm)],[f13672,f1551]) ).
fof(f13858,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ143_spl
| ~ sQ137_spl
| implies(X0,or(X1,X1)) = implies(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f1551,f13791]) ).
fof(f14868,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ143_spl
| ~ sQ137_spl
| strict_implies(X0,or(X1,X1)) = necessarily(implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f13858,f948]) ).
fof(f14926,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ143_spl
| ~ sQ137_spl
| strict_implies(X0,or(X1,X1)) = strict_implies(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f948,f14868]) ).
fof(f14929,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| X0 = or(X0,X0)
| ~ is_a_theorem(strict_implies(X0,X0)) ),
inference(backward_demodulation,[status(thm)],[f14926,f1996]) ).
fof(f15016,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| X0 = or(X0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f14929,f1310]) ).
fof(f15097,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| strict_implies(X0,X1) = strict_implies(not(X1),not(X0)) ),
inference(backward_demodulation,[status(thm)],[f15016,f1829]) ).
fof(f15098,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| implies(X0,not(X1)) = not(and(X1,X0)) ),
inference(backward_demodulation,[status(thm)],[f15016,f1761]) ).
fof(f15101,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| X0 = not(not(X0)) ),
inference(backward_demodulation,[status(thm)],[f15016,f1343]) ).
fof(f16134,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| strict_implies(X0,not(X1)) = strict_implies(X1,not(X0)) ),
inference(paramodulation,[status(thm)],[f15101,f15097]) ).
fof(f19577,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(X0,not(and(not(X0),X1)))) ),
inference(paramodulation,[status(thm)],[f16134,f835]) ).
fof(f19719,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(X0,implies(X1,not(not(X0))))) ),
inference(forward_demodulation,[status(thm)],[f15098,f19577]) ).
fof(f19720,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(X0,implies(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f15101,f19719]) ).
fof(f19760,plain,
! [X0,X1] :
( ~ sQ93_spl
| ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ146_spl
| is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f19720,f672]) ).
fof(f19796,plain,
( sQ173_spl
| ~ sQ93_spl
| ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ146_spl
| ~ is_a_theorem(sK1_skl) ),
inference(resolution,[status(thm)],[f19760,f1649]) ).
fof(f19811,plain,
( sQ173_spl
| ~ sQ93_spl
| ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ146_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19796,f337]) ).
fof(f19812,plain,
( sQ173_spl
| ~ sQ93_spl
| ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ146_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f19811]) ).
fof(f19814,plain,
( ~ sQ2_spl
| ~ sQ175_spl
| is_a_theorem(sK0_skl) ),
inference(backward_demodulation,[status(thm)],[f2370,f337]) ).
fof(f19815,plain,
( ~ sQ2_spl
| ~ sQ175_spl
| sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f19814,f346]) ).
fof(f19816,plain,
( ~ sQ2_spl
| ~ sQ175_spl
| sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f19815]) ).
fof(f19817,plain,
$false,
inference(sat_refutation,[status(thm)],[f339,f343,f347,f354,f624,f638,f652,f674,f693,f712,f826,f837,f859,f870,f950,f957,f959,f961,f963,f967,f969,f971,f973,f975,f977,f983,f1000,f1004,f1014,f1048,f2372,f19812,f19816]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL550+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 00:38:02 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 51.43/6.95 % Refutation found
% 51.43/6.95 % SZS status Theorem for theBenchmark: Theorem is valid
% 51.43/6.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 44.76/7.10 % Elapsed time: 6.728444 seconds
% 44.76/7.10 % CPU time: 52.396951 seconds
% 44.76/7.10 % Total memory used: 550.935 MB
% 44.76/7.10 % Net memory used: 528.412 MB
%------------------------------------------------------------------------------