%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KRS102+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 12:59:41 PM UTC 2026
% Result : Unsatisfiable 0.14s 10.45s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 56
% Syntax : Number of formulae : 246 ( 3 unt; 22 def)
% Number of atoms : 783 ( 427 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 823 ( 286 ~; 470 |; 36 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 23 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 18 con; 0-0 aty)
% Number of variables : 104 ( 104 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X] :
( cTorF(X)
<=> ( X = iminus1
| X = iplus1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( cTorF(X)
<=> ( X = iplus4
| X = iminus4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] :
( cTorF(X)
<=> ( X = iminus2
| X = iplus2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] :
( cTorF(X)
<=> ( X = iminus7
| X = iplus7 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X] :
( cTorF(X)
<=> ( X = iminus3
| X = iplus3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X] :
( cTorF(X)
<=> ( X = iF
| X = iT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X] :
( cTorF(X)
<=> ( X = iminus8
| X = iplus8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X] :
( cTorF(X)
<=> ( X = iplus6
| X = iminus6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X] :
( cTorF(X)
<=> ( X = iplus9
| X = iminus9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
( iT = iplus1
| iT = iplus2
| iT = iminus6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
( iT = iplus7
| iT = iminus3
| iT = iplus8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
( iT = iplus4
| iT = iminus9
| iT = iplus3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
( iT = iplus9
| iT = iminus4
| iT = iminus8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
( iT = iplus4
| iT = iplus6
| iT = iplus3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
( iT = iminus2
| iT = iminus8
| iT = iplus3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
( iT = iplus4
| iT = iplus6
| iT = iminus8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
( iT = iminus2
| iT = iminus9
| iT = iplus3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
( iT = iminus7
| iT = iminus2
| iT = iplus6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
( iT = iplus9
| iT = iminus4
| iT = iplus1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
( iT = iminus4
| iT = iplus2
| iT = iplus8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
( iT = iminus7
| iT = iminus3
| iT = iminus4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
( iT = iminus1
| iT = iplus4
| iT = iplus2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
( iT = iminus3
| iT = iplus1
| iT = iminus2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
( iT = iminus4
| iT = iminus9
| iT = iminus8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
( iT = iplus4
| iT = iplus1
| iT = iplus3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
( iT = iminus3
| iT = iplus2
| iT = iplus8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
( iT = iminus7
| iT = iplus3
| iT = iplus8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,axiom,
( iT = iplus4
| iT = iplus9
| iT = iplus3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,axiom,
( iT = iplus7
| iT = iminus2
| iT = iminus9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,axiom,
( iT = iminus1
| iT = iminus4
| iT = iplus6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,axiom,
( iT = iplus4
| iT = iminus2
| iT = iminus6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,axiom,
( iT = iminus4
| iT = iplus6
| iT = iplus8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,axiom,
( iT = iplus9
| iT = iplus7
| iT = iminus4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f83,axiom,
iT != iF,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f106,plain,
! [X] :
( ( ( X != iminus1
& X != iplus1 )
| cTorF(X) )
& ( X = iminus1
| X = iplus1
| ~ cTorF(X) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f107,plain,
( ! [X] :
( ( X != iminus1
& X != iplus1 )
| cTorF(X) )
& ! [X] :
( X = iminus1
| X = iplus1
| ~ cTorF(X) ) ),
inference(miniscoping,[status(thm)],[f106]) ).
fof(f108,plain,
! [X0] :
( X0 = iminus1
| X0 = iplus1
| ~ cTorF(X0) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
! [X0] :
( X0 != iplus1
| cTorF(X0) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f111,plain,
! [X] :
( ( ( X != iplus4
& X != iminus4 )
| cTorF(X) )
& ( X = iplus4
| X = iminus4
| ~ cTorF(X) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f112,plain,
( ! [X] :
( ( X != iplus4
& X != iminus4 )
| cTorF(X) )
& ! [X] :
( X = iplus4
| X = iminus4
| ~ cTorF(X) ) ),
inference(miniscoping,[status(thm)],[f111]) ).
fof(f113,plain,
! [X0] :
( X0 = iplus4
| X0 = iminus4
| ~ cTorF(X0) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f114,plain,
! [X0] :
( X0 != iminus4
| cTorF(X0) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f115,plain,
! [X0] :
( X0 != iplus4
| cTorF(X0) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f116,plain,
! [X] :
( ( ( X != iminus2
& X != iplus2 )
| cTorF(X) )
& ( X = iminus2
| X = iplus2
| ~ cTorF(X) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f117,plain,
( ! [X] :
( ( X != iminus2
& X != iplus2 )
| cTorF(X) )
& ! [X] :
( X = iminus2
| X = iplus2
| ~ cTorF(X) ) ),
inference(miniscoping,[status(thm)],[f116]) ).
fof(f118,plain,
! [X0] :
( X0 = iminus2
| X0 = iplus2
| ~ cTorF(X0) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f120,plain,
! [X0] :
( X0 != iminus2
| cTorF(X0) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f121,plain,
! [X] :
( ( ( X != iminus7
& X != iplus7 )
| cTorF(X) )
& ( X = iminus7
| X = iplus7
| ~ cTorF(X) ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f122,plain,
( ! [X] :
( ( X != iminus7
& X != iplus7 )
| cTorF(X) )
& ! [X] :
( X = iminus7
| X = iplus7
| ~ cTorF(X) ) ),
inference(miniscoping,[status(thm)],[f121]) ).
fof(f123,plain,
! [X0] :
( X0 = iminus7
| X0 = iplus7
| ~ cTorF(X0) ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f125,plain,
! [X0] :
( X0 != iminus7
| cTorF(X0) ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f131,plain,
! [X] :
( ( ( X != iminus3
& X != iplus3 )
| cTorF(X) )
& ( X = iminus3
| X = iplus3
| ~ cTorF(X) ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f132,plain,
( ! [X] :
( ( X != iminus3
& X != iplus3 )
| cTorF(X) )
& ! [X] :
( X = iminus3
| X = iplus3
| ~ cTorF(X) ) ),
inference(miniscoping,[status(thm)],[f131]) ).
fof(f133,plain,
! [X0] :
( X0 = iminus3
| X0 = iplus3
| ~ cTorF(X0) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f135,plain,
! [X0] :
( X0 != iminus3
| cTorF(X0) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f136,plain,
! [X] :
( ( ( X != iF
& X != iT )
| cTorF(X) )
& ( X = iF
| X = iT
| ~ cTorF(X) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f137,plain,
( ! [X] :
( ( X != iF
& X != iT )
| cTorF(X) )
& ! [X] :
( X = iF
| X = iT
| ~ cTorF(X) ) ),
inference(miniscoping,[status(thm)],[f136]) ).
fof(f140,plain,
! [X0] :
( X0 != iF
| cTorF(X0) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f141,plain,
! [X] :
( ( ( X != iminus8
& X != iplus8 )
| cTorF(X) )
& ( X = iminus8
| X = iplus8
| ~ cTorF(X) ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f142,plain,
( ! [X] :
( ( X != iminus8
& X != iplus8 )
| cTorF(X) )
& ! [X] :
( X = iminus8
| X = iplus8
| ~ cTorF(X) ) ),
inference(miniscoping,[status(thm)],[f141]) ).
fof(f143,plain,
! [X0] :
( X0 = iminus8
| X0 = iplus8
| ~ cTorF(X0) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f144,plain,
! [X0] :
( X0 != iplus8
| cTorF(X0) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f146,plain,
! [X] :
( ( ( X != iplus6
& X != iminus6 )
| cTorF(X) )
& ( X = iplus6
| X = iminus6
| ~ cTorF(X) ) ),
inference(NNF_transformation,[status(thm)],[f16]) ).
fof(f147,plain,
( ! [X] :
( ( X != iplus6
& X != iminus6 )
| cTorF(X) )
& ! [X] :
( X = iplus6
| X = iminus6
| ~ cTorF(X) ) ),
inference(miniscoping,[status(thm)],[f146]) ).
fof(f148,plain,
! [X0] :
( X0 = iplus6
| X0 = iminus6
| ~ cTorF(X0) ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f151,plain,
! [X] :
( ( ( X != iplus9
& X != iminus9 )
| cTorF(X) )
& ( X = iplus9
| X = iminus9
| ~ cTorF(X) ) ),
inference(NNF_transformation,[status(thm)],[f17]) ).
fof(f152,plain,
( ! [X] :
( ( X != iplus9
& X != iminus9 )
| cTorF(X) )
& ! [X] :
( X = iplus9
| X = iminus9
| ~ cTorF(X) ) ),
inference(miniscoping,[status(thm)],[f151]) ).
fof(f153,plain,
! [X0] :
( X0 = iplus9
| X0 = iminus9
| ~ cTorF(X0) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f154,plain,
! [X0] :
( X0 != iminus9
| cTorF(X0) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f157,plain,
( iT = iplus1
| iT = iplus2
| iT = iminus6 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f159,plain,
( iT = iplus7
| iT = iminus3
| iT = iplus8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f162,plain,
( iT = iplus4
| iT = iminus9
| iT = iplus3 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f165,plain,
( iT = iplus9
| iT = iminus4
| iT = iminus8 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f166,plain,
( iT = iplus4
| iT = iplus6
| iT = iplus3 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f168,plain,
( iT = iminus2
| iT = iminus8
| iT = iplus3 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f169,plain,
( iT = iplus4
| iT = iplus6
| iT = iminus8 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f170,plain,
( iT = iminus2
| iT = iminus9
| iT = iplus3 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f171,plain,
( iT = iminus7
| iT = iminus2
| iT = iplus6 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f174,plain,
( iT = iplus9
| iT = iminus4
| iT = iplus1 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f175,plain,
( iT = iminus4
| iT = iplus2
| iT = iplus8 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f180,plain,
( iT = iminus7
| iT = iminus3
| iT = iminus4 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f181,plain,
( iT = iminus1
| iT = iplus4
| iT = iplus2 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f182,plain,
( iT = iminus3
| iT = iplus1
| iT = iminus2 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f184,plain,
( iT = iminus4
| iT = iminus9
| iT = iminus8 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f185,plain,
( iT = iplus4
| iT = iplus1
| iT = iplus3 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f186,plain,
( iT = iminus3
| iT = iplus2
| iT = iplus8 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f188,plain,
( iT = iminus7
| iT = iplus3
| iT = iplus8 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f190,plain,
( iT = iplus4
| iT = iplus9
| iT = iplus3 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f192,plain,
( iT = iplus7
| iT = iminus2
| iT = iminus9 ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f197,plain,
( iT = iminus1
| iT = iminus4
| iT = iplus6 ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f200,plain,
( iT = iplus4
| iT = iminus2
| iT = iminus6 ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f201,plain,
( iT = iminus4
| iT = iplus6
| iT = iplus8 ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f202,plain,
( iT = iplus9
| iT = iplus7
| iT = iminus4 ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f221,plain,
iT != iF,
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f222,definition,
( sQ0_spl
<=> iT = iminus6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f223,plain,
( ~ sQ0_spl
| iT = iminus6 ),
inference(component_clause,[status(thm)],[f222]) ).
fof(f225,definition,
( sQ1_spl
<=> iT = iplus2 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f226,plain,
( ~ sQ1_spl
| iT = iplus2 ),
inference(component_clause,[status(thm)],[f225]) ).
fof(f228,definition,
( sQ2_spl
<=> iT = iplus1 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f229,plain,
( ~ sQ2_spl
| iT = iplus1 ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f231,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f157,f222,f225,f228]) ).
fof(f232,definition,
( sQ3_spl
<=> iT = iplus9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( ~ sQ3_spl
| iT = iplus9 ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f235,definition,
( sQ4_spl
<=> iT = iminus7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f236,plain,
( ~ sQ4_spl
| iT = iminus7 ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f237,plain,
( sQ4_spl
| iT != iminus7 ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f239,definition,
( sQ5_spl
<=> iT = iplus8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f240,plain,
( ~ sQ5_spl
| iT = iplus8 ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f242,definition,
( sQ6_spl
<=> iT = iminus3 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( ~ sQ6_spl
| iT = iminus3 ),
inference(component_clause,[status(thm)],[f242]) ).
fof(f245,definition,
( sQ7_spl
<=> iT = iplus7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f246,plain,
( ~ sQ7_spl
| iT = iplus7 ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,plain,
( sQ7_spl
| sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f159,f239,f242,f245]) ).
fof(f254,definition,
( sQ9_spl
<=> iT = iplus3 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( ~ sQ9_spl
| iT = iplus3 ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f257,definition,
( sQ10_spl
<=> iT = iminus9 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f258,plain,
( ~ sQ10_spl
| iT = iminus9 ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,definition,
( sQ11_spl
<=> iT = iplus4 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f261,plain,
( ~ sQ11_spl
| iT = iplus4 ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f263,plain,
( sQ11_spl
| sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f162,f254,f257,f260]) ).
fof(f265,definition,
( sQ12_spl
<=> iT = iminus8 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f266,plain,
( ~ sQ12_spl
| iT = iminus8 ),
inference(component_clause,[status(thm)],[f265]) ).
fof(f268,definition,
( sQ13_spl
<=> iT = iminus4 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f269,plain,
( ~ sQ13_spl
| iT = iminus4 ),
inference(component_clause,[status(thm)],[f268]) ).
fof(f270,plain,
( sQ13_spl
| iT != iminus4 ),
inference(component_clause,[status(thm)],[f268]) ).
fof(f271,plain,
( sQ3_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f165,f265,f268,f232]) ).
fof(f272,definition,
( sQ14_spl
<=> iT = iplus6 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f273,plain,
( ~ sQ14_spl
| iT = iplus6 ),
inference(component_clause,[status(thm)],[f272]) ).
fof(f275,plain,
( sQ11_spl
| sQ14_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f166,f254,f272,f260]) ).
fof(f277,definition,
( sQ15_spl
<=> iT = iminus2 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f278,plain,
( ~ sQ15_spl
| iT = iminus2 ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f280,plain,
( sQ15_spl
| sQ12_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f168,f254,f265,f277]) ).
fof(f281,plain,
( sQ11_spl
| sQ14_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f169,f265,f272,f260]) ).
fof(f282,plain,
( sQ15_spl
| sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f170,f254,f257,f277]) ).
fof(f283,plain,
( sQ4_spl
| sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f171,f272,f277,f235]) ).
fof(f286,plain,
( sQ3_spl
| sQ13_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f174,f228,f268,f232]) ).
fof(f287,plain,
( sQ13_spl
| sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f175,f239,f225,f268]) ).
fof(f295,plain,
( sQ4_spl
| sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f180,f268,f242,f235]) ).
fof(f296,definition,
( sQ17_spl
<=> iT = iminus1 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f299,plain,
( sQ17_spl
| sQ11_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f181,f225,f260,f296]) ).
fof(f300,plain,
( sQ6_spl
| sQ2_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f182,f277,f228,f242]) ).
fof(f302,plain,
( sQ13_spl
| sQ10_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f184,f265,f257,f268]) ).
fof(f303,plain,
( sQ11_spl
| sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f185,f254,f228,f260]) ).
fof(f304,plain,
( sQ6_spl
| sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f186,f239,f225,f242]) ).
fof(f306,plain,
( sQ4_spl
| sQ9_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f188,f239,f254,f235]) ).
fof(f308,plain,
( sQ11_spl
| sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f190,f254,f232,f260]) ).
fof(f310,plain,
( sQ7_spl
| sQ15_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f192,f257,f277,f245]) ).
fof(f315,plain,
( sQ17_spl
| sQ13_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f197,f272,f268,f296]) ).
fof(f318,plain,
( sQ11_spl
| sQ15_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f200,f222,f277,f260]) ).
fof(f319,plain,
( sQ13_spl
| sQ14_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f201,f239,f272,f268]) ).
fof(f320,plain,
( sQ3_spl
| sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f202,f268,f245,f232]) ).
fof(f324,plain,
! [X0] :
( X0 != iplus1
| X0 = iplus4
| X0 = iminus4 ),
inference(resolution,[status(thm)],[f113,f109]) ).
fof(f328,plain,
! [X0] :
( X0 = iminus1
| X0 = iplus1
| X0 != iplus4 ),
inference(resolution,[status(thm)],[f115,f108]) ).
fof(f330,plain,
! [X0] :
( X0 != iminus4
| X0 = iminus2
| X0 = iplus2 ),
inference(resolution,[status(thm)],[f118,f114]) ).
fof(f339,plain,
! [X0] :
( X0 != iminus2
| X0 = iminus7
| X0 = iplus7 ),
inference(resolution,[status(thm)],[f123,f120]) ).
fof(f522,plain,
! [X0] :
( ~ sQ13_spl
| X0 = iplus4
| X0 = iT
| ~ cTorF(X0) ),
inference(backward_demodulation,[status(thm)],[f269,f113]) ).
fof(f524,plain,
! [X0] :
( ~ sQ3_spl
| X0 = iT
| X0 = iminus9
| ~ cTorF(X0) ),
inference(backward_demodulation,[status(thm)],[f233,f153]) ).
fof(f526,plain,
! [X0] :
( ~ sQ14_spl
| X0 = iT
| X0 = iminus6
| ~ cTorF(X0) ),
inference(backward_demodulation,[status(thm)],[f273,f148]) ).
fof(f528,plain,
! [X0] :
( ~ sQ9_spl
| X0 = iminus3
| X0 = iT
| ~ cTorF(X0) ),
inference(backward_demodulation,[status(thm)],[f255,f133]) ).
fof(f533,plain,
! [X0] :
( ~ sQ15_spl
| X0 = iT
| X0 = iplus2
| ~ cTorF(X0) ),
inference(backward_demodulation,[status(thm)],[f278,f118]) ).
fof(f535,plain,
! [X0] :
( ~ sQ12_spl
| X0 = iT
| X0 = iplus8
| ~ cTorF(X0) ),
inference(backward_demodulation,[status(thm)],[f266,f143]) ).
fof(f542,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ11_spl
| X0 = iT
| X0 = iT
| ~ cTorF(X0) ),
inference(forward_demodulation,[status(thm)],[f261,f522]) ).
fof(f543,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ11_spl
| X0 = iT
| ~ cTorF(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f542]) ).
fof(f545,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ11_spl
| X0 != iF
| X0 = iT ),
inference(resolution,[status(thm)],[f543,f140]) ).
fof(f552,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ10_spl
| X0 = iT
| X0 = iT
| ~ cTorF(X0) ),
inference(forward_demodulation,[status(thm)],[f258,f524]) ).
fof(f553,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ10_spl
| X0 = iT
| ~ cTorF(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f552]) ).
fof(f556,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ6_spl
| X0 = iT
| X0 = iT
| ~ cTorF(X0) ),
inference(forward_demodulation,[status(thm)],[f243,f528]) ).
fof(f557,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ6_spl
| X0 = iT
| ~ cTorF(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f556]) ).
fof(f558,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| iF = iT ),
inference(equality_resolution,[status(thm)],[f545]) ).
fof(f559,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f558,f221]) ).
fof(f560,plain,
( ~ sQ13_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f559]) ).
fof(f561,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ1_spl
| X0 = iT
| X0 = iT
| ~ cTorF(X0) ),
inference(forward_demodulation,[status(thm)],[f226,f533]) ).
fof(f562,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ1_spl
| X0 = iT
| ~ cTorF(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f561]) ).
fof(f563,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ1_spl
| X0 != iF
| X0 = iT ),
inference(resolution,[status(thm)],[f562,f140]) ).
fof(f569,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| X0 = iT
| X0 = iT
| ~ cTorF(X0) ),
inference(forward_demodulation,[status(thm)],[f240,f535]) ).
fof(f570,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| X0 = iT
| ~ cTorF(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f569]) ).
fof(f596,plain,
! [X0] :
( ~ sQ2_spl
| X0 != iT
| X0 = iplus4
| X0 = iminus4 ),
inference(forward_demodulation,[status(thm)],[f229,f324]) ).
fof(f597,plain,
! [X0] :
( ~ sQ2_spl
| X0 = iminus4
| iplus4 != iminus4
| X0 != iT ),
inference(equality_factoring,[status(thm)],[f596]) ).
fof(f598,definition,
! [X0] :
( sQ20_spl
<=> ( X0 = iminus4
| X0 != iT ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f599,plain,
! [X0] :
( ~ sQ20_spl
| X0 = iminus4
| X0 != iT ),
inference(component_clause,[status(thm)],[f598]) ).
fof(f601,definition,
( sQ21_spl
<=> iplus4 = iminus4 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f604,plain,
( ~ sQ2_spl
| ~ sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f597,f598,f601,f228]) ).
fof(f607,plain,
( ~ sQ15_spl
| ~ sQ1_spl
| iF = iT ),
inference(equality_resolution,[status(thm)],[f563]) ).
fof(f608,definition,
( sQ22_spl
<=> iF = iminus4 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f609,plain,
( ~ sQ22_spl
| iF = iminus4 ),
inference(component_clause,[status(thm)],[f608]) ).
fof(f615,plain,
( ~ sQ15_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f607,f221]) ).
fof(f616,plain,
( ~ sQ15_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f615]) ).
fof(f630,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ10_spl
| X0 != iF
| X0 = iT ),
inference(resolution,[status(thm)],[f553,f140]) ).
fof(f635,plain,
( sQ13_spl
| ~ sQ20_spl
| iT != iT ),
inference(resolution,[status(thm)],[f599,f270]) ).
fof(f636,plain,
( sQ13_spl
| ~ sQ20_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f635]) ).
fof(f637,plain,
( sQ13_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f636]) ).
fof(f660,plain,
! [X0] :
( ~ sQ2_spl
| X0 = iminus1
| X0 = iT
| X0 != iplus4 ),
inference(forward_demodulation,[status(thm)],[f229,f328]) ).
fof(f661,plain,
! [X0] :
( ~ sQ2_spl
| X0 = iT
| iminus1 != iT
| X0 != iplus4 ),
inference(equality_factoring,[status(thm)],[f660]) ).
fof(f662,definition,
! [X0] :
( sQ24_spl
<=> ( X0 = iT
| X0 != iplus4 ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f663,plain,
! [X0] :
( ~ sQ24_spl
| X0 = iT
| X0 != iplus4 ),
inference(component_clause,[status(thm)],[f662]) ).
fof(f665,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f661,f662,f296,f228]) ).
fof(f690,plain,
! [X0] :
( ~ sQ1_spl
| X0 != iminus4
| X0 = iminus2
| X0 = iT ),
inference(forward_demodulation,[status(thm)],[f226,f330]) ).
fof(f692,plain,
( ~ sQ1_spl
| iminus4 = iminus2
| iminus4 = iT ),
inference(equality_resolution,[status(thm)],[f690]) ).
fof(f697,definition,
( sQ26_spl
<=> iminus4 = iminus2 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f698,plain,
( ~ sQ26_spl
| iminus4 = iminus2 ),
inference(component_clause,[status(thm)],[f697]) ).
fof(f700,plain,
( ~ sQ1_spl
| sQ26_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f692,f268,f697,f225]) ).
fof(f769,plain,
! [X0] :
( ~ sQ7_spl
| X0 = iminus7
| X0 = iT
| ~ cTorF(X0) ),
inference(forward_demodulation,[status(thm)],[f246,f123]) ).
fof(f795,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| X0 = iT
| X0 = iT
| ~ cTorF(X0) ),
inference(forward_demodulation,[status(thm)],[f223,f526]) ).
fof(f796,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| X0 = iT
| ~ cTorF(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f795]) ).
fof(f799,plain,
! [X0] :
( ~ sQ12_spl
| X0 != iplus4
| X0 = iT
| X0 = iplus8 ),
inference(resolution,[status(thm)],[f535,f115]) ).
fof(f810,plain,
! [X0] :
( ~ sQ7_spl
| X0 != iplus8
| X0 = iminus7
| X0 = iT ),
inference(resolution,[status(thm)],[f769,f144]) ).
fof(f830,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ6_spl
| X0 != iplus4
| X0 = iT ),
inference(resolution,[status(thm)],[f557,f115]) ).
fof(f832,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ6_spl
| X0 != iminus7
| X0 = iT ),
inference(resolution,[status(thm)],[f557,f125]) ).
fof(f840,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| iplus4 = iT ),
inference(equality_resolution,[status(thm)],[f830]) ).
fof(f841,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f840,f260,f242,f254]) ).
fof(f855,plain,
! [X0] :
( ~ sQ7_spl
| X0 != iminus2
| X0 = iminus7
| X0 = iT ),
inference(forward_demodulation,[status(thm)],[f246,f339]) ).
fof(f856,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ26_spl
| X0 != iminus4
| X0 = iminus7
| X0 = iT ),
inference(forward_demodulation,[status(thm)],[f698,f855]) ).
fof(f857,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ26_spl
| X0 = iT
| iminus7 != iT
| X0 != iminus4 ),
inference(equality_factoring,[status(thm)],[f856]) ).
fof(f858,definition,
! [X0] :
( sQ28_spl
<=> ( X0 = iT
| X0 != iminus4 ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f859,plain,
! [X0] :
( ~ sQ28_spl
| X0 = iT
| X0 != iminus4 ),
inference(component_clause,[status(thm)],[f858]) ).
fof(f861,plain,
( ~ sQ7_spl
| ~ sQ26_spl
| ~ sQ4_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f857,f858,f235,f697,f245]) ).
fof(f880,plain,
( sQ4_spl
| ~ sQ9_spl
| ~ sQ6_spl
| iminus7 != iminus7 ),
inference(resolution,[status(thm)],[f832,f237]) ).
fof(f884,plain,
( sQ4_spl
| ~ sQ9_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f880]) ).
fof(f885,plain,
( sQ4_spl
| ~ sQ9_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f884]) ).
fof(f925,plain,
( ~ sQ22_spl
| iT != iminus4 ),
inference(backward_demodulation,[status(thm)],[f609,f221]) ).
fof(f936,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| X0 != iminus9
| X0 = iT ),
inference(resolution,[status(thm)],[f570,f154]) ).
fof(f937,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| X0 != iminus4
| X0 = iT ),
inference(resolution,[status(thm)],[f570,f114]) ).
fof(f946,plain,
( ~ sQ28_spl
| iminus4 = iT ),
inference(equality_resolution,[status(thm)],[f859]) ).
fof(f948,plain,
( ~ sQ28_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f946,f268,f858]) ).
fof(f949,plain,
( ~ sQ22_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f925,f268,f608]) ).
fof(f998,plain,
( ~ sQ12_spl
| ~ sQ5_spl
| iminus9 = iT ),
inference(equality_resolution,[status(thm)],[f936]) ).
fof(f999,plain,
( ~ sQ12_spl
| ~ sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f998,f257,f239,f265]) ).
fof(f1068,plain,
( ~ sQ12_spl
| ~ sQ5_spl
| iminus4 = iT ),
inference(equality_resolution,[status(thm)],[f937]) ).
fof(f1071,plain,
( ~ sQ12_spl
| ~ sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f1068,f268,f239,f265]) ).
fof(f1135,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| X0 != iminus3
| X0 = iT ),
inference(resolution,[status(thm)],[f796,f135]) ).
fof(f1221,plain,
( ~ sQ14_spl
| ~ sQ0_spl
| iminus3 = iT ),
inference(equality_resolution,[status(thm)],[f1135]) ).
fof(f1222,plain,
( ~ sQ14_spl
| ~ sQ0_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f1221,f242,f222,f272]) ).
fof(f1227,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| X0 != iplus4
| X0 = iT
| X0 = iT ),
inference(forward_demodulation,[status(thm)],[f240,f799]) ).
fof(f1228,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| X0 != iplus4
| X0 = iT ),
inference(duplicate_literals_removal,[status(thm)],[f1227]) ).
fof(f1272,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| iF = iT ),
inference(equality_resolution,[status(thm)],[f630]) ).
fof(f1273,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1272,f221]) ).
fof(f1274,plain,
( ~ sQ3_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f1273]) ).
fof(f1317,plain,
( ~ sQ12_spl
| ~ sQ5_spl
| iplus4 = iT ),
inference(equality_resolution,[status(thm)],[f1228]) ).
fof(f1318,plain,
( ~ sQ12_spl
| ~ sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f1317,f260,f239,f265]) ).
fof(f1334,plain,
( ~ sQ24_spl
| iplus4 = iT ),
inference(equality_resolution,[status(thm)],[f663]) ).
fof(f1335,plain,
( ~ sQ24_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f1334,f260,f662]) ).
fof(f1337,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ4_spl
| X0 != iplus8
| X0 = iT
| X0 = iT ),
inference(forward_demodulation,[status(thm)],[f236,f810]) ).
fof(f1338,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ4_spl
| X0 != iplus8
| X0 = iT ),
inference(duplicate_literals_removal,[status(thm)],[f1337]) ).
fof(f1525,plain,
( ~ sQ7_spl
| ~ sQ4_spl
| iplus8 = iT ),
inference(equality_resolution,[status(thm)],[f1338]) ).
fof(f1526,plain,
( ~ sQ7_spl
| ~ sQ4_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f1525,f239,f235,f245]) ).
fof(f1527,plain,
$false,
inference(sat_refutation,[status(thm)],[f231,f248,f263,f271,f275,f280,f281,f282,f283,f286,f287,f295,f299,f300,f302,f303,f304,f306,f308,f310,f315,f318,f319,f320,f560,f604,f616,f637,f665,f700,f841,f861,f885,f948,f949,f999,f1071,f1222,f1274,f1318,f1335,f1526]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS102+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.37 % Computer : n013.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Sun Sep 20 22:53:19 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.38 % Drodi V4.1.1
% 0.14/10.45 % Refutation found
% 0.14/10.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/10.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/10.47 % Elapsed time: 0.085566 seconds
% 0.14/10.47 % CPU time: 0.479991 seconds
% 0.14/10.47 % Total memory used: 17.144 MB
% 0.14/10.47 % Net memory used: 16.729 MB
%------------------------------------------------------------------------------