%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL894+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 01:09:02 PM UTC 2026
% Result : Theorem 149.75s 19.30s
% Output : CNFRefutation 112.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 37
% Syntax : Number of formulae : 194 ( 49 unt; 26 def)
% Number of atoms : 388 ( 49 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 339 ( 145 ~; 152 |; 9 &)
% ( 29 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 27 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 251 ( 251 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : '+'('+'(A,B),C) = '+'(A,'+'(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : '+'(A,B) = '+'(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : '+'(A,'0') = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : '>='(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( '>='(X1,X2)
& '>='(X0,X1) )
=> '>='(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X3,X4] :
( ( '>='(X4,X3)
& '>='(X3,X4) )
=> X3 = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X5,X6,X7] :
( '>='('+'(X5,X6),X7)
<=> '>='(X6,'==>'(X5,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] : '>='(A,'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X8,X9,X10] :
( '>='(X8,X9)
=> '>='('+'(X8,X10),'+'(X9,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] : '+'(A,'==>'(A,B)) = '+'(B,'==>'(B,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
( ( '>='(c,b)
& '>='(c,a) )
<=> '>='(c,'+'(a,'==>'(a,b))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ( ( '>='(c,b)
& '>='(c,a) )
<=> '>='(c,'+'(a,'==>'(a,b))) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X1,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
! [X0] : '+'(X0,'0') = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
! [X0] : '>='(X0,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f19,plain,
! [X0,X1,X2] :
( '>='(X0,X2)
| ~ '>='(X1,X2)
| ~ '>='(X0,X1) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f20,plain,
! [X0,X2] :
( '>='(X0,X2)
| ! [X1] :
( ~ '>='(X1,X2)
| ~ '>='(X0,X1) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( '>='(X0,X2)
| ~ '>='(X1,X2)
| ~ '>='(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
! [X3,X4] :
( X3 = X4
| ~ '>='(X4,X3)
| ~ '>='(X3,X4) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f23,plain,
! [X0,X1] :
( X0 = X1
| ~ '>='(X1,X0)
| ~ '>='(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X5,X6,X7] :
( ( ~ '>='(X6,'==>'(X5,X7))
| '>='('+'(X5,X6),X7) )
& ( '>='(X6,'==>'(X5,X7))
| ~ '>='('+'(X5,X6),X7) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f25,plain,
( ! [X5,X6,X7] :
( ~ '>='(X6,'==>'(X5,X7))
| '>='('+'(X5,X6),X7) )
& ! [X5,X6,X7] :
( '>='(X6,'==>'(X5,X7))
| ~ '>='('+'(X5,X6),X7) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( '>='(X1,'==>'(X0,X2))
| ~ '>='('+'(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ '>='(X1,'==>'(X0,X2))
| '>='('+'(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f28,plain,
! [X0] : '>='(X0,'0'),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f29,plain,
! [X8,X9,X10] :
( '>='('+'(X8,X10),'+'(X9,X10))
| ~ '>='(X8,X9) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f30,plain,
! [X8,X9] :
( ! [X10] : '>='('+'(X8,X10),'+'(X9,X10))
| ~ '>='(X8,X9) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( '>='('+'(X0,X2),'+'(X1,X2))
| ~ '>='(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f38,plain,
! [X0,X1] : '+'(X0,'==>'(X0,X1)) = '+'(X1,'==>'(X1,X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f39,plain,
( ( '>='(c,b)
& '>='(c,a) )
<~> '>='(c,'+'(a,'==>'(a,b))) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f40,plain,
( ( ~ '>='(c,'+'(a,'==>'(a,b)))
| ~ '>='(c,b)
| ~ '>='(c,a) )
& ( '>='(c,'+'(a,'==>'(a,b)))
| ( '>='(c,b)
& '>='(c,a) ) ) ),
inference(NNF_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
( '>='(c,'+'(a,'==>'(a,b)))
| '>='(c,a) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
( '>='(c,'+'(a,'==>'(a,b)))
| '>='(c,b) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f43,plain,
( ~ '>='(c,'+'(a,'==>'(a,b)))
| ~ '>='(c,b)
| ~ '>='(c,a) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f44,definition,
( sQ0_spl
<=> '>='(c,a) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f45,plain,
( ~ sQ0_spl
| '>='(c,a) ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f46,plain,
( sQ0_spl
| ~ '>='(c,a) ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,definition,
( sQ1_spl
<=> '>='(c,'+'(a,'==>'(a,b))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f48,plain,
( ~ sQ1_spl
| '>='(c,'+'(a,'==>'(a,b))) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f49,plain,
( sQ1_spl
| ~ '>='(c,'+'(a,'==>'(a,b))) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f44,f47]) ).
fof(f51,definition,
( sQ2_spl
<=> '>='(c,b) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f52,plain,
( ~ sQ2_spl
| '>='(c,b) ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f53,plain,
( sQ2_spl
| ~ '>='(c,b) ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,plain,
( sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f42,f51,f47]) ).
fof(f55,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f44,f51,f47]) ).
fof(f64,plain,
( ~ sQ1_spl
| '>='(c,'+'('==>'(a,b),a)) ),
inference(backward_demodulation,[status(thm)],[f16,f48]) ).
fof(f65,plain,
! [X0,X1,X2] : '+'(X0,'+'(X1,X2)) = '+'(X2,'+'(X0,X1)),
inference(paramodulation,[status(thm)],[f15,f16]) ).
fof(f66,plain,
! [X0,X1,X2] : '+'('+'(X0,X1),X2) = '+'('+'(X1,X2),X0),
inference(paramodulation,[status(thm)],[f15,f16]) ).
fof(f84,plain,
! [X0] :
( sQ0_spl
| ~ '>='(X0,a)
| ~ '>='(c,X0) ),
inference(resolution,[status(thm)],[f21,f46]) ).
fof(f86,plain,
! [X0,X1,X2] :
( X2 = X0
| ~ '>='(X2,X0)
| ~ '>='(X1,X2)
| ~ '>='(X0,X1) ),
inference(resolution,[status(thm)],[f21,f23]) ).
fof(f90,plain,
! [X0,X1] : '>='(X0,'==>'(X1,'+'(X1,X0))),
inference(resolution,[status(thm)],[f26,f18]) ).
fof(f95,plain,
! [X0,X1,X2] : '>='(X0,'==>'(X1,'==>'(X2,'+'(X2,'+'(X1,X0))))),
inference(resolution,[status(thm)],[f90,f26]) ).
fof(f121,plain,
! [X0,X1] : '>='(X0,'==>'(X1,'0')),
inference(resolution,[status(thm)],[f28,f26]) ).
fof(f124,plain,
! [X0] :
( '0' = X0
| ~ '>='('0',X0) ),
inference(resolution,[status(thm)],[f28,f23]) ).
fof(f126,plain,
! [X0] : '+'('0',X0) = X0,
inference(paramodulation,[status(thm)],[f16,f17]) ).
fof(f131,plain,
! [X0,X1] :
( ~ '>='('0','==>'(X0,X1))
| '>='(X0,X1) ),
inference(paramodulation,[status(thm)],[f17,f27]) ).
fof(f145,plain,
! [X0,X1] :
( '>='('+'(X0,X1),X1)
| ~ '>='(X0,'0') ),
inference(paramodulation,[status(thm)],[f126,f31]) ).
fof(f146,plain,
! [X0,X1] :
( '>='(X1,'+'(X0,X1))
| ~ '>='('0',X0) ),
inference(paramodulation,[status(thm)],[f126,f31]) ).
fof(f153,plain,
! [X0,X1] : '>='('+'(X0,X1),X1),
inference(forward_subsumption_resolution,[status(thm)],[f145,f28]) ).
fof(f154,plain,
! [X0,X1] : '>='(X0,'==>'(X1,X0)),
inference(resolution,[status(thm)],[f153,f26]) ).
fof(f158,plain,
! [X0,X1,X2] : '>='('+'(X0,'+'(X1,X2)),X2),
inference(paramodulation,[status(thm)],[f15,f153]) ).
fof(f161,plain,
! [X0,X1] : '>='('+'(X0,X1),X0),
inference(paramodulation,[status(thm)],[f16,f153]) ).
fof(f165,plain,
! [X0,X1,X2] :
( '>='(X0,'==>'(X2,X1))
| ~ '>='(X0,X1) ),
inference(resolution,[status(thm)],[f154,f21]) ).
fof(f166,plain,
! [X0,X1] :
( '==>'(X0,X1) = X1
| ~ '>='('==>'(X0,X1),X1) ),
inference(resolution,[status(thm)],[f154,f23]) ).
fof(f175,plain,
! [X0,X1] : '+'('==>'(X0,X1),X0) = '+'(X1,'==>'(X1,X0)),
inference(paramodulation,[status(thm)],[f16,f38]) ).
fof(f215,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ '>='('+'('==>'(a,b),a),a) ),
inference(resolution,[status(thm)],[f64,f84]) ).
fof(f218,plain,
( sQ0_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f215,f153]) ).
fof(f219,plain,
( sQ0_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f218]) ).
fof(f227,plain,
( sQ1_spl
| ~ '>='(c,'+'('==>'(a,b),a)) ),
inference(forward_demodulation,[status(thm)],[f16,f49]) ).
fof(f228,plain,
! [X0] :
( ~ sQ0_spl
| '>='(X0,a)
| ~ '>='(X0,c) ),
inference(resolution,[status(thm)],[f45,f21]) ).
fof(f244,plain,
! [X0,X1] : '>='('+'(X0,'==>'(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f38,f161]) ).
fof(f247,plain,
! [X0,X1,X2] : '>='('+'('+'(X0,X1),X2),X0),
inference(paramodulation,[status(thm)],[f15,f161]) ).
fof(f352,plain,
! [X0] : '0' = '==>'(X0,'0'),
inference(resolution,[status(thm)],[f124,f121]) ).
fof(f353,plain,
! [X0] : '0' = '==>'(X0,'+'(X0,'0')),
inference(resolution,[status(thm)],[f124,f90]) ).
fof(f358,plain,
! [X0] : '0' = '==>'(X0,X0),
inference(forward_demodulation,[status(thm)],[f17,f353]) ).
fof(f651,plain,
! [X0,X1] :
( ~ sQ0_spl
| '>='(X1,'==>'(X0,a))
| ~ '>='('+'(X0,X1),c) ),
inference(resolution,[status(thm)],[f228,f26]) ).
fof(f662,plain,
! [X0] :
( ~ sQ2_spl
| '>='(X0,b)
| ~ '>='(X0,c) ),
inference(resolution,[status(thm)],[f52,f21]) ).
fof(f671,plain,
! [X0] :
( sQ2_spl
| ~ '>='(X0,b)
| ~ '>='(c,X0) ),
inference(resolution,[status(thm)],[f53,f21]) ).
fof(f696,plain,
! [X0,X1,X2] : '>='('+'(X0,X1),'==>'(X2,X1)),
inference(resolution,[status(thm)],[f158,f26]) ).
fof(f708,plain,
! [X0,X1,X2] : '>='('+'('+'(X0,X1),X2),X1),
inference(paramodulation,[status(thm)],[f16,f158]) ).
fof(f722,plain,
! [X0,X1,X2] : '>='('+'(X0,'+'(X1,X2)),X1),
inference(paramodulation,[status(thm)],[f16,f158]) ).
fof(f912,plain,
! [X0,X1] : '>='('+'('==>'(X0,X1),X0),X1),
inference(paramodulation,[status(thm)],[f16,f244]) ).
fof(f921,plain,
! [X0,X1,X2] : '>='(X0,'==>'('+'(X1,X2),X1)),
inference(resolution,[status(thm)],[f247,f26]) ).
fof(f982,definition,
( sQ12_spl
<=> '>='(c,c) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f984,plain,
( sQ12_spl
| ~ '>='(c,c) ),
inference(component_clause,[status(thm)],[f982]) ).
fof(f1007,plain,
! [X0,X1,X2] : '>='('+'(X0,X1),'==>'(X2,X0)),
inference(paramodulation,[status(thm)],[f16,f696]) ).
fof(f1014,plain,
! [X0] :
( sQ1_spl
| ~ '>='(X0,'+'('==>'(a,b),a))
| ~ '>='(c,X0) ),
inference(resolution,[status(thm)],[f227,f21]) ).
fof(f1395,plain,
! [X0,X1] :
( ~ sQ2_spl
| '>='(X1,'==>'(X0,b))
| ~ '>='('+'(X0,X1),c) ),
inference(resolution,[status(thm)],[f662,f26]) ).
fof(f1731,plain,
! [X0,X1] : '0' = '==>'('+'(X0,X1),X0),
inference(resolution,[status(thm)],[f921,f124]) ).
fof(f1773,plain,
! [X0,X1] : '0' = '==>'('+'(X0,'==>'(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f38,f1731]) ).
fof(f1780,plain,
! [X0,X1,X2] : '0' = '==>'('+'(X0,'+'(X1,X2)),X2),
inference(paramodulation,[status(thm)],[f65,f1731]) ).
fof(f1781,plain,
! [X0,X1,X2] : '0' = '==>'('+'(X0,'+'(X1,X2)),X1),
inference(paramodulation,[status(thm)],[f65,f1731]) ).
fof(f1782,plain,
! [X0,X1,X2] : '0' = '==>'('+'('+'(X0,X1),X2),X0),
inference(paramodulation,[status(thm)],[f15,f1731]) ).
fof(f1783,plain,
! [X0,X1] : '0' = '==>'('+'(X0,X1),X1),
inference(paramodulation,[status(thm)],[f16,f1731]) ).
fof(f1812,plain,
! [X0,X1,X2] : '0' = '==>'('+'('+'(X0,X1),X2),X1),
inference(paramodulation,[status(thm)],[f66,f1783]) ).
fof(f1844,plain,
( ~ sQ1_spl
| sQ2_spl
| ~ '>='('+'('==>'(a,b),a),b) ),
inference(resolution,[status(thm)],[f671,f64]) ).
fof(f1853,plain,
( ~ sQ1_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1844,f912]) ).
fof(f1854,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f1853]) ).
fof(f1882,plain,
! [X0,X1,X2] : '>='(X0,'==>'(X1,'==>'(X2,X1))),
inference(resolution,[status(thm)],[f1007,f26]) ).
fof(f2438,plain,
! [X0] :
( sQ1_spl
| ~ '>='(X0,'==>'(a,b))
| ~ '>='(c,'+'(X0,a)) ),
inference(resolution,[status(thm)],[f1014,f31]) ).
fof(f2446,plain,
! [X0,X1] : '0' = '==>'(X0,'==>'(X1,X0)),
inference(resolution,[status(thm)],[f1882,f124]) ).
fof(f2528,plain,
! [X0,X1] :
( '0' = '==>'(X1,X0)
| ~ '>='('0',X0) ),
inference(resolution,[status(thm)],[f165,f124]) ).
fof(f2683,plain,
( '0' = '0'
| ~ '>='('0','0') ),
inference(paramodulation,[status(thm)],[f352,f2528]) ).
fof(f2688,definition,
( sQ17_spl
<=> '0' = '0' ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f2697,definition,
( sQ19_spl
<=> '>='('0','0') ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f2699,plain,
( sQ19_spl
| ~ '>='('0','0') ),
inference(component_clause,[status(thm)],[f2697]) ).
fof(f2700,plain,
( sQ17_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2683,f2697,f2688]) ).
fof(f3282,definition,
! [X0] :
( sQ27_spl
<=> '>='(X0,'0') ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f3369,plain,
! [X0,X1] :
( ~ '>='('0','0')
| '>='('+'(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f1783,f131]) ).
fof(f3370,plain,
! [X0,X1] :
( ~ '>='('0','0')
| '>='('+'(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f1731,f131]) ).
fof(f3372,plain,
! [X0,X1] :
( ~ '>='('0','0')
| '>='(X0,'==>'(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2446,f131]) ).
fof(f3373,plain,
! [X0] :
( ~ '>='('0','0')
| '>='(X0,'0') ),
inference(paramodulation,[status(thm)],[f352,f131]) ).
fof(f3374,plain,
! [X0] :
( ~ '>='('0','0')
| '>='(X0,X0) ),
inference(paramodulation,[status(thm)],[f358,f131]) ).
fof(f3379,definition,
! [X0,X1] :
( sQ33_spl
<=> '>='('+'(X0,X1),X1) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f3382,plain,
( ~ sQ19_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f3369,f3379,f2697]) ).
fof(f3383,definition,
! [X0,X1] :
( sQ34_spl
<=> '>='('+'(X0,X1),X0) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f3386,plain,
( ~ sQ19_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f3370,f3383,f2697]) ).
fof(f3387,definition,
! [X0,X1] :
( sQ35_spl
<=> '>='(X0,'==>'(X1,X0)) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f3390,plain,
( ~ sQ19_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f3372,f3387,f2697]) ).
fof(f3391,plain,
( ~ sQ19_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f3373,f3282,f2697]) ).
fof(f3392,definition,
! [X0] :
( sQ36_spl
<=> '>='(X0,X0) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f3395,plain,
( ~ sQ19_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f3374,f3392,f2697]) ).
fof(f3396,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2699,f28]) ).
fof(f3397,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f3396]) ).
fof(f3488,plain,
! [X0,X1] :
( '+'(X0,X1) = X1
| ~ '>='('+'(X0,X1),X1)
| ~ '>='('0',X0) ),
inference(resolution,[status(thm)],[f146,f23]) ).
fof(f3523,plain,
! [X0,X1] :
( '+'(X0,X1) = X1
| ~ '>='('0',X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3488,f153]) ).
fof(f3525,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f984,f18]) ).
fof(f3526,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f3525]) ).
fof(f3548,plain,
! [X0] :
( X0 = X0
| ~ '>='('0','0') ),
inference(paramodulation,[status(thm)],[f126,f3523]) ).
fof(f3574,definition,
! [X0] :
( sQ38_spl
<=> X0 = X0 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f3577,plain,
( sQ38_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f3548,f2697,f3574]) ).
fof(f3970,plain,
! [X0] :
( '==>'(X0,'0') = '0'
| ~ '>='('0','0') ),
inference(paramodulation,[status(thm)],[f352,f166]) ).
fof(f3975,definition,
! [X0] :
( sQ41_spl
<=> '==>'(X0,'0') = '0' ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f3978,plain,
( sQ41_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f3970,f2697,f3975]) ).
fof(f4580,plain,
! [X0,X1] : '0' = '==>'('+'('==>'(X0,X1),X0),X1),
inference(paramodulation,[status(thm)],[f16,f1773]) ).
fof(f4603,plain,
! [X0,X1] :
( ~ '>='('0','0')
| '>='('+'(X0,'==>'(X0,X1)),X1) ),
inference(paramodulation,[status(thm)],[f1773,f131]) ).
fof(f4631,definition,
! [X0,X1] :
( sQ44_spl
<=> '>='('+'(X0,'==>'(X0,X1)),X1) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f4634,plain,
( ~ sQ19_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f4603,f4631,f2697]) ).
fof(f4713,plain,
! [X0,X1,X2] :
( ~ '>='('0','0')
| '>='('+'(X0,'+'(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f1780,f131]) ).
fof(f4737,definition,
! [X0,X1,X2] :
( sQ46_spl
<=> '>='('+'(X0,'+'(X1,X2)),X2) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f4740,plain,
( ~ sQ19_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f4713,f4737,f2697]) ).
fof(f4985,plain,
! [X0,X1,X2] :
( ~ '>='('0','0')
| '>='('+'(X0,'+'(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f1781,f131]) ).
fof(f5009,definition,
! [X0,X1,X2] :
( sQ48_spl
<=> '>='('+'(X0,'+'(X1,X2)),X1) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f5012,plain,
( ~ sQ19_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f4985,f5009,f2697]) ).
fof(f5099,plain,
! [X0,X1,X2] :
( ~ '>='('0','0')
| '>='('+'('+'(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f1782,f131]) ).
fof(f5123,definition,
! [X0,X1,X2] :
( sQ50_spl
<=> '>='('+'('+'(X0,X1),X2),X0) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f5126,plain,
( ~ sQ19_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f5099,f5123,f2697]) ).
fof(f5215,plain,
! [X0,X1,X2] :
( ~ '>='('0','0')
| '>='('+'('+'(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f1812,f131]) ).
fof(f5239,definition,
! [X0,X1,X2] :
( sQ52_spl
<=> '>='('+'('+'(X0,X1),X2),X1) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f5242,plain,
( ~ sQ19_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f5215,f5239,f2697]) ).
fof(f6726,plain,
! [X0,X1] :
( ~ sQ0_spl
| '>='(X0,'==>'('+'(X1,c),a)) ),
inference(resolution,[status(thm)],[f651,f708]) ).
fof(f6730,plain,
! [X0,X1] :
( ~ sQ0_spl
| '>='('+'(c,X0),'==>'(X1,a)) ),
inference(resolution,[status(thm)],[f651,f722]) ).
fof(f6735,plain,
! [X0] :
( ~ sQ0_spl
| '>='(X0,'==>'(c,a)) ),
inference(resolution,[status(thm)],[f651,f161]) ).
fof(f6783,plain,
( ~ sQ0_spl
| '0' = '==>'(c,a) ),
inference(resolution,[status(thm)],[f6735,f124]) ).
fof(f6792,plain,
( ~ sQ0_spl
| '==>'(c,a) = '==>'(c,a)
| ~ '>='('==>'(c,a),'==>'(c,a)) ),
inference(resolution,[status(thm)],[f6735,f86]) ).
fof(f6802,definition,
( sQ57_spl
<=> '>='('==>'(c,a),'==>'(c,a)) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f6804,plain,
( sQ57_spl
| ~ '>='('==>'(c,a),'==>'(c,a)) ),
inference(component_clause,[status(thm)],[f6802]) ).
fof(f6805,definition,
( sQ58_spl
<=> '==>'(c,a) = '==>'(c,a) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f6808,plain,
( ~ sQ0_spl
| sQ58_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f6792,f6802,f6805,f44]) ).
fof(f6810,plain,
( sQ57_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6804,f6735]) ).
fof(f6811,plain,
( sQ57_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f6810]) ).
fof(f6817,plain,
( ~ sQ0_spl
| '+'('==>'(a,c),a) = '+'(c,'0') ),
inference(paramodulation,[status(thm)],[f6783,f175]) ).
fof(f6851,plain,
( ~ sQ0_spl
| '+'('==>'(a,c),a) = c ),
inference(forward_demodulation,[status(thm)],[f17,f6817]) ).
fof(f7084,plain,
! [X0,X1] :
( ~ '>='('0','0')
| '>='('+'('==>'(X0,X1),X0),X1) ),
inference(paramodulation,[status(thm)],[f4580,f131]) ).
fof(f7139,definition,
! [X0,X1] :
( sQ62_spl
<=> '>='('+'('==>'(X0,X1),X0),X1) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f7142,plain,
( ~ sQ19_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f7084,f7139,f2697]) ).
fof(f8999,plain,
! [X0] :
( ~ sQ0_spl
| '0' = '==>'('+'(X0,c),a) ),
inference(resolution,[status(thm)],[f6726,f124]) ).
fof(f9054,plain,
! [X0] :
( ~ sQ0_spl
| '0' = '==>'('+'(c,X0),a) ),
inference(paramodulation,[status(thm)],[f16,f8999]) ).
fof(f9094,plain,
! [X0] :
( ~ sQ0_spl
| ~ '>='('0','0')
| '>='('+'(X0,c),a) ),
inference(paramodulation,[status(thm)],[f8999,f131]) ).
fof(f9161,definition,
! [X0] :
( sQ67_spl
<=> '>='('+'(X0,c),a) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f9164,plain,
( ~ sQ0_spl
| ~ sQ19_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f9094,f9161,f2697,f44]) ).
fof(f9281,plain,
! [X0] :
( ~ sQ0_spl
| ~ '>='('0','0')
| '>='('+'(c,X0),a) ),
inference(paramodulation,[status(thm)],[f9054,f131]) ).
fof(f9358,definition,
! [X0] :
( sQ71_spl
<=> '>='('+'(c,X0),a) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f9361,plain,
( ~ sQ0_spl
| ~ sQ19_spl
| sQ71_spl ),
inference(split_clause,[status(thm)],[f9281,f9358,f2697,f44]) ).
fof(f9427,plain,
! [X0,X1] :
( ~ sQ0_spl
| '>='(X0,'==>'(c,'==>'(X1,a))) ),
inference(resolution,[status(thm)],[f6730,f26]) ).
fof(f9878,plain,
! [X0,X1] : '0' = '==>'(X0,'==>'(X1,'+'(X1,'+'(X0,'0')))),
inference(resolution,[status(thm)],[f95,f124]) ).
fof(f9964,plain,
! [X0,X1] : '0' = '==>'(X0,'==>'(X1,'+'(X1,X0))),
inference(forward_demodulation,[status(thm)],[f17,f9878]) ).
fof(f10187,plain,
! [X0] :
( ~ sQ2_spl
| '>='('==>'(X0,c),'==>'(X0,b)) ),
inference(resolution,[status(thm)],[f1395,f244]) ).
fof(f16163,plain,
! [X0] :
( ~ sQ0_spl
| '0' = '==>'(c,'==>'(X0,a)) ),
inference(resolution,[status(thm)],[f9427,f124]) ).
fof(f16254,plain,
! [X0] :
( ~ sQ0_spl
| ~ '>='('0','0')
| '>='(c,'==>'(X0,a)) ),
inference(paramodulation,[status(thm)],[f16163,f131]) ).
fof(f16325,definition,
! [X0] :
( sQ104_spl
<=> '>='(c,'==>'(X0,a)) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f16328,plain,
( ~ sQ0_spl
| ~ sQ19_spl
| sQ104_spl ),
inference(split_clause,[status(thm)],[f16254,f16325,f2697,f44]) ).
fof(f18357,plain,
! [X0,X1] :
( ~ '>='('0','0')
| '>='(X0,'==>'(X1,'+'(X1,X0))) ),
inference(paramodulation,[status(thm)],[f9964,f131]) ).
fof(f18428,definition,
! [X0,X1] :
( sQ108_spl
<=> '>='(X0,'==>'(X1,'+'(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f18431,plain,
( ~ sQ19_spl
| sQ108_spl ),
inference(split_clause,[status(thm)],[f18357,f18428,f2697]) ).
fof(f23215,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ '>='('==>'(a,c),'==>'(a,b))
| ~ '>='(c,c) ),
inference(paramodulation,[status(thm)],[f6851,f2438]) ).
fof(f23241,definition,
( sQ116_spl
<=> '>='('==>'(a,c),'==>'(a,b)) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f23243,plain,
( sQ116_spl
| ~ '>='('==>'(a,c),'==>'(a,b)) ),
inference(component_clause,[status(thm)],[f23241]) ).
fof(f23244,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ sQ116_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f23215,f982,f23241,f47,f44]) ).
fof(f23246,plain,
( sQ116_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f23243,f10187]) ).
fof(f23247,plain,
( sQ116_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f23246]) ).
fof(f23248,plain,
$false,
inference(sat_refutation,[status(thm)],[f50,f54,f55,f219,f1854,f2700,f3382,f3386,f3390,f3391,f3395,f3397,f3526,f3577,f3978,f4634,f4740,f5012,f5126,f5242,f6808,f6811,f7142,f9164,f9361,f16328,f18431,f23244,f23247]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL894+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 21 01:09:51 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 149.75/19.30 % Refutation found
% 149.75/19.30 % SZS status Theorem for theBenchmark: Theorem is valid
% 149.75/19.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 112.48/19.34 % Elapsed time: 19.031108 seconds
% 112.48/19.34 % CPU time: 150.906862 seconds
% 112.48/19.34 % Total memory used: 537.591 MB
% 112.48/19.34 % Net memory used: 484.887 MB
%------------------------------------------------------------------------------