%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM022+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n015.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 : Fri Sep 25 01:04:20 PM UTC 2026
% Result : Theorem 1.79s 1.29s
% Output : CNFRefutation 1.79s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f156ERROR: Could not build tree for root c_7940ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aRewritingSystem0(X1)
& aElement0(X0) )
=> ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCRDef) ).
fof(f13,axiom,
! [X0,X1] :
( ( aRewritingSystem0(X1)
& aElement0(X0) )
=> ! [X2] :
( aNormalFormOfIn0(X2,X0,X1)
<=> ( ~ ? [X3] : aReductOfIn0(X3,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNFRDef) ).
fof(f15,axiom,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).
fof(f17,axiom,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__731) ).
fof(f19,conjecture,
( ( ( sdtmndtplgtdt0(xa,xR,xc)
& sdtmndtplgtdt0(xa,xR,xb) )
=> ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( sdtmndtasgtdt0(xc,xR,X3)
& sdtmndtasgtdt0(xb,xR,X3)
& aNormalFormOfIn0(X3,X2,xR) )
& sdtmndtasgtdt0(X1,xR,X2)
& sdtmndtasgtdt0(X0,xR,X2)
& aElement0(X2) )
& sdtmndtasgtdt0(X1,xR,xc)
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) )
& sdtmndtasgtdt0(X0,xR,xb)
& aReductOfIn0(X0,xa,xR)
& aElement0(X0) ) )
=> ( ( sdtmndtasgtdt0(xa,xR,xc)
& sdtmndtasgtdt0(xa,xR,xb) )
=> ? [X0] :
( sdtmndtasgtdt0(xc,xR,X0)
& sdtmndtasgtdt0(xb,xR,X0)
& aElement0(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f20,negated_conjecture,
~ ( ( ( sdtmndtplgtdt0(xa,xR,xc)
& sdtmndtplgtdt0(xa,xR,xb) )
=> ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( sdtmndtasgtdt0(xc,xR,X3)
& sdtmndtasgtdt0(xb,xR,X3)
& aNormalFormOfIn0(X3,X2,xR) )
& sdtmndtasgtdt0(X1,xR,X2)
& sdtmndtasgtdt0(X0,xR,X2)
& aElement0(X2) )
& sdtmndtasgtdt0(X1,xR,xc)
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) )
& sdtmndtasgtdt0(X0,xR,xb)
& aReductOfIn0(X0,xa,xR)
& aElement0(X0) ) )
=> ( ( sdtmndtasgtdt0(xa,xR,xc)
& sdtmndtasgtdt0(xa,xR,xb) )
=> ? [X0] :
( sdtmndtasgtdt0(xc,xR,X0)
& sdtmndtasgtdt0(xb,xR,X0)
& aElement0(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f25,plain,
~ ( ( ( sdtmndtplgtdt0(xa,xR,xc)
& sdtmndtplgtdt0(xa,xR,xb) )
=> ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( sdtmndtasgtdt0(xc,xR,X3)
& sdtmndtasgtdt0(xb,xR,X3)
& aNormalFormOfIn0(X3,X2,xR) )
& sdtmndtasgtdt0(X1,xR,X2)
& sdtmndtasgtdt0(X0,xR,X2)
& aElement0(X2) )
& sdtmndtasgtdt0(X1,xR,xc)
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) )
& sdtmndtasgtdt0(X0,xR,xb)
& aReductOfIn0(X0,xa,xR)
& aElement0(X0) ) )
=> ( ( sdtmndtasgtdt0(xa,xR,xc)
& sdtmndtasgtdt0(xa,xR,xb) )
=> ? [X4] :
( sdtmndtasgtdt0(xc,xR,X4)
& sdtmndtasgtdt0(xb,xR,X4)
& aElement0(X4) ) ) ),
inference(rectify,[],[f20]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ) ) ),
inference(flattening,[],[f32]) ).
fof(f42,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( aNormalFormOfIn0(X2,X0,X1)
<=> ( ! [X3] : ~ aReductOfIn0(X3,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f43,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( aNormalFormOfIn0(X2,X0,X1)
<=> ( ! [X3] : ~ aReductOfIn0(X3,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) ) ) ),
inference(flattening,[],[f42]) ).
fof(f48,plain,
( ( ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( sdtmndtasgtdt0(xc,xR,X3)
& sdtmndtasgtdt0(xb,xR,X3)
& aNormalFormOfIn0(X3,X2,xR) )
& sdtmndtasgtdt0(X1,xR,X2)
& sdtmndtasgtdt0(X0,xR,X2)
& aElement0(X2) )
& sdtmndtasgtdt0(X1,xR,xc)
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) )
& sdtmndtasgtdt0(X0,xR,xb)
& aReductOfIn0(X0,xa,xR)
& aElement0(X0) ) )
& sdtmndtasgtdt0(xa,xR,xc)
& sdtmndtasgtdt0(xa,xR,xb)
& ! [X4] :
( ~ sdtmndtasgtdt0(xc,xR,X4)
| ~ sdtmndtasgtdt0(xb,xR,X4)
| ~ aElement0(X4) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f49,plain,
( ( ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( sdtmndtasgtdt0(xc,xR,X3)
& sdtmndtasgtdt0(xb,xR,X3)
& aNormalFormOfIn0(X3,X2,xR) )
& sdtmndtasgtdt0(X1,xR,X2)
& sdtmndtasgtdt0(X0,xR,X2)
& aElement0(X2) )
& sdtmndtasgtdt0(X1,xR,xc)
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) )
& sdtmndtasgtdt0(X0,xR,xb)
& aReductOfIn0(X0,xa,xR)
& aElement0(X0) ) )
& sdtmndtasgtdt0(xa,xR,xc)
& sdtmndtasgtdt0(xa,xR,xb)
& ! [X4] :
( ~ sdtmndtasgtdt0(xc,xR,X4)
| ~ sdtmndtasgtdt0(xb,xR,X4)
| ~ aElement0(X4) ) ),
inference(flattening,[],[f48]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ( ( ~ sdtmndtasgtdt0(X0,X1,X2)
| sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 )
& ( ( ~ sdtmndtplgtdt0(X0,X1,X2)
& X0 != X2 )
| sdtmndtasgtdt0(X0,X1,X2) ) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ( ( ~ sdtmndtasgtdt0(X0,X1,X2)
| sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 )
& ( ( ~ sdtmndtplgtdt0(X0,X1,X2)
& X0 != X2 )
| sdtmndtasgtdt0(X0,X1,X2) ) ) ),
inference(flattening,[],[f62]) ).
fof(f75,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ( ~ aNormalFormOfIn0(X2,X0,X1)
| ( ! [X3] : ~ aReductOfIn0(X3,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) ) )
& ( ? [X3] : aReductOfIn0(X3,X2,X1)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| aNormalFormOfIn0(X2,X0,X1) ) ) ),
inference(nnf_transformation,[],[f43]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ( ~ aNormalFormOfIn0(X2,X0,X1)
| ( ! [X3] : ~ aReductOfIn0(X3,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) ) )
& ( ? [X3] : aReductOfIn0(X3,X2,X1)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| aNormalFormOfIn0(X2,X0,X1) ) ) ),
inference(flattening,[],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ( ~ aNormalFormOfIn0(X2,X0,X1)
| ( ! [X4] : ~ aReductOfIn0(X4,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) ) )
& ( ? [X3] : aReductOfIn0(X3,X2,X1)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| aNormalFormOfIn0(X2,X0,X1) ) ) ),
inference(rectify,[],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ( ~ aNormalFormOfIn0(X2,X0,X1)
| ( ! [X4] : ~ aReductOfIn0(X4,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) ) )
& ( aReductOfIn0(sK16(X1,X2),X2,X1)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| aNormalFormOfIn0(X2,X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X3,sK16(X1,X2))],[f77]) ).
fof(f83,plain,
( ( ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ? [X1] :
( ? [X2] :
( sP4(X1,X2)
& sdtmndtasgtdt0(X2,xR,xc)
& aReductOfIn0(X2,xa,xR)
& aElement0(X2) )
& sdtmndtasgtdt0(X1,xR,xb)
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) ) )
& sdtmndtasgtdt0(xa,xR,xc)
& sdtmndtasgtdt0(xa,xR,xb)
& ! [X0] :
( ~ sdtmndtasgtdt0(xc,xR,X0)
| ~ sdtmndtasgtdt0(xb,xR,X0)
| ~ aElement0(X0) ) ),
inference(rectify,[],[f57]) ).
fof(f84,plain,
( ( ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ( sP4(sK21,sK22)
& sdtmndtasgtdt0(sK22,xR,xc)
& aReductOfIn0(sK22,xa,xR)
& aElement0(sK22)
& sdtmndtasgtdt0(sK21,xR,xb)
& aReductOfIn0(sK21,xa,xR)
& aElement0(sK21) ) )
& sdtmndtasgtdt0(xa,xR,xc)
& sdtmndtasgtdt0(xa,xR,xb)
& ! [X0] :
( ~ sdtmndtasgtdt0(xc,xR,X0)
| ~ sdtmndtasgtdt0(xb,xR,X0)
| ~ aElement0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21,sK22]),skolemize(X1,sK21),skolemize(X2,sK22)],[f83]) ).
fof(f92,plain,
! [X2,X0,X1] :
( ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ),
inference(cnf_transformation,[],[f63]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ aNormalFormOfIn0(X2,X0,X1)
| aElement0(X2) ),
inference(cnf_transformation,[],[f78]) ).
fof(f130,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f15]) ).
fof(f133,plain,
aElement0(xc),
inference(cnf_transformation,[],[f17]) ).
fof(f134,plain,
aElement0(xb),
inference(cnf_transformation,[],[f17]) ).
fof(f135,plain,
aElement0(xa),
inference(cnf_transformation,[],[f17]) ).
fof(f145,plain,
( ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| sP4(sK21,sK22) ),
inference(cnf_transformation,[],[f84]) ).
fof(f152,plain,
sdtmndtasgtdt0(xa,xR,xc),
inference(cnf_transformation,[],[f84]) ).
fof(f153,plain,
sdtmndtasgtdt0(xa,xR,xb),
inference(cnf_transformation,[],[f84]) ).
fof(f154,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xc,xR,X0)
| ~ sdtmndtasgtdt0(xb,xR,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( sdtmndtasgtdt0(X0,X1,X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtplgtdt0(X0,X1,X2)
| ( X0 = X2 )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X0,X1,X2) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElement0(X0)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1)
| ~ aNormalFormOfIn0(X0,X1,X2) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_94,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f130]) ).
tcf(c_97,plain,
aElement0(xa),
inference(cnf_transformation,[],[f135]) ).
tcf(c_98,plain,
aElement0(xb),
inference(cnf_transformation,[],[f134]) ).
tcf(c_99,plain,
aElement0(xc),
inference(cnf_transformation,[],[f133]) ).
tcf(c_109,negated_conjecture,
! [X0: $i] :
( ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xc,xR,X0)
| ~ sdtmndtasgtdt0(xb,xR,X0) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_110,negated_conjecture,
sdtmndtasgtdt0(xa,xR,xb),
inference(cnf_transformation,[],[f153]) ).
tcf(c_111,negated_conjecture,
sdtmndtasgtdt0(xa,xR,xc),
inference(cnf_transformation,[],[f152]) ).
tcf(c_118,negated_conjecture,
( sP4(sK21,sK22)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_1893,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtplgtdt0(X1,X0,X2)
| ( X1 = X2 )
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ sdtmndtasgtdt0(X1,X0,X2)
| ( X0 != xR ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_94]) ).
tcf(c_1894,plain,
! [X0: $i,X1: $i] :
( sdtmndtplgtdt0(X0,xR,X1)
| ( X0 = X1 )
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X0,xR,X1) ),
inference(unflattening,[status(thm)],[c_1893]) ).
tcf(c_1926,plain,
! [X0: $i,X1: $i] :
( sdtmndtasgtdt0(X1,X0,X1)
| ~ aElement0(X1)
| ( X0 != xR ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_94]) ).
tcf(c_1927,plain,
! [X0: $i] :
( sdtmndtasgtdt0(X0,xR,X0)
| ~ aElement0(X0) ),
inference(unflattening,[status(thm)],[c_1926]) ).
tcf(c_5418,negated_conjecture,
sdtmndtasgtdt0(xa,xR,xc),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_5419,negated_conjecture,
sdtmndtasgtdt0(xa,xR,xb),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_5420,negated_conjecture,
! [X0: $i] :
( ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xc,xR,X0)
| ~ sdtmndtasgtdt0(xb,xR,X0) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_6547,plain,
( ~ aElement0(xb)
| ~ sdtmndtasgtdt0(xc,xR,xb) ),
inference(superposition,[status(thm)],[c_1927,c_5420]) ).
tcf(c_6548,plain,
~ sdtmndtasgtdt0(xc,xR,xb),
inference(forward_subsumption_resolution,[status(thm)],[c_6547,c_98]) ).
tcf(c_6742,plain,
( sdtmndtplgtdt0(xa,xR,xb)
| ( xa = xb )
| ~ aElement0(xb)
| ~ aElement0(xa) ),
inference(superposition,[status(thm)],[c_5419,c_1894]) ).
tcf(c_6743,plain,
( sdtmndtplgtdt0(xa,xR,xc)
| ( xa = xc )
| ~ aElement0(xc)
| ~ aElement0(xa) ),
inference(superposition,[status(thm)],[c_5418,c_1894]) ).
tcf(c_6746,plain,
( sdtmndtplgtdt0(xa,xR,xc)
| ( xa = xc ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6743,c_99,c_97]) ).
tcf(c_6749,plain,
( sdtmndtplgtdt0(xa,xR,xb)
| ( xa = xb ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6742,c_98,c_97]) ).
fof(f56,definition,
! [X0,X1] :
( ~ sP4(X0,X1)
| ? [X2] :
( ? [X3] :
( sdtmndtasgtdt0(xc,xR,X3)
& sdtmndtasgtdt0(xb,xR,X3)
& aNormalFormOfIn0(X3,X2,xR) )
& sdtmndtasgtdt0(X1,xR,X2)
& sdtmndtasgtdt0(X0,xR,X2)
& aElement0(X2) ) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
fof(f57,plain,
( ( ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ? [X0] :
( ? [X1] :
( sP4(X0,X1)
& sdtmndtasgtdt0(X1,xR,xc)
& aReductOfIn0(X1,xa,xR)
& aElement0(X1) )
& sdtmndtasgtdt0(X0,xR,xb)
& aReductOfIn0(X0,xa,xR)
& aElement0(X0) ) )
& sdtmndtasgtdt0(xa,xR,xc)
& sdtmndtasgtdt0(xa,xR,xb)
& ! [X4] :
( ~ sdtmndtasgtdt0(xc,xR,X4)
| ~ sdtmndtasgtdt0(xb,xR,X4)
| ~ aElement0(X4) ) ),
inference(definition_folding,[],[f49,f56]) ).
fof(f81,plain,
! [X0,X1] :
( ~ sP4(X0,X1)
| ? [X2] :
( ? [X3] :
( sdtmndtasgtdt0(xc,xR,X3)
& sdtmndtasgtdt0(xb,xR,X3)
& aNormalFormOfIn0(X3,X2,xR) )
& sdtmndtasgtdt0(X1,xR,X2)
& sdtmndtasgtdt0(X0,xR,X2)
& aElement0(X2) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f82,plain,
! [X0,X1] :
( ~ sP4(X0,X1)
| ( sdtmndtasgtdt0(xc,xR,sK20(X0,X1))
& sdtmndtasgtdt0(xb,xR,sK20(X0,X1))
& aNormalFormOfIn0(sK20(X0,X1),sK19(X0,X1),xR)
& sdtmndtasgtdt0(X1,xR,sK19(X0,X1))
& sdtmndtasgtdt0(X0,xR,sK19(X0,X1))
& aElement0(sK19(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20]),skolemize(X2,sK19(X0,X1)),skolemize(X3,sK20(X0,X1))],[f81]) ).
fof(f139,plain,
! [X0,X1] :
( ~ sP4(X0,X1)
| sdtmndtasgtdt0(xc,xR,sK20(X0,X1)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f140,plain,
! [X0,X1] :
( ~ sP4(X0,X1)
| sdtmndtasgtdt0(xb,xR,sK20(X0,X1)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f141,plain,
! [X0,X1] :
( ~ sP4(X0,X1)
| aNormalFormOfIn0(sK20(X0,X1),sK19(X0,X1),xR) ),
inference(cnf_transformation,[],[f82]) ).
fof(f144,plain,
! [X0,X1] :
( ~ sP4(X0,X1)
| aElement0(sK19(X0,X1)) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] :
( aElement0(sK19(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( aNormalFormOfIn0(sK20(X0,X1),sK19(X0,X1),xR)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( sdtmndtasgtdt0(xb,xR,sK20(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( sdtmndtasgtdt0(xc,xR,sK20(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_1173,plain,
! [X0: $i,X1: $i] :
( sdtmndtasgtdt0(xc,xR,sK20(X0,X1))
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ( X1 != sK22 )
| ( X0 != sK21 ) ),
inference(resolution_lifted,[status(thm)],[c_108,c_118]) ).
tcf(c_1174,plain,
( sdtmndtasgtdt0(xc,xR,sK20(sK21,sK22))
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(unflattening,[status(thm)],[c_1173]) ).
tcf(c_1184,plain,
! [X0: $i,X1: $i] :
( sdtmndtasgtdt0(xb,xR,sK20(X0,X1))
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ( X1 != sK22 )
| ( X0 != sK21 ) ),
inference(resolution_lifted,[status(thm)],[c_107,c_118]) ).
tcf(c_1185,plain,
( sdtmndtasgtdt0(xb,xR,sK20(sK21,sK22))
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(unflattening,[status(thm)],[c_1184]) ).
tcf(c_1195,plain,
! [X0: $i,X1: $i] :
( aNormalFormOfIn0(sK20(X0,X1),sK19(X0,X1),xR)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ( X1 != sK22 )
| ( X0 != sK21 ) ),
inference(resolution_lifted,[status(thm)],[c_106,c_118]) ).
tcf(c_1196,plain,
( aNormalFormOfIn0(sK20(sK21,sK22),sK19(sK21,sK22),xR)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(unflattening,[status(thm)],[c_1195]) ).
tcf(c_1228,plain,
! [X0: $i,X1: $i] :
( aElement0(sK19(X0,X1))
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ( X1 != sK22 )
| ( X0 != sK21 ) ),
inference(resolution_lifted,[status(thm)],[c_103,c_118]) ).
tcf(c_1229,plain,
( aElement0(sK19(sK21,sK22))
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(unflattening,[status(thm)],[c_1228]) ).
tcf(c_1672,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElement0(X0)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ( X2 != xR )
| ( sK20(sK21,sK22) != X0 )
| ( sK19(sK21,sK22) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_90,c_1196]) ).
tcf(c_1673,plain,
( aElement0(sK20(sK21,sK22))
| ~ aRewritingSystem0(xR)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ aElement0(sK19(sK21,sK22)) ),
inference(unflattening,[status(thm)],[c_1672]) ).
tcf(c_1674,plain,
( aElement0(sK20(sK21,sK22))
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) ),
inference(global_subsumption_just,[status(thm)],[c_1673,c_94,c_1229,c_1673]) ).
tcf(c_1675,plain,
( aElement0(sK20(sK21,sK22))
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(renaming,[status(thm)],[c_1674]) ).
tcf(c_5405,plain,
( aElement0(iPr_def_11)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(demodulation,[status(thm)],[c_1675]) ).
tcf(c_5410,plain,
( sdtmndtasgtdt0(xb,xR,iPr_def_11)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(demodulation,[status(thm)],[c_1185]) ).
tcf(c_5411,plain,
( sdtmndtasgtdt0(xc,xR,iPr_def_11)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(demodulation,[status(thm)],[c_1174]) ).
tcf(c_6777,plain,
( aElement0(iPr_def_11)
| ( xa = xb )
| ~ sdtmndtplgtdt0(xa,xR,xc) ),
inference(superposition,[status(thm)],[c_6749,c_5405]) ).
tcf(c_6779,plain,
( sdtmndtasgtdt0(xc,xR,iPr_def_11)
| ( xa = xb )
| ~ sdtmndtplgtdt0(xa,xR,xc) ),
inference(superposition,[status(thm)],[c_6749,c_5411]) ).
tcf(c_6780,plain,
( sdtmndtasgtdt0(xb,xR,iPr_def_11)
| ( xa = xb )
| ~ sdtmndtplgtdt0(xa,xR,xc) ),
inference(superposition,[status(thm)],[c_6749,c_5410]) ).
tcf(c_7565,plain,
( aElement0(iPr_def_11)
| ( xa = xc )
| ( xa = xb ) ),
inference(superposition,[status(thm)],[c_6746,c_6777]) ).
tcf(c_7636,plain,
( sdtmndtasgtdt0(xc,xR,iPr_def_11)
| ( xa = xc )
| ( xa = xb ) ),
inference(superposition,[status(thm)],[c_6746,c_6779]) ).
tcf(c_7772,plain,
( sdtmndtasgtdt0(xb,xR,iPr_def_11)
| ( xa = xc )
| ( xa = xb ) ),
inference(superposition,[status(thm)],[c_6746,c_6780]) ).
tcf(c_7787,plain,
( ( xa = xc )
| ( xa = xb )
| ~ aElement0(iPr_def_11)
| ~ sdtmndtasgtdt0(xc,xR,iPr_def_11) ),
inference(superposition,[status(thm)],[c_7772,c_5420]) ).
tcf(c_7812,plain,
( ( xa = xc )
| ( xa = xb ) ),
inference(global_subsumption_just,[status(thm)],[c_7787,c_7565,c_7636,c_7787]) ).
tcf(c_7832,plain,
( ( xa = xb )
| ~ sdtmndtasgtdt0(xa,xR,xb) ),
inference(superposition,[status(thm)],[c_7812,c_6548]) ).
tcf(c_7837,plain,
xa = xb,
inference(forward_subsumption_resolution,[status(thm)],[c_7832,c_5419]) ).
tcf(c_7854,plain,
! [X0: $i] :
( ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xc,xR,X0)
| ~ sdtmndtasgtdt0(xa,xR,X0) ),
inference(demodulation,[status(thm)],[c_5420,c_7837]) ).
tcf(c_7939,plain,
( ~ aElement0(xc)
| ~ sdtmndtasgtdt0(xa,xR,xc) ),
inference(superposition,[status(thm)],[c_1927,c_7854]) ).
tcf(c_7940,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7939,c_99,c_5418]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM022+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 07:52:57 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 1.79/1.29 % SZS status Started for theBenchmark.p
% 1.79/1.29 % SZS status Theorem for theBenchmark.p
% 1.79/1.29
% 1.79/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.79/1.29
% 1.79/1.29 % ------ iProver source info
% 1.79/1.29
% 1.79/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.79/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.79/1.29 % git: non_committed_changes: false
% 1.79/1.29
% 1.79/1.29 % ------ Parsing...
% 1.79/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.79/1.29
% 1.79/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 7 0s sf_e pe_s pe_e %
% 1.79/1.29
% 1.79/1.29 % ------ Preprocessing... gs_s sp: 1 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.79/1.29
% 1.79/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.79/1.29 % ------ Proving...
% 1.79/1.29 % ------ Problem Properties
% 1.79/1.29
% 1.79/1.29 %
% 1.79/1.29 % clauses 60
% 1.79/1.29 % conjectures 9
% 1.79/1.29 % EPR 30
% 1.79/1.29 % Horn 46
% 1.79/1.29 % unary 8
% 1.79/1.29 % binary 15
% 1.79/1.29 % lits 206
% 1.79/1.29 % lits eq 3
% 1.79/1.29 % fd_pure 0
% 1.79/1.29 % fd_pseudo 0
% 1.79/1.29 % fd_cond 0
% 1.79/1.29 % fd_pseudo_cond 1
% 1.79/1.29 % AC symbols 0
% 1.79/1.29
% 1.79/1.29 % ------ Schedule dynamic 5 is on
% 1.79/1.29
% 1.79/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.79/1.29
% 1.79/1.29
% 1.79/1.29 % ------
% 1.79/1.29 % Current options:
% 1.79/1.29 % ------
% 1.79/1.29
% 1.79/1.29
% 1.79/1.29 %
% 1.79/1.29
% 1.79/1.29 % ------ Proving...
% 1.79/1.29 %
% 1.79/1.29
% 1.79/1.29 % SZS status Theorem for theBenchmark.p
% 1.79/1.29
% 1.79/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.79/1.29
% 1.79/1.29
%------------------------------------------------------------------------------