%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM019+4 : 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 : n002.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 10.45s 2.50s
% Output : CNFRefutation 10.45s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f60ERROR: Could not build tree for root c_25723ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( ( aRewritingSystem0(X1)
& aElement0(X0) )
=> ! [X2] :
( aReductOfIn0(X2,X0,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mReduct) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( ( aElement0(X3)
& aElement0(X2)
& aRewritingSystem0(X1)
& aElement0(X0) )
=> ( ( sdtmndtasgtdt0(X2,X1,X3)
& sdtmndtasgtdt0(X0,X1,X2) )
=> sdtmndtasgtdt0(X0,X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCRTrans) ).
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(f18,axiom,
! [X0,X1,X2] :
( ( ( sdtmndtasgtdt0(X0,xR,X2)
| sdtmndtplgtdt0(X0,xR,X2)
| ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X0,xR)
| X0 = X2 )
& ( sdtmndtasgtdt0(X0,xR,X1)
| sdtmndtplgtdt0(X0,xR,X1)
| ? [X3] :
( sdtmndtplgtdt0(X3,xR,X1)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X1,X0,xR)
| X0 = X1 )
& aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ( iLess0(X0,xa)
=> ? [X3] :
( sdtmndtasgtdt0(X2,xR,X3)
& ( ( sdtmndtplgtdt0(X2,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X2,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X2,xR) ) )
| X2 = X3 )
& sdtmndtasgtdt0(X1,xR,X3)
& ( ( sdtmndtplgtdt0(X1,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X1,xR) ) )
| X1 = X3 )
& aElement0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__715) ).
fof(f20,axiom,
( sdtmndtasgtdt0(xu,xR,xb)
& ( ( sdtmndtplgtdt0(xu,xR,xb)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xb)
& aReductOfIn0(X0,xu,xR)
& aElement0(X0) )
| aReductOfIn0(xb,xu,xR) ) )
| xu = xb )
& aReductOfIn0(xu,xa,xR)
& aElement0(xu) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__755) ).
fof(f22,axiom,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xw)
& aReductOfIn0(X0,xv,xR)
& aElement0(X0) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xw)
& aReductOfIn0(X0,xu,xR)
& aElement0(X0) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).
fof(f23,axiom,
( aNormalFormOfIn0(xd,xw,xR)
& ~ ? [X0] : aReductOfIn0(X0,xd,xR)
& sdtmndtasgtdt0(xw,xR,xd)
& ( ( sdtmndtplgtdt0(xw,xR,xd)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xd)
& aReductOfIn0(X0,xw,xR)
& aElement0(X0) )
| aReductOfIn0(xd,xw,xR) ) )
| xw = xd )
& aElement0(xd) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__818) ).
fof(f24,conjecture,
( sdtmndtasgtdt0(xb,xR,xd)
| sdtmndtplgtdt0(xb,xR,xd)
| ? [X0] :
( sdtmndtplgtdt0(X0,xR,xd)
& aReductOfIn0(X0,xb,xR)
& aElement0(X0) )
| aReductOfIn0(xd,xb,xR)
| xb = xd ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f25,negated_conjecture,
~ ( sdtmndtasgtdt0(xb,xR,xd)
| sdtmndtplgtdt0(xb,xR,xd)
| ? [X0] :
( sdtmndtplgtdt0(X0,xR,xd)
& aReductOfIn0(X0,xb,xR)
& aElement0(X0) )
| aReductOfIn0(xd,xb,xR)
| xb = xd ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( ( sdtmndtasgtdt0(X0,xR,X2)
| sdtmndtplgtdt0(X0,xR,X2)
| ? [X4] :
( sdtmndtplgtdt0(X4,xR,X2)
& aReductOfIn0(X4,X0,xR)
& aElement0(X4) )
| aReductOfIn0(X2,X0,xR)
| X0 = X2 )
& ( sdtmndtasgtdt0(X0,xR,X1)
| sdtmndtplgtdt0(X0,xR,X1)
| ? [X3] :
( sdtmndtplgtdt0(X3,xR,X1)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X1,X0,xR)
| X0 = X1 )
& aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ( iLess0(X0,xa)
=> ? [X5] :
( sdtmndtasgtdt0(X2,xR,X5)
& ( ( sdtmndtplgtdt0(X2,xR,X5)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X5)
& aReductOfIn0(X7,X2,xR)
& aElement0(X7) )
| aReductOfIn0(X5,X2,xR) ) )
| X2 = X5 )
& sdtmndtasgtdt0(X1,xR,X5)
& ( ( sdtmndtplgtdt0(X1,xR,X5)
& ( ? [X6] :
( sdtmndtplgtdt0(X6,xR,X5)
& aReductOfIn0(X6,X1,xR)
& aElement0(X6) )
| aReductOfIn0(X5,X1,xR) ) )
| X1 = X5 )
& aElement0(X5) ) ) ),
inference(rectify,[],[f18]) ).
fof(f29,plain,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xw)
& aReductOfIn0(X1,xv,xR)
& aElement0(X1) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xw)
& aReductOfIn0(X0,xu,xR)
& aElement0(X0) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
inference(rectify,[],[f22]) ).
fof(f30,plain,
( aNormalFormOfIn0(xd,xw,xR)
& ~ ? [X1] : aReductOfIn0(X1,xd,xR)
& sdtmndtasgtdt0(xw,xR,xd)
& ( ( sdtmndtplgtdt0(xw,xR,xd)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xd)
& aReductOfIn0(X0,xw,xR)
& aElement0(X0) )
| aReductOfIn0(xd,xw,xR) ) )
| xw = xd )
& aElement0(xd) ),
inference(rectify,[],[f23]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( ~ sdtmndtasgtdt0(X0,xR,X2)
& ~ sdtmndtplgtdt0(X0,xR,X2)
& ! [X4] :
( ~ sdtmndtplgtdt0(X4,xR,X2)
| ~ aReductOfIn0(X4,X0,xR)
| ~ aElement0(X4) )
& ~ aReductOfIn0(X2,X0,xR)
& X0 != X2 )
| ( ~ sdtmndtasgtdt0(X0,xR,X1)
& ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X3] :
( ~ sdtmndtplgtdt0(X3,xR,X1)
| ~ aReductOfIn0(X3,X0,xR)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X1,X0,xR)
& X0 != X1 )
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ iLess0(X0,xa)
| ? [X5] :
( sdtmndtasgtdt0(X2,xR,X5)
& ( ( sdtmndtplgtdt0(X2,xR,X5)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X5)
& aReductOfIn0(X7,X2,xR)
& aElement0(X7) )
| aReductOfIn0(X5,X2,xR) ) )
| X2 = X5 )
& sdtmndtasgtdt0(X1,xR,X5)
& ( ( sdtmndtplgtdt0(X1,xR,X5)
& ( ? [X6] :
( sdtmndtplgtdt0(X6,xR,X5)
& aReductOfIn0(X6,X1,xR)
& aElement0(X6) )
| aReductOfIn0(X5,X1,xR) ) )
| X1 = X5 )
& aElement0(X5) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( ~ sdtmndtasgtdt0(X0,xR,X2)
& ~ sdtmndtplgtdt0(X0,xR,X2)
& ! [X4] :
( ~ sdtmndtplgtdt0(X4,xR,X2)
| ~ aReductOfIn0(X4,X0,xR)
| ~ aElement0(X4) )
& ~ aReductOfIn0(X2,X0,xR)
& X0 != X2 )
| ( ~ sdtmndtasgtdt0(X0,xR,X1)
& ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X3] :
( ~ sdtmndtplgtdt0(X3,xR,X1)
| ~ aReductOfIn0(X3,X0,xR)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X1,X0,xR)
& X0 != X1 )
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ iLess0(X0,xa)
| ? [X5] :
( sdtmndtasgtdt0(X2,xR,X5)
& ( ( sdtmndtplgtdt0(X2,xR,X5)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X5)
& aReductOfIn0(X7,X2,xR)
& aElement0(X7) )
| aReductOfIn0(X5,X2,xR) ) )
| X2 = X5 )
& sdtmndtasgtdt0(X1,xR,X5)
& ( ( sdtmndtplgtdt0(X1,xR,X5)
& ( ? [X6] :
( sdtmndtplgtdt0(X6,xR,X5)
& aReductOfIn0(X6,X1,xR)
& aElement0(X6) )
| aReductOfIn0(X5,X1,xR) ) )
| X1 = X5 )
& aElement0(X5) ) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
( aNormalFormOfIn0(xd,xw,xR)
& ! [X1] : ~ aReductOfIn0(X1,xd,xR)
& sdtmndtasgtdt0(xw,xR,xd)
& ( ( sdtmndtplgtdt0(xw,xR,xd)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xd)
& aReductOfIn0(X0,xw,xR)
& aElement0(X0) )
| aReductOfIn0(xd,xw,xR) ) )
| xw = xd )
& aElement0(xd) ),
inference(ennf_transformation,[],[f30]) ).
fof(f40,plain,
( ~ sdtmndtasgtdt0(xb,xR,xd)
& ~ sdtmndtplgtdt0(xb,xR,xd)
& ! [X0] :
( ~ sdtmndtplgtdt0(X0,xR,xd)
| ~ aReductOfIn0(X0,xb,xR)
| ~ aElement0(X0) )
& ~ aReductOfIn0(xd,xb,xR)
& xb != xd ),
inference(ennf_transformation,[],[f25]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| sdtmndtasgtdt0(X0,X1,X3) ),
inference(ennf_transformation,[],[f9]) ).
fof(f42,plain,
! [X0,X1,X2,X3] :
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| sdtmndtasgtdt0(X0,X1,X3) ),
inference(flattening,[],[f41]) ).
fof(f47,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f48,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2) ) ),
inference(flattening,[],[f47]) ).
fof(f71,plain,
( isTerminating0(xR)
& ! [X5,X6] :
( ~ aElement0(X6)
| ~ aElement0(X5)
| ( ~ sdtmndtplgtdt0(X5,xR,X6)
& ! [X7] :
( ~ sdtmndtplgtdt0(X7,xR,X6)
| ~ aReductOfIn0(X7,X5,xR)
| ~ aElement0(X7) )
& ~ aReductOfIn0(X6,X5,xR) )
| iLess0(X6,X5) )
& isLocallyConfluent0(xR)
& ! [X0,X1,X2] :
( ~ aReductOfIn0(X2,X0,xR)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ? [X3] :
( sdtmndtasgtdt0(X2,xR,X3)
& sP0(X3,X2)
& sdtmndtasgtdt0(X1,xR,X3)
& ( ( sdtmndtplgtdt0(X1,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X1,xR) ) )
| X1 = X3 )
& aElement0(X3) ) ) ),
inference(rectify,[],[f60]) ).
fof(f72,plain,
( isTerminating0(xR)
& ! [X5,X6] :
( ~ aElement0(X6)
| ~ aElement0(X5)
| ( ~ sdtmndtplgtdt0(X5,xR,X6)
& ! [X7] :
( ~ sdtmndtplgtdt0(X7,xR,X6)
| ~ aReductOfIn0(X7,X5,xR)
| ~ aElement0(X7) )
& ~ aReductOfIn0(X6,X5,xR) )
| iLess0(X6,X5) )
& isLocallyConfluent0(xR)
& ! [X0,X1,X2] :
( ~ aReductOfIn0(X2,X0,xR)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ( sdtmndtasgtdt0(X2,xR,sK7(X1,X2))
& sP0(sK7(X1,X2),X2)
& sdtmndtasgtdt0(X1,xR,sK7(X1,X2))
& ( ( sdtmndtplgtdt0(X1,xR,sK7(X1,X2))
& ( ( sdtmndtplgtdt0(sK8(X1,X2),xR,sK7(X1,X2))
& aReductOfIn0(sK8(X1,X2),X1,xR)
& aElement0(sK8(X1,X2)) )
| aReductOfIn0(sK7(X1,X2),X1,xR) ) )
| sK7(X1,X2) = X1 )
& aElement0(sK7(X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X3,sK7(X1,X2)),skolemize(X4,sK8(X1,X2))],[f71]) ).
fof(f73,plain,
! [X2,X0] :
( ~ sP3(X2,X0)
| ( ~ sdtmndtasgtdt0(X0,xR,X2)
& ~ sdtmndtplgtdt0(X0,xR,X2)
& ! [X4] :
( ~ sdtmndtplgtdt0(X4,xR,X2)
| ~ aReductOfIn0(X4,X0,xR)
| ~ aElement0(X4) )
& ~ aReductOfIn0(X2,X0,xR)
& X0 != X2 ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f74,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| ( ~ sdtmndtasgtdt0(X1,xR,X0)
& ~ sdtmndtplgtdt0(X1,xR,X0)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X0)
| ~ aReductOfIn0(X2,X1,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X0,X1,xR)
& X0 != X1 ) ),
inference(rectify,[],[f73]) ).
fof(f75,plain,
! [X1,X2] :
( ~ sP2(X1,X2)
| ? [X5] :
( sdtmndtasgtdt0(X2,xR,X5)
& sP1(X5,X2)
& sdtmndtasgtdt0(X1,xR,X5)
& ( ( sdtmndtplgtdt0(X1,xR,X5)
& ( ? [X6] :
( sdtmndtplgtdt0(X6,xR,X5)
& aReductOfIn0(X6,X1,xR)
& aElement0(X6) )
| aReductOfIn0(X5,X1,xR) ) )
| X1 = X5 )
& aElement0(X5) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f76,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| ? [X2] :
( sdtmndtasgtdt0(X1,xR,X2)
& sP1(X2,X1)
& sdtmndtasgtdt0(X0,xR,X2)
& ( ( sdtmndtplgtdt0(X0,xR,X2)
& ( ? [X3] :
( sdtmndtplgtdt0(X3,xR,X2)
& aReductOfIn0(X3,X0,xR)
& aElement0(X3) )
| aReductOfIn0(X2,X0,xR) ) )
| X0 = X2 )
& aElement0(X2) ) ),
inference(rectify,[],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| ( sdtmndtasgtdt0(X1,xR,sK9(X0,X1))
& sP1(sK9(X0,X1),X1)
& sdtmndtasgtdt0(X0,xR,sK9(X0,X1))
& ( ( sdtmndtplgtdt0(X0,xR,sK9(X0,X1))
& ( ( sdtmndtplgtdt0(sK10(X0,X1),xR,sK9(X0,X1))
& aReductOfIn0(sK10(X0,X1),X0,xR)
& aElement0(sK10(X0,X1)) )
| aReductOfIn0(sK9(X0,X1),X0,xR) ) )
| sK9(X0,X1) = X0 )
& aElement0(sK9(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X2,sK9(X0,X1)),skolemize(X3,sK10(X0,X1))],[f76]) ).
fof(f82,plain,
( sdtmndtasgtdt0(xu,xR,xb)
& ( ( sdtmndtplgtdt0(xu,xR,xb)
& ( ( sdtmndtplgtdt0(sK14,xR,xb)
& aReductOfIn0(sK14,xu,xR)
& aElement0(sK14) )
| aReductOfIn0(xb,xu,xR) ) )
| xu = xb )
& aReductOfIn0(xu,xa,xR)
& aElement0(xu) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f20]) ).
fof(f84,plain,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(sK17,xR,xw)
& aReductOfIn0(sK17,xv,xR)
& aElement0(sK17) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(sK16,xR,xw)
& aReductOfIn0(sK16,xu,xR)
& aElement0(sK16) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17]),skolemize(X0,sK16),skolemize(X1,sK17)],[f29]) ).
fof(f85,plain,
( aNormalFormOfIn0(xd,xw,xR)
& ! [X1] : ~ aReductOfIn0(X1,xd,xR)
& sdtmndtasgtdt0(xw,xR,xd)
& ( ( sdtmndtplgtdt0(xw,xR,xd)
& ( ( sdtmndtplgtdt0(sK18,xR,xd)
& aReductOfIn0(sK18,xw,xR)
& aElement0(sK18) )
| aReductOfIn0(xd,xw,xR) ) )
| xw = xd )
& aElement0(xd) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X0,sK18)],[f39]) ).
fof(f104,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f15]) ).
fof(f112,plain,
! [X6,X5] :
( ~ aElement0(X6)
| ~ aElement0(X5)
| ~ aReductOfIn0(X6,X5,xR)
| iLess0(X6,X5) ),
inference(cnf_transformation,[],[f72]) ).
fof(f123,plain,
aElement0(xb),
inference(cnf_transformation,[],[f17]) ).
fof(f124,plain,
aElement0(xa),
inference(cnf_transformation,[],[f17]) ).
fof(f125,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| ~ sdtmndtasgtdt0(X1,xR,X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f131,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| sP1(sK9(X0,X1),X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f132,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| sdtmndtasgtdt0(X0,xR,sK9(X0,X1)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f142,plain,
! [X2,X0,X1] :
( sP3(X2,X0)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ iLess0(X0,xa)
| sP2(X1,X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f155,plain,
sdtmndtasgtdt0(xu,xR,xb),
inference(cnf_transformation,[],[f82]) ).
fof(f160,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf_transformation,[],[f82]) ).
fof(f161,plain,
aElement0(xu),
inference(cnf_transformation,[],[f82]) ).
fof(f174,plain,
sdtmndtasgtdt0(xu,xR,xw),
inference(cnf_transformation,[],[f84]) ).
fof(f179,plain,
aElement0(xw),
inference(cnf_transformation,[],[f84]) ).
fof(f181,plain,
! [X1] : ~ aReductOfIn0(X1,xd,xR),
inference(cnf_transformation,[],[f85]) ).
fof(f182,plain,
sdtmndtasgtdt0(xw,xR,xd),
inference(cnf_transformation,[],[f85]) ).
fof(f187,plain,
aElement0(xd),
inference(cnf_transformation,[],[f85]) ).
fof(f188,plain,
~ sdtmndtasgtdt0(xb,xR,xd),
inference(cnf_transformation,[],[f40]) ).
fof(f193,plain,
! [X2,X3,X0,X1] :
( ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| sdtmndtasgtdt0(X0,X1,X3) ),
inference(cnf_transformation,[],[f42]) ).
fof(f200,plain,
! [X2,X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_49,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f104]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( iLess0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ aReductOfIn0(X0,X1,xR) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_67,plain,
aElement0(xa),
inference(cnf_transformation,[],[f124]) ).
tcf(c_68,plain,
aElement0(xb),
inference(cnf_transformation,[],[f123]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( ~ sP3(X1,X0)
| ~ sdtmndtasgtdt0(X0,xR,X1) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( sdtmndtasgtdt0(X0,xR,sK9(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( sP1(sK9(X0,X1),X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP2(X1,X2)
| sP3(X2,X0)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ iLess0(X0,xa)
| ~ sdtmndtasgtdt0(X0,xR,X1) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_100,plain,
aElement0(xu),
inference(cnf_transformation,[],[f161]) ).
tcf(c_101,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf_transformation,[],[f160]) ).
tcf(c_106,plain,
sdtmndtasgtdt0(xu,xR,xb),
inference(cnf_transformation,[],[f155]) ).
tcf(c_114,plain,
aElement0(xw),
inference(cnf_transformation,[],[f179]) ).
tcf(c_119,plain,
sdtmndtasgtdt0(xu,xR,xw),
inference(cnf_transformation,[],[f174]) ).
tcf(c_125,plain,
aElement0(xd),
inference(cnf_transformation,[],[f187]) ).
tcf(c_130,plain,
sdtmndtasgtdt0(xw,xR,xd),
inference(cnf_transformation,[],[f182]) ).
tcf(c_131,plain,
! [X0: $i] : ~ aReductOfIn0(X0,xd,xR),
inference(cnf_transformation,[],[f181]) ).
tcf(c_137,negated_conjecture,
~ sdtmndtasgtdt0(xb,xR,xd),
inference(cnf_transformation,[],[f188]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtmndtasgtdt0(X0,X1,X3)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2) ),
inference(cnf_transformation,[],[f193]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElement0(X0)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aReductOfIn0(X0,X1,X2) ),
inference(cnf_transformation,[],[f200]) ).
tcf(c_2244,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtmndtasgtdt0(X1,X0,X3)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ sdtmndtasgtdt0(X2,X0,X3)
| ~ sdtmndtasgtdt0(X1,X0,X2)
| ( X0 != xR ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_138]) ).
tcf(c_2245,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtasgtdt0(X0,xR,X2)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X1,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1) ),
inference(unflattening,[status(thm)],[c_2244]) ).
tcf(c_2311,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElement0(X1)
| ~ aElement0(X2)
| ~ aReductOfIn0(X1,X2,X0)
| ( X0 != xR ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_145]) ).
tcf(c_2312,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aElement0(X1)
| ~ aReductOfIn0(X0,X1,xR) ),
inference(unflattening,[status(thm)],[c_2311]) ).
tcf(c_2427,plain,
! [X0: $i,X1: $i] :
( iLess0(X0,X1)
| ~ aElement0(X1)
| ~ aReductOfIn0(X0,X1,xR) ),
inference(backward_subsumption_resolution,[status(thm)],[c_63,c_2312]) ).
tcf(c_12206,plain,
( iLess0(xu,xa)
| ~ aElement0(xa) ),
inference(superposition,[status(thm)],[c_101,c_2427]) ).
tcf(c_12217,plain,
iLess0(xu,xa),
inference(forward_subsumption_resolution,[status(thm)],[c_12206,c_67]) ).
tcf(c_12726,plain,
! [X0: $i] :
( sdtmndtasgtdt0(xu,xR,X0)
| ~ aElement0(xw)
| ~ aElement0(xu)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xw,xR,X0) ),
inference(superposition,[status(thm)],[c_119,c_2245]) ).
tcf(c_12751,plain,
! [X0: $i] :
( sdtmndtasgtdt0(xu,xR,X0)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xw,xR,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12726,c_114,c_100]) ).
tcf(c_14994,plain,
! [X0: $i] :
( sP2(xb,X0)
| sP3(X0,xu)
| ~ aElement0(xu)
| ~ aElement0(xb)
| ~ aElement0(X0)
| ~ iLess0(xu,xa) ),
inference(superposition,[status(thm)],[c_106,c_91]) ).
tcf(c_15024,plain,
! [X0: $i] :
( sP2(xb,X0)
| sP3(X0,xu)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14994,c_100,c_68,c_12217]) ).
tcf(c_22332,plain,
( sdtmndtasgtdt0(xu,xR,xd)
| ~ aElement0(xd) ),
inference(superposition,[status(thm)],[c_130,c_12751]) ).
tcf(c_22343,plain,
sdtmndtasgtdt0(xu,xR,xd),
inference(forward_subsumption_resolution,[status(thm)],[c_22332,c_125]) ).
tcf(c_22421,plain,
~ sP3(xd,xu),
inference(superposition,[status(thm)],[c_22343,c_74]) ).
tcf(c_23246,plain,
( sP2(xb,xd)
| ~ aElement0(xd) ),
inference(superposition,[status(thm)],[c_15024,c_22421]) ).
tcf(c_23250,plain,
sP2(xb,xd),
inference(forward_subsumption_resolution,[status(thm)],[c_23246,c_125]) ).
fof(f61,definition,
! [X5,X2] :
( ~ sP1(X5,X2)
| ( sdtmndtplgtdt0(X2,xR,X5)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X5)
& aReductOfIn0(X7,X2,xR)
& aElement0(X7) )
| aReductOfIn0(X5,X2,xR) ) )
| X2 = X5 ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f62,definition,
! [X1,X2] :
( ~ sP2(X1,X2)
| ? [X5] :
( sdtmndtasgtdt0(X2,xR,X5)
& sP1(X5,X2)
& sdtmndtasgtdt0(X1,xR,X5)
& ( ( sdtmndtplgtdt0(X1,xR,X5)
& ( ? [X6] :
( sdtmndtplgtdt0(X6,xR,X5)
& aReductOfIn0(X6,X1,xR)
& aElement0(X6) )
| aReductOfIn0(X5,X1,xR) ) )
| X1 = X5 )
& aElement0(X5) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f63,definition,
! [X2,X0] :
( ~ sP3(X2,X0)
| ( ~ sdtmndtasgtdt0(X0,xR,X2)
& ~ sdtmndtplgtdt0(X0,xR,X2)
& ! [X4] :
( ~ sdtmndtplgtdt0(X4,xR,X2)
| ~ aReductOfIn0(X4,X0,xR)
| ~ aElement0(X4) )
& ~ aReductOfIn0(X2,X0,xR)
& X0 != X2 ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f64,plain,
! [X0,X1,X2] :
( sP3(X2,X0)
| ( ~ sdtmndtasgtdt0(X0,xR,X1)
& ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X3] :
( ~ sdtmndtplgtdt0(X3,xR,X1)
| ~ aReductOfIn0(X3,X0,xR)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X1,X0,xR)
& X0 != X1 )
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ iLess0(X0,xa)
| sP2(X1,X2) ),
inference(definition_folding,[],[f38,f63,f62,f61]) ).
fof(f78,plain,
! [X5,X2] :
( ~ sP1(X5,X2)
| ( sdtmndtplgtdt0(X2,xR,X5)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X5)
& aReductOfIn0(X7,X2,xR)
& aElement0(X7) )
| aReductOfIn0(X5,X2,xR) ) )
| X2 = X5 ),
inference(nnf_transformation,[],[f61]) ).
fof(f79,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| ( sdtmndtplgtdt0(X1,xR,X0)
& ( ? [X2] :
( sdtmndtplgtdt0(X2,xR,X0)
& aReductOfIn0(X2,X1,xR)
& aElement0(X2) )
| aReductOfIn0(X0,X1,xR) ) )
| X0 = X1 ),
inference(rectify,[],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| ( sdtmndtplgtdt0(X1,xR,X0)
& ( ( sdtmndtplgtdt0(sK11(X0,X1),xR,X0)
& aReductOfIn0(sK11(X0,X1),X1,xR)
& aElement0(sK11(X0,X1)) )
| aReductOfIn0(X0,X1,xR) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f79]) ).
fof(f140,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| aReductOfIn0(sK11(X0,X1),X1,xR)
| aReductOfIn0(X0,X1,xR)
| X0 = X1 ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( aReductOfIn0(X0,X1,xR)
| aReductOfIn0(sK11(X0,X1),X1,xR)
| ( X0 = X1 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_14186,plain,
! [X0: $i] :
( aReductOfIn0(X0,xd,xR)
| ( X0 = xd )
| ~ sP1(X0,xd) ),
inference(superposition,[status(thm)],[c_84,c_131]) ).
tcf(c_14189,plain,
! [X0: $i] :
( ( X0 = xd )
| ~ sP1(X0,xd) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14186,c_131]) ).
tcf(c_14376,plain,
! [X0: $i] :
( ( sK9(X0,xd) = xd )
| ~ sP2(X0,xd) ),
inference(superposition,[status(thm)],[c_81,c_14189]) ).
tcf(c_23485,plain,
sK9(xb,xd) = xd,
inference(superposition,[status(thm)],[c_23250,c_14376]) ).
tcf(c_25691,plain,
( sdtmndtasgtdt0(xb,xR,xd)
| ~ sP2(xb,xd) ),
inference(superposition,[status(thm)],[c_23485,c_80]) ).
tcf(c_25723,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_25691,c_137,c_23250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM019+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.58 % Computer : n002.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Fri Sep 25 07:51:05 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.62 Running first-order theorem proving
% 0.10/0.62 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
% 0.15/0.63
% 0.15/0.63 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.63
% 0.15/0.63 % Detected problem language: tptp
% 0.15/0.64 % Proving...
% 10.45/2.50 % SZS status Started for theBenchmark.p
% 10.45/2.50 % SZS status Theorem for theBenchmark.p
% 10.45/2.50
% 10.45/2.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.45/2.50
% 10.45/2.50 % ------ iProver source info
% 10.45/2.50
% 10.45/2.50 % git: date: 2026-07-19 20:42:38 +0200
% 10.45/2.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.45/2.50 % git: non_committed_changes: false
% 10.45/2.50
% 10.45/2.50 % ------ Parsing...
% 10.45/2.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.45/2.50
% 10.45/2.50 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 10.45/2.50
% 10.45/2.50 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.45/2.50
% 10.45/2.50 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.45/2.50 % ------ Proving...
% 10.45/2.50 % ------ Problem Properties
% 10.45/2.50
% 10.45/2.50 %
% 10.45/2.50 % clauses 110
% 10.45/2.50 % conjectures 5
% 10.45/2.50 % EPR 72
% 10.45/2.50 % Horn 54
% 10.45/2.50 % unary 23
% 10.45/2.50 % binary 27
% 10.45/2.50 % lits 335
% 10.45/2.50 % lits eq 38
% 10.45/2.50 % fd_pure 0
% 10.45/2.50 % fd_pseudo 0
% 10.45/2.50 % fd_cond 0
% 10.45/2.50 % fd_pseudo_cond 9
% 10.45/2.50 % AC symbols 0
% 10.45/2.50
% 10.45/2.50 % ------ Schedule dynamic 5 is on
% 10.45/2.50
% 10.45/2.50 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.45/2.50
% 10.45/2.50
% 10.45/2.50 % ------
% 10.45/2.50 % Current options:
% 10.45/2.50 % ------
% 10.45/2.50
% 10.45/2.50
% 10.45/2.50 %
% 10.45/2.50
% 10.45/2.50 % ------ Proving...
% 10.45/2.50 %
% 10.45/2.50
% 10.45/2.50 % SZS status Theorem for theBenchmark.p
% 10.45/2.50
% 10.45/2.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.45/2.50
% 10.45/2.50
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