%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM020+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 : n009.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 7.25s 2.27s
% Output : CNFRefutation 7.25s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f73ERROR: Could not build tree for root c_27886ERROR: 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(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,
? [X0] :
( ( sdtmndtasgtdt0(xd,xR,X0)
| sdtmndtplgtdt0(xd,xR,X0)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,X0)
& aReductOfIn0(X1,xd,xR)
& aElement0(X1) )
| aReductOfIn0(X0,xd,xR)
| xd = X0 )
& ( sdtmndtasgtdt0(xb,xR,X0)
| sdtmndtplgtdt0(xb,xR,X0)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,X0)
& aReductOfIn0(X1,xb,xR)
& aElement0(X1) )
| aReductOfIn0(X0,xb,xR)
| xb = X0 )
& aElement0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f25,negated_conjecture,
~ ? [X0] :
( ( sdtmndtasgtdt0(xd,xR,X0)
| sdtmndtplgtdt0(xd,xR,X0)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,X0)
& aReductOfIn0(X1,xd,xR)
& aElement0(X1) )
| aReductOfIn0(X0,xd,xR)
| xd = X0 )
& ( sdtmndtasgtdt0(xb,xR,X0)
| sdtmndtplgtdt0(xb,xR,X0)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,X0)
& aReductOfIn0(X1,xb,xR)
& aElement0(X1) )
| aReductOfIn0(X0,xb,xR)
| xb = X0 )
& aElement0(X0) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f33,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(f34,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(f35,plain,
~ ? [X0] :
( ( sdtmndtasgtdt0(xd,xR,X0)
| sdtmndtplgtdt0(xd,xR,X0)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X0)
& aReductOfIn0(X2,xd,xR)
& aElement0(X2) )
| aReductOfIn0(X0,xd,xR)
| xd = X0 )
& ( sdtmndtasgtdt0(xb,xR,X0)
| sdtmndtplgtdt0(xb,xR,X0)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,X0)
& aReductOfIn0(X1,xb,xR)
& aElement0(X1) )
| aReductOfIn0(X0,xb,xR)
| xb = X0 )
& aElement0(X0) ),
inference(rectify,[],[f25]) ).
fof(f36,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f37,plain,
! [X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ! [X2] :
( ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2) ) ),
inference(flattening,[],[f36]) ).
fof(f44,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(f45,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,[],[f44]) ).
fof(f60,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,[],[f34]) ).
fof(f61,plain,
! [X0] :
( ( ~ sdtmndtasgtdt0(xd,xR,X0)
& ~ sdtmndtplgtdt0(xd,xR,X0)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X0)
| ~ aReductOfIn0(X2,xd,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X0,xd,xR)
& xd != X0 )
| ( ~ sdtmndtasgtdt0(xb,xR,X0)
& ~ sdtmndtplgtdt0(xb,xR,X0)
& ! [X1] :
( ~ sdtmndtplgtdt0(X1,xR,X0)
| ~ aReductOfIn0(X1,xb,xR)
| ~ aElement0(X1) )
& ~ aReductOfIn0(X0,xb,xR)
& xb != X0 )
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f101,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)
& sP4(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,[],[f69]) ).
fof(f102,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,sK23(X1,X2))
& sP4(sK23(X1,X2),X2)
& sdtmndtasgtdt0(X1,xR,sK23(X1,X2))
& ( ( sdtmndtplgtdt0(X1,xR,sK23(X1,X2))
& ( ( sdtmndtplgtdt0(sK24(X1,X2),xR,sK23(X1,X2))
& aReductOfIn0(sK24(X1,X2),X1,xR)
& aElement0(sK24(X1,X2)) )
| aReductOfIn0(sK23(X1,X2),X1,xR) ) )
| sK23(X1,X2) = X1 )
& aElement0(sK23(X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23,sK24]),skolemize(X3,sK23(X1,X2)),skolemize(X4,sK24(X1,X2))],[f101]) ).
fof(f103,plain,
! [X2,X0] :
( ~ sP7(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,[],[f72]) ).
fof(f104,plain,
! [X0,X1] :
( ~ sP7(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,[],[f103]) ).
fof(f105,plain,
! [X1,X2] :
( ~ sP6(X1,X2)
| ? [X5] :
( sdtmndtasgtdt0(X2,xR,X5)
& sP5(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,[],[f71]) ).
fof(f106,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| ? [X2] :
( sdtmndtasgtdt0(X1,xR,X2)
& sP5(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,[],[f105]) ).
fof(f107,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| ( sdtmndtasgtdt0(X1,xR,sK25(X0,X1))
& sP5(sK25(X0,X1),X1)
& sdtmndtasgtdt0(X0,xR,sK25(X0,X1))
& ( ( sdtmndtplgtdt0(X0,xR,sK25(X0,X1))
& ( ( sdtmndtplgtdt0(sK26(X0,X1),xR,sK25(X0,X1))
& aReductOfIn0(sK26(X0,X1),X0,xR)
& aElement0(sK26(X0,X1)) )
| aReductOfIn0(sK25(X0,X1),X0,xR) ) )
| sK25(X0,X1) = X0 )
& aElement0(sK25(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26]),skolemize(X2,sK25(X0,X1)),skolemize(X3,sK26(X0,X1))],[f106]) ).
fof(f112,plain,
( sdtmndtasgtdt0(xu,xR,xb)
& ( ( sdtmndtplgtdt0(xu,xR,xb)
& ( ( sdtmndtplgtdt0(sK30,xR,xb)
& aReductOfIn0(sK30,xu,xR)
& aElement0(sK30) )
| aReductOfIn0(xb,xu,xR) ) )
| xu = xb )
& aReductOfIn0(xu,xa,xR)
& aElement0(xu) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(X0,sK30)],[f20]) ).
fof(f114,plain,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(sK33,xR,xw)
& aReductOfIn0(sK33,xv,xR)
& aElement0(sK33) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(sK32,xR,xw)
& aReductOfIn0(sK32,xu,xR)
& aElement0(sK32) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32,sK33]),skolemize(X0,sK32),skolemize(X1,sK33)],[f33]) ).
fof(f115,plain,
( aNormalFormOfIn0(xd,xw,xR)
& ! [X1] : ~ aReductOfIn0(X1,xd,xR)
& sdtmndtasgtdt0(xw,xR,xd)
& ( ( sdtmndtplgtdt0(xw,xR,xd)
& ( ( sdtmndtplgtdt0(sK34,xR,xd)
& aReductOfIn0(sK34,xw,xR)
& aElement0(sK34) )
| aReductOfIn0(xd,xw,xR) ) )
| xw = xd )
& aElement0(xd) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(X0,sK34)],[f60]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ aReductOfIn0(X2,X0,X1)
| aElement0(X2) ),
inference(cnf_transformation,[],[f37]) ).
fof(f128,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,[],[f45]) ).
fof(f163,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f15]) ).
fof(f171,plain,
! [X6,X5] :
( ~ aElement0(X6)
| ~ aElement0(X5)
| ~ aReductOfIn0(X6,X5,xR)
| iLess0(X6,X5) ),
inference(cnf_transformation,[],[f102]) ).
fof(f182,plain,
aElement0(xb),
inference(cnf_transformation,[],[f17]) ).
fof(f183,plain,
aElement0(xa),
inference(cnf_transformation,[],[f17]) ).
fof(f184,plain,
! [X0,X1] :
( ~ sP7(X0,X1)
| ~ sdtmndtasgtdt0(X1,xR,X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f189,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| sdtmndtasgtdt0(X1,xR,sK25(X0,X1)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f191,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| sdtmndtasgtdt0(X0,xR,sK25(X0,X1)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f196,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| aElement0(sK25(X0,X1)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f201,plain,
! [X2,X0,X1] :
( sP7(X2,X0)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ iLess0(X0,xa)
| sP6(X1,X2) ),
inference(cnf_transformation,[],[f73]) ).
fof(f214,plain,
sdtmndtasgtdt0(xu,xR,xb),
inference(cnf_transformation,[],[f112]) ).
fof(f219,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf_transformation,[],[f112]) ).
fof(f220,plain,
aElement0(xu),
inference(cnf_transformation,[],[f112]) ).
fof(f233,plain,
sdtmndtasgtdt0(xu,xR,xw),
inference(cnf_transformation,[],[f114]) ).
fof(f238,plain,
aElement0(xw),
inference(cnf_transformation,[],[f114]) ).
fof(f241,plain,
sdtmndtasgtdt0(xw,xR,xd),
inference(cnf_transformation,[],[f115]) ).
fof(f246,plain,
aElement0(xd),
inference(cnf_transformation,[],[f115]) ).
fof(f252,plain,
! [X0] :
( sP8(X0)
| ~ sdtmndtasgtdt0(xb,xR,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElement0(X0)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1)
| ~ aReductOfIn0(X0,X1,X2) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtmndtasgtdt0(X3,X1,X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X3,X1,X0)
| ~ sdtmndtasgtdt0(X0,X1,X2) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_94,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f163]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( iLess0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ aReductOfIn0(X0,X1,xR) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_112,plain,
aElement0(xa),
inference(cnf_transformation,[],[f183]) ).
tcf(c_113,plain,
aElement0(xb),
inference(cnf_transformation,[],[f182]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] :
( ~ sP7(X1,X0)
| ~ sdtmndtasgtdt0(X0,xR,X1) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i] :
( aElement0(sK25(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] :
( sdtmndtasgtdt0(X0,xR,sK25(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i] :
( sdtmndtasgtdt0(X1,xR,sK25(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP6(X1,X2)
| sP7(X2,X0)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ iLess0(X0,xa)
| ~ sdtmndtasgtdt0(X0,xR,X1) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_145,plain,
aElement0(xu),
inference(cnf_transformation,[],[f220]) ).
tcf(c_146,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf_transformation,[],[f219]) ).
tcf(c_151,plain,
sdtmndtasgtdt0(xu,xR,xb),
inference(cnf_transformation,[],[f214]) ).
tcf(c_159,plain,
aElement0(xw),
inference(cnf_transformation,[],[f238]) ).
tcf(c_164,plain,
sdtmndtasgtdt0(xu,xR,xw),
inference(cnf_transformation,[],[f233]) ).
tcf(c_170,plain,
aElement0(xd),
inference(cnf_transformation,[],[f246]) ).
tcf(c_175,plain,
sdtmndtasgtdt0(xw,xR,xd),
inference(cnf_transformation,[],[f241]) ).
tcf(c_187,negated_conjecture,
! [X0: $i] :
( sP8(X0)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xb,xR,X0) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_2633,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_94]) ).
tcf(c_2634,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aElement0(X1)
| ~ aReductOfIn0(X0,X1,xR) ),
inference(unflattening,[status(thm)],[c_2633]) ).
tcf(c_2684,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtmndtasgtdt0(X3,X0,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ sdtmndtasgtdt0(X3,X0,X1)
| ~ sdtmndtasgtdt0(X1,X0,X2)
| ( X0 != xR ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_94]) ).
tcf(c_2685,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtmndtasgtdt0(X2,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X2,xR,X0)
| ~ sdtmndtasgtdt0(X0,xR,X1) ),
inference(unflattening,[status(thm)],[c_2684]) ).
tcf(c_2852,plain,
! [X0: $i,X1: $i] :
( iLess0(X0,X1)
| ~ aElement0(X1)
| ~ aReductOfIn0(X0,X1,xR) ),
inference(backward_subsumption_resolution,[status(thm)],[c_108,c_2634]) ).
tcf(c_12234,negated_conjecture,
! [X0: $i] :
( sP8(X0)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xb,xR,X0) ),
inference(demodulation,[status(thm)],[c_187]) ).
tcf(c_14461,plain,
! [X0: $i] :
( sP8(sK25(xb,X0))
| ~ sP6(xb,X0)
| ~ aElement0(sK25(xb,X0)) ),
inference(superposition,[status(thm)],[c_125,c_12234]) ).
tcf(c_14475,plain,
! [X0: $i] :
( sP8(sK25(xb,X0))
| ~ sP6(xb,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14461,c_120]) ).
tcf(c_14676,plain,
! [X0: $i] :
( sdtmndtasgtdt0(X0,xR,xd)
| ~ aElement0(xd)
| ~ aElement0(xw)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X0,xR,xw) ),
inference(superposition,[status(thm)],[c_175,c_2685]) ).
tcf(c_14679,plain,
! [X0: $i] :
( sdtmndtasgtdt0(X0,xR,xd)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X0,xR,xw) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14676,c_170,c_159]) ).
tcf(c_14922,plain,
( iLess0(xu,xa)
| ~ aElement0(xa) ),
inference(superposition,[status(thm)],[c_146,c_2852]) ).
tcf(c_14930,plain,
iLess0(xu,xa),
inference(forward_subsumption_resolution,[status(thm)],[c_14922,c_112]) ).
tcf(c_19333,plain,
! [X0: $i] :
( sP6(xb,X0)
| sP7(X0,xu)
| ~ aElement0(xu)
| ~ aElement0(xb)
| ~ aElement0(X0)
| ~ iLess0(xu,xa) ),
inference(superposition,[status(thm)],[c_151,c_136]) ).
tcf(c_19361,plain,
! [X0: $i] :
( sP6(xb,X0)
| sP7(X0,xu)
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19333,c_145,c_113,c_14930]) ).
tcf(c_27634,plain,
( sdtmndtasgtdt0(xu,xR,xd)
| ~ aElement0(xu) ),
inference(superposition,[status(thm)],[c_164,c_14679]) ).
tcf(c_27640,plain,
sdtmndtasgtdt0(xu,xR,xd),
inference(forward_subsumption_resolution,[status(thm)],[c_27634,c_145]) ).
tcf(c_27750,plain,
~ sP7(xd,xu),
inference(superposition,[status(thm)],[c_27640,c_119]) ).
tcf(c_27882,plain,
( sP6(xb,xd)
| ~ aElement0(xd) ),
inference(superposition,[status(thm)],[c_19361,c_27750]) ).
fof(f74,definition,
! [X0] :
( ~ sP8(X0)
| ( ~ sdtmndtasgtdt0(xd,xR,X0)
& ~ sdtmndtplgtdt0(xd,xR,X0)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X0)
| ~ aReductOfIn0(X2,xd,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X0,xd,xR)
& xd != X0 ) ),
introduced(definition,[new_symbols(definition,[sP8])],[predicate_definition_introduction]) ).
fof(f75,plain,
! [X0] :
( sP8(X0)
| ( ~ sdtmndtasgtdt0(xb,xR,X0)
& ~ sdtmndtplgtdt0(xb,xR,X0)
& ! [X1] :
( ~ sdtmndtplgtdt0(X1,xR,X0)
| ~ aReductOfIn0(X1,xb,xR)
| ~ aElement0(X1) )
& ~ aReductOfIn0(X0,xb,xR)
& xb != X0 )
| ~ aElement0(X0) ),
inference(definition_folding,[],[f61,f74]) ).
fof(f116,plain,
! [X0] :
( ~ sP8(X0)
| ( ~ sdtmndtasgtdt0(xd,xR,X0)
& ~ sdtmndtplgtdt0(xd,xR,X0)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X0)
| ~ aReductOfIn0(X2,xd,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X0,xd,xR)
& xd != X0 ) ),
inference(nnf_transformation,[],[f74]) ).
fof(f117,plain,
! [X0] :
( ~ sP8(X0)
| ( ~ sdtmndtasgtdt0(xd,xR,X0)
& ~ sdtmndtplgtdt0(xd,xR,X0)
& ! [X1] :
( ~ sdtmndtplgtdt0(X1,xR,X0)
| ~ aReductOfIn0(X1,xd,xR)
| ~ aElement0(X1) )
& ~ aReductOfIn0(X0,xd,xR)
& xd != X0 ) ),
inference(rectify,[],[f116]) ).
fof(f247,plain,
! [X0] :
( ~ sP8(X0)
| ~ sdtmndtasgtdt0(xd,xR,X0) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_182,plain,
! [X0: $i] :
( ~ sP8(X0)
| ~ sdtmndtasgtdt0(xd,xR,X0) ),
inference(cnf_transformation,[],[f247]) ).
tcf(c_14541,plain,
! [X0: $i] :
( ~ sP6(X0,xd)
| ~ sP8(sK25(X0,xd)) ),
inference(superposition,[status(thm)],[c_127,c_182]) ).
tcf(c_14850,plain,
~ sP6(xb,xd),
inference(superposition,[status(thm)],[c_14475,c_14541]) ).
tcf(c_27886,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_27882,c_14850,c_170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM020+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 07:48:13 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 7.25/2.27 % SZS status Started for theBenchmark.p
% 7.25/2.27 % SZS status Theorem for theBenchmark.p
% 7.25/2.27
% 7.25/2.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.25/2.27
% 7.25/2.27 % ------ iProver source info
% 7.25/2.27
% 7.25/2.27 % git: date: 2026-07-19 20:42:38 +0200
% 7.25/2.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.25/2.27 % git: non_committed_changes: false
% 7.25/2.27
% 7.25/2.27 % ------ Parsing...
% 7.25/2.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.25/2.27
% 7.25/2.27 % ------ 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 %
% 7.25/2.27
% 7.25/2.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.25/2.27
% 7.25/2.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.25/2.27 % ------ Proving...
% 7.25/2.27 % ------ Problem Properties
% 7.25/2.27
% 7.25/2.27 %
% 7.25/2.27 % clauses 122
% 7.25/2.27 % conjectures 5
% 7.25/2.27 % EPR 75
% 7.25/2.27 % Horn 61
% 7.25/2.27 % unary 21
% 7.25/2.27 % binary 34
% 7.25/2.27 % lits 383
% 7.25/2.27 % lits eq 37
% 7.25/2.27 % fd_pure 0
% 7.25/2.27 % fd_pseudo 0
% 7.25/2.27 % fd_cond 0
% 7.25/2.27 % fd_pseudo_cond 9
% 7.25/2.27 % AC symbols 0
% 7.25/2.27
% 7.25/2.27 % ------ Schedule dynamic 5 is on
% 7.25/2.27
% 7.25/2.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.25/2.27
% 7.25/2.27
% 7.25/2.27 % ------
% 7.25/2.27 % Current options:
% 7.25/2.27 % ------
% 7.25/2.27
% 7.25/2.27
% 7.25/2.27 %
% 7.25/2.27
% 7.25/2.27 % ------ Proving...
% 7.25/2.27 %
% 7.25/2.27
% 7.25/2.27 % SZS status Theorem for theBenchmark.p
% 7.25/2.27
% 7.25/2.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.25/2.27
% 7.25/2.27
%------------------------------------------------------------------------------