%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM527+3 : 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 : n007.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 02:25:50 PM UTC 2026
% Result : Theorem 98.35s 26.71s
% Output : CNFRefutation 98.35s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f258ERROR: Could not build tree for root c_74057ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(f16,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtpldt0(X0,X1) = sz00
=> ( X1 = sz00
& X0 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(f25,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2
& X0 != sz00 )
=> ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).
fof(f40,axiom,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2987) ).
fof(f47,conjecture,
( ( sdtlseqdt0(xn,xm)
& ? [X0] :
( sdtpldt0(xn,X0) = xm
& aNaturalNumber0(X0) ) )
=> ( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ? [X0] :
( sdtpldt0(sdtasdt0(xn,xn),X0) = sdtasdt0(xm,xm)
& aNaturalNumber0(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f48,negated_conjecture,
~ ( ( sdtlseqdt0(xn,xm)
& ? [X0] :
( sdtpldt0(xn,X0) = xm
& aNaturalNumber0(X0) ) )
=> ( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ? [X0] :
( sdtpldt0(sdtasdt0(xn,xn),X0) = sdtasdt0(xm,xm)
& aNaturalNumber0(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f52,plain,
~ ( ( sdtlseqdt0(xn,xm)
& ? [X0] :
( sdtpldt0(xn,X0) = xm
& aNaturalNumber0(X0) ) )
=> ( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ? [X1] :
( sdtasdt0(xm,xm) = sdtpldt0(sdtasdt0(xn,xn),X1)
& aNaturalNumber0(X1) ) ) ),
inference(rectify,[],[f48]) ).
fof(f53,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f54,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f56,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f55]) ).
fof(f61,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f74,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f75,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(flattening,[],[f74]) ).
fof(f78,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f79,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f78]) ).
fof(f83,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f84,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f88,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f87]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ),
inference(flattening,[],[f91]) ).
fof(f123,plain,
( sdtlseqdt0(xn,xm)
& ? [X0] :
( sdtpldt0(xn,X0) = xm
& aNaturalNumber0(X0) )
& ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
& ! [X1] :
( sdtasdt0(xm,xm) != sdtpldt0(sdtasdt0(xn,xn),X1)
| ~ aNaturalNumber0(X1) ) ),
inference(ennf_transformation,[],[f52]) ).
fof(f124,plain,
( sdtlseqdt0(xn,xm)
& ? [X0] :
( sdtpldt0(xn,X0) = xm
& aNaturalNumber0(X0) )
& ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
& ! [X1] :
( sdtasdt0(xm,xm) != sdtpldt0(sdtasdt0(xn,xn),X1)
| ~ aNaturalNumber0(X1) ) ),
inference(flattening,[],[f123]) ).
fof(f125,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f79]) ).
fof(f126,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(rectify,[],[f125]) ).
fof(f127,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ( sdtpldt0(X0,sK0(X0,X1)) = X1
& aNaturalNumber0(sK0(X0,X1)) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f126]) ).
fof(f142,plain,
( sdtlseqdt0(xn,xm)
& ? [X1] :
( xm = sdtpldt0(xn,X1)
& aNaturalNumber0(X1) )
& ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
& ! [X0] :
( sdtasdt0(xm,xm) != sdtpldt0(sdtasdt0(xn,xn),X0)
| ~ aNaturalNumber0(X0) ) ),
inference(rectify,[],[f124]) ).
fof(f143,plain,
( sdtlseqdt0(xn,xm)
& xm = sdtpldt0(xn,sK8)
& aNaturalNumber0(sK8)
& ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
& ! [X0] :
( sdtasdt0(xm,xm) != sdtpldt0(sdtasdt0(xn,xn),X0)
| ~ aNaturalNumber0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X1,sK8)],[f142]) ).
fof(f144,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f147,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f148,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f151,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f61]) ).
fof(f165,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f75]) ).
fof(f170,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f175,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f84]) ).
fof(f176,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f86]) ).
fof(f177,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f183,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ),
inference(cnf_transformation,[],[f92]) ).
fof(f185,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(cnf_transformation,[],[f92]) ).
fof(f214,plain,
sz00 != xm,
inference(cnf_transformation,[],[f40]) ).
fof(f215,plain,
sz00 != xn,
inference(cnf_transformation,[],[f40]) ).
fof(f217,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f40]) ).
fof(f218,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f40]) ).
fof(f241,plain,
sdtlseqdt0(xn,xm),
inference(cnf_transformation,[],[f143]) ).
fof(f244,plain,
~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)),
inference(cnf_transformation,[],[f143]) ).
fof(f246,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f170]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f144]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f165]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f246]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_82,plain,
! [X0: $i] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f258]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(sdtasdt0(X2,X0),sdtasdt0(X2,X1))
| ( X2 = sz00 )
| ( X0 = X1 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
| ( X2 = sz00 )
| ( X0 = X1 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_117,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f218]) ).
tcf(c_118,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f217]) ).
tcf(c_120,plain,
sz00 != xn,
inference(cnf_transformation,[],[f215]) ).
tcf(c_121,plain,
sz00 != xm,
inference(cnf_transformation,[],[f214]) ).
tcf(c_146,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)),
inference(cnf_transformation,[],[f244]) ).
tcf(c_149,negated_conjecture,
sdtlseqdt0(xn,xm),
inference(cnf_transformation,[],[f241]) ).
tcf(c_150,plain,
( sdtlseqdt0(sz00,sz00)
| ~ aNaturalNumber0(sz00) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_154,plain,
( ( sdtpldt0(sz00,sz00) = sz00 )
| ~ aNaturalNumber0(sz00) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_174,plain,
( ( sz00 = sz00 )
| ~ aNaturalNumber0(sz00)
| ( sdtpldt0(sz00,sz00) != sz00 ) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
tcf(c_3654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtasdt0(X0,X2) = sdtasdt0(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3655,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_5239,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ~ sdtlseqdt0(X0,X1)
| ( sdtasdt0(xm,xm) != X1 )
| ( sdtasdt0(xn,xn) != X0 ) ),
inference(instantiation,[status(thm)],[c_3655]) ).
tcf(c_5271,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xn) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_5301,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ~ sdtlseqdt0(sdtasdt0(X0,X1),X2)
| ( sdtasdt0(xm,xm) != X2 )
| ( sdtasdt0(xn,xn) != sdtasdt0(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_5239]) ).
tcf(c_5305,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xm) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_5763,plain,
! [X0: $i] :
( sdtlseqdt0(X0,sdtasdt0(xm,xm))
| sdtlseqdt0(sdtasdt0(xm,xm),X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_5811,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ~ sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X1))
| ( sdtasdt0(xm,xm) != sdtasdt0(X0,X1) )
| ( sdtasdt0(xn,xn) != sdtasdt0(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_5301]) ).
tcf(c_6527,plain,
( ( sdtasdt0(xn,xn) = sdtasdt0(xm,xm) )
| ( xn != xm ) ),
inference(instantiation,[status(thm)],[c_3654]) ).
tcf(c_6732,plain,
sdtpldt0(sz00,xn) = xn,
inference(superposition,[status(thm)],[c_117,c_57]) ).
tcf(c_6733,plain,
sdtpldt0(sz00,xm) = xm,
inference(superposition,[status(thm)],[c_118,c_57]) ).
tcf(c_7626,plain,
( sdtlseqdt0(sz00,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_6732,c_209]) ).
tcf(c_7627,plain,
( sdtlseqdt0(sz00,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_6733,c_209]) ).
tcf(c_12782,plain,
( sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(instantiation,[status(thm)],[c_5763]) ).
tcf(c_13175,plain,
sdtpldt0(sz00,xn) = xn,
inference(superposition,[status(thm)],[c_117,c_57]) ).
tcf(c_13176,plain,
sdtpldt0(sz00,xm) = xm,
inference(superposition,[status(thm)],[c_118,c_57]) ).
tcf(c_13296,plain,
( sdtlseqdt0(sz00,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_13175,c_209]) ).
tcf(c_13297,plain,
( sdtlseqdt0(sz00,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_13176,c_209]) ).
tcf(c_14263,plain,
( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ~ sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xm,xm))
| ( sdtasdt0(xm,xm) != sdtasdt0(xm,xm) )
| ( sdtasdt0(xn,xn) != sdtasdt0(xm,xm) ) ),
inference(instantiation,[status(thm)],[c_5811]) ).
tcf(c_14264,plain,
( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ~ sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xm,xm))
| ( sdtasdt0(xn,xn) != sdtasdt0(xm,xm) ) ),
inference(equality_resolution_simp,[status(thm)],[c_14263]) ).
tcf(c_16444,plain,
sdtlseqdt0(sz00,xn),
inference(global_subsumption_just,[status(thm)],[c_13296,c_117,c_49,c_7626]) ).
tcf(c_16446,plain,
( ( sz00 = xn )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00)
| ~ sdtlseqdt0(xn,sz00) ),
inference(superposition,[status(thm)],[c_16444,c_80]) ).
tcf(c_16531,plain,
sdtlseqdt0(sz00,xm),
inference(global_subsumption_just,[status(thm)],[c_13297,c_118,c_49,c_7627]) ).
tcf(c_16533,plain,
( ( sz00 = xm )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| ~ sdtlseqdt0(xm,sz00) ),
inference(superposition,[status(thm)],[c_16531,c_80]) ).
tcf(c_44782,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(xm,X0)
| ~ sdtlseqdt0(X2,X1)
| ( xm != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_3655]) ).
tcf(c_44783,plain,
( sdtlseqdt0(xm,sz00)
| ~ sdtlseqdt0(sz00,sz00)
| ( xm != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_44782]) ).
tcf(c_47359,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ sdtlseqdt0(X0,sdtasdt0(xm,xm))
| ~ sdtlseqdt0(sdtasdt0(xn,xn),X0) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_47383,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(X0,xn))
| ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(X0,xn))
| ~ sdtlseqdt0(sdtasdt0(X0,xn),sdtasdt0(xm,xm)) ),
inference(instantiation,[status(thm)],[c_47359]) ).
tcf(c_47628,plain,
! [X0: $i] :
( aNaturalNumber0(sdtasdt0(X0,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_48525,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(X0,xn))
| ( xn = sz00 )
| ( xn = X0 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xn,X0) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_49032,plain,
( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xm,xm))
| ~ sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xn)) ),
inference(instantiation,[status(thm)],[c_47383]) ).
tcf(c_57344,plain,
( aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(instantiation,[status(thm)],[c_47628]) ).
tcf(c_61226,plain,
( sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xm,xm))
| ( xm = sz00 )
| ( xn = xm )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xn,xm) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_74052,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(xn,X0)
| ~ sdtlseqdt0(X2,X1)
| ( xn != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_3655]) ).
tcf(c_74053,plain,
( sdtlseqdt0(xn,sz00)
| ~ sdtlseqdt0(sz00,sz00)
| ( xn != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_74052]) ).
tcf(c_74056,plain,
( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xn))
| ( xn = xm )
| ( xn = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xn,xm) ),
inference(instantiation,[status(thm)],[c_48525]) ).
tcf(c_74057,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_74056,c_74053,c_61226,c_57344,c_49032,c_44783,c_16533,c_16446,c_14264,c_12782,c_6527,c_5305,c_5271,c_174,c_154,c_146,c_150,c_120,c_121,c_149,c_49,c_117,c_118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM527+3 : 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 : n007.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 : Thu Sep 24 04:25:53 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.43
% 0.14/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.43
% 0.14/0.43 % Detected problem language: tptp
% 0.14/0.44 % Proving...
% 98.35/26.71 % SZS status Started for theBenchmark.p
% 98.35/26.71 % SZS status Theorem for theBenchmark.p
% 98.35/26.71
% 98.35/26.71 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 98.35/26.71
% 98.35/26.71 % ------ iProver source info
% 98.35/26.71
% 98.35/26.71 % git: date: 2026-07-19 20:42:38 +0200
% 98.35/26.71 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 98.35/26.71 % git: non_committed_changes: false
% 98.35/26.71
% 98.35/26.71 % ------ Parsing...
% 98.35/26.71 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 98.35/26.71
% 98.35/26.71 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 98.35/26.71
% 98.35/26.71 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 98.35/26.71
% 98.35/26.71 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 98.35/26.71 % ------ Proving...
% 98.35/26.71 % ------ Problem Properties
% 98.35/26.71
% 98.35/26.71 %
% 98.35/26.71 % clauses 96
% 98.35/26.71 % conjectures 5
% 98.35/26.71 % EPR 29
% 98.35/26.71 % Horn 62
% 98.35/26.71 % unary 28
% 98.35/26.71 % binary 8
% 98.35/26.71 % lits 360
% 98.35/26.71 % lits eq 125
% 98.35/26.71 % fd_pure 0
% 98.35/26.71 % fd_pseudo 0
% 98.35/26.71 % fd_cond 23
% 98.35/26.71 % fd_pseudo_cond 11
% 98.35/26.71 % AC symbols 0
% 98.35/26.71
% 98.35/26.71 % ------ Input Options Time Limit: Unbounded
% 98.35/26.71
% 98.35/26.71
% 98.35/26.71 % ------
% 98.35/26.71 % Current options:
% 98.35/26.71 % ------
% 98.35/26.71
% 98.35/26.71
% 98.35/26.71 %
% 98.35/26.71
% 98.35/26.71 % ------ Proving...
% 98.35/26.71 %
% 98.35/26.71
% 98.35/26.71 % SZS status Theorem for theBenchmark.p
% 98.35/26.71
% 98.35/26.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 98.35/26.71
% 98.35/26.71
%------------------------------------------------------------------------------