%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM463+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 : n011.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 02:24:33 PM UTC 2026
% Result : Theorem 8.08s 1.65s
% Output : CNFRefutation 8.08s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f134ERROR: Could not build tree for root c_10873ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
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(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
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(f17,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(X0,X1) = sz00
=> ( X1 = sz00
| X0 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).
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(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
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(f26,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| X0 = sz10
| X0 = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLENTr) ).
fof(f27,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__987) ).
fof(f28,conjecture,
( xm != sz00
=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f29,negated_conjecture,
~ ( xm != sz00
=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f31,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f32,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f34,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f33]) ).
fof(f39,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f44,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f52,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f53,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(ennf_transformation,[],[f17]) ).
fof(f55,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f57,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f59,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f58]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f66,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f65]) ).
fof(f69,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(f70,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,[],[f69]) ).
fof(f71,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| X0 = sz10
| X0 = sz00 ),
inference(ennf_transformation,[],[f26]) ).
fof(f72,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| X0 = sz10
| X0 = sz00 ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
( xm != sz00
& ~ sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(ennf_transformation,[],[f29]) ).
fof(f74,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,[],[f57]) ).
fof(f75,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,[],[f74]) ).
fof(f76,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))],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( ( sdtmndt0(X1,X0) != X2
| ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
& ( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtmndt0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f78,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( ( sdtmndt0(X1,X0) != X2
| ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
& ( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtmndt0(X1,X0) ) ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f81,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f82,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f83,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f86,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f87,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f91,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f44]) ).
fof(f100,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f53]) ).
fof(f101,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| sz00 = X0 ),
inference(cnf_transformation,[],[f53]) ).
fof(f102,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| sz00 = X1
| sz00 = X0 ),
inference(cnf_transformation,[],[f55]) ).
fof(f105,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f106,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtmndt0(X1,X0) != X2
| sdtpldt0(X0,X2) = X1 ),
inference(cnf_transformation,[],[f78]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f112,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f120,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,[],[f70]) ).
fof(f122,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtlseqdt0(sz10,X0)
| sz10 = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f72]) ).
fof(f124,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f27]) ).
fof(f125,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f27]) ).
fof(f126,plain,
sz00 != xm,
inference(cnf_transformation,[],[f73]) ).
fof(f127,plain,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f73]) ).
fof(f128,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f105]) ).
fof(f131,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 ),
inference(equality_resolution,[],[f106]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f79]) ).
tcf(c_50,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f81]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_56,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_60,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz10) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f131]) ).
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,[],[f111]) ).
tcf(c_82,plain,
! [X0: $i] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f112]) ).
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,[],[f120]) ).
tcf(c_92,plain,
! [X0: $i] :
( sdtlseqdt0(sz10,X0)
| ( X0 = sz10 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_93,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f125]) ).
tcf(c_94,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f124]) ).
tcf(c_95,negated_conjecture,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f127]) ).
tcf(c_96,negated_conjecture,
sz00 != xm,
inference(cnf_transformation,[],[f126]) ).
tcf(c_97,plain,
( sdtlseqdt0(sz00,sz00)
| ~ aNaturalNumber0(sz00) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_101,plain,
( ( sdtpldt0(sz00,sz00) = sz00 )
| ~ aNaturalNumber0(sz00) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_110,plain,
( ( sz00 = sz00 )
| ~ aNaturalNumber0(sz00)
| ( sdtpldt0(sz00,sz00) != sz00 ) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_122,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_1328,definition,
iPr_def_10 = sdtasdt0(xn,xm),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1329,negated_conjecture,
sz00 != xm,
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_1330,negated_conjecture,
~ sdtlseqdt0(xn,iPr_def_10),
inference(demodulation,[status(thm)],[c_95,c_1328]) ).
tcf(c_1331,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1333,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2055,plain,
sdtasdt0(xn,sz10) = xn,
inference(superposition,[status(thm)],[c_94,c_60]) ).
tcf(c_2129,plain,
( aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_1328,c_53]) ).
tcf(c_2142,plain,
aNaturalNumber0(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2129,c_94,c_93]) ).
tcf(c_2171,plain,
sdtpldt0(sz00,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_2142,c_57]) ).
tcf(c_2172,plain,
sdtpldt0(iPr_def_10,sz00) = iPr_def_10,
inference(superposition,[status(thm)],[c_2142,c_56]) ).
tcf(c_2198,plain,
( sdtlseqdt0(sz00,iPr_def_10)
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_2171,c_122]) ).
tcf(c_2199,plain,
( sdtlseqdt0(iPr_def_10,iPr_def_10)
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_2172,c_122]) ).
tcf(c_2201,plain,
sdtlseqdt0(iPr_def_10,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2199,c_2142,c_49]) ).
tcf(c_2202,plain,
sdtlseqdt0(sz00,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2198,c_2142,c_49]) ).
tcf(c_2222,plain,
( sdtlseqdt0(iPr_def_10,xn)
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_83,c_1330]) ).
tcf(c_2226,plain,
sdtlseqdt0(iPr_def_10,xn),
inference(forward_subsumption_resolution,[status(thm)],[c_2222,c_2142,c_94]) ).
tcf(c_2311,plain,
! [X0: $i] :
( sdtlseqdt0(xn,iPr_def_10)
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xn,X0)
| ~ sdtlseqdt0(X0,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_2312,plain,
( sdtlseqdt0(xn,iPr_def_10)
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00)
| ~ sdtlseqdt0(xn,sz00)
| ~ sdtlseqdt0(sz00,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_2311]) ).
tcf(c_2681,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(xn,X0)
| ~ sdtlseqdt0(X2,X1)
| ( xn != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1337]) ).
tcf(c_2682,plain,
( sdtlseqdt0(xn,sz00)
| ~ sdtlseqdt0(sz00,sz00)
| ( xn != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_2681]) ).
tcf(c_2725,plain,
xn = xn,
inference(instantiation,[status(thm)],[c_1331]) ).
tcf(c_2727,plain,
! [X0: $i,X1: $i] :
( ( xn = X0 )
| ( xn != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1333]) ).
tcf(c_2910,plain,
( ( sdtpldt0(iPr_def_10,sdtmndt0(xn,iPr_def_10)) = xn )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_2226,c_78]) ).
tcf(c_2921,plain,
sdtpldt0(iPr_def_10,sdtmndt0(xn,iPr_def_10)) = xn,
inference(forward_subsumption_resolution,[status(thm)],[c_2910,c_2142,c_94]) ).
tcf(c_3043,plain,
( ( sz00 = iPr_def_10 )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(sdtmndt0(xn,iPr_def_10))
| ( sz00 != xn ) ),
inference(superposition,[status(thm)],[c_2921,c_70]) ).
tcf(c_3046,plain,
( ( sz00 = iPr_def_10 )
| ~ aNaturalNumber0(sdtmndt0(xn,iPr_def_10))
| ( sz00 != xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3043,c_2142]) ).
tcf(c_3736,plain,
( ( sz00 = xn )
| ( sz00 = xm )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ( sz00 != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_1328,c_72]) ).
tcf(c_3760,plain,
( ( sz00 = xn )
| ( sz00 != iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3736,c_1329,c_94,c_93]) ).
tcf(c_4135,plain,
! [X0: $i] :
( ( xn = X0 )
| ( xn != xn )
| ( X0 != xn ) ),
inference(instantiation,[status(thm)],[c_2727]) ).
tcf(c_4136,plain,
( ( xn = sz00 )
| ( xn != xn )
| ( sz00 != xn ) ),
inference(instantiation,[status(thm)],[c_4135]) ).
tcf(c_4401,plain,
sz00 != iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_3760,c_94,c_49,c_97,c_101,c_110,c_1330,c_2142,c_2202,c_2312,c_2682,c_2725,c_3760,c_4136]) ).
tcf(c_4403,plain,
( ~ aNaturalNumber0(sdtmndt0(xn,iPr_def_10))
| ( sz00 != xn ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3046,c_4401]) ).
tcf(c_4409,plain,
sz00 != xn,
inference(global_subsumption_just,[status(thm)],[c_4403,c_94,c_49,c_97,c_101,c_110,c_1330,c_2142,c_2202,c_2312,c_2682,c_2725,c_4136]) ).
tcf(c_6506,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(xn,X0),iPr_def_10)
| ( sz00 = xn )
| ( X0 = xm )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xm) ),
inference(superposition,[status(thm)],[c_1328,c_89]) ).
tcf(c_6595,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(xn,X0),iPr_def_10)
| ( X0 = xm )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xm) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6506,c_4409,c_94,c_93]) ).
tcf(c_10700,plain,
( sdtlseqdt0(xn,iPr_def_10)
| ( sz10 = xm )
| ~ aNaturalNumber0(sz10)
| ~ sdtlseqdt0(sz10,xm) ),
inference(superposition,[status(thm)],[c_2055,c_6595]) ).
tcf(c_10706,plain,
( ( sz10 = xm )
| ~ sdtlseqdt0(sz10,xm) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10700,c_1330,c_50]) ).
tcf(c_10745,plain,
( ( sz10 = xm )
| ( sz00 = xm )
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_92,c_10706]) ).
tcf(c_10746,plain,
sz10 = xm,
inference(forward_subsumption_resolution,[status(thm)],[c_10745,c_1329,c_93]) ).
tcf(c_10812,plain,
sdtasdt0(xn,sz10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_1328,c_10746]) ).
tcf(c_10815,plain,
xn = iPr_def_10,
inference(demodulation,[status(thm)],[c_2055,c_10812]) ).
tcf(c_10872,plain,
~ sdtlseqdt0(iPr_def_10,iPr_def_10),
inference(demodulation,[status(thm)],[c_1330,c_10815]) ).
tcf(c_10873,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_10872,c_2201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM463+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 04:06:28 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 8.08/1.65 % SZS status Started for theBenchmark.p
% 8.08/1.65 % SZS status Theorem for theBenchmark.p
% 8.08/1.65
% 8.08/1.65 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.08/1.65
% 8.08/1.65 % ------ iProver source info
% 8.08/1.65
% 8.08/1.65 % git: date: 2026-07-19 20:42:38 +0200
% 8.08/1.65 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.08/1.65 % git: non_committed_changes: false
% 8.08/1.65
% 8.08/1.65 % ------ Parsing...
% 8.08/1.65 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.08/1.65
% 8.08/1.65 % ------ 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 %
% 8.08/1.65
% 8.08/1.65 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.08/1.65
% 8.08/1.65 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.08/1.65 % ------ Proving...
% 8.08/1.65 % ------ Problem Properties
% 8.08/1.65
% 8.08/1.65 %
% 8.08/1.65 % clauses 44
% 8.08/1.65 % conjectures 2
% 8.08/1.65 % EPR 12
% 8.08/1.65 % Horn 35
% 8.08/1.65 % unary 8
% 8.08/1.65 % binary 7
% 8.08/1.65 % lits 152
% 8.08/1.65 % lits eq 44
% 8.08/1.65 % fd_pure 0
% 8.08/1.65 % fd_pseudo 0
% 8.08/1.65 % fd_cond 4
% 8.08/1.65 % fd_pseudo_cond 9
% 8.08/1.65 % AC symbols 0
% 8.08/1.65
% 8.08/1.65 % ------ Schedule dynamic 5 is on
% 8.08/1.65
% 8.08/1.65 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.08/1.65
% 8.08/1.65
% 8.08/1.65 % ------
% 8.08/1.65 % Current options:
% 8.08/1.65 % ------
% 8.08/1.65
% 8.08/1.65
% 8.08/1.65 %
% 8.08/1.65
% 8.08/1.65 % ------ Proving...
% 8.08/1.65 %
% 8.08/1.65
% 8.08/1.65 % SZS status Theorem for theBenchmark.p
% 8.08/1.65
% 8.08/1.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.08/1.65
% 8.08/1.65
%------------------------------------------------------------------------------