TSTP Solution File: NUM463+2 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM463+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:30:40 EDT 2023
% Result : Theorem 24.55s 4.22s
% Output : CNFRefutation 24.55s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f137)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
( sz00 != sz10
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f16,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 = sdtpldt0(X0,X1)
=> ( sz00 = X1
& sz00 = X0 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
fof(f25,axiom,
! [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) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
fof(f26,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| sz10 = X0
| sz00 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLENTr) ).
fof(f27,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__987) ).
fof(f28,conjecture,
( sz00 != xm
=> ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ? [X0] :
( sdtpldt0(xn,X0) = sdtasdt0(xn,xm)
& aNaturalNumber0(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f29,negated_conjecture,
~ ( sz00 != xm
=> ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ? [X0] :
( sdtpldt0(xn,X0) = sdtasdt0(xn,xm)
& aNaturalNumber0(X0) ) ) ),
inference(negated_conjecture,[],[f28]) ).
fof(f31,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f32,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f34,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f33]) ).
fof(f39,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f44,plain,
! [X0] :
( ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f52,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f53,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f57,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f56]) ).
fof(f61,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f62,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f64,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f66,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f65]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ( 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) )
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ( 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) )
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0] :
( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f72,plain,
! [X0] :
( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
& ! [X0] :
( sdtpldt0(xn,X0) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X0) )
& sz00 != xm ),
inference(ennf_transformation,[],[f29]) ).
fof(f74,plain,
( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
& ! [X0] :
( sdtpldt0(xn,X0) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X0) )
& sz00 != xm ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f57]) ).
fof(f76,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtpldt0(X0,sK0(X0,X1)) = X1
& aNaturalNumber0(sK0(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ( sdtpldt0(X0,sK0(X0,X1)) = X1
& aNaturalNumber0(sK0(X0,X1)) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f76,f77]) ).
fof(f81,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f82,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f84,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f85,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f88,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f89,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f92,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f102,plain,
! [X0,X1] :
( sz00 = X0
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f106,plain,
! [X0,X1] :
( sdtpldt0(X0,sK0(X0,X1)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f107,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f112,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f113,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f115,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f121,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f125,plain,
! [X0] :
( sdtlseqdt0(sz10,X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f126,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f27]) ).
fof(f127,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f27]) ).
fof(f128,plain,
sz00 != xm,
inference(cnf_transformation,[],[f74]) ).
fof(f130,plain,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f74]) ).
fof(f131,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f107]) ).
cnf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f81]) ).
cnf(c_51,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f82]) ).
cnf(c_52,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f84]) ).
cnf(c_53,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f85]) ).
cnf(c_56,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f89]) ).
cnf(c_57,plain,
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f88]) ).
cnf(c_61,plain,
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f92]) ).
cnf(c_71,plain,
( sdtpldt0(X0,X1) != sz00
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = sz00 ),
inference(cnf_transformation,[],[f102]) ).
cnf(c_73,plain,
( ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f131]) ).
cnf(c_74,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X0,sK0(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f106]) ).
cnf(c_80,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f112]) ).
cnf(c_81,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f113]) ).
cnf(c_82,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,X1)
| sdtlseqdt0(X1,X0) ),
inference(cnf_transformation,[],[f115]) ).
cnf(c_83,plain,
( ~ aNaturalNumber0(X0)
| sdtlseqdt0(X0,X0) ),
inference(cnf_transformation,[],[f137]) ).
cnf(c_90,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| X0 = X1
| X2 = sz00
| sdtlseqdt0(sdtasdt0(X2,X0),sdtasdt0(X2,X1)) ),
inference(cnf_transformation,[],[f121]) ).
cnf(c_92,plain,
( ~ aNaturalNumber0(X0)
| X0 = sz00
| X0 = sz10
| sdtlseqdt0(sz10,X0) ),
inference(cnf_transformation,[],[f125]) ).
cnf(c_93,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f127]) ).
cnf(c_94,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f126]) ).
cnf(c_95,negated_conjecture,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f130]) ).
cnf(c_97,negated_conjecture,
sz00 != xm,
inference(cnf_transformation,[],[f128]) ).
cnf(c_98,plain,
( ~ aNaturalNumber0(sz00)
| sdtlseqdt0(sz00,sz00) ),
inference(instantiation,[status(thm)],[c_83]) ).
cnf(c_102,plain,
( ~ aNaturalNumber0(sz00)
| sdtpldt0(sz00,sz00) = sz00 ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_112,plain,
( sdtpldt0(sz00,sz00) != sz00
| ~ aNaturalNumber0(sz00)
| sz00 = sz00 ),
inference(instantiation,[status(thm)],[c_71]) ).
cnf(c_124,plain,
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,sdtpldt0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
cnf(c_156,plain,
X0 = X0,
theory(equality) ).
cnf(c_158,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_161,plain,
( X0 != X1
| X2 != X3
| sdtasdt0(X0,X2) = sdtasdt0(X1,X3) ),
theory(equality) ).
cnf(c_162,plain,
( X0 != X1
| X2 != X3
| ~ sdtlseqdt0(X1,X3)
| sdtlseqdt0(X0,X2) ),
theory(equality) ).
cnf(c_171,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(sdtasdt0(xn,xm),xn)
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_82]) ).
cnf(c_176,plain,
( sz00 != X0
| xm != X0
| sz00 = xm ),
inference(instantiation,[status(thm)],[c_158]) ).
cnf(c_177,plain,
( sz00 != sz00
| xm != sz00
| sz00 = xm ),
inference(instantiation,[status(thm)],[c_176]) ).
cnf(c_184,plain,
( sdtasdt0(xn,xm) != X0
| xn != X1
| ~ sdtlseqdt0(X1,X0)
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_162]) ).
cnf(c_185,plain,
( sdtasdt0(xn,xm) != sz00
| xn != sz00
| ~ sdtlseqdt0(sz00,sz00)
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_184]) ).
cnf(c_198,plain,
( ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_81]) ).
cnf(c_213,plain,
sdtpldt0(sz00,sz10) = sz10,
inference(superposition,[status(thm)],[c_51,c_56]) ).
cnf(c_237,plain,
sdtpldt0(xn,sz00) = xn,
inference(superposition,[status(thm)],[c_93,c_57]) ).
cnf(c_261,plain,
( X0 != X1
| xm != X1
| xm = X0 ),
inference(instantiation,[status(thm)],[c_158]) ).
cnf(c_264,plain,
sdtasdt0(xn,sz10) = xn,
inference(superposition,[status(thm)],[c_93,c_61]) ).
cnf(c_272,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_368,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(xn,xn) ),
inference(superposition,[status(thm)],[c_237,c_124]) ).
cnf(c_371,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10)
| sdtlseqdt0(sz00,sz10) ),
inference(superposition,[status(thm)],[c_213,c_124]) ).
cnf(c_422,plain,
( xn != X0
| xm != X1
| sdtasdt0(xn,xm) = sdtasdt0(X0,X1) ),
inference(instantiation,[status(thm)],[c_161]) ).
cnf(c_425,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(sdtasdt0(xn,xm),xn) ),
inference(superposition,[status(thm)],[c_82,c_95]) ).
cnf(c_513,plain,
xn = xn,
inference(instantiation,[status(thm)],[c_156]) ).
cnf(c_515,plain,
( X0 != X1
| xn != X1
| xn = X0 ),
inference(instantiation,[status(thm)],[c_158]) ).
cnf(c_690,plain,
( ~ aNaturalNumber0(xm)
| xm = sz00
| xm = sz10
| sdtlseqdt0(sz10,xm) ),
inference(instantiation,[status(thm)],[c_92]) ).
cnf(c_1025,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(xn,xm) = sz00
| sdtasdt0(xn,xm) = sz10
| sdtlseqdt0(sz10,sdtasdt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_92]) ).
cnf(c_1183,plain,
( X0 != X1
| xn != X2
| ~ sdtlseqdt0(X2,X1)
| sdtlseqdt0(xn,X0) ),
inference(instantiation,[status(thm)],[c_162]) ).
cnf(c_1184,plain,
( sz00 != sz00
| xn != sz00
| ~ sdtlseqdt0(sz00,sz00)
| sdtlseqdt0(xn,sz00) ),
inference(instantiation,[status(thm)],[c_1183]) ).
cnf(c_1226,plain,
sdtlseqdt0(sdtasdt0(xn,xm),xn),
inference(global_subsumption_just,[status(thm)],[c_425,c_94,c_93,c_95,c_171,c_272]) ).
cnf(c_1614,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| sdtpldt0(sdtasdt0(xn,xm),sK0(sdtasdt0(xn,xm),xn)) = xn ),
inference(superposition,[status(thm)],[c_1226,c_74]) ).
cnf(c_1740,plain,
( X0 != xm
| xm != xm
| xm = X0 ),
inference(instantiation,[status(thm)],[c_261]) ).
cnf(c_1741,plain,
xm = xm,
inference(instantiation,[status(thm)],[c_156]) ).
cnf(c_1804,plain,
( ~ sdtlseqdt0(sdtasdt0(xn,xm),X0)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(sdtasdt0(xn,xm),X1) ),
inference(instantiation,[status(thm)],[c_81]) ).
cnf(c_1908,plain,
( X0 != xn
| xn != xn
| xn = X0 ),
inference(instantiation,[status(thm)],[c_515]) ).
cnf(c_1909,plain,
( sz00 != xn
| xn != xn
| xn = sz00 ),
inference(instantiation,[status(thm)],[c_1908]) ).
cnf(c_2125,plain,
sdtpldt0(sdtasdt0(xn,xm),sK0(sdtasdt0(xn,xm),xn)) = xn,
inference(global_subsumption_just,[status(thm)],[c_1614,c_94,c_93,c_272,c_1614]) ).
cnf(c_2127,plain,
( sz00 != xn
| ~ aNaturalNumber0(sK0(sdtasdt0(xn,xm),xn))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sdtasdt0(xn,xm) = sz00 ),
inference(superposition,[status(thm)],[c_2125,c_71]) ).
cnf(c_2210,plain,
( sz00 != xn
| ~ aNaturalNumber0(sK0(sdtasdt0(xn,xm),xn)) ),
inference(global_subsumption_just,[status(thm)],[c_2127,c_94,c_93,c_49,c_95,c_98,c_185,c_272,c_513,c_1909,c_2127]) ).
cnf(c_2242,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sdtlseqdt0(sdtasdt0(xn,xm),X0) ),
inference(superposition,[status(thm)],[c_1226,c_81]) ).
cnf(c_2893,plain,
( ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xn,X0)
| sdtlseqdt0(sdtasdt0(xn,xm),X0) ),
inference(global_subsumption_just,[status(thm)],[c_2242,c_94,c_93,c_272,c_2242]) ).
cnf(c_2894,plain,
( ~ sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(sdtasdt0(xn,xm),X0) ),
inference(renaming,[status(thm)],[c_2893]) ).
cnf(c_3232,plain,
sdtlseqdt0(sz00,sz10),
inference(global_subsumption_just,[status(thm)],[c_371,c_51,c_49,c_371]) ).
cnf(c_3515,plain,
( xn != X0
| xm != sz10
| sdtasdt0(xn,xm) = sdtasdt0(X0,sz10) ),
inference(instantiation,[status(thm)],[c_422]) ).
cnf(c_3878,plain,
( ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xn,xm) = X0 ),
inference(superposition,[status(thm)],[c_2894,c_80]) ).
cnf(c_3896,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(sdtasdt0(xn,xm),X1) ),
inference(superposition,[status(thm)],[c_2894,c_81]) ).
cnf(c_4141,plain,
( ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xn,X0)
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm)) ),
inference(global_subsumption_just,[status(thm)],[c_3878,c_94,c_93,c_95,c_198,c_272]) ).
cnf(c_4142,plain,
( ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0) ),
inference(renaming,[status(thm)],[c_4141]) ).
cnf(c_4149,plain,
( ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(sdtasdt0(xn,xm),X1) ),
inference(global_subsumption_just,[status(thm)],[c_3896,c_94,c_93,c_272,c_1804,c_2242]) ).
cnf(c_4159,plain,
( ~ sdtlseqdt0(xn,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz10)
| sdtlseqdt0(sdtasdt0(xn,xm),sz10) ),
inference(superposition,[status(thm)],[c_3232,c_4149]) ).
cnf(c_4341,plain,
( ~ sdtlseqdt0(xn,sz00)
| sdtlseqdt0(sdtasdt0(xn,xm),sz10) ),
inference(global_subsumption_just,[status(thm)],[c_4159,c_51,c_49,c_4159]) ).
cnf(c_4345,plain,
( ~ sdtlseqdt0(sz10,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(xn,sz00)
| ~ aNaturalNumber0(sz10)
| sdtasdt0(xn,xm) = sz10 ),
inference(superposition,[status(thm)],[c_4341,c_80]) ).
cnf(c_5382,plain,
( sdtasdt0(xn,xm) != sz10
| xn != X0
| ~ sdtlseqdt0(X0,sz10)
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_184]) ).
cnf(c_5383,plain,
( sdtasdt0(xn,xm) != sz10
| xn != sz00
| ~ sdtlseqdt0(sz00,sz10)
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_5382]) ).
cnf(c_6149,plain,
sz00 != xn,
inference(global_subsumption_just,[status(thm)],[c_2210,c_94,c_93,c_51,c_49,c_95,c_98,c_102,c_112,c_185,c_272,c_371,c_513,c_1025,c_1184,c_1909,c_4345,c_5383]) ).
cnf(c_6155,plain,
( ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xn,X0)
| sdtlseqdt0(sdtasdt0(xn,xm),X0) ),
inference(global_subsumption_just,[status(thm)],[c_2242,c_2894]) ).
cnf(c_6156,plain,
( ~ sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(sdtasdt0(xn,xm),X0) ),
inference(renaming,[status(thm)],[c_6155]) ).
cnf(c_6171,plain,
sdtasdt0(xn,sz10) = xn,
inference(superposition,[status(thm)],[c_93,c_61]) ).
cnf(c_6677,plain,
( ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0)
| sdtasdt0(xn,xm) = X0 ),
inference(superposition,[status(thm)],[c_6156,c_80]) ).
cnf(c_6730,plain,
( ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(xn,X0)
| ~ sdtlseqdt0(X0,sdtasdt0(xn,xm)) ),
inference(global_subsumption_just,[status(thm)],[c_6677,c_4142]) ).
cnf(c_6731,plain,
( ~ sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ sdtlseqdt0(xn,X0)
| ~ aNaturalNumber0(X0) ),
inference(renaming,[status(thm)],[c_6730]) ).
cnf(c_8478,plain,
( ~ sdtlseqdt0(xn,sdtasdt0(xn,X0))
| ~ aNaturalNumber0(sdtasdt0(xn,X0))
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| X0 = xm
| sz00 = xn ),
inference(superposition,[status(thm)],[c_90,c_6731]) ).
cnf(c_10637,plain,
( X0 = xm
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(sdtasdt0(xn,X0))
| ~ sdtlseqdt0(xn,sdtasdt0(xn,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_8478,c_94,c_93,c_6149,c_8478]) ).
cnf(c_10638,plain,
( ~ sdtlseqdt0(xn,sdtasdt0(xn,X0))
| ~ aNaturalNumber0(sdtasdt0(xn,X0))
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0)
| X0 = xm ),
inference(renaming,[status(thm)],[c_10637]) ).
cnf(c_10643,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,sz10))
| ~ sdtlseqdt0(sz10,xm)
| ~ sdtlseqdt0(xn,xn)
| ~ aNaturalNumber0(sz10)
| sz10 = xm ),
inference(superposition,[status(thm)],[c_6171,c_10638]) ).
cnf(c_11145,plain,
( ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn)
| aNaturalNumber0(sdtasdt0(xn,sz10)) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_11618,plain,
( sdtasdt0(xn,sz10) != xn
| xn != xn
| xn = sdtasdt0(xn,sz10) ),
inference(instantiation,[status(thm)],[c_1908]) ).
cnf(c_12422,plain,
( sz10 != xm
| xm != xm
| xm = sz10 ),
inference(instantiation,[status(thm)],[c_1740]) ).
cnf(c_19812,plain,
( xn != xn
| xm != sz10
| sdtasdt0(xn,xm) = sdtasdt0(xn,sz10) ),
inference(instantiation,[status(thm)],[c_3515]) ).
cnf(c_25037,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xn,sz10)
| xn != X0
| ~ sdtlseqdt0(X0,sdtasdt0(xn,sz10))
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_184]) ).
cnf(c_33472,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xn,sz10)
| xn != sdtasdt0(xn,sz10)
| ~ sdtlseqdt0(sdtasdt0(xn,sz10),sdtasdt0(xn,sz10))
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_25037]) ).
cnf(c_33473,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,sz10))
| sdtlseqdt0(sdtasdt0(xn,sz10),sdtasdt0(xn,sz10)) ),
inference(instantiation,[status(thm)],[c_83]) ).
cnf(c_33474,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_33473,c_33472,c_19812,c_12422,c_11618,c_11145,c_10643,c_1741,c_690,c_513,c_368,c_264,c_177,c_112,c_102,c_95,c_97,c_49,c_51,c_93,c_94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM463+2 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 13:29:08 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.55/4.22 % SZS status Started for theBenchmark.p
% 24.55/4.22 % SZS status Theorem for theBenchmark.p
% 24.55/4.22
% 24.55/4.22 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 24.55/4.22
% 24.55/4.22 ------ iProver source info
% 24.55/4.22
% 24.55/4.22 git: date: 2023-05-31 18:12:56 +0000
% 24.55/4.22 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 24.55/4.22 git: non_committed_changes: false
% 24.55/4.22 git: last_make_outside_of_git: false
% 24.55/4.22
% 24.55/4.22 ------ Parsing...
% 24.55/4.22 ------ Clausification by vclausify_rel & Parsing by iProver...
% 24.55/4.22
% 24.55/4.22 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e sup_sim: 0 sf_s rm: 1 0s sf_e
% 24.55/4.22
% 24.55/4.22 ------ Preprocessing...
% 24.55/4.22
% 24.55/4.22 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 24.55/4.22 ------ Proving...
% 24.55/4.22 ------ Problem Properties
% 24.55/4.22
% 24.55/4.22
% 24.55/4.22 clauses 44
% 24.55/4.22 conjectures 4
% 24.55/4.22 EPR 11
% 24.55/4.22 Horn 35
% 24.55/4.22 unary 7
% 24.55/4.22 binary 8
% 24.55/4.22 lits 153
% 24.55/4.22 lits eq 44
% 24.55/4.22 fd_pure 0
% 24.55/4.22 fd_pseudo 0
% 24.55/4.22 fd_cond 4
% 24.55/4.22 fd_pseudo_cond 9
% 24.55/4.22 AC symbols 0
% 24.55/4.22
% 24.55/4.22 ------ Input Options Time Limit: Unbounded
% 24.55/4.22
% 24.55/4.22
% 24.55/4.22 ------
% 24.55/4.22 Current options:
% 24.55/4.22 ------
% 24.55/4.22
% 24.55/4.22
% 24.55/4.22
% 24.55/4.22
% 24.55/4.22 ------ Proving...
% 24.55/4.22
% 24.55/4.22
% 24.55/4.22 % SZS status Theorem for theBenchmark.p
% 24.55/4.22
% 24.55/4.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 24.55/4.22
% 24.55/4.24
%------------------------------------------------------------------------------