%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM463+2 : 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 27.58s 6.32s
% Output : CNFRefutation 27.58s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f136ERROR: Could not build tree for root c_88001ERROR: 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(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
| sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
fof(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 != sz00
=> ! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtasdt0(X1,X0) = sdtasdt0(X2,X0)
| sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
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(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(f24,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> ! [X2] :
( aNaturalNumber0(X2)
=> ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonAdd) ).
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))
| ? [X0] :
( sdtpldt0(xn,X0) = sdtasdt0(xn,xm)
& aNaturalNumber0(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f29,negated_conjecture,
~ ( xm != sz00
=> ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ? [X0] :
( sdtpldt0(xn,X0) = sdtasdt0(xn,xm)
& aNaturalNumber0(X0) ) ) ),
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(f40,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f41,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f40]) ).
fof(f44,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f45,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| X1 = X2 ),
inference(ennf_transformation,[],[f14]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| X1 = X2 ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ! [X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| X1 = X2 ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f51,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ! [X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| X1 = X2 ) ),
inference(flattening,[],[f50]) ).
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(f61,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f62,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f61]) ).
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(f67,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ! [X2] :
( ~ aNaturalNumber0(X2)
| ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f68,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ! [X2] :
( ~ aNaturalNumber0(X2)
| ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ),
inference(flattening,[],[f67]) ).
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))
& ! [X0] :
( sdtpldt0(xn,X0) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X0) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f74,plain,
( xm != sz00
& ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
& ! [X0] :
( sdtpldt0(xn,X0) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X0) ) ),
inference(flattening,[],[f73]) ).
fof(f75,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(f76,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,[],[f75]) ).
fof(f77,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))],[f76]) ).
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(nnf_transformation,[],[f59]) ).
fof(f79,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,[],[f78]) ).
fof(f80,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f82,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f83,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f84,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f87,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f88,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f89,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f91,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz10,X0) = X0 ),
inference(cnf_transformation,[],[f44]) ).
fof(f92,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f44]) ).
fof(f93,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f94,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f45]) ).
fof(f98,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f49]) ).
fof(f99,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f51]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f51]) ).
fof(f101,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f53]) ).
fof(f102,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| sz00 = X0 ),
inference(cnf_transformation,[],[f53]) ).
fof(f103,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| sz00 = X1
| sz00 = X0 ),
inference(cnf_transformation,[],[f55]) ).
fof(f104,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,sK0(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f77]) ).
fof(f106,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtmndt0(X1,X0) != X2
| sdtpldt0(X0,X2) = X1 ),
inference(cnf_transformation,[],[f79]) ).
fof(f111,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f62]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f113,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f117,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f119,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,[],[f70]) ).
fof(f121,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(f123,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtlseqdt0(sz10,X0)
| sz10 = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f72]) ).
fof(f125,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f27]) ).
fof(f126,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f27]) ).
fof(f127,plain,
sz00 != xm,
inference(cnf_transformation,[],[f74]) ).
fof(f128,plain,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f74]) ).
fof(f129,plain,
! [X0] :
( sdtpldt0(xn,X0) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f130,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f106]) ).
fof(f133,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 ),
inference(equality_resolution,[],[f107]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f80]) ).
tcf(c_50,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f82]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_56,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_60,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz10) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_61,plain,
! [X0: $i] :
( ( sdtasdt0(sz10,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_62,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz00) = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_63,plain,
! [X0: $i] :
( ( sdtasdt0(sz00,X0) = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sdtpldt0(X0,X2) ) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = sz00 )
| ( X0 = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sdtasdt0(X2,X1) ) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,sK0(X0,X1)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
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,[],[f112]) ).
tcf(c_82,plain,
! [X0: $i] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
| ( X0 = X1 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
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,[],[f121]) ).
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,[],[f119]) ).
tcf(c_92,plain,
! [X0: $i] :
( sdtlseqdt0(sz10,X0)
| ( X0 = sz10 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_93,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f126]) ).
tcf(c_94,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f125]) ).
tcf(c_95,negated_conjecture,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ( sdtpldt0(xn,X0) != sdtasdt0(xn,xm) ) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_96,negated_conjecture,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f128]) ).
tcf(c_97,negated_conjecture,
sz00 != xm,
inference(cnf_transformation,[],[f127]) ).
tcf(c_98,plain,
( sdtlseqdt0(sz00,sz00)
| ~ aNaturalNumber0(sz00) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_102,plain,
( ( sdtpldt0(sz00,sz00) = sz00 )
| ~ aNaturalNumber0(sz00) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_112,plain,
( ( sz00 = sz00 )
| ~ aNaturalNumber0(sz00)
| ( sdtpldt0(sz00,sz00) != sz00 ) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_124,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_1346,definition,
iPr_def_10 = sdtasdt0(xn,xm),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1347,negated_conjecture,
sz00 != xm,
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_1348,negated_conjecture,
~ sdtlseqdt0(xn,iPr_def_10),
inference(demodulation,[status(thm)],[c_96,c_1346]) ).
tcf(c_1349,negated_conjecture,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ( sdtpldt0(xn,X0) != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_1350,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1352,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2071,plain,
sdtpldt0(xn,sz00) = xn,
inference(superposition,[status(thm)],[c_94,c_56]) ).
tcf(c_2078,plain,
sdtpldt0(sz00,xm) = xm,
inference(superposition,[status(thm)],[c_93,c_57]) ).
tcf(c_2088,plain,
( ~ aNaturalNumber0(sz00)
| ( xn != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_2071,c_1349]) ).
tcf(c_2089,plain,
xn != iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_2088,c_49]) ).
tcf(c_2101,plain,
( sdtlseqdt0(sz00,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_2078,c_124]) ).
tcf(c_2105,plain,
sdtlseqdt0(sz00,xm),
inference(forward_subsumption_resolution,[status(thm)],[c_2101,c_93,c_49]) ).
tcf(c_2124,plain,
sdtasdt0(xm,sz00) = sz00,
inference(superposition,[status(thm)],[c_93,c_62]) ).
tcf(c_2132,plain,
sdtasdt0(sz00,xm) = sz00,
inference(superposition,[status(thm)],[c_93,c_63]) ).
tcf(c_2183,plain,
( aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_1346,c_53]) ).
tcf(c_2200,plain,
aNaturalNumber0(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2183,c_94,c_93]) ).
tcf(c_2233,plain,
( sdtlseqdt0(iPr_def_10,xn)
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_83,c_1348]) ).
tcf(c_2237,plain,
( sdtlseqdt0(iPr_def_10,xn)
| ~ aNaturalNumber0(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2233,c_94]) ).
tcf(c_2275,plain,
! [X0: $i] :
( ( sz00 = xm )
| ( xm != X0 )
| ( sz00 != X0 ) ),
inference(instantiation,[status(thm)],[c_1352]) ).
tcf(c_2276,plain,
( ( sz00 = xm )
| ( xm != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_2275]) ).
tcf(c_2289,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xm) = sdtasdt0(xm,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_93,c_58]) ).
tcf(c_2323,plain,
sdtpldt0(sz00,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_2200,c_57]) ).
tcf(c_2354,plain,
( sdtlseqdt0(sz00,iPr_def_10)
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_2323,c_124]) ).
tcf(c_2355,plain,
sdtlseqdt0(sz00,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2354,c_2200,c_49]) ).
tcf(c_2396,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_2397,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_2396]) ).
tcf(c_2494,plain,
! [X0: $i,X1: $i] :
( ( sz10 = X0 )
| ( sz10 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1352]) ).
tcf(c_2659,plain,
( sdtlseqdt0(sz10,xm)
| ( xm = sz10 )
| ( xm = sz00 )
| ~ aNaturalNumber0(xm) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_2777,plain,
! [X0: $i] :
( sdtlseqdt0(xn,sdtpldt0(xn,X0))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(instantiation,[status(thm)],[c_124]) ).
tcf(c_2783,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(xn,X0)
| ~ sdtlseqdt0(X2,X1)
| ( xn != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1356]) ).
tcf(c_2784,plain,
( sdtlseqdt0(xn,sz00)
| ~ sdtlseqdt0(sz00,sz00)
| ( xn != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_2783]) ).
tcf(c_2914,plain,
! [X0: $i] :
( aNaturalNumber0(sdtpldt0(xn,X0))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_2937,plain,
xn = xn,
inference(instantiation,[status(thm)],[c_1350]) ).
tcf(c_2939,plain,
! [X0: $i,X1: $i] :
( ( xn = X0 )
| ( xn != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1352]) ).
tcf(c_3563,plain,
( ( sz00 = xn )
| ( sz00 = xm )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ( sz00 != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_1346,c_72]) ).
tcf(c_3580,plain,
( ( sz00 = xn )
| ( sz00 != iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3563,c_1347,c_94,c_93]) ).
tcf(c_3793,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xn,X0) != xn ) ),
inference(superposition,[status(thm)],[c_2071,c_66]) ).
tcf(c_3842,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(xn,X0) != xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3793,c_94,c_49]) ).
tcf(c_4201,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(xn,X0) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sdtpldt0(xn,X0))
| ~ sdtlseqdt0(X1,sdtpldt0(xn,X0))
| ~ sdtlseqdt0(sdtpldt0(xn,X0),X1) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_4578,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xn,X0),xn)
| ( X0 = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(superposition,[status(thm)],[c_2071,c_85]) ).
tcf(c_4643,plain,
! [X0: $i] :
( sdtlseqdt0(sdtpldt0(xn,X0),xn)
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4578,c_94,c_49]) ).
tcf(c_4971,plain,
! [X0: $i] :
( ( xn = X0 )
| ( xn != xn )
| ( X0 != xn ) ),
inference(instantiation,[status(thm)],[c_2939]) ).
tcf(c_4972,plain,
( ( xn = sz00 )
| ( xn != xn )
| ( sz00 != xn ) ),
inference(instantiation,[status(thm)],[c_4971]) ).
tcf(c_5658,plain,
! [X0: $i] :
( ( sz00 = xm )
| ( X0 = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,xm) != sz00 ) ),
inference(superposition,[status(thm)],[c_2132,c_69]) ).
tcf(c_5698,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,xm) != sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5658,c_1347,c_93,c_49]) ).
tcf(c_6204,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,sdtasdt0(xm,X0))
| ( sz00 = xm )
| ( X0 = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(superposition,[status(thm)],[c_2124,c_89]) ).
tcf(c_6346,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,sdtasdt0(xm,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6204,c_1347,c_93,c_49]) ).
tcf(c_6708,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,sdtasdt0(X0,xm))
| ( sz00 = xm )
| ( X0 = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(superposition,[status(thm)],[c_2132,c_91]) ).
tcf(c_6735,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(X0,xm),sz00)
| ( sz00 = xm )
| ( X0 = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(superposition,[status(thm)],[c_2132,c_91]) ).
tcf(c_6788,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(X0,xm),sz00)
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6735,c_1347,c_93,c_49]) ).
tcf(c_6847,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,sdtasdt0(X0,xm))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6708,c_1347,c_93,c_49]) ).
tcf(c_7094,plain,
! [X0: $i] :
( ( sz10 = X0 )
| ( sz10 != sz10 )
| ( X0 != sz10 ) ),
inference(instantiation,[status(thm)],[c_2494]) ).
tcf(c_7095,plain,
sz10 = sz10,
inference(instantiation,[status(thm)],[c_1350]) ).
tcf(c_7507,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ( sdtpldt0(sz00,sdtmndt0(sdtasdt0(xm,X0),sz00)) = sdtasdt0(xm,X0) )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(sdtasdt0(xm,X0)) ),
inference(superposition,[status(thm)],[c_6346,c_78]) ).
tcf(c_7515,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ( sdtpldt0(sz00,sdtmndt0(sdtasdt0(xm,X0),sz00)) = sdtasdt0(xm,X0) )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(sdtasdt0(xm,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7507,c_49]) ).
tcf(c_7606,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ( sdtasdt0(X0,xm) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ~ sdtlseqdt0(sz00,sdtasdt0(X0,xm)) ),
inference(superposition,[status(thm)],[c_6788,c_80]) ).
tcf(c_7622,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ( sdtasdt0(X0,xm) = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ~ sdtlseqdt0(sz00,sdtasdt0(X0,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7606,c_49]) ).
tcf(c_7803,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sz00,X1)
| ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ~ sdtlseqdt0(sdtasdt0(X0,xm),X1) ),
inference(superposition,[status(thm)],[c_6847,c_81]) ).
tcf(c_7826,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sz00,X1)
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ~ sdtlseqdt0(sdtasdt0(X0,xm),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7803,c_49]) ).
tcf(c_10349,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ( sdtpldt0(sz00,sdtmndt0(sdtasdt0(xm,X0),sz00)) = sdtasdt0(xm,X0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(superposition,[status(thm)],[c_53,c_7515]) ).
tcf(c_10353,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ( sdtpldt0(sz00,sdtmndt0(sdtasdt0(xm,X0),sz00)) = sdtasdt0(xm,X0) )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10349,c_93]) ).
tcf(c_12478,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ sdtlseqdt0(sz00,sdtasdt0(X0,xm))
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_7622,c_5698,c_7622]) ).
tcf(c_12479,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ~ sdtlseqdt0(sz00,sdtasdt0(X0,xm)) ),
inference(renaming,[status(thm)],[c_12478]) ).
tcf(c_15188,plain,
! [X0: $i] :
( ( sdtpldt0(xn,X0) = xn )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtpldt0(xn,X0))
| ~ sdtlseqdt0(xn,sdtpldt0(xn,X0))
| ~ sdtlseqdt0(sdtpldt0(xn,X0),xn) ),
inference(instantiation,[status(thm)],[c_4201]) ).
tcf(c_17044,plain,
sdtasdt0(xm,xn) = sdtasdt0(xn,xm),
inference(superposition,[status(thm)],[c_94,c_2289]) ).
tcf(c_17045,plain,
sdtasdt0(xm,iPr_def_10) = sdtasdt0(iPr_def_10,xm),
inference(superposition,[status(thm)],[c_2200,c_2289]) ).
tcf(c_17057,plain,
sdtasdt0(xm,xn) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_17044,c_1346]) ).
tcf(c_17108,plain,
! [X0: $i] :
( ( sz00 = xm )
| ( X0 = xn )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(xm,X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_17057,c_68]) ).
tcf(c_17110,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(xm,X0),iPr_def_10)
| ( sz00 = xm )
| ( X0 = xn )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn) ),
inference(superposition,[status(thm)],[c_17057,c_89]) ).
tcf(c_17138,plain,
! [X0: $i] :
( ( X0 = xn )
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(xm,X0) != iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17108,c_1347,c_94,c_93]) ).
tcf(c_17148,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(xm,X0),iPr_def_10)
| ( X0 = xn )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17110,c_1347,c_94,c_93]) ).
tcf(c_17192,plain,
( aNaturalNumber0(sdtasdt0(iPr_def_10,xm))
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_17045,c_53]) ).
tcf(c_17197,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(xm,X0),sdtasdt0(iPr_def_10,xm))
| ( sz00 = xm )
| ( X0 = iPr_def_10 )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_17045,c_89]) ).
tcf(c_17211,plain,
( sdtlseqdt0(sz00,sdtasdt0(iPr_def_10,xm))
| ( sz00 = iPr_def_10 )
| ~ aNaturalNumber0(iPr_def_10)
| ~ sdtlseqdt0(sz00,iPr_def_10) ),
inference(superposition,[status(thm)],[c_17045,c_6346]) ).
tcf(c_17216,plain,
aNaturalNumber0(sdtasdt0(iPr_def_10,xm)),
inference(forward_subsumption_resolution,[status(thm)],[c_17192,c_2200,c_93]) ).
tcf(c_17227,plain,
( sdtlseqdt0(sz00,sdtasdt0(iPr_def_10,xm))
| ( sz00 = iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17211,c_2200,c_2355]) ).
tcf(c_17290,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(xm,X0),sdtasdt0(iPr_def_10,xm))
| ( X0 = iPr_def_10 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17197,c_1347,c_2200,c_93]) ).
tcf(c_17732,plain,
( ( xn = iPr_def_10 )
| ~ aNaturalNumber0(iPr_def_10)
| ( sdtasdt0(iPr_def_10,xm) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_17045,c_17138]) ).
tcf(c_17733,plain,
sdtasdt0(iPr_def_10,xm) != iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_17732,c_2089,c_2200]) ).
tcf(c_17747,plain,
! [X0: $i] :
( ( X0 = xn )
| ( sdtasdt0(xm,X0) = iPr_def_10 )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ~ sdtlseqdt0(iPr_def_10,sdtasdt0(xm,X0)) ),
inference(superposition,[status(thm)],[c_17148,c_80]) ).
tcf(c_17774,plain,
! [X0: $i] :
( ( X0 = xn )
| ( sdtasdt0(xm,X0) = iPr_def_10 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ~ sdtlseqdt0(iPr_def_10,sdtasdt0(xm,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17747,c_2200]) ).
tcf(c_17892,plain,
( sdtlseqdt0(sz00,sdtasdt0(iPr_def_10,xm))
| ( xm = iPr_def_10 )
| ( sz00 = xm )
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xm,iPr_def_10)
| ~ sdtlseqdt0(sz00,xm)
| ~ aNaturalNumber0(sdtasdt0(iPr_def_10,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(superposition,[status(thm)],[c_17290,c_7826]) ).
tcf(c_17894,plain,
( sdtlseqdt0(sz00,sdtasdt0(iPr_def_10,xm))
| ( xm = iPr_def_10 )
| ~ sdtlseqdt0(xm,iPr_def_10)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17892,c_1347,c_93,c_2105,c_17216]) ).
tcf(c_17992,plain,
sdtlseqdt0(sz00,sdtasdt0(iPr_def_10,xm)),
inference(global_subsumption_just,[status(thm)],[c_17894,c_94,c_49,c_98,c_102,c_112,c_1348,c_2200,c_2355,c_2397,c_2784,c_2937,c_3580,c_4972,c_17227]) ).
tcf(c_17994,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(iPr_def_10,xm))
| ~ sdtlseqdt0(sdtasdt0(iPr_def_10,xm),X0) ),
inference(superposition,[status(thm)],[c_17992,c_81]) ).
tcf(c_18004,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sdtasdt0(iPr_def_10,xm),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17994,c_49,c_17216]) ).
tcf(c_18531,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,sdtasdt0(X0,xm))
| ( sz00 = xm )
| ( X0 = iPr_def_10 )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(iPr_def_10,X0)
| ~ aNaturalNumber0(sdtasdt0(X0,xm)) ),
inference(superposition,[status(thm)],[c_91,c_18004]) ).
tcf(c_18565,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,sdtasdt0(X0,xm))
| ( X0 = iPr_def_10 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(iPr_def_10,X0)
| ~ aNaturalNumber0(sdtasdt0(X0,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18531,c_1347,c_2200,c_93]) ).
tcf(c_18597,plain,
! [X0: $i] :
( ( X0 = iPr_def_10 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(iPr_def_10,X0)
| ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(sdtasdt0(X0,xm)) ),
inference(superposition,[status(thm)],[c_18565,c_12479]) ).
tcf(c_19427,plain,
! [X0: $i] :
( ~ sdtlseqdt0(X0,sz00)
| ~ aNaturalNumber0(X0)
| ( X0 = sz00 ) ),
inference(global_subsumption_just,[status(thm)],[c_18597,c_94,c_2777,c_2914,c_3842,c_4643,c_15188]) ).
tcf(c_19428,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sz00) ),
inference(renaming,[status(thm)],[c_19427]) ).
tcf(c_19437,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,X0)
| ( X0 = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_83,c_19428]) ).
tcf(c_19448,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,X0)
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19437,c_49]) ).
tcf(c_20134,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,sdtasdt0(xm,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_6346,c_19448]) ).
tcf(c_22248,plain,
! [X0: $i] :
( ( X0 = xn )
| ~ sdtlseqdt0(iPr_def_10,sdtasdt0(xm,X0))
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_17774,c_17138,c_17774]) ).
tcf(c_22249,plain,
! [X0: $i] :
( ( X0 = xn )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ~ sdtlseqdt0(iPr_def_10,sdtasdt0(xm,X0)) ),
inference(renaming,[status(thm)],[c_22248]) ).
tcf(c_28061,plain,
sdtpldt0(xn,sz00) = xn,
inference(superposition,[status(thm)],[c_94,c_56]) ).
tcf(c_28070,plain,
( ~ aNaturalNumber0(sz00)
| ( xn != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_28061,c_1349]) ).
tcf(c_28071,plain,
xn != iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_28070,c_49]) ).
tcf(c_28094,plain,
sdtasdt0(xm,sz00) = sz00,
inference(superposition,[status(thm)],[c_93,c_62]) ).
tcf(c_28282,plain,
( aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_1346,c_53]) ).
tcf(c_28306,plain,
aNaturalNumber0(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_28282,c_94,c_93]) ).
tcf(c_28378,plain,
( sdtlseqdt0(iPr_def_10,xn)
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_83,c_1348]) ).
tcf(c_28382,plain,
( sdtlseqdt0(iPr_def_10,xn)
| ~ aNaturalNumber0(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28378,c_94]) ).
tcf(c_28421,plain,
sdtasdt0(sz10,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_28306,c_61]) ).
tcf(c_28422,plain,
sdtasdt0(iPr_def_10,sz10) = iPr_def_10,
inference(superposition,[status(thm)],[c_28306,c_60]) ).
tcf(c_28423,plain,
sdtpldt0(sz00,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_28306,c_57]) ).
tcf(c_28442,plain,
sdtlseqdt0(iPr_def_10,xn),
inference(global_subsumption_just,[status(thm)],[c_28382,c_2200,c_2237]) ).
tcf(c_28528,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xm) = sdtasdt0(xm,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_93,c_58]) ).
tcf(c_28896,plain,
sdtasdt0(xm,xn) = sdtasdt0(xn,xm),
inference(superposition,[status(thm)],[c_94,c_28528]) ).
tcf(c_28897,plain,
sdtasdt0(xm,iPr_def_10) = sdtasdt0(iPr_def_10,xm),
inference(superposition,[status(thm)],[c_28306,c_28528]) ).
tcf(c_28898,plain,
sdtasdt0(xm,xn) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_28896,c_1346]) ).
tcf(c_29028,plain,
( ( sdtpldt0(iPr_def_10,sK0(iPr_def_10,xn)) = xn )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_28442,c_75]) ).
tcf(c_29039,plain,
sdtpldt0(iPr_def_10,sK0(iPr_def_10,xn)) = xn,
inference(forward_subsumption_resolution,[status(thm)],[c_29028,c_28306,c_94]) ).
tcf(c_29145,plain,
( ( sz00 = iPr_def_10 )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(sK0(iPr_def_10,xn))
| ( sz00 != xn ) ),
inference(superposition,[status(thm)],[c_29039,c_70]) ).
tcf(c_29148,plain,
( ( sz00 = iPr_def_10 )
| ~ aNaturalNumber0(sK0(iPr_def_10,xn))
| ( sz00 != xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29145,c_28306]) ).
tcf(c_29168,plain,
sz00 != xn,
inference(global_subsumption_just,[status(thm)],[c_29148,c_94,c_49,c_98,c_102,c_112,c_1348,c_2200,c_2355,c_2397,c_2784,c_2937,c_4972]) ).
tcf(c_29667,plain,
( ( sz00 = xn )
| ( sz00 = xm )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ( sz00 != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_28898,c_72]) ).
tcf(c_29668,plain,
sz00 != iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_29667,c_29168,c_1347,c_94,c_93]) ).
tcf(c_29708,plain,
! [X0: $i] :
( ( X0 = iPr_def_10 )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sz00,X0) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_28423,c_66]) ).
tcf(c_29730,plain,
! [X0: $i] :
( ( X0 = iPr_def_10 )
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(sz00,X0) != iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29708,c_28306,c_49]) ).
tcf(c_33638,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,sdtasdt0(xm,X0))
| ( sz00 = xm )
| ( X0 = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(superposition,[status(thm)],[c_28094,c_89]) ).
tcf(c_33672,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(xm,X0),iPr_def_10)
| ( sz00 = xm )
| ( X0 = xn )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn) ),
inference(superposition,[status(thm)],[c_28898,c_89]) ).
tcf(c_33687,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(xm,X0),iPr_def_10)
| ( X0 = xn )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33672,c_1347,c_94,c_93]) ).
tcf(c_33772,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,sdtasdt0(xm,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz00,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33638,c_1347,c_93,c_49]) ).
tcf(c_36605,plain,
! [X0: $i] :
( sdtlseqdt0(iPr_def_10,sdtasdt0(X0,iPr_def_10))
| ( sz00 = iPr_def_10 )
| ( X0 = sz10 )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz10,X0) ),
inference(superposition,[status(thm)],[c_28421,c_91]) ).
tcf(c_36718,plain,
! [X0: $i] :
( sdtlseqdt0(iPr_def_10,sdtasdt0(X0,iPr_def_10))
| ( X0 = sz10 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36605,c_29668,c_28306,c_50]) ).
tcf(c_39294,plain,
! [X0: $i] :
( ( X0 = xn )
| ( sdtasdt0(xm,X0) = iPr_def_10 )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ~ sdtlseqdt0(iPr_def_10,sdtasdt0(xm,X0)) ),
inference(superposition,[status(thm)],[c_33687,c_80]) ).
tcf(c_39313,plain,
! [X0: $i] :
( ( X0 = xn )
| ( sdtasdt0(xm,X0) = iPr_def_10 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ~ sdtlseqdt0(iPr_def_10,sdtasdt0(xm,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39294,c_28306]) ).
tcf(c_39463,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,sdtasdt0(xm,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_33772,c_20134]) ).
tcf(c_39476,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ( sdtpldt0(sz00,sdtmndt0(sdtasdt0(xm,X0),sz00)) = sdtasdt0(xm,X0) )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xm,X0)) ),
inference(superposition,[status(thm)],[c_39463,c_78]) ).
tcf(c_39483,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ( sdtpldt0(sz00,sdtmndt0(sdtasdt0(xm,X0),sz00)) = sdtasdt0(xm,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xm,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39476,c_49]) ).
tcf(c_62842,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ( sdtpldt0(sz00,sdtmndt0(sdtasdt0(xm,X0),sz00)) = sdtasdt0(xm,X0) )
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_39483,c_10353,c_19448]) ).
tcf(c_62858,plain,
( ( sz00 = iPr_def_10 )
| ( sdtpldt0(sz00,sdtmndt0(sdtasdt0(xm,iPr_def_10),sz00)) = sdtasdt0(xm,iPr_def_10) ) ),
inference(superposition,[status(thm)],[c_28306,c_62842]) ).
tcf(c_62865,plain,
( ( sz00 = iPr_def_10 )
| ( sdtpldt0(sz00,sdtmndt0(sdtasdt0(iPr_def_10,xm),sz00)) = sdtasdt0(iPr_def_10,xm) ) ),
inference(light_normalisation,[status(thm)],[c_62858,c_28897]) ).
tcf(c_62866,plain,
sdtpldt0(sz00,sdtmndt0(sdtasdt0(iPr_def_10,xm),sz00)) = sdtasdt0(iPr_def_10,xm),
inference(forward_subsumption_resolution,[status(thm)],[c_62865,c_29668]) ).
tcf(c_75373,plain,
( ( sdtmndt0(sdtasdt0(iPr_def_10,xm),sz00) = iPr_def_10 )
| ~ aNaturalNumber0(sdtmndt0(sdtasdt0(iPr_def_10,xm),sz00))
| ( sdtasdt0(iPr_def_10,xm) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_62866,c_29730]) ).
tcf(c_76773,plain,
sdtasdt0(iPr_def_10,xm) != iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_75373,c_17733]) ).
tcf(c_81424,plain,
( ( sz10 = xm )
| ( xm != sz10 )
| ( sz10 != sz10 ) ),
inference(instantiation,[status(thm)],[c_7094]) ).
tcf(c_85675,plain,
! [X0: $i] :
( ( X0 = xn )
| ~ sdtlseqdt0(iPr_def_10,sdtasdt0(xm,X0))
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_39313,c_22249]) ).
tcf(c_85676,plain,
! [X0: $i] :
( ( X0 = xn )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(sdtasdt0(xm,X0))
| ~ sdtlseqdt0(iPr_def_10,sdtasdt0(xm,X0)) ),
inference(renaming,[status(thm)],[c_85675]) ).
tcf(c_85693,plain,
( ( xn = iPr_def_10 )
| ( sz10 = xm )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(iPr_def_10,xn)
| ~ sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(sdtasdt0(xm,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_36718,c_85676]) ).
tcf(c_85713,plain,
( ( xn = iPr_def_10 )
| ( sz10 = xm )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(iPr_def_10,xn)
| ~ sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(sdtasdt0(iPr_def_10,xm)) ),
inference(light_normalisation,[status(thm)],[c_85693,c_28897]) ).
tcf(c_85714,plain,
( ( sz10 = xm )
| ~ sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(sdtasdt0(iPr_def_10,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85713,c_28071,c_28306,c_93,c_28442]) ).
tcf(c_87856,plain,
sz10 = xm,
inference(global_subsumption_just,[status(thm)],[c_85714,c_93,c_49,c_97,c_102,c_112,c_2276,c_2659,c_7095,c_17216,c_81424,c_85714]) ).
tcf(c_87890,plain,
sdtasdt0(iPr_def_10,sz10) != iPr_def_10,
inference(demodulation,[status(thm)],[c_76773,c_87856]) ).
tcf(c_88001,plain,
$false,
inference(ground_joinability,[status(thm)],[c_87890,c_28422]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM463+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 04:06:44 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 27.58/6.32 % SZS status Started for theBenchmark.p
% 27.58/6.32 % SZS status Theorem for theBenchmark.p
% 27.58/6.32
% 27.58/6.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 27.58/6.32
% 27.58/6.32 % ------ iProver source info
% 27.58/6.32
% 27.58/6.32 % git: date: 2026-07-19 20:42:38 +0200
% 27.58/6.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 27.58/6.32 % git: non_committed_changes: false
% 27.58/6.32
% 27.58/6.32 % ------ Parsing...
% 27.58/6.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 27.58/6.32
% 27.58/6.32 % ------ 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 %
% 27.58/6.32
% 27.58/6.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 27.58/6.32
% 27.58/6.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 27.58/6.32 % ------ Proving...
% 27.58/6.32 % ------ Problem Properties
% 27.58/6.32
% 27.58/6.32 %
% 27.58/6.32 % clauses 45
% 27.58/6.32 % conjectures 3
% 27.58/6.32 % EPR 12
% 27.58/6.32 % Horn 36
% 27.58/6.32 % unary 8
% 27.58/6.32 % binary 8
% 27.58/6.32 % lits 154
% 27.58/6.32 % lits eq 45
% 27.58/6.32 % fd_pure 0
% 27.58/6.32 % fd_pseudo 0
% 27.58/6.32 % fd_cond 4
% 27.58/6.32 % fd_pseudo_cond 9
% 27.58/6.32 % AC symbols 0
% 27.58/6.32
% 27.58/6.32 % ------ Schedule dynamic 5 is on
% 27.58/6.32
% 27.58/6.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 27.58/6.32
% 27.58/6.32
% 27.58/6.32 % ------
% 27.58/6.32 % Current options:
% 27.58/6.32 % ------
% 27.58/6.32
% 27.58/6.32
% 27.58/6.32 %
% 27.58/6.32
% 27.58/6.32 % ------ Proving...
% 27.58/6.32 %
% 27.58/6.32
% 27.58/6.32 % SZS status Theorem for theBenchmark.p
% 27.58/6.32
% 27.58/6.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 27.58/6.32
% 27.58/6.32
%------------------------------------------------------------------------------