%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM465+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n014.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 7.22s 2.02s
% Output : CNFRefutation 7.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 22
% Syntax : Number of formulae : 175 ( 38 unt; 1 def)
% Number of atoms : 746 ( 235 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 828 ( 361 ~; 367 |; 69 &)
% ( 6 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 222 ( 0 sgn 213 !; 9 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
( sz10 != sz00
& 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)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(f16,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtpldt0(X0,X1) = sz00
=> ( X1 = sz00
& X0 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).
fof(f17,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(X0,X1) = sz00
=> ( X1 = sz00
| X0 = sz00 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
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(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| 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
& 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/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
fof(f27,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__987) ).
fof(f28,axiom,
( xm != sz00
=> ( sdtlseqdt0(sz10,xm)
& ? [X0] :
( sdtpldt0(sz10,X0) = xm
& aNaturalNumber0(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1007) ).
fof(f29,conjecture,
( xm != sz00
=> ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ? [X0] :
( sdtpldt0(xn,X0) = sdtasdt0(xn,xm)
& aNaturalNumber0(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f30,negated_conjecture,
~ ( xm != sz00
=> ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ? [X0] :
( sdtpldt0(xn,X0) = sdtasdt0(xn,xm)
& aNaturalNumber0(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f32,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f33,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f35,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f34]) ).
fof(f40,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f45,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
inference(ennf_transformation,[],[f11]) ).
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(ennf_transformation,[],[f14]) ).
fof(f50,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,[],[f49]) ).
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(ennf_transformation,[],[f15]) ).
fof(f52,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,[],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f54,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(ennf_transformation,[],[f17]) ).
fof(f56,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f58,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f57]) ).
fof(f59,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(f60,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f59]) ).
fof(f62,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f63,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f62]) ).
fof(f66,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f67,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f66]) ).
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(ennf_transformation,[],[f25]) ).
fof(f71,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,[],[f70]) ).
fof(f74,plain,
( sz00 = xm
| ( sdtlseqdt0(sz10,xm)
& ? [X0] :
( sdtpldt0(sz10,X0) = xm
& aNaturalNumber0(X0) ) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f75,plain,
( xm != sz00
& ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
& ! [X0] :
( sdtpldt0(xn,X0) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X0) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f76,plain,
( xm != sz00
& ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
& ! [X0] :
( sdtpldt0(xn,X0) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X0) ) ),
inference(flattening,[],[f75]) ).
fof(f77,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,[],[f58]) ).
fof(f78,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,[],[f77]) ).
fof(f79,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))],[f78]) ).
fof(f80,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,[],[f60]) ).
fof(f81,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,[],[f80]) ).
fof(f82,plain,
( sz00 = xm
| ( sdtlseqdt0(sz10,xm)
& xm = sdtpldt0(sz10,sK1)
& aNaturalNumber0(sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f74]) ).
fof(f83,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f85,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f86,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f87,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f90,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f40]) ).
fof(f91,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f40]) ).
fof(f95,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f45]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f50]) ).
fof(f102,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f52]) ).
fof(f105,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| sz00 = X0 ),
inference(cnf_transformation,[],[f54]) ).
fof(f106,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| sz00 = X1
| sz00 = X0 ),
inference(cnf_transformation,[],[f56]) ).
fof(f107,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,sK0(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f79]) ).
fof(f108,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| aNaturalNumber0(sK0(X0,X1)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtmndt0(X1,X0) != X2
| sdtpldt0(X0,X2) = X1 ),
inference(cnf_transformation,[],[f81]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtmndt0(X1,X0) != X2
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f81]) ).
fof(f114,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f63]) ).
fof(f116,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f122,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,[],[f71]) ).
fof(f124,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,[],[f71]) ).
fof(f128,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f27]) ).
fof(f129,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f27]) ).
fof(f130,plain,
( sz00 = xm
| sdtlseqdt0(sz10,xm) ),
inference(cnf_transformation,[],[f82]) ).
fof(f133,plain,
sz00 != xm,
inference(cnf_transformation,[],[f76]) ).
fof(f134,plain,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f76]) ).
fof(f135,plain,
! [X0] :
( sdtpldt0(xn,X0) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f136,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f109]) ).
fof(f138,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| aNaturalNumber0(sdtmndt0(X1,X0)) ),
inference(equality_resolution,[],[f111]) ).
fof(f139,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 ),
inference(equality_resolution,[],[f110]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f83]) ).
tcf(c_50,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f85]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_56,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_60,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz10) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f95]) ).
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,[],[f101]) ).
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,[],[f102]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sK0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,sK0(X0,X1)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f116]) ).
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,[],[f124]) ).
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,[],[f122]) ).
tcf(c_93,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f129]) ).
tcf(c_94,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f128]) ).
tcf(c_97,plain,
( sdtlseqdt0(sz10,xm)
| ( sz00 = xm ) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_98,negated_conjecture,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ( sdtpldt0(xn,X0) != sdtasdt0(xn,xm) ) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_99,negated_conjecture,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f134]) ).
tcf(c_100,negated_conjecture,
sz00 != xm,
inference(cnf_transformation,[],[f133]) ).
tcf(c_129,plain,
sdtlseqdt0(sz10,xm),
inference(global_subsumption_just,[status(thm)],[c_97,c_100,c_97]) ).
tcf(c_133,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_1367,definition,
iPr_def_10 = sdtasdt0(xn,xm),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1368,negated_conjecture,
sz00 != xm,
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_1369,negated_conjecture,
~ sdtlseqdt0(xn,iPr_def_10),
inference(demodulation,[status(thm)],[c_99,c_1367]) ).
tcf(c_1370,negated_conjecture,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ( sdtpldt0(xn,X0) != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_1371,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1373,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2104,plain,
sdtpldt0(xn,sz00) = xn,
inference(superposition,[status(thm)],[c_94,c_56]) ).
tcf(c_2106,plain,
( ~ aNaturalNumber0(sz00)
| ( xn != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_2104,c_1370]) ).
tcf(c_2107,plain,
xn != iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_2106,c_49]) ).
tcf(c_2149,plain,
sdtasdt0(xn,sz10) = xn,
inference(superposition,[status(thm)],[c_94,c_60]) ).
tcf(c_2230,plain,
( aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_1367,c_53]) ).
tcf(c_2241,plain,
aNaturalNumber0(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2230,c_94,c_93]) ).
tcf(c_2266,plain,
( sdtlseqdt0(iPr_def_10,xn)
| sdtlseqdt0(xn,iPr_def_10)
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xn) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_2275,plain,
( sdtlseqdt0(iPr_def_10,xn)
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_83,c_1369]) ).
tcf(c_2279,plain,
( sdtlseqdt0(iPr_def_10,xn)
| ~ aNaturalNumber0(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2275,c_94]) ).
tcf(c_2334,plain,
sdtasdt0(iPr_def_10,sz10) = iPr_def_10,
inference(superposition,[status(thm)],[c_2241,c_60]) ).
tcf(c_2335,plain,
sdtpldt0(sz00,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_2241,c_57]) ).
tcf(c_2340,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(xn,iPr_def_10)
| ~ sdtlseqdt0(X0,X1)
| ( iPr_def_10 != X1 )
| ( xn != X0 ) ),
inference(instantiation,[status(thm)],[c_1377]) ).
tcf(c_2357,plain,
sdtlseqdt0(iPr_def_10,xn),
inference(global_subsumption_just,[status(thm)],[c_2279,c_94,c_1369,c_2241,c_2266]) ).
tcf(c_2575,plain,
( sdtlseqdt0(sz00,iPr_def_10)
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_2335,c_133]) ).
tcf(c_2576,plain,
sdtlseqdt0(sz00,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2575,c_2241,c_49]) ).
tcf(c_2806,plain,
( ( sdtpldt0(iPr_def_10,sK0(iPr_def_10,xn)) = xn )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_2357,c_75]) ).
tcf(c_2818,plain,
sdtpldt0(iPr_def_10,sK0(iPr_def_10,xn)) = xn,
inference(forward_subsumption_resolution,[status(thm)],[c_2806,c_2241,c_94]) ).
tcf(c_2893,plain,
! [X0: $i] :
( sdtlseqdt0(xn,iPr_def_10)
| ~ sdtlseqdt0(sz00,X0)
| ( iPr_def_10 != X0 )
| ( xn != sz00 ) ),
inference(instantiation,[status(thm)],[c_2340]) ).
tcf(c_2908,plain,
xn = xn,
inference(instantiation,[status(thm)],[c_1371]) ).
tcf(c_2910,plain,
! [X0: $i,X1: $i] :
( ( xn = X0 )
| ( xn != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1373]) ).
tcf(c_3049,plain,
( ( sdtpldt0(iPr_def_10,sdtmndt0(xn,iPr_def_10)) = xn )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_2357,c_78]) ).
tcf(c_3065,plain,
sdtpldt0(iPr_def_10,sdtmndt0(xn,iPr_def_10)) = xn,
inference(forward_subsumption_resolution,[status(thm)],[c_3049,c_2241,c_94]) ).
tcf(c_3518,plain,
( ( sz00 = iPr_def_10 )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(sdtmndt0(xn,iPr_def_10))
| ( sz00 != xn ) ),
inference(superposition,[status(thm)],[c_3065,c_70]) ).
tcf(c_3521,plain,
( ( sz00 = iPr_def_10 )
| ~ aNaturalNumber0(sdtmndt0(xn,iPr_def_10))
| ( sz00 != xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3518,c_2241]) ).
tcf(c_3814,plain,
( ( sz00 = xn )
| ( sz00 = xm )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ( sz00 != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_1367,c_72]) ).
tcf(c_3835,plain,
( ( sz00 = xn )
| ( sz00 != iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3814,c_1368,c_94,c_93]) ).
tcf(c_3885,plain,
! [X0: $i] :
( ( sdtmndt0(xn,iPr_def_10) = X0 )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtmndt0(xn,iPr_def_10))
| ( sdtpldt0(iPr_def_10,X0) != xn ) ),
inference(superposition,[status(thm)],[c_3065,c_66]) ).
tcf(c_3951,plain,
! [X0: $i] :
( ( sdtmndt0(xn,iPr_def_10) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtmndt0(xn,iPr_def_10))
| ( sdtpldt0(iPr_def_10,X0) != xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3885,c_2241]) ).
tcf(c_4217,plain,
( sdtlseqdt0(xn,iPr_def_10)
| ~ sdtlseqdt0(sz00,iPr_def_10)
| ( iPr_def_10 != iPr_def_10 )
| ( xn != sz00 ) ),
inference(instantiation,[status(thm)],[c_2893]) ).
tcf(c_4218,plain,
iPr_def_10 = iPr_def_10,
inference(instantiation,[status(thm)],[c_1371]) ).
tcf(c_4361,plain,
( ( sK0(iPr_def_10,xn) = sdtmndt0(xn,iPr_def_10) )
| ~ aNaturalNumber0(sdtmndt0(xn,iPr_def_10))
| ~ aNaturalNumber0(sK0(iPr_def_10,xn)) ),
inference(superposition,[status(thm)],[c_2818,c_3951]) ).
tcf(c_4373,plain,
( ( sK0(iPr_def_10,xn) = sdtmndt0(xn,iPr_def_10) )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(iPr_def_10,xn)
| ~ aNaturalNumber0(sdtmndt0(xn,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_74,c_4361]) ).
tcf(c_4374,plain,
( ( sK0(iPr_def_10,xn) = sdtmndt0(xn,iPr_def_10) )
| ~ aNaturalNumber0(sdtmndt0(xn,iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4373,c_2241,c_94,c_2357]) ).
tcf(c_4383,plain,
( ( sK0(iPr_def_10,xn) = sdtmndt0(xn,iPr_def_10) )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(iPr_def_10,xn) ),
inference(superposition,[status(thm)],[c_77,c_4374]) ).
tcf(c_4384,plain,
sK0(iPr_def_10,xn) = sdtmndt0(xn,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_4383,c_2241,c_94,c_2357]) ).
tcf(c_4388,plain,
( aNaturalNumber0(sdtmndt0(xn,iPr_def_10))
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(iPr_def_10,xn) ),
inference(superposition,[status(thm)],[c_4384,c_74]) ).
tcf(c_4389,plain,
aNaturalNumber0(sdtmndt0(xn,iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_4388,c_2241,c_94,c_2357]) ).
tcf(c_4392,plain,
( ( sz00 = iPr_def_10 )
| ( sz00 != xn ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3521,c_4389]) ).
tcf(c_5253,plain,
! [X0: $i] :
( ( xn = X0 )
| ( xn != xn )
| ( X0 != xn ) ),
inference(instantiation,[status(thm)],[c_2910]) ).
tcf(c_5254,plain,
( ( xn = sz00 )
| ( xn != xn )
| ( sz00 != xn ) ),
inference(instantiation,[status(thm)],[c_5253]) ).
tcf(c_6055,plain,
sz00 != xn,
inference(global_subsumption_just,[status(thm)],[c_4392,c_1369,c_2576,c_2908,c_4217,c_4218,c_5254]) ).
tcf(c_6057,plain,
sz00 != iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_3835,c_6055]) ).
tcf(c_6521,plain,
! [X0: $i] :
( ( sz00 = xm )
| ( X0 = xn )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,xm) != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_1367,c_69]) ).
tcf(c_6605,plain,
! [X0: $i] :
( ( X0 = xn )
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,xm) != iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6521,c_1368,c_94,c_93]) ).
tcf(c_6705,plain,
! [X0: $i] :
( sdtlseqdt0(iPr_def_10,sdtasdt0(iPr_def_10,X0))
| ( sz00 = iPr_def_10 )
| ( X0 = sz10 )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz10,X0) ),
inference(superposition,[status(thm)],[c_2334,c_89]) ).
tcf(c_6821,plain,
! [X0: $i] :
( sdtlseqdt0(iPr_def_10,sdtasdt0(iPr_def_10,X0))
| ( X0 = sz10 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(sz10,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6705,c_6057,c_2241,c_50]) ).
tcf(c_7136,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(X0,xm),iPr_def_10)
| ( sz00 = xm )
| ( X0 = xn )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn) ),
inference(superposition,[status(thm)],[c_1367,c_91]) ).
tcf(c_7242,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(X0,xm),iPr_def_10)
| ( X0 = xn )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7136,c_1368,c_94,c_93]) ).
tcf(c_8639,plain,
! [X0: $i] :
( ( X0 = xn )
| ( sdtasdt0(X0,xm) = iPr_def_10 )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ~ sdtlseqdt0(iPr_def_10,sdtasdt0(X0,xm)) ),
inference(superposition,[status(thm)],[c_7242,c_80]) ).
tcf(c_8658,plain,
! [X0: $i] :
( ( X0 = xn )
| ( sdtasdt0(X0,xm) = iPr_def_10 )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ~ sdtlseqdt0(iPr_def_10,sdtasdt0(X0,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8639,c_2241]) ).
tcf(c_13853,plain,
! [X0: $i] :
( ( X0 = xn )
| ~ sdtlseqdt0(iPr_def_10,sdtasdt0(X0,xm))
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_8658,c_6605,c_8658]) ).
tcf(c_13854,plain,
! [X0: $i] :
( ( X0 = xn )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(sdtasdt0(X0,xm))
| ~ sdtlseqdt0(iPr_def_10,sdtasdt0(X0,xm)) ),
inference(renaming,[status(thm)],[c_13853]) ).
tcf(c_13869,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(superposition,[status(thm)],[c_6821,c_13854]) ).
tcf(c_13890,plain,
( ( sz10 = xm )
| ~ aNaturalNumber0(sdtasdt0(iPr_def_10,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13869,c_2107,c_2241,c_93,c_2357,c_129]) ).
tcf(c_14189,plain,
( ( sz10 = xm )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_53,c_13890]) ).
tcf(c_14190,plain,
sz10 = xm,
inference(forward_subsumption_resolution,[status(thm)],[c_14189,c_2241,c_93]) ).
tcf(c_14299,plain,
sdtasdt0(xn,xm) = xn,
inference(demodulation,[status(thm)],[c_2149,c_14190]) ).
tcf(c_14317,plain,
xn = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_14299,c_1367]) ).
tcf(c_14318,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_14317,c_2107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM465+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.44 % Computer : n014.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Thu Sep 24 04:06:48 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.28/0.51 Running first-order theorem proving
% 0.28/0.51 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.28/0.53
% 0.28/0.53 % ======== iProver multi-core TPTP/SMT =========
% 0.28/0.53
% 0.28/0.53 % Detected problem language: tptp
% 0.28/0.55 % Proving...
% 7.22/2.02 % SZS status Started for theBenchmark.p
% 7.22/2.02 % SZS status Theorem for theBenchmark.p
% 7.22/2.02
% 7.22/2.02 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.22/2.02
% 7.22/2.02 % ------ iProver source info
% 7.22/2.02
% 7.22/2.02 % git: date: 2026-07-19 20:42:38 +0200
% 7.22/2.02 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.22/2.02 % git: non_committed_changes: false
% 7.22/2.02
% 7.22/2.02 % ------ Parsing...
% 7.22/2.02 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.22/2.02
% 7.22/2.02 % ------ 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 %
% 7.22/2.02
% 7.22/2.02 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.22/2.02
% 7.22/2.02 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.22/2.02 % ------ Proving...
% 7.22/2.02 % ------ Problem Properties
% 7.22/2.02
% 7.22/2.02 %
% 7.22/2.02 % clauses 48
% 7.22/2.02 % conjectures 3
% 7.22/2.02 % EPR 14
% 7.22/2.02 % Horn 39
% 7.22/2.02 % unary 11
% 7.22/2.02 % binary 8
% 7.22/2.02 % lits 157
% 7.22/2.02 % lits eq 46
% 7.22/2.02 % fd_pure 0
% 7.22/2.02 % fd_pseudo 0
% 7.22/2.02 % fd_cond 4
% 7.22/2.02 % fd_pseudo_cond 9
% 7.22/2.02 % AC symbols 0
% 7.22/2.02
% 7.22/2.02 % ------ Schedule dynamic 5 is on
% 7.22/2.02
% 7.22/2.02 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.22/2.02
% 7.22/2.02
% 7.22/2.02 % ------
% 7.22/2.02 % Current options:
% 7.22/2.02 % ------
% 7.22/2.02
% 7.22/2.02
% 7.22/2.02 %
% 7.22/2.02
% 7.22/2.02 % ------ Proving...
% 7.22/2.02 %
% 7.22/2.02
% 7.22/2.02 % SZS status Theorem for theBenchmark.p
% 7.22/2.02
% 7.22/2.02 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.22/2.02
% 7.22/2.02
%------------------------------------------------------------------------------