%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM528+1 : 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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:25:50 PM UTC 2026
% Result : Theorem 8.69s 28.50s
% Output : CNFRefutation 8.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 26
% Syntax : Number of formulae : 200 ( 61 unt; 0 def)
% Number of atoms : 687 ( 244 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 836 ( 349 ~; 363 |; 88 &)
% ( 12 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 231 ( 0 sgn 218 !; 13 ?; 55 :)
% 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(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
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(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(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(f27,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( X0 != sz00
=> sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& X0 != sz00 )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(f36,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& X0 != sz00 )
=> ! [X2] :
( aNaturalNumber0(X2)
=> sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivAsso) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( ! [X1] :
( ( doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( X1 = X0
| X1 = sz10 ) )
& X0 != sz10
& X0 != sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(f40,axiom,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
fof(f42,axiom,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
fof(f43,axiom,
isPrime0(xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3025) ).
fof(f44,axiom,
( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).
fof(f45,axiom,
xq = sdtsldt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
fof(f46,axiom,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3082) ).
fof(f47,axiom,
( sdtlseqdt0(xn,xm)
=> sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3152) ).
fof(f48,conjecture,
( sdtlseqdt0(xm,xn)
& xm != xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f49,negated_conjecture,
~ ( sdtlseqdt0(xm,xn)
& xm != xn ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f52,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f53,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f55,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f54]) ).
fof(f60,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f61,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f62,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f61]) ).
fof(f65,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtasdt0(sz10,X0)
& sdtasdt0(X0,sz10) = X0 ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f71,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(f72,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,[],[f71]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f78,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f77]) ).
fof(f82,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f83,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f82]) ).
fof(f86,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f87,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f86]) ).
fof(f94,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(ennf_transformation,[],[f27]) ).
fof(f95,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(flattening,[],[f94]) ).
fof(f98,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f99,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f101,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f100]) ).
fof(f110,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0) ) ),
inference(ennf_transformation,[],[f36]) ).
fof(f111,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0) ) ),
inference(flattening,[],[f110]) ).
fof(f112,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( isPrime0(X0)
<=> ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f113,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( isPrime0(X0)
<=> ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) ) ),
inference(flattening,[],[f112]) ).
fof(f120,plain,
( ~ sdtlseqdt0(xn,xm)
| sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
inference(ennf_transformation,[],[f47]) ).
fof(f121,plain,
( ~ sdtlseqdt0(xm,xn)
| xn = xm ),
inference(ennf_transformation,[],[f49]) ).
fof(f122,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,[],[f78]) ).
fof(f123,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,[],[f122]) ).
fof(f124,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))],[f123]) ).
fof(f127,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ doDivides0(X0,X1)
| ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f99]) ).
fof(f128,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ doDivides0(X0,X1)
| ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(rectify,[],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ doDivides0(X0,X1)
| ( sdtasdt0(X0,sK1(X0,X1)) = X1
& aNaturalNumber0(sK1(X0,X1)) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f128]) ).
fof(f130,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( ( sdtsldt0(X1,X0) != X2
| ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtsldt0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f101]) ).
fof(f131,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( ( sdtsldt0(X1,X0) != X2
| ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtsldt0(X1,X0) ) ) ),
inference(flattening,[],[f130]) ).
fof(f132,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) )
& ( ? [X1] :
( doDivides0(X1,X0)
& aNaturalNumber0(X1)
& X0 != X1
& sz10 != X1 )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(nnf_transformation,[],[f113]) ).
fof(f133,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) )
& ( ? [X1] :
( doDivides0(X1,X0)
& aNaturalNumber0(X1)
& X0 != X1
& sz10 != X1 )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(flattening,[],[f132]) ).
fof(f134,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X2] :
( ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2)
| X0 = X2
| sz10 = X2 )
& X0 != sz10
& X0 != sz00 ) )
& ( ? [X1] :
( doDivides0(X1,X0)
& aNaturalNumber0(X1)
& X0 != X1
& sz10 != X1 )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(rectify,[],[f133]) ).
fof(f135,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X2] :
( ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2)
| X0 = X2
| sz10 = X2 )
& X0 != sz10
& X0 != sz00 ) )
& ( ( doDivides0(sK2(X0),X0)
& aNaturalNumber0(sK2(X0))
& sK2(X0) != X0
& sz10 != sK2(X0) )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f134]) ).
fof(f137,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f139,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f140,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f141,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f145,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f60]) ).
fof(f146,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f148,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz10,X0) = X0 ),
inference(cnf_transformation,[],[f65]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f72]) ).
fof(f163,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f124]) ).
fof(f168,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f83]) ).
fof(f170,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f182,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f186,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f187,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| sdtasdt0(X0,X2) = X1 ),
inference(cnf_transformation,[],[f131]) ).
fof(f188,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f131]) ).
fof(f189,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtsldt0(X1,X0) = X2 ),
inference(cnf_transformation,[],[f131]) ).
fof(f194,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f196,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| sz10 != X0 ),
inference(cnf_transformation,[],[f135]) ).
fof(f206,plain,
sz00 != xp,
inference(cnf_transformation,[],[f40]) ).
fof(f208,plain,
sz00 != xn,
inference(cnf_transformation,[],[f40]) ).
fof(f209,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f40]) ).
fof(f210,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f40]) ).
fof(f211,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f40]) ).
fof(f213,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f214,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f43]) ).
fof(f215,plain,
doDivides0(xp,xn),
inference(cnf_transformation,[],[f44]) ).
fof(f217,plain,
xq = sdtsldt0(xn,xp),
inference(cnf_transformation,[],[f45]) ).
fof(f218,plain,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(cnf_transformation,[],[f46]) ).
fof(f219,plain,
( ~ sdtlseqdt0(xn,xm)
| sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f220,plain,
( ~ sdtlseqdt0(xm,xn)
| xn = xm ),
inference(cnf_transformation,[],[f121]) ).
fof(f221,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f163]) ).
fof(f227,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f186]) ).
fof(f228,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| sz00 = X0
| ~ aNaturalNumber0(X2)
| sdtsldt0(sdtasdt0(X0,X2),X0) = X2 ),
inference(equality_resolution,[],[f189]) ).
fof(f229,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(equality_resolution,[],[f188]) ).
fof(f230,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1 ),
inference(equality_resolution,[],[f187]) ).
fof(f232,plain,
( ~ aNaturalNumber0(sz10)
| ~ isPrime0(sz10) ),
inference(equality_resolution,[],[f196]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f137]) ).
tcf(c_50,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f139]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_56,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_61,plain,
! [X0: $i] :
( ( sdtasdt0(sz10,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f148]) ).
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,[],[f156]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ( sdtsldt0(sdtasdt0(X0,X1),X0) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ doDivides0(X0,sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f228]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f229]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f230]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = sz00 )
| ( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_111,plain,
( ~ isPrime0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_117,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f211]) ).
tcf(c_118,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f210]) ).
tcf(c_119,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f209]) ).
tcf(c_120,plain,
sz00 != xn,
inference(cnf_transformation,[],[f208]) ).
tcf(c_122,plain,
sz00 != xp,
inference(cnf_transformation,[],[f206]) ).
tcf(c_124,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnf_transformation,[],[f213]) ).
tcf(c_125,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f214]) ).
tcf(c_127,plain,
doDivides0(xp,xn),
inference(cnf_transformation,[],[f215]) ).
tcf(c_128,plain,
sdtsldt0(xn,xp) = xq,
inference(cnf_transformation,[],[f217]) ).
tcf(c_129,plain,
sdtasdt0(xp,sdtasdt0(xq,xq)) = sdtasdt0(xm,xm),
inference(cnf_transformation,[],[f218]) ).
tcf(c_130,plain,
( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
| ~ sdtlseqdt0(xn,xm) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_131,negated_conjecture,
( ( xn = xm )
| ~ sdtlseqdt0(xm,xn) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_175,plain,
~ isPrime0(sz10),
inference(global_subsumption_just,[status(thm)],[c_111,c_50,c_111]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_95,c_53,c_95]) ).
tcf(c_182,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_192,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ( sdtsldt0(sdtasdt0(X0,X1),X0) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_98,c_53,c_98,c_179]) ).
tcf(c_1885,plain,
sz10 != xp,
inference(resolution_lifted,[status(thm)],[c_175,c_125]) ).
tcf(c_3817,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_3823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_5083,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(xn,xm)
| ~ sdtlseqdt0(X0,X1)
| ( xm != X1 )
| ( xn != X0 ) ),
inference(instantiation,[status(thm)],[c_3823]) ).
tcf(c_5140,plain,
sdtpldt0(xm,sz00) = xm,
inference(superposition,[status(thm)],[c_118,c_56]) ).
tcf(c_5201,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xn) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_5340,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xq,xq)) ),
inference(superposition,[status(thm)],[c_129,c_53]) ).
tcf(c_5341,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xq,xq)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5340,c_119]) ).
tcf(c_5362,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xq) ),
inference(superposition,[status(thm)],[c_53,c_5341]) ).
tcf(c_5448,plain,
( sdtlseqdt0(xm,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_5140,c_182]) ).
tcf(c_5452,plain,
sdtlseqdt0(xm,xm),
inference(forward_subsumption_resolution,[status(thm)],[c_5448,c_118,c_49]) ).
tcf(c_5499,plain,
( sdtlseqdt0(xn,xm)
| ( xn = xm )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_83,c_131]) ).
tcf(c_5503,plain,
( sdtlseqdt0(xn,xm)
| ( xn = xm ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5499,c_118,c_117]) ).
tcf(c_5845,plain,
! [X0: $i] :
( sdtlseqdt0(xn,xm)
| ~ sdtlseqdt0(X0,xm)
| ( xm != xm )
| ( xn != X0 ) ),
inference(instantiation,[status(thm)],[c_5083]) ).
tcf(c_5846,plain,
xm = xm,
inference(instantiation,[status(thm)],[c_3817]) ).
tcf(c_7979,plain,
( sdtlseqdt0(xn,xm)
| ~ sdtlseqdt0(xm,xm)
| ( xm != xm )
| ( xn != xm ) ),
inference(instantiation,[status(thm)],[c_5845]) ).
tcf(c_8778,plain,
( aNaturalNumber0(xq)
| ( sz00 = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn) ),
inference(superposition,[status(thm)],[c_128,c_99]) ).
tcf(c_8797,plain,
aNaturalNumber0(xq),
inference(forward_subsumption_resolution,[status(thm)],[c_8778,c_122,c_119,c_117,c_127]) ).
tcf(c_10397,plain,
sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)),
inference(global_subsumption_just,[status(thm)],[c_130,c_130,c_5452,c_5503,c_5846,c_7979]) ).
tcf(c_116138,plain,
sdtasdt0(sz10,xn) = xn,
inference(superposition,[status(thm)],[c_117,c_61]) ).
tcf(c_116200,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(superposition,[status(thm)],[c_124,c_53]) ).
tcf(c_116201,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_116200,c_119]) ).
tcf(c_116202,plain,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(global_subsumption_just,[status(thm)],[c_116201,c_117,c_5201]) ).
tcf(c_116241,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xq,xq)) ),
inference(superposition,[status(thm)],[c_129,c_53]) ).
tcf(c_116242,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xq,xq)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_116241,c_119]) ).
tcf(c_116243,plain,
sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)),
inference(global_subsumption_just,[status(thm)],[c_130,c_10397]) ).
tcf(c_116322,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xn) = sdtasdt0(xn,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_117,c_58]) ).
tcf(c_116324,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xp) = sdtasdt0(xp,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_119,c_58]) ).
tcf(c_116396,plain,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(global_subsumption_just,[status(thm)],[c_116242,c_5362,c_8797]) ).
tcf(c_116835,plain,
( ( sdtasdt0(xn,xn) = sdtasdt0(xm,xm) )
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn)) ),
inference(superposition,[status(thm)],[c_116243,c_80]) ).
tcf(c_116870,plain,
( ( sdtasdt0(xn,xn) = sdtasdt0(xm,xm) )
| ~ sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_116835,c_116396,c_116202]) ).
tcf(c_116972,plain,
( aNaturalNumber0(xq)
| ( sz00 = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn) ),
inference(superposition,[status(thm)],[c_128,c_99]) ).
tcf(c_116989,plain,
aNaturalNumber0(xq),
inference(forward_subsumption_resolution,[status(thm)],[c_116972,c_122,c_119,c_117,c_127]) ).
tcf(c_117004,plain,
! [X0: $i] :
( ( sz00 = xn )
| ( sdtsldt0(sdtasdt0(xn,X0),xn) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_117,c_192]) ).
tcf(c_117006,plain,
! [X0: $i] :
( ( sz00 = xp )
| ( sdtsldt0(sdtasdt0(xp,X0),xp) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_119,c_192]) ).
tcf(c_117014,plain,
! [X0: $i] :
( ( sdtsldt0(sdtasdt0(xp,X0),xp) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_117006,c_122]) ).
tcf(c_117016,plain,
! [X0: $i] :
( ( sdtsldt0(sdtasdt0(xn,X0),xn) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_117004,c_120]) ).
tcf(c_117619,plain,
( ( sz00 = xp )
| ( sdtasdt0(xp,sdtsldt0(xn,xp)) = xn )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_127,c_100]) ).
tcf(c_117645,plain,
sdtasdt0(xp,sdtsldt0(xn,xp)) = xn,
inference(forward_subsumption_resolution,[status(thm)],[c_117619,c_122,c_119,c_117]) ).
tcf(c_118556,plain,
! [X0: $i] :
( ( sz00 = xn )
| ( X0 = sz10 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,xn) != xn ) ),
inference(superposition,[status(thm)],[c_116138,c_69]) ).
tcf(c_118580,plain,
! [X0: $i] :
( ( X0 = sz10 )
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,xn) != xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_118556,c_120,c_117,c_50]) ).
tcf(c_118984,plain,
! [X0: $i] :
( ( sz00 = xp )
| ( sdtasdt0(X0,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(X0,xn),xp) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_127,c_105]) ).
tcf(c_119014,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(X0,xn),xp) )
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_118984,c_122,c_119,c_117]) ).
tcf(c_119370,plain,
sdtasdt0(xp,xq) = xn,
inference(light_normalisation,[status(thm)],[c_117645,c_128]) ).
tcf(c_129617,plain,
! [X0: $i] :
( ( sdtsldt0(sdtasdt0(X0,xn),xp) = sdtasdt0(X0,xq) )
| ~ aNaturalNumber0(X0) ),
inference(light_normalisation,[status(thm)],[c_119014,c_128]) ).
tcf(c_129632,plain,
sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xn,xq),
inference(superposition,[status(thm)],[c_117,c_129617]) ).
tcf(c_142635,plain,
sdtasdt0(xn,xp) = sdtasdt0(xp,xn),
inference(superposition,[status(thm)],[c_119,c_116322]) ).
tcf(c_143229,plain,
( ( sz10 = xp )
| ~ aNaturalNumber0(xp)
| ( sdtasdt0(xn,xp) != xn ) ),
inference(superposition,[status(thm)],[c_142635,c_118580]) ).
tcf(c_143242,plain,
( ( sz10 = xp )
| ( sdtasdt0(xn,xp) != xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_143229,c_119]) ).
tcf(c_200015,plain,
sdtasdt0(sdtasdt0(xm,xm),xp) = sdtasdt0(xp,sdtasdt0(xm,xm)),
inference(superposition,[status(thm)],[c_116396,c_116324]) ).
tcf(c_200016,plain,
sdtasdt0(xp,xq) = sdtasdt0(xq,xp),
inference(superposition,[status(thm)],[c_116989,c_116324]) ).
tcf(c_201092,plain,
sdtasdt0(xq,xp) = xn,
inference(light_normalisation,[status(thm)],[c_200016,c_119370]) ).
tcf(c_205659,plain,
sdtasdt0(sdtasdt0(xm,xm),xp) = sdtasdt0(xn,xn),
inference(light_normalisation,[status(thm)],[c_200015,c_124]) ).
tcf(c_205665,plain,
( sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn))
| ( sz00 = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(superposition,[status(thm)],[c_205659,c_93]) ).
tcf(c_205676,plain,
sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn)),
inference(forward_subsumption_resolution,[status(thm)],[c_205665,c_122,c_119,c_116396]) ).
tcf(c_205683,plain,
sdtasdt0(xn,xn) = sdtasdt0(xm,xm),
inference(backward_subsumption_resolution,[status(thm)],[c_116870,c_205676]) ).
tcf(c_207589,plain,
sdtasdt0(xp,sdtasdt0(xn,xn)) = sdtasdt0(xn,xn),
inference(demodulation,[status(thm)],[c_124,c_205683]) ).
tcf(c_237411,plain,
sdtsldt0(sdtasdt0(xp,sdtasdt0(xn,xn)),xp) = sdtasdt0(xn,xn),
inference(superposition,[status(thm)],[c_116202,c_117014]) ).
tcf(c_237534,plain,
sdtasdt0(xn,xn) = sdtasdt0(xn,xq),
inference(light_normalisation,[status(thm)],[c_237411,c_129632,c_207589]) ).
tcf(c_239073,plain,
sdtsldt0(sdtasdt0(xn,xn),xn) = xn,
inference(superposition,[status(thm)],[c_117,c_117016]) ).
tcf(c_239077,plain,
sdtsldt0(sdtasdt0(xn,xq),xn) = xq,
inference(superposition,[status(thm)],[c_116989,c_117016]) ).
tcf(c_239116,plain,
xn = xq,
inference(light_normalisation,[status(thm)],[c_239077,c_239073,c_237534]) ).
tcf(c_239196,plain,
sdtasdt0(xn,xp) = xn,
inference(demodulation,[status(thm)],[c_201092,c_239116]) ).
tcf(c_239260,plain,
sz10 = xp,
inference(backward_subsumption_resolution,[status(thm)],[c_143242,c_239196]) ).
tcf(c_239491,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_239260,c_1885]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM528+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.39 % Computer : n008.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Thu Sep 24 04:28:46 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.43 Running first-order theorem proving
% 0.16/5.43 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
% 0.16/5.44
% 0.16/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.44
% 0.16/5.44 % Detected problem language: tptp
% 0.16/5.45 % Proving...
% 8.69/28.50 % SZS status Started for theBenchmark.p
% 8.69/28.50 % SZS status Theorem for theBenchmark.p
% 8.69/28.50
% 8.69/28.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.69/28.50
% 8.69/28.50 % ------ iProver source info
% 8.69/28.50
% 8.69/28.50 % git: date: 2026-07-19 20:42:38 +0200
% 8.69/28.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.69/28.50 % git: non_committed_changes: false
% 8.69/28.50
% 8.69/28.50 % ------ Parsing...
% 8.69/28.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.69/28.50
% 8.69/28.50 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 8.69/28.50
% 8.69/28.50 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.69/28.50
% 8.69/28.50 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.69/28.50 % ------ Proving...
% 8.69/28.50 % ------ Problem Properties
% 8.69/28.50
% 8.69/28.50 %
% 8.69/28.50 % clauses 77
% 8.69/28.50 % conjectures 1
% 8.69/28.50 % EPR 22
% 8.69/28.50 % Horn 52
% 8.69/28.50 % unary 17
% 8.69/28.50 % binary 9
% 8.69/28.50 % lits 278
% 8.69/28.50 % lits eq 82
% 8.69/28.50 % fd_pure 0
% 8.69/28.50 % fd_pseudo 0
% 8.69/28.50 % fd_cond 16
% 8.69/28.50 % fd_pseudo_cond 10
% 8.69/28.50 % AC symbols 0
% 8.69/28.50
% 8.69/28.50 % ------ Input Options Time Limit: Unbounded
% 8.69/28.50
% 8.69/28.50
% 8.69/28.50 % ------
% 8.69/28.50 % Current options:
% 8.69/28.50 % ------
% 8.69/28.50
% 8.69/28.50
% 8.69/28.50 %
% 8.69/28.50
% 8.69/28.50 % ------ Proving...
% 8.69/28.50 %
% 8.69/28.50
% 8.69/28.50 % SZS status Theorem for theBenchmark.p
% 8.69/28.50
% 8.69/28.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.69/28.50
% 8.69/28.50
%------------------------------------------------------------------------------