%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM529+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:25:51 PM UTC 2026
% Result : Theorem 69.21s 10.87s
% Output : CNFRefutation 69.21s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f232ERROR: Could not build tree for root c_64410ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
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(f26,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| X0 = sz10
| X0 = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLENTr) ).
fof(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).
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/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(f40,axiom,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2987) ).
fof(f41,axiom,
! [X0,X1,X2] :
( ( X2 != sz00
& X1 != sz00
& X0 != sz00
& aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(X2,sdtasdt0(X1,X1)) = sdtasdt0(X0,X0)
=> ( iLess0(X0,xn)
=> ~ isPrime0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2963) ).
fof(f43,axiom,
isPrime0(xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3025) ).
fof(f44,axiom,
( doDivides0(xp,xn)
& doDivides0(xp,sdtasdt0(xn,xn)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3046) ).
fof(f45,axiom,
xq = sdtsldt0(xn,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3059) ).
fof(f46,axiom,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3082) ).
fof(f47,axiom,
( sdtlseqdt0(xm,xn)
& xm != xn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3124) ).
fof(f61,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f67,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f12]) ).
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(ennf_transformation,[],[f15]) ).
fof(f73,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,[],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f75,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(ennf_transformation,[],[f17]) ).
fof(f77,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| X1 = sz00
| X0 = sz00 ),
inference(flattening,[],[f76]) ).
fof(f93,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| X0 = sz10
| X0 = sz00 ),
inference(ennf_transformation,[],[f26]) ).
fof(f94,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| X0 = sz10
| X0 = sz00 ),
inference(flattening,[],[f93]) ).
fof(f97,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f98,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(flattening,[],[f97]) ).
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(ennf_transformation,[],[f31]) ).
fof(f102,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,[],[f101]) ).
fof(f119,plain,
! [X0,X1,X2] :
( sz00 = X2
| sz00 = X1
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X2,sdtasdt0(X1,X1)) != sdtasdt0(X0,X0)
| ~ iLess0(X0,xn)
| ~ isPrime0(X2) ),
inference(ennf_transformation,[],[f41]) ).
fof(f120,plain,
! [X0,X1,X2] :
( sz00 = X2
| sz00 = X1
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X2,sdtasdt0(X1,X1)) != sdtasdt0(X0,X0)
| ~ iLess0(X0,xn)
| ~ isPrime0(X2) ),
inference(flattening,[],[f119]) ).
fof(f129,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,[],[f102]) ).
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(flattening,[],[f129]) ).
fof(f136,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f143,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f61]) ).
fof(f149,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f150,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f67]) ).
fof(f155,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f73]) ).
fof(f157,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f75]) ).
fof(f159,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtasdt0(X0,X1)
| sz00 = X1
| sz00 = X0 ),
inference(cnf_transformation,[],[f77]) ).
fof(f179,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtlseqdt0(sz10,X0)
| sz10 = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f94]) ).
fof(f182,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f187,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f130]) ).
fof(f205,plain,
sz00 != xp,
inference(cnf_transformation,[],[f40]) ).
fof(f206,plain,
sz00 != xm,
inference(cnf_transformation,[],[f40]) ).
fof(f208,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f40]) ).
fof(f209,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f40]) ).
fof(f210,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f40]) ).
fof(f211,plain,
! [X2,X0,X1] :
( sz00 = X2
| sz00 = X1
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X2,sdtasdt0(X1,X1)) != sdtasdt0(X0,X0)
| ~ iLess0(X0,xn)
| ~ isPrime0(X2) ),
inference(cnf_transformation,[],[f120]) ).
fof(f213,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f43]) ).
fof(f214,plain,
doDivides0(xp,xn),
inference(cnf_transformation,[],[f44]) ).
fof(f216,plain,
xq = sdtsldt0(xn,xp),
inference(cnf_transformation,[],[f45]) ).
fof(f217,plain,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(cnf_transformation,[],[f46]) ).
fof(f218,plain,
sdtlseqdt0(xm,xn),
inference(cnf_transformation,[],[f47]) ).
fof(f219,plain,
xn != xm,
inference(cnf_transformation,[],[f47]) ).
fof(f228,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(equality_resolution,[],[f187]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f136]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_62,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz00) = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_63,plain,
! [X0: $i] :
( ( sdtasdt0(sz00,X0) = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f149]) ).
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,[],[f155]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f157]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_82,plain,
! [X0: $i] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f232]) ).
tcf(c_92,plain,
! [X0: $i] :
( sdtlseqdt0(sz10,X0)
| ( X0 = sz10 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( iLess0(X0,X1)
| ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
tcf(c_117,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f210]) ).
tcf(c_118,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f209]) ).
tcf(c_119,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f208]) ).
tcf(c_121,plain,
sz00 != xm,
inference(cnf_transformation,[],[f206]) ).
tcf(c_122,plain,
sz00 != xp,
inference(cnf_transformation,[],[f205]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = sz00 )
| ( X1 = sz00 )
| ( X0 = sz00 )
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ iLess0(X2,xn)
| ( sdtasdt0(X0,sdtasdt0(X1,X1)) != sdtasdt0(X2,X2) ) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_125,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f213]) ).
tcf(c_127,plain,
doDivides0(xp,xn),
inference(cnf_transformation,[],[f214]) ).
tcf(c_128,plain,
sdtsldt0(xn,xp) = xq,
inference(cnf_transformation,[],[f216]) ).
tcf(c_129,plain,
sdtasdt0(xp,sdtasdt0(xq,xq)) = sdtasdt0(xm,xm),
inference(cnf_transformation,[],[f217]) ).
tcf(c_130,plain,
xn != xm,
inference(cnf_transformation,[],[f219]) ).
tcf(c_131,plain,
sdtlseqdt0(xm,xn),
inference(cnf_transformation,[],[f218]) ).
tcf(c_137,plain,
( ( sdtpldt0(sz00,sz00) = sz00 )
| ~ aNaturalNumber0(sz00) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_155,plain,
( ( sz00 = sz00 )
| ~ aNaturalNumber0(sz00)
| ( sdtpldt0(sz00,sz00) != sz00 ) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_224,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_226,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_230,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_259,plain,
! [X0: $i] :
( ( sz00 = xm )
| ( xm != X0 )
| ( sz00 != X0 ) ),
inference(instantiation,[status(thm)],[c_226]) ).
tcf(c_260,plain,
( ( sz00 = xm )
| ( xm != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_259]) ).
tcf(c_261,plain,
! [X0: $i] :
( ( sz00 = xp )
| ( xp != X0 )
| ( sz00 != X0 ) ),
inference(instantiation,[status(thm)],[c_226]) ).
tcf(c_262,plain,
( ( sz00 = xp )
| ( xp != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_261]) ).
tcf(c_820,plain,
! [X0: $i] :
( aNaturalNumber0(sdtsldt0(X0,xp))
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,X0) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_876,plain,
! [X0: $i] :
( ( xm = sz00 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,xm) != sz00 ) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_1375,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_226,c_224]) ).
tcf(c_1649,plain,
! [X0: $i] :
( sdtlseqdt0(sz10,X0)
| ( sz10 = X0 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(resolution,[status(thm)],[c_1375,c_92]) ).
tcf(c_1653,plain,
xq = sdtsldt0(xn,xp),
inference(resolution,[status(thm)],[c_1375,c_128]) ).
tcf(c_1693,plain,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(sdtsldt0(xn,xp)) ),
inference(resolution,[status(thm)],[c_1653,c_227]) ).
tcf(c_2863,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,xq)
| ~ sdtlseqdt0(X1,sdtsldt0(xn,xp))
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_230,c_1653]) ).
tcf(c_2871,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_230,c_224]) ).
tcf(c_2897,plain,
( aNaturalNumber0(sdtsldt0(xn,xp))
| ( xp = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn) ),
inference(instantiation,[status(thm)],[c_820]) ).
tcf(c_2968,plain,
( ( xm = sz00 )
| ~ aNaturalNumber0(xm)
| ( sdtasdt0(xm,xm) != sz00 ) ),
inference(instantiation,[status(thm)],[c_876]) ).
tcf(c_4212,plain,
! [X0: $i] :
( sdtlseqdt0(xq,X0)
| ~ sdtlseqdt0(sdtsldt0(xn,xp),X0) ),
inference(resolution,[status(thm)],[c_2871,c_1653]) ).
tcf(c_6990,plain,
( sdtlseqdt0(xq,sdtsldt0(xn,xp))
| ~ aNaturalNumber0(sdtsldt0(xn,xp)) ),
inference(resolution,[status(thm)],[c_4212,c_82]) ).
tcf(c_7809,plain,
sdtlseqdt0(xq,sdtsldt0(xn,xp)),
inference(global_subsumption_just,[status(thm)],[c_6990,c_119,c_117,c_49,c_127,c_122,c_137,c_155,c_262,c_2897,c_6990]) ).
tcf(c_16390,plain,
( ( xq = sz00 )
| ( xp = sz00 )
| ( xm = sz00 )
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ iLess0(xm,xn) ),
inference(resolution,[status(thm)],[c_123,c_129]) ).
tcf(c_27921,plain,
( iLess0(xm,xn)
| ( xn = xm )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_131,c_94]) ).
tcf(c_31561,plain,
sdtasdt0(sz00,sz00) = sz00,
inference(superposition,[status(thm)],[c_49,c_62]) ).
tcf(c_31567,plain,
sdtasdt0(xp,sz00) = sz00,
inference(superposition,[status(thm)],[c_119,c_62]) ).
tcf(c_33736,plain,
! [X0: $i] :
( sdtlseqdt0(X0,xq)
| ( X0 != xq ) ),
inference(resolution,[status(thm)],[c_2863,c_7809]) ).
tcf(c_33827,plain,
( sdtlseqdt0(sz10,xq)
| ( xq = sz00 )
| ~ aNaturalNumber0(xq) ),
inference(resolution,[status(thm)],[c_33736,c_1649]) ).
tcf(c_35001,plain,
( ( sz00 = xp )
| ( sdtasdt0(xq,xq) = sz00 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xq,xq))
| ( sdtasdt0(xm,xm) != sz00 ) ),
inference(superposition,[status(thm)],[c_129,c_72]) ).
tcf(c_35026,plain,
sdtasdt0(xm,xm) != sz00,
inference(global_subsumption_just,[status(thm)],[c_35001,c_118,c_49,c_121,c_137,c_155,c_260,c_2968]) ).
tcf(c_40451,plain,
xq = sz00,
inference(global_subsumption_just,[status(thm)],[c_33827,c_125,c_119,c_118,c_117,c_49,c_127,c_130,c_122,c_121,c_137,c_155,c_260,c_262,c_1693,c_2897,c_16390,c_27921]) ).
tcf(c_40465,plain,
sz00 = xq,
inference(resolution,[status(thm)],[c_40451,c_1375]) ).
tcf(c_63487,plain,
( aNaturalNumber0(xq)
| ( sz00 = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn) ),
inference(superposition,[status(thm)],[c_128,c_99]) ).
tcf(c_63500,plain,
aNaturalNumber0(xq),
inference(global_subsumption_just,[status(thm)],[c_63487,c_119,c_117,c_49,c_127,c_122,c_137,c_155,c_262,c_1693,c_2897]) ).
tcf(c_64145,plain,
sdtasdt0(sz00,xq) = sz00,
inference(superposition,[status(thm)],[c_63500,c_63]) ).
tcf(c_64381,plain,
! [X0: $i] :
( ( sz00 = xq )
| ( X0 = sz00 )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,xq) != sz00 ) ),
inference(superposition,[status(thm)],[c_64145,c_69]) ).
tcf(c_64384,plain,
sz00 = xq,
inference(global_subsumption_just,[status(thm)],[c_64381,c_40465]) ).
tcf(c_64408,plain,
sdtasdt0(xp,sdtasdt0(sz00,sz00)) = sdtasdt0(xm,xm),
inference(superposition,[status(thm)],[c_64384,c_129]) ).
tcf(c_64409,plain,
sdtasdt0(xm,xm) = sz00,
inference(light_normalisation,[status(thm)],[c_64408,c_31561,c_31567]) ).
tcf(c_64410,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_35026,c_64409]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM529+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 04:28:27 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 69.21/10.87 % SZS status Started for theBenchmark.p
% 69.21/10.87 % SZS status Theorem for theBenchmark.p
% 69.21/10.87
% 69.21/10.87 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 69.21/10.87
% 69.21/10.87 % ------ iProver source info
% 69.21/10.87
% 69.21/10.87 % git: date: 2026-07-19 20:42:38 +0200
% 69.21/10.87 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 69.21/10.87 % git: non_committed_changes: false
% 69.21/10.87
% 69.21/10.87 % ------ Parsing...
% 69.21/10.87 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 69.21/10.87
% 69.21/10.87 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 1 0s sf_e %
% 69.21/10.87
% 69.21/10.87 % ------ Preprocessing...%
% 69.21/10.87
% 69.21/10.87 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 69.21/10.87 % ------ Proving...
% 69.21/10.87 % ------ Problem Properties
% 69.21/10.87
% 69.21/10.87 %
% 69.21/10.87 % clauses 78
% 69.21/10.87 % conjectures 0
% 69.21/10.87 % EPR 24
% 69.21/10.87 % Horn 52
% 69.21/10.87 % unary 19
% 69.21/10.87 % binary 7
% 69.21/10.87 % lits 280
% 69.21/10.87 % lits eq 82
% 69.21/10.87 % fd_pure 0
% 69.21/10.87 % fd_pseudo 0
% 69.21/10.87 % fd_cond 16
% 69.21/10.87 % fd_pseudo_cond 11
% 69.21/10.87 % AC symbols 0
% 69.21/10.87
% 69.21/10.87 % ------ Input Options Time Limit: Unbounded
% 69.21/10.87
% 69.21/10.87
% 69.21/10.87 % ------
% 69.21/10.87 % Current options:
% 69.21/10.87 % ------
% 69.21/10.87
% 69.21/10.87
% 69.21/10.87 %
% 69.21/10.87
% 69.21/10.87 % ------ Proving...
% 69.21/10.87 %
% 69.21/10.87
% 69.21/10.87 % SZS status Theorem for theBenchmark.p
% 69.21/10.87
% 69.21/10.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 69.21/10.87
% 69.21/10.87
%------------------------------------------------------------------------------