%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM471+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 : n019.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 02:24:44 PM UTC 2026
% Result : Theorem 93.48s 25.99s
% Output : CNFRefutation 93.48s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f180ERROR: Could not build tree for root c_398983ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
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(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(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(f34,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
fof(f35,axiom,
( doDivides0(xl,sdtpldt0(xm,xn))
& doDivides0(xl,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324_04) ).
fof(f36,axiom,
xl != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1347) ).
fof(f37,axiom,
xp = sdtsldt0(xm,xl),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1360) ).
fof(f38,axiom,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1379) ).
fof(f39,conjecture,
sdtlseqdt0(xp,xq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f40,negated_conjecture,
~ sdtlseqdt0(xp,xq),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f43,plain,
~ sdtlseqdt0(xp,xq),
inference(flattening,[],[f40]) ).
fof(f45,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f46,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f48,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f50,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(flattening,[],[f49]) ).
fof(f54,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f55,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f54]) ).
fof(f64,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(f65,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,[],[f64]) ).
fof(f70,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f71,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f70]) ).
fof(f75,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f75]) ).
fof(f79,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f80,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f79]) ).
fof(f83,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(f84,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,[],[f83]) ).
fof(f91,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(f92,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,[],[f91]) ).
fof(f97,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,[],[f71]) ).
fof(f98,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,[],[f97]) ).
fof(f99,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))],[f98]) ).
fof(f105,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,[],[f92]) ).
fof(f106,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,[],[f105]) ).
fof(f110,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f111,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f48]) ).
fof(f112,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f116,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f126,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f65]) ).
fof(f131,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,sK0(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f99]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f138,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f76]) ).
fof(f140,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f146,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,[],[f84]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| sdtasdt0(X0,X2) = X1 ),
inference(cnf_transformation,[],[f106]) ).
fof(f157,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f106]) ).
fof(f161,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f34]) ).
fof(f162,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f34]) ).
fof(f163,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f34]) ).
fof(f164,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f35]) ).
fof(f165,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f35]) ).
fof(f166,plain,
sz00 != xl,
inference(cnf_transformation,[],[f36]) ).
fof(f167,plain,
xp = sdtsldt0(xm,xl),
inference(cnf_transformation,[],[f37]) ).
fof(f168,plain,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(cnf_transformation,[],[f38]) ).
fof(f169,plain,
~ sdtlseqdt0(xp,xq),
inference(cnf_transformation,[],[f43]) ).
fof(f170,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f133]) ).
fof(f178,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(equality_resolution,[],[f157]) ).
fof(f179,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1 ),
inference(equality_resolution,[],[f156]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f116]) ).
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,[],[f126]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,sK0(X0,X1)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_82,plain,
! [X0: $i] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f140]) ).
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,[],[f146]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f178]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_102,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f163]) ).
tcf(c_103,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f162]) ).
tcf(c_104,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f161]) ).
tcf(c_105,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f165]) ).
tcf(c_106,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f164]) ).
tcf(c_107,plain,
sz00 != xl,
inference(cnf_transformation,[],[f166]) ).
tcf(c_108,plain,
sdtsldt0(xm,xl) = xp,
inference(cnf_transformation,[],[f167]) ).
tcf(c_109,plain,
sdtsldt0(sdtpldt0(xm,xn),xl) = xq,
inference(cnf_transformation,[],[f168]) ).
tcf(c_110,negated_conjecture,
~ sdtlseqdt0(xp,xq),
inference(cnf_transformation,[],[f169]) ).
tcf(c_147,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_1708,negated_conjecture,
~ sdtlseqdt0(xp,xq),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_1709,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2835,plain,
( sdtlseqdt0(xq,xp)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_83,c_1708]) ).
tcf(c_2842,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(xp,xq)
| ~ sdtlseqdt0(X0,X1)
| ( xq != X1 )
| ( xp != X0 ) ),
inference(instantiation,[status(thm)],[c_1715]) ).
tcf(c_2863,plain,
! [X0: $i] :
( ( sdtpldt0(X0,xm) = sdtpldt0(xm,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_103,c_54]) ).
tcf(c_3150,plain,
( ( sdtpldt0(xq,sK0(xq,xp)) = xp )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_2835,c_75]) ).
tcf(c_3839,plain,
( aNaturalNumber0(xp)
| ( sz00 = xl )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm) ),
inference(superposition,[status(thm)],[c_108,c_98]) ).
tcf(c_3840,plain,
( aNaturalNumber0(xq)
| ( sz00 = xl )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(superposition,[status(thm)],[c_109,c_98]) ).
tcf(c_3851,plain,
aNaturalNumber0(xp),
inference(forward_subsumption_resolution,[status(thm)],[c_3839,c_107,c_103,c_102,c_105]) ).
tcf(c_3852,plain,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3840,c_107,c_102,c_106]) ).
tcf(c_6056,plain,
( ( sz00 = xl )
| ( sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl)) = sdtpldt0(xm,xn) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(superposition,[status(thm)],[c_106,c_99]) ).
tcf(c_6096,plain,
( ( sz00 = xl )
| ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(light_normalisation,[status(thm)],[c_6056,c_109]) ).
tcf(c_6097,plain,
( ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6096,c_107,c_102]) ).
tcf(c_6172,plain,
! [X0: $i] :
( sdtlseqdt0(xp,xq)
| ~ sdtlseqdt0(X0,xq)
| ( xq != xq )
| ( xp != X0 ) ),
inference(instantiation,[status(thm)],[c_2842]) ).
tcf(c_6173,plain,
xq = xq,
inference(instantiation,[status(thm)],[c_1709]) ).
tcf(c_8426,plain,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_52,c_3852]) ).
tcf(c_8427,plain,
aNaturalNumber0(xq),
inference(forward_subsumption_resolution,[status(thm)],[c_8426,c_104,c_103]) ).
tcf(c_10010,plain,
( sdtlseqdt0(xp,xq)
| ~ sdtlseqdt0(xq,xq)
| ( xq != xq )
| ( xp != xq ) ),
inference(instantiation,[status(thm)],[c_6172]) ).
tcf(c_10011,plain,
( sdtlseqdt0(xq,xq)
| ~ aNaturalNumber0(xq) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_40151,plain,
sdtpldt0(xm,xn) = sdtpldt0(xn,xm),
inference(superposition,[status(thm)],[c_104,c_2863]) ).
tcf(c_40192,plain,
( aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_40151,c_52]) ).
tcf(c_40200,plain,
aNaturalNumber0(sdtpldt0(xm,xn)),
inference(forward_subsumption_resolution,[status(thm)],[c_40192,c_104,c_103]) ).
tcf(c_169939,plain,
( sdtlseqdt0(xq,xp)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_83,c_1708]) ).
tcf(c_169997,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xl) = sdtasdt0(xl,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_102,c_58]) ).
tcf(c_170085,plain,
sdtlseqdt0(xq,xp),
inference(global_subsumption_just,[status(thm)],[c_169939,c_2835,c_3851,c_8427]) ).
tcf(c_170114,plain,
( ( sdtpldt0(xq,sK0(xq,xp)) = xp )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_170085,c_75]) ).
tcf(c_170357,plain,
sdtpldt0(xq,sK0(xq,xp)) = xp,
inference(global_subsumption_just,[status(thm)],[c_170114,c_3150,c_3851,c_8427]) ).
tcf(c_170360,plain,
( aNaturalNumber0(xp)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(sK0(xq,xp)) ),
inference(superposition,[status(thm)],[c_170357,c_52]) ).
tcf(c_170364,plain,
aNaturalNumber0(xp),
inference(global_subsumption_just,[status(thm)],[c_170360,c_3851]) ).
tcf(c_170367,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xp) = sdtasdt0(xp,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_170364,c_58]) ).
tcf(c_170756,plain,
( aNaturalNumber0(xq)
| ( sz00 = xl )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(superposition,[status(thm)],[c_109,c_98]) ).
tcf(c_170766,plain,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_170756,c_107,c_102,c_106]) ).
tcf(c_171030,plain,
aNaturalNumber0(xq),
inference(global_subsumption_just,[status(thm)],[c_170766,c_8427]) ).
tcf(c_172428,plain,
( ( sz00 = xl )
| ( sdtasdt0(xl,sdtsldt0(xm,xl)) = xm )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_105,c_99]) ).
tcf(c_172477,plain,
( ( sz00 = xl )
| ( sdtasdt0(xl,xp) = xm )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(light_normalisation,[status(thm)],[c_172428,c_108]) ).
tcf(c_172478,plain,
sdtasdt0(xl,xp) = xm,
inference(forward_subsumption_resolution,[status(thm)],[c_172477,c_107,c_103,c_102]) ).
tcf(c_172762,plain,
sdtasdt0(xl,xp) = sdtasdt0(xp,xl),
inference(superposition,[status(thm)],[c_102,c_170367]) ).
tcf(c_172767,plain,
sdtasdt0(xp,xl) = xm,
inference(light_normalisation,[status(thm)],[c_172762,c_172478]) ).
tcf(c_174988,plain,
! [X0: $i] :
( ( sz00 = xl )
| ( X0 = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,xl) != xm ) ),
inference(superposition,[status(thm)],[c_172767,c_69]) ).
tcf(c_175028,plain,
! [X0: $i] :
( ( X0 = xp )
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,xl) != xm ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_174988,c_107,c_170364,c_102]) ).
tcf(c_175957,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(X0,xl),xm)
| ( sz00 = xl )
| ( X0 = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xp) ),
inference(superposition,[status(thm)],[c_172767,c_91]) ).
tcf(c_176011,plain,
! [X0: $i] :
( sdtlseqdt0(sdtasdt0(X0,xl),xm)
| ( X0 = xp )
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xp) ),
inference(forward_subsumption_resolution,[status(thm)],[c_175957,c_107,c_170364,c_102]) ).
tcf(c_200568,plain,
( ( sz00 = xl )
| ( sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl)) = sdtpldt0(xm,xn) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(superposition,[status(thm)],[c_106,c_99]) ).
tcf(c_200602,plain,
( ( sz00 = xl )
| ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq) )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(light_normalisation,[status(thm)],[c_200568,c_109]) ).
tcf(c_200603,plain,
( ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_200602,c_107,c_102]) ).
tcf(c_246245,plain,
sdtasdt0(xl,xq) = sdtasdt0(xq,xl),
inference(superposition,[status(thm)],[c_171030,c_169997]) ).
tcf(c_251069,plain,
( aNaturalNumber0(sdtasdt0(xl,xq))
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_246245,c_53]) ).
tcf(c_251078,plain,
( sdtlseqdt0(sdtasdt0(xl,xq),xm)
| ( xp = xq )
| ~ aNaturalNumber0(xq)
| ~ sdtlseqdt0(xq,xp) ),
inference(superposition,[status(thm)],[c_246245,c_176011]) ).
tcf(c_251079,plain,
( ( xp = xq )
| ~ aNaturalNumber0(xq)
| ( sdtasdt0(xl,xq) != xm ) ),
inference(superposition,[status(thm)],[c_246245,c_175028]) ).
tcf(c_251081,plain,
aNaturalNumber0(sdtasdt0(xl,xq)),
inference(forward_subsumption_resolution,[status(thm)],[c_251069,c_171030,c_102]) ).
tcf(c_251083,plain,
( ( xp = xq )
| ( sdtasdt0(xl,xq) != xm ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_251079,c_171030]) ).
tcf(c_251087,plain,
( sdtlseqdt0(sdtasdt0(xl,xq),xm)
| ( xp = xq ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_251078,c_171030,c_170085]) ).
tcf(c_251698,plain,
sdtlseqdt0(sdtasdt0(xl,xq),xm),
inference(global_subsumption_just,[status(thm)],[c_251087,c_110,c_6173,c_8427,c_10010,c_10011,c_251087]) ).
tcf(c_251704,plain,
( ( sdtasdt0(xl,xq) = xm )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xq))
| ~ sdtlseqdt0(xm,sdtasdt0(xl,xq)) ),
inference(superposition,[status(thm)],[c_251698,c_80]) ).
tcf(c_251709,plain,
( ( sdtasdt0(xl,xq) = xm )
| ~ sdtlseqdt0(xm,sdtasdt0(xl,xq)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_251704,c_103,c_251081]) ).
tcf(c_398926,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(global_subsumption_just,[status(thm)],[c_200603,c_6097,c_40200]) ).
tcf(c_398940,plain,
( sdtlseqdt0(xm,sdtasdt0(xl,xq))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_398926,c_147]) ).
tcf(c_398949,plain,
sdtlseqdt0(xm,sdtasdt0(xl,xq)),
inference(forward_subsumption_resolution,[status(thm)],[c_398940,c_104,c_103]) ).
tcf(c_398983,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_398949,c_251709,c_251083,c_10011,c_10010,c_8427,c_6173,c_110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM471+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 04:09:34 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 93.48/25.99 % SZS status Started for theBenchmark.p
% 93.48/25.99 % SZS status Theorem for theBenchmark.p
% 93.48/25.99
% 93.48/25.99 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 93.48/25.99
% 93.48/25.99 % ------ iProver source info
% 93.48/25.99
% 93.48/25.99 % git: date: 2026-07-19 20:42:38 +0200
% 93.48/25.99 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 93.48/25.99 % git: non_committed_changes: false
% 93.48/25.99
% 93.48/25.99 % ------ Parsing...
% 93.48/25.99 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 93.48/25.99
% 93.48/25.99 % ------ 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 %
% 93.48/25.99
% 93.48/25.99 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 93.48/25.99
% 93.48/25.99 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 93.48/25.99 % ------ Proving...
% 93.48/25.99 % ------ Problem Properties
% 93.48/25.99
% 93.48/25.99 %
% 93.48/25.99 % clauses 57
% 93.48/25.99 % conjectures 1
% 93.48/25.99 % EPR 15
% 93.48/25.99 % Horn 44
% 93.48/25.99 % unary 12
% 93.48/25.99 % binary 7
% 93.48/25.99 % lits 197
% 93.48/25.99 % lits eq 52
% 93.48/25.99 % fd_pure 0
% 93.48/25.99 % fd_pseudo 0
% 93.48/25.99 % fd_cond 6
% 93.48/25.99 % fd_pseudo_cond 9
% 93.48/25.99 % AC symbols 0
% 93.48/25.99
% 93.48/25.99 % ------ Schedule dynamic 5 is on
% 93.48/25.99
% 93.48/25.99 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 93.48/25.99
% 93.48/25.99
% 93.48/25.99 % ------
% 93.48/25.99 % Current options:
% 93.48/25.99 % ------
% 93.48/25.99
% 93.48/25.99
% 93.48/25.99 %
% 93.48/25.99
% 93.48/25.99 % ------ Proving...
% 93.48/25.99 % Proof_search_loop: time out after: 5288 full_loop iterations
% 93.48/25.99
% 93.48/25.99 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 93.48/25.99
% 93.48/25.99
% 93.48/25.99 % ------
% 93.48/25.99 % Current options:
% 93.48/25.99 % ------
% 93.48/25.99
% 93.48/25.99
% 93.48/25.99 %
% 93.48/25.99
% 93.48/25.99 % ------ Proving...
% 93.48/25.99 %
% 93.48/25.99
% 93.48/25.99 % SZS status Theorem for theBenchmark.p
% 93.48/25.99
% 93.48/25.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 93.48/25.99
% 93.48/25.99
%------------------------------------------------------------------------------