%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM512+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 : n017.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 02:25:34 PM UTC 2026
% Result : Theorem 136.35s 31.03s
% Output : CNFRefutation 136.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 22
% Syntax : Number of formulae : 139 ( 63 unt; 7 def)
% Number of atoms : 516 ( 187 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 452 ( 184 ~; 201 |; 52 &)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 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 : 13 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn 96 !; 3 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
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(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/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(f45,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(f48,axiom,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(f49,axiom,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtlseqdt0(xr,xk) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2362) ).
fof(f52,axiom,
doDivides0(xr,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2487) ).
fof(f54,conjecture,
( sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
& sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f55,negated_conjecture,
~ ( sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
& sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) ),
inference(negated_conjecture,[status(cth)],[f54]) ).
fof(f60,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f61,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f60]) ).
fof(f67,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f68,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f67]) ).
fof(f106,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(f107,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,[],[f106]) ).
fof(f116,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(f117,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,[],[f116]) ).
fof(f118,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(f119,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( isPrime0(X0)
<=> ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) ) ),
inference(flattening,[],[f118]) ).
fof(f125,plain,
( sdtasdt0(xn,xm) != sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
| sdtasdt0(xn,xm) != sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) ),
inference(ennf_transformation,[],[f55]) ).
fof(f134,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,[],[f107]) ).
fof(f135,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,[],[f134]) ).
fof(f136,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,[],[f119]) ).
fof(f137,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,[],[f136]) ).
fof(f138,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,[],[f137]) ).
fof(f139,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))],[f138]) ).
fof(f141,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f145,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f150,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f191,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| sdtasdt0(X0,X2) = X1 ),
inference(cnf_transformation,[],[f135]) ).
fof(f192,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f135]) ).
fof(f198,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,[],[f117]) ).
fof(f201,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| sz00 != X0 ),
inference(cnf_transformation,[],[f139]) ).
fof(f209,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f210,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f211,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f213,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f214,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f221,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f226,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f228,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f229,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f49]) ).
fof(f234,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f52]) ).
fof(f237,plain,
( sdtasdt0(xn,xm) != sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
| sdtasdt0(xn,xm) != sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) ),
inference(cnf_transformation,[],[f125]) ).
fof(f246,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(equality_resolution,[],[f192]) ).
fof(f247,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1 ),
inference(equality_resolution,[],[f191]) ).
fof(f248,plain,
( ~ aNaturalNumber0(sz00)
| ~ isPrime0(sz00) ),
inference(equality_resolution,[],[f201]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f141]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ 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,[],[f150]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f246]) ).
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,[],[f247]) ).
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,[],[f198]) ).
tcf(c_110,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(cnf_transformation,[],[f248]) ).
tcf(c_116,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f211]) ).
tcf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f210]) ).
tcf(c_118,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f209]) ).
tcf(c_120,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f214]) ).
tcf(c_121,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f213]) ).
tcf(c_128,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(cnf_transformation,[],[f221]) ).
tcf(c_133,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f228]) ).
tcf(c_135,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f226]) ).
tcf(c_137,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f229]) ).
tcf(c_141,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f234]) ).
tcf(c_144,negated_conjecture,
( ( sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr) != sdtasdt0(xn,xm) )
| ( sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) != sdtasdt0(xn,xm) ) ),
inference(cnf_transformation,[],[f237]) ).
tcf(c_192,plain,
~ isPrime0(sz00),
inference(global_subsumption_just,[status(thm)],[c_110,c_49,c_110]) ).
tcf(c_1607,plain,
sz00 != xp,
inference(resolution_lifted,[status(thm)],[c_192,c_120]) ).
tcf(c_1611,plain,
sz00 != xr,
inference(resolution_lifted,[status(thm)],[c_192,c_135]) ).
tcf(c_3567,definition,
iPr_def_10 = sdtsldt0(xn,xr),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3568,definition,
iPr_def_11 = sdtasdt0(iPr_def_10,xm),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_3569,definition,
iPr_def_12 = sdtasdt0(iPr_def_11,xr),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_3570,definition,
iPr_def_13 = sdtasdt0(xn,xm),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_3571,definition,
iPr_def_14 = sdtasdt0(xp,xk),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_3572,definition,
iPr_def_15 = sdtsldt0(iPr_def_14,xr),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_3573,definition,
iPr_def_16 = sdtasdt0(iPr_def_15,xr),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_3574,negated_conjecture,
( ( iPr_def_16 != iPr_def_13 )
| ( iPr_def_12 != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_144,c_3571,c_3572,c_3573,c_3570,c_3567,c_3568,c_3569]) ).
tcf(c_3575,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_3577,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_4893,plain,
doDivides0(xp,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_121,c_3570]) ).
tcf(c_4894,plain,
doDivides0(xr,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_137,c_3570]) ).
tcf(c_4901,plain,
sdtsldt0(iPr_def_13,xp) = xk,
inference(light_normalisation,[status(thm)],[c_128,c_3570]) ).
tcf(c_5015,plain,
( aNaturalNumber0(iPr_def_13)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_3570,c_53]) ).
tcf(c_5044,plain,
aNaturalNumber0(iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_5015,c_117,c_116]) ).
tcf(c_5229,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xr) = sdtasdt0(xr,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_133,c_58]) ).
tcf(c_5276,plain,
! [X0: $i] :
( ( iPr_def_12 = iPr_def_13 )
| ( iPr_def_13 != X0 )
| ( iPr_def_12 != X0 ) ),
inference(instantiation,[status(thm)],[c_3577]) ).
tcf(c_6967,plain,
( aNaturalNumber0(iPr_def_10)
| ( sz00 = xr )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,xn) ),
inference(superposition,[status(thm)],[c_3567,c_99]) ).
tcf(c_6988,plain,
( aNaturalNumber0(iPr_def_10)
| ( sz00 = xr ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6967,c_133,c_116,c_141]) ).
tcf(c_8844,plain,
( ( sz00 = xp )
| ( sdtasdt0(xp,sdtsldt0(iPr_def_13,xp)) = iPr_def_13 )
| ~ aNaturalNumber0(iPr_def_13)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_4893,c_100]) ).
tcf(c_8845,plain,
( ( sz00 = xr )
| ( sdtasdt0(xr,sdtsldt0(iPr_def_13,xr)) = iPr_def_13 )
| ~ aNaturalNumber0(iPr_def_13)
| ~ aNaturalNumber0(xr) ),
inference(superposition,[status(thm)],[c_4894,c_100]) ).
tcf(c_8929,plain,
( ( sz00 = xr )
| ( sdtasdt0(xr,sdtsldt0(iPr_def_13,xr)) = iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8845,c_5044,c_133]) ).
tcf(c_8932,plain,
( ( iPr_def_13 = iPr_def_14 )
| ( sz00 = xp )
| ~ aNaturalNumber0(iPr_def_13)
| ~ aNaturalNumber0(xp) ),
inference(light_normalisation,[status(thm)],[c_8844,c_3571,c_4901]) ).
tcf(c_8933,plain,
( ( iPr_def_13 = iPr_def_14 )
| ( sz00 = xp ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8932,c_5044,c_118]) ).
tcf(c_14578,plain,
! [X0: $i] :
( ( sz00 = xr )
| ( sdtasdt0(X0,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(X0,xn),xr) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_141,c_105]) ).
tcf(c_14763,plain,
! [X0: $i] :
( ( sz00 = xr )
| ( sdtsldt0(sdtasdt0(X0,xn),xr) = sdtasdt0(X0,iPr_def_10) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(light_normalisation,[status(thm)],[c_14578,c_3567]) ).
tcf(c_14764,plain,
! [X0: $i] :
( ( sz00 = xr )
| ( sdtsldt0(sdtasdt0(X0,xn),xr) = sdtasdt0(X0,iPr_def_10) )
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14763,c_133,c_116]) ).
tcf(c_15501,plain,
! [X0: $i] :
( ( iPr_def_16 = iPr_def_13 )
| ( iPr_def_16 != X0 )
| ( iPr_def_13 != X0 ) ),
inference(instantiation,[status(thm)],[c_3577]) ).
tcf(c_23214,plain,
iPr_def_13 = iPr_def_14,
inference(global_subsumption_just,[status(thm)],[c_8933,c_1607,c_8933]) ).
tcf(c_23244,plain,
sdtsldt0(iPr_def_13,xr) = iPr_def_15,
inference(demodulation,[status(thm)],[c_3572,c_23214]) ).
tcf(c_23278,plain,
( aNaturalNumber0(iPr_def_15)
| ( sz00 = xr )
| ~ aNaturalNumber0(iPr_def_13)
| ~ aNaturalNumber0(xr)
| ~ doDivides0(xr,iPr_def_13) ),
inference(superposition,[status(thm)],[c_23244,c_99]) ).
tcf(c_23279,plain,
( aNaturalNumber0(iPr_def_15)
| ( sz00 = xr ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23278,c_5044,c_133,c_4894]) ).
tcf(c_23431,plain,
aNaturalNumber0(iPr_def_15),
inference(global_subsumption_just,[status(thm)],[c_23279,c_1611,c_23279]) ).
tcf(c_27492,plain,
( ( iPr_def_16 = iPr_def_13 )
| ( iPr_def_16 != iPr_def_16 )
| ( iPr_def_13 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_15501]) ).
tcf(c_27493,plain,
iPr_def_16 = iPr_def_16,
inference(instantiation,[status(thm)],[c_3575]) ).
tcf(c_41415,plain,
sdtasdt0(xr,sdtsldt0(iPr_def_13,xr)) = iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_8929,c_1611,c_8929]) ).
tcf(c_41417,plain,
sdtasdt0(xr,iPr_def_15) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_41415,c_23244]) ).
tcf(c_121131,plain,
sdtasdt0(xr,iPr_def_15) = sdtasdt0(iPr_def_15,xr),
inference(superposition,[status(thm)],[c_23431,c_5229]) ).
tcf(c_121212,plain,
iPr_def_13 = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_121131,c_3573,c_41417]) ).
tcf(c_140831,plain,
( ( iPr_def_12 = iPr_def_13 )
| ( iPr_def_13 != iPr_def_16 )
| ( iPr_def_12 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_5276]) ).
tcf(c_350636,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xn) = sdtasdt0(xn,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_116,c_58]) ).
tcf(c_350637,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xm) = sdtasdt0(xm,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_117,c_58]) ).
tcf(c_351128,plain,
doDivides0(xp,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_121,c_3570]) ).
tcf(c_351944,plain,
( aNaturalNumber0(iPr_def_10)
| ( sz00 = xr )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,xn) ),
inference(superposition,[status(thm)],[c_3567,c_99]) ).
tcf(c_351945,plain,
( aNaturalNumber0(iPr_def_10)
| ( sz00 = xr ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_351944,c_133,c_116,c_141]) ).
tcf(c_352039,plain,
( ( sz00 = xp )
| ( sdtasdt0(xp,sdtsldt0(iPr_def_13,xp)) = iPr_def_13 )
| ~ aNaturalNumber0(iPr_def_13)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_351128,c_100]) ).
tcf(c_352045,plain,
( ( sz00 = xp )
| ( sdtasdt0(xp,sdtsldt0(iPr_def_13,xp)) = iPr_def_13 )
| ~ aNaturalNumber0(iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_352039,c_118]) ).
tcf(c_352311,plain,
! [X0: $i] :
( ( sz00 = xr )
| ( sdtasdt0(X0,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(X0,xn),xr) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_141,c_105]) ).
tcf(c_352324,plain,
! [X0: $i] :
( ( sz00 = xr )
| ( sdtsldt0(sdtasdt0(X0,xn),xr) = sdtasdt0(X0,iPr_def_10) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0) ),
inference(light_normalisation,[status(thm)],[c_352311,c_3567]) ).
tcf(c_352325,plain,
! [X0: $i] :
( ( sz00 = xr )
| ( sdtsldt0(sdtasdt0(X0,xn),xr) = sdtasdt0(X0,iPr_def_10) )
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_352324,c_133,c_116]) ).
tcf(c_353205,plain,
sdtsldt0(iPr_def_13,xp) = xk,
inference(light_normalisation,[status(thm)],[c_128,c_3570]) ).
tcf(c_358402,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(superposition,[status(thm)],[c_117,c_350636]) ).
tcf(c_358410,plain,
sdtasdt0(xm,xn) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_358402,c_3570]) ).
tcf(c_362879,plain,
aNaturalNumber0(iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_351945,c_1611,c_6988]) ).
tcf(c_362900,plain,
sdtasdt0(xm,iPr_def_10) = sdtasdt0(iPr_def_10,xm),
inference(superposition,[status(thm)],[c_362879,c_350637]) ).
tcf(c_362940,plain,
sdtasdt0(xm,iPr_def_10) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_362900,c_3568]) ).
tcf(c_412134,plain,
sdtasdt0(xp,sdtsldt0(iPr_def_13,xp)) = iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_352045,c_1607,c_5044,c_352045]) ).
tcf(c_412136,plain,
iPr_def_13 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_412134,c_3571,c_353205]) ).
tcf(c_412155,plain,
sdtsldt0(iPr_def_13,xr) = iPr_def_15,
inference(demodulation,[status(thm)],[c_3572,c_412136]) ).
tcf(c_421163,plain,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ( sdtsldt0(sdtasdt0(X0,xn),xr) = sdtasdt0(X0,iPr_def_10) ) ),
inference(global_subsumption_just,[status(thm)],[c_352325,c_1611,c_14764]) ).
tcf(c_421164,plain,
! [X0: $i] :
( ( sdtsldt0(sdtasdt0(X0,xn),xr) = sdtasdt0(X0,iPr_def_10) )
| ~ aNaturalNumber0(X0) ),
inference(renaming,[status(thm)],[c_421163]) ).
tcf(c_421181,plain,
sdtsldt0(sdtasdt0(xm,xn),xr) = sdtasdt0(xm,iPr_def_10),
inference(superposition,[status(thm)],[c_117,c_421164]) ).
tcf(c_421194,plain,
iPr_def_11 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_421181,c_412155,c_358410,c_362940]) ).
tcf(c_421232,plain,
sdtasdt0(iPr_def_11,xr) = iPr_def_16,
inference(demodulation,[status(thm)],[c_3573,c_421194]) ).
tcf(c_421233,plain,
iPr_def_12 = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_421232,c_3569]) ).
tcf(c_421248,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_421233,c_140831,c_121212,c_27493,c_27492,c_3574]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM512+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n017.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 04:17:45 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 136.35/31.03 % SZS status Started for theBenchmark.p
% 136.35/31.03 % SZS status Theorem for theBenchmark.p
% 136.35/31.03
% 136.35/31.03 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 136.35/31.03
% 136.35/31.03 % ------ iProver source info
% 136.35/31.03
% 136.35/31.03 % git: date: 2026-07-19 20:42:38 +0200
% 136.35/31.03 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 136.35/31.03 % git: non_committed_changes: false
% 136.35/31.03
% 136.35/31.03 % ------ Parsing...
% 136.35/31.03 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 136.35/31.03
% 136.35/31.03 % ------ 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 %
% 136.35/31.03
% 136.35/31.03 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 136.35/31.03
% 136.35/31.03 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 136.35/31.03 % ------ Proving...
% 136.35/31.03 % ------ Problem Properties
% 136.35/31.03
% 136.35/31.03 %
% 136.35/31.03 % clauses 95
% 136.35/31.03 % conjectures 1
% 136.35/31.03 % EPR 34
% 136.35/31.03 % Horn 70
% 136.35/31.03 % unary 36
% 136.35/31.03 % binary 8
% 136.35/31.03 % lits 291
% 136.35/31.03 % lits eq 87
% 136.35/31.03 % fd_pure 0
% 136.35/31.03 % fd_pseudo 0
% 136.35/31.03 % fd_cond 15
% 136.35/31.03 % fd_pseudo_cond 11
% 136.35/31.03 % AC symbols 0
% 136.35/31.03
% 136.35/31.03 % ------ Schedule dynamic 5 is on
% 136.35/31.03
% 136.35/31.03 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 136.35/31.03
% 136.35/31.03
% 136.35/31.03 % ------
% 136.35/31.03 % Current options:
% 136.35/31.03 % ------
% 136.35/31.03
% 136.35/31.03
% 136.35/31.03 %
% 136.35/31.03
% 136.35/31.03 % ------ Proving...
% 136.35/31.03 % Proof_search_loop: time out after: 7570 full_loop iterations
% 136.35/31.03
% 136.35/31.03 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 136.35/31.03
% 136.35/31.03
% 136.35/31.03 % ------
% 136.35/31.03 % Current options:
% 136.35/31.03 % ------
% 136.35/31.03
% 136.35/31.03
% 136.35/31.03 %
% 136.35/31.03
% 136.35/31.03 % ------ Proving...
% 136.35/31.03 % Proof_search_loop: time out after: 7561 full_loop iterations
% 136.35/31.03
% 136.35/31.03 % ------ Option_1: Negative Selections Time Limit: 35.
% 136.35/31.03
% 136.35/31.03
% 136.35/31.03 % ------
% 136.35/31.03 % Current options:
% 136.35/31.03 % ------
% 136.35/31.03
% 136.35/31.03
% 136.35/31.03 %
% 136.35/31.03
% 136.35/31.03 % ------ Proving...
% 136.35/31.03 %
% 136.35/31.03
% 136.35/31.03 % SZS status Theorem for theBenchmark.p
% 136.35/31.03
% 136.35/31.03 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 136.35/31.03
% 136.35/31.03
%------------------------------------------------------------------------------