%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM501+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 : n005.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 02:25:21 PM UTC 2026
% Result : Theorem 22.06s 4.29s
% Output : CNFRefutation 22.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 97 ( 38 unt; 1 def)
% Number of atoms : 386 ( 108 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 451 ( 186 ~; 187 |; 60 &)
% ( 9 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 113 ( 0 sgn 105 !; 8 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
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(f32,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).
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(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(f45,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(f48,axiom,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(f49,conjecture,
doDivides0(xr,sdtasdt0(xn,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f50,negated_conjecture,
~ doDivides0(xr,sdtasdt0(xn,xm)),
inference(negated_conjecture,[status(cth)],[f49]) ).
fof(f53,plain,
~ doDivides0(xr,sdtasdt0(xn,xm)),
inference(flattening,[],[f50]) ).
fof(f56,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f57,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f56]) ).
fof(f63,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f64,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f63]) ).
fof(f100,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f101,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f100]) ).
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(ennf_transformation,[],[f31]) ).
fof(f103,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,[],[f102]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(flattening,[],[f104]) ).
fof(f114,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(f115,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( isPrime0(X0)
<=> ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) ) ),
inference(flattening,[],[f114]) ).
fof(f126,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,[],[f101]) ).
fof(f127,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,[],[f126]) ).
fof(f128,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))],[f127]) ).
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,[],[f103]) ).
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(f131,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,[],[f115]) ).
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(flattening,[],[f131]) ).
fof(f133,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,[],[f132]) ).
fof(f134,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))],[f133]) ).
fof(f136,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f140,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f57]) ).
fof(f145,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f185,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f128]) ).
fof(f186,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| sdtasdt0(X0,X2) = X1 ),
inference(cnf_transformation,[],[f130]) ).
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(f189,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(cnf_transformation,[],[f105]) ).
fof(f196,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| sz00 != X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f204,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f205,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f206,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f208,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f209,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f216,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f222,plain,
doDivides0(xr,xk),
inference(cnf_transformation,[],[f48]) ).
fof(f223,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f224,plain,
~ doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f53]) ).
fof(f231,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f185]) ).
fof(f233,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(equality_resolution,[],[f187]) ).
fof(f234,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1 ),
inference(equality_resolution,[],[f186]) ).
fof(f235,plain,
( ~ aNaturalNumber0(sz00)
| ~ isPrime0(sz00) ),
inference(equality_resolution,[],[f196]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f136]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f233]) ).
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,[],[f234]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_110,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_116,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f206]) ).
tcf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f205]) ).
tcf(c_118,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f204]) ).
tcf(c_120,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f209]) ).
tcf(c_121,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f208]) ).
tcf(c_128,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(cnf_transformation,[],[f216]) ).
tcf(c_133,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f223]) ).
tcf(c_134,plain,
doDivides0(xr,xk),
inference(cnf_transformation,[],[f222]) ).
tcf(c_136,negated_conjecture,
~ doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f224]) ).
tcf(c_182,plain,
~ isPrime0(sz00),
inference(global_subsumption_just,[status(thm)],[c_110,c_49,c_110]) ).
tcf(c_184,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_1577,plain,
sz00 != xp,
inference(resolution_lifted,[status(thm)],[c_182,c_120]) ).
tcf(c_3517,definition,
iPr_def_10 = sdtasdt0(xn,xm),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3518,negated_conjecture,
~ doDivides0(xr,iPr_def_10),
inference(demodulation,[status(thm)],[c_136,c_3517]) ).
tcf(c_4779,plain,
doDivides0(xp,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_121,c_3517]) ).
tcf(c_4782,plain,
sdtsldt0(iPr_def_10,xp) = xk,
inference(light_normalisation,[status(thm)],[c_128,c_3517]) ).
tcf(c_4789,plain,
( aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_3517,c_53]) ).
tcf(c_4790,plain,
aNaturalNumber0(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_4789,c_117,c_116]) ).
tcf(c_5061,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xp) = sdtasdt0(xp,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_118,c_58]) ).
tcf(c_5097,plain,
! [X0: $i] :
( doDivides0(xr,iPr_def_10)
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xr,X0)
| ~ doDivides0(X0,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_5582,plain,
( doDivides0(xr,iPr_def_10)
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk)
| ~ doDivides0(xr,xk)
| ~ doDivides0(xk,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_5097]) ).
tcf(c_6722,plain,
( aNaturalNumber0(xk)
| ( sz00 = xp )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,iPr_def_10) ),
inference(superposition,[status(thm)],[c_4782,c_99]) ).
tcf(c_6734,plain,
( aNaturalNumber0(xk)
| ( sz00 = xp ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6722,c_4790,c_118,c_4779]) ).
tcf(c_6814,plain,
aNaturalNumber0(xk),
inference(global_subsumption_just,[status(thm)],[c_6734,c_1577,c_6734]) ).
tcf(c_8674,plain,
( ( sz00 = xp )
| ( sdtasdt0(xp,sdtsldt0(iPr_def_10,xp)) = iPr_def_10 )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_4779,c_100]) ).
tcf(c_8731,plain,
( ( sz00 = xp )
| ( sdtasdt0(xp,xk) = iPr_def_10 )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xp) ),
inference(light_normalisation,[status(thm)],[c_8674,c_4782]) ).
tcf(c_8732,plain,
( ( sz00 = xp )
| ( sdtasdt0(xp,xk) = iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8731,c_4790,c_118]) ).
tcf(c_21629,plain,
sdtasdt0(xp,xk) = iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_8732,c_1577,c_8732]) ).
tcf(c_55065,plain,
sdtasdt0(xp,xk) = sdtasdt0(xk,xp),
inference(superposition,[status(thm)],[c_6814,c_5061]) ).
tcf(c_55095,plain,
sdtasdt0(xk,xp) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_55065,c_21629]) ).
tcf(c_55190,plain,
( doDivides0(xk,iPr_def_10)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_55095,c_184]) ).
tcf(c_55199,plain,
doDivides0(xk,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_55190,c_6814,c_118]) ).
tcf(c_55229,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_55199,c_6734,c_5582,c_4790,c_3518,c_1577,c_134,c_133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM501+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 04:18:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 22.06/4.29 % SZS status Started for theBenchmark.p
% 22.06/4.29 % SZS status Theorem for theBenchmark.p
% 22.06/4.29
% 22.06/4.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 22.06/4.29
% 22.06/4.29 % ------ iProver source info
% 22.06/4.29
% 22.06/4.29 % git: date: 2026-07-19 20:42:38 +0200
% 22.06/4.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 22.06/4.29 % git: non_committed_changes: false
% 22.06/4.29
% 22.06/4.29 % ------ Parsing...
% 22.06/4.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 22.06/4.29
% 22.06/4.29 % ------ 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 %
% 22.06/4.29
% 22.06/4.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 22.06/4.29
% 22.06/4.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 22.06/4.29 % ------ Proving...
% 22.06/4.29 % ------ Problem Properties
% 22.06/4.29
% 22.06/4.29 %
% 22.06/4.29 % clauses 82
% 22.06/4.29 % conjectures 1
% 22.06/4.29 % EPR 30
% 22.06/4.29 % Horn 57
% 22.06/4.29 % unary 24
% 22.06/4.29 % binary 7
% 22.06/4.29 % lits 277
% 22.06/4.29 % lits eq 77
% 22.06/4.29 % fd_pure 0
% 22.06/4.29 % fd_pseudo 0
% 22.06/4.29 % fd_cond 15
% 22.06/4.29 % fd_pseudo_cond 11
% 22.06/4.29 % AC symbols 0
% 22.06/4.29
% 22.06/4.29 % ------ Schedule dynamic 5 is on
% 22.06/4.29
% 22.06/4.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 22.06/4.29
% 22.06/4.29
% 22.06/4.29 % ------
% 22.06/4.29 % Current options:
% 22.06/4.29 % ------
% 22.06/4.29
% 22.06/4.29
% 22.06/4.29 %
% 22.06/4.29
% 22.06/4.29 % ------ Proving...
% 22.06/4.29 %
% 22.06/4.29
% 22.06/4.29 % SZS status Theorem for theBenchmark.p
% 22.06/4.29
% 22.06/4.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 22.06/4.29
% 22.06/4.29
%------------------------------------------------------------------------------