%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM513+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 : n018.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 02:25:46 PM UTC 2026
% Result : Theorem 181.26s 28.95s
% Output : CNFRefutation 181.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 130 ( 58 unt; 4 def)
% Number of atoms : 450 ( 166 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 458 ( 187 ~; 206 |; 50 &)
% ( 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 : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 100 ( 0 sgn 97 !; 3 ?; 29 :)
% 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(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& X0 != sz00 )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(f36,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& X0 != sz00 )
=> ! [X2] :
( aNaturalNumber0(X2)
=> sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivAsso) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( ! [X1] :
( ( doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( X1 = X0
| X1 = sz10 ) )
& X0 != sz10
& X0 != sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(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(f52,axiom,
doDivides0(xr,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
fof(f54,axiom,
( sdtasdt0(xn,xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp,xk),xr),xr)
& sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2576) ).
fof(f55,conjecture,
sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f56,negated_conjecture,
sdtasdt0(xp,sdtsldt0(xk,xr)) != sdtasdt0(sdtsldt0(xn,xr),xm),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f59,plain,
sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(xk,xr)),
inference(flattening,[],[f56]) ).
fof(f62,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f63,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f62]) ).
fof(f69,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f70,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f69]) ).
fof(f108,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(f109,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,[],[f108]) ).
fof(f118,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(f119,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,[],[f118]) ).
fof(f120,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(f121,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( isPrime0(X0)
<=> ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) ) ),
inference(flattening,[],[f120]) ).
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(nnf_transformation,[],[f109]) ).
fof(f136,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,[],[f135]) ).
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(nnf_transformation,[],[f121]) ).
fof(f138,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,[],[f137]) ).
fof(f139,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,[],[f138]) ).
fof(f140,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))],[f139]) ).
fof(f142,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f146,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f151,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f192,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| sdtasdt0(X0,X2) = X1 ),
inference(cnf_transformation,[],[f136]) ).
fof(f193,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f136]) ).
fof(f199,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,[],[f119]) ).
fof(f202,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| sz00 != X0 ),
inference(cnf_transformation,[],[f140]) ).
fof(f210,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f211,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f212,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f214,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f215,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f222,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f227,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f228,plain,
doDivides0(xr,xk),
inference(cnf_transformation,[],[f48]) ).
fof(f229,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f235,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f52]) ).
fof(f239,plain,
sdtasdt0(xn,xm) = sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr),
inference(cnf_transformation,[],[f54]) ).
fof(f240,plain,
sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(xk,xr)),
inference(cnf_transformation,[],[f59]) ).
fof(f249,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(equality_resolution,[],[f193]) ).
fof(f250,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1 ),
inference(equality_resolution,[],[f192]) ).
fof(f251,plain,
( ~ aNaturalNumber0(sz00)
| ~ isPrime0(sz00) ),
inference(equality_resolution,[],[f202]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f142]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f249]) ).
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,[],[f250]) ).
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,[],[f199]) ).
tcf(c_110,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(cnf_transformation,[],[f251]) ).
tcf(c_116,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f212]) ).
tcf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f211]) ).
tcf(c_118,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f210]) ).
tcf(c_120,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f215]) ).
tcf(c_121,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f214]) ).
tcf(c_128,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(cnf_transformation,[],[f222]) ).
tcf(c_133,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f229]) ).
tcf(c_134,plain,
doDivides0(xr,xk),
inference(cnf_transformation,[],[f228]) ).
tcf(c_135,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f227]) ).
tcf(c_141,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f235]) ).
tcf(c_144,plain,
sdtasdt0(sdtasdt0(sdtsldt0(xn,xr),xm),xr) = sdtasdt0(xn,xm),
inference(cnf_transformation,[],[f239]) ).
tcf(c_146,negated_conjecture,
sdtasdt0(sdtsldt0(xn,xr),xm) != sdtasdt0(xp,sdtsldt0(xk,xr)),
inference(cnf_transformation,[],[f240]) ).
tcf(c_194,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_194,c_120]) ).
tcf(c_1611,plain,
sz00 != xr,
inference(resolution_lifted,[status(thm)],[c_194,c_135]) ).
tcf(c_3565,definition,
iPr_def_10 = sdtsldt0(xn,xr),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3566,definition,
iPr_def_11 = sdtasdt0(iPr_def_10,xm),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_3567,definition,
iPr_def_12 = sdtsldt0(xk,xr),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_3568,definition,
iPr_def_13 = sdtasdt0(xp,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_3569,negated_conjecture,
iPr_def_11 != iPr_def_13,
inference(demodulation,[status(thm)],[c_146,c_3567,c_3568,c_3565,c_3566]) ).
tcf(c_4892,plain,
sdtasdt0(xn,xm) = sdtasdt0(iPr_def_11,xr),
inference(light_normalisation,[status(thm)],[c_144,c_3565,c_3566]) ).
tcf(c_4893,plain,
sdtsldt0(sdtasdt0(iPr_def_11,xr),xp) = xk,
inference(demodulation,[status(thm)],[c_128,c_4892]) ).
tcf(c_4895,plain,
doDivides0(xp,sdtasdt0(iPr_def_11,xr)),
inference(demodulation,[status(thm)],[c_121,c_4892]) ).
tcf(c_5000,plain,
( aNaturalNumber0(sdtasdt0(iPr_def_11,xr))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_4892,c_53]) ).
tcf(c_5035,plain,
aNaturalNumber0(sdtasdt0(iPr_def_11,xr)),
inference(forward_subsumption_resolution,[status(thm)],[c_5000,c_117,c_116]) ).
tcf(c_7196,plain,
( aNaturalNumber0(iPr_def_10)
| ( sz00 = xr )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,xn) ),
inference(superposition,[status(thm)],[c_3565,c_99]) ).
tcf(c_7198,plain,
( aNaturalNumber0(xk)
| ( sz00 = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(iPr_def_11,xr))
| ~ doDivides0(xp,sdtasdt0(iPr_def_11,xr)) ),
inference(superposition,[status(thm)],[c_4893,c_99]) ).
tcf(c_7215,plain,
( aNaturalNumber0(iPr_def_10)
| ( sz00 = xr ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7196,c_133,c_116,c_141]) ).
tcf(c_7218,plain,
( aNaturalNumber0(xk)
| ( sz00 = xp ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7198,c_118,c_5035,c_4895]) ).
tcf(c_7627,plain,
aNaturalNumber0(xk),
inference(global_subsumption_just,[status(thm)],[c_7218,c_1607,c_7218]) ).
tcf(c_15087,plain,
! [X0: $i] :
( ( sz00 = xr )
| ( sdtasdt0(X0,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(X0,xk),xr) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_134,c_105]) ).
tcf(c_15088,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_15206,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_15088,c_3565]) ).
tcf(c_15207,plain,
! [X0: $i] :
( ( sz00 = xr )
| ( sdtsldt0(sdtasdt0(X0,xn),xr) = sdtasdt0(X0,iPr_def_10) )
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15206,c_133,c_116]) ).
tcf(c_15211,plain,
! [X0: $i] :
( ( sz00 = xr )
| ( sdtsldt0(sdtasdt0(X0,xk),xr) = sdtasdt0(X0,iPr_def_12) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X0) ),
inference(light_normalisation,[status(thm)],[c_15087,c_3567]) ).
tcf(c_15212,plain,
! [X0: $i] :
( ( sz00 = xr )
| ( sdtsldt0(sdtasdt0(X0,xk),xr) = sdtasdt0(X0,iPr_def_12) )
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15211,c_133,c_7627]) ).
tcf(c_423732,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xn) = sdtasdt0(xn,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_116,c_58]) ).
tcf(c_423733,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xm) = sdtasdt0(xm,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_117,c_58]) ).
tcf(c_425038,plain,
( aNaturalNumber0(iPr_def_10)
| ( sz00 = xr )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,xn) ),
inference(superposition,[status(thm)],[c_3565,c_99]) ).
tcf(c_425039,plain,
( aNaturalNumber0(iPr_def_10)
| ( sz00 = xr ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_425038,c_133,c_116,c_141]) ).
tcf(c_425052,plain,
( ( sz00 = xp )
| ( sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtasdt0(xn,xm) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_121,c_100]) ).
tcf(c_425069,plain,
( ( sz00 = xp )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xk) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(light_normalisation,[status(thm)],[c_425052,c_128]) ).
tcf(c_425070,plain,
( ( sz00 = xp )
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xk) )
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_425069,c_118]) ).
tcf(c_425357,plain,
! [X0: $i] :
( ( sz00 = xr )
| ( sdtasdt0(X0,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(X0,xk),xr) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_134,c_105]) ).
tcf(c_425359,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_425360,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_425359,c_3565]) ).
tcf(c_425361,plain,
! [X0: $i] :
( ( sz00 = xr )
| ( sdtsldt0(sdtasdt0(X0,xn),xr) = sdtasdt0(X0,iPr_def_10) )
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_425360,c_133,c_116]) ).
tcf(c_425365,plain,
! [X0: $i] :
( ( sz00 = xr )
| ( sdtsldt0(sdtasdt0(X0,xk),xr) = sdtasdt0(X0,iPr_def_12) )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X0) ),
inference(light_normalisation,[status(thm)],[c_425357,c_3567]) ).
tcf(c_425366,plain,
! [X0: $i] :
( ( sz00 = xr )
| ( sdtsldt0(sdtasdt0(X0,xk),xr) = sdtasdt0(X0,iPr_def_12) )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_425365,c_133]) ).
tcf(c_426204,plain,
sdtasdt0(xn,xm) = sdtasdt0(iPr_def_11,xr),
inference(light_normalisation,[status(thm)],[c_144,c_3565,c_3566]) ).
tcf(c_426211,plain,
( aNaturalNumber0(sdtasdt0(iPr_def_11,xr))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_426204,c_53]) ).
tcf(c_426219,plain,
aNaturalNumber0(sdtasdt0(iPr_def_11,xr)),
inference(forward_subsumption_resolution,[status(thm)],[c_426211,c_117,c_116]) ).
tcf(c_431020,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(superposition,[status(thm)],[c_117,c_423732]) ).
tcf(c_431026,plain,
sdtasdt0(xm,xn) = sdtasdt0(iPr_def_11,xr),
inference(light_normalisation,[status(thm)],[c_431020,c_426204]) ).
tcf(c_435518,plain,
aNaturalNumber0(iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_425039,c_1611,c_7215]) ).
tcf(c_435540,plain,
sdtasdt0(xm,iPr_def_10) = sdtasdt0(iPr_def_10,xm),
inference(superposition,[status(thm)],[c_435518,c_423733]) ).
tcf(c_435580,plain,
sdtasdt0(xm,iPr_def_10) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_435540,c_3566]) ).
tcf(c_475338,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ( sdtasdt0(xn,xm) = sdtasdt0(xp,xk) ) ),
inference(global_subsumption_just,[status(thm)],[c_425070,c_1607,c_425070]) ).
tcf(c_475339,plain,
( ( sdtasdt0(xn,xm) = sdtasdt0(xp,xk) )
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(renaming,[status(thm)],[c_475338]) ).
tcf(c_475340,plain,
( ( sdtasdt0(xp,xk) = sdtasdt0(iPr_def_11,xr) )
| ~ aNaturalNumber0(sdtasdt0(iPr_def_11,xr)) ),
inference(light_normalisation,[status(thm)],[c_475339,c_426204]) ).
tcf(c_475341,plain,
sdtasdt0(xp,xk) = sdtasdt0(iPr_def_11,xr),
inference(forward_subsumption_resolution,[status(thm)],[c_475340,c_426219]) ).
tcf(c_483797,plain,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ( sdtsldt0(sdtasdt0(X0,xn),xr) = sdtasdt0(X0,iPr_def_10) ) ),
inference(global_subsumption_just,[status(thm)],[c_425361,c_1611,c_15207]) ).
tcf(c_483798,plain,
! [X0: $i] :
( ( sdtsldt0(sdtasdt0(X0,xn),xr) = sdtasdt0(X0,iPr_def_10) )
| ~ aNaturalNumber0(X0) ),
inference(renaming,[status(thm)],[c_483797]) ).
tcf(c_483815,plain,
sdtsldt0(sdtasdt0(xm,xn),xr) = sdtasdt0(xm,iPr_def_10),
inference(superposition,[status(thm)],[c_117,c_483798]) ).
tcf(c_483827,plain,
sdtsldt0(sdtasdt0(iPr_def_11,xr),xr) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_483815,c_431026,c_435580]) ).
tcf(c_483870,plain,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ( sdtsldt0(sdtasdt0(X0,xk),xr) = sdtasdt0(X0,iPr_def_12) ) ),
inference(global_subsumption_just,[status(thm)],[c_425366,c_1611,c_15212]) ).
tcf(c_483871,plain,
! [X0: $i] :
( ( sdtsldt0(sdtasdt0(X0,xk),xr) = sdtasdt0(X0,iPr_def_12) )
| ~ aNaturalNumber0(X0) ),
inference(renaming,[status(thm)],[c_483870]) ).
tcf(c_483889,plain,
sdtsldt0(sdtasdt0(xp,xk),xr) = sdtasdt0(xp,iPr_def_12),
inference(superposition,[status(thm)],[c_118,c_483871]) ).
tcf(c_483897,plain,
iPr_def_11 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_483889,c_3568,c_475341,c_483827]) ).
tcf(c_483898,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_483897,c_3569]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM513+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 04:25:18 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 181.26/28.95 % SZS status Started for theBenchmark.p
% 181.26/28.95 % SZS status Theorem for theBenchmark.p
% 181.26/28.95
% 181.26/28.95 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 181.26/28.95
% 181.26/28.95 % ------ iProver source info
% 181.26/28.95
% 181.26/28.95 % git: date: 2026-07-19 20:42:38 +0200
% 181.26/28.95 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 181.26/28.95 % git: non_committed_changes: false
% 181.26/28.95
% 181.26/28.95 % ------ Parsing...
% 181.26/28.95 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 181.26/28.95
% 181.26/28.95 % ------ 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 %
% 181.26/28.95
% 181.26/28.95 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 181.26/28.95
% 181.26/28.95 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 181.26/28.95 % ------ Proving...
% 181.26/28.95 % ------ Problem Properties
% 181.26/28.95
% 181.26/28.95 %
% 181.26/28.95 % clauses 94
% 181.26/28.95 % conjectures 1
% 181.26/28.95 % EPR 34
% 181.26/28.95 % Horn 69
% 181.26/28.95 % unary 36
% 181.26/28.95 % binary 7
% 181.26/28.95 % lits 289
% 181.26/28.95 % lits eq 85
% 181.26/28.95 % fd_pure 0
% 181.26/28.95 % fd_pseudo 0
% 181.26/28.95 % fd_cond 15
% 181.26/28.95 % fd_pseudo_cond 11
% 181.26/28.95 % AC symbols 0
% 181.26/28.95
% 181.26/28.95 % ------ Schedule dynamic 5 is on
% 181.26/28.95
% 181.26/28.95 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 181.26/28.95
% 181.26/28.95
% 181.26/28.95 % ------
% 181.26/28.95 % Current options:
% 181.26/28.95 % ------
% 181.26/28.95
% 181.26/28.95
% 181.26/28.95 %
% 181.26/28.95
% 181.26/28.95 % ------ Proving...
% 181.26/28.95 % Proof_search_loop: time out after: 9629 full_loop iterations
% 181.26/28.95
% 181.26/28.95 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 181.26/28.95
% 181.26/28.95
% 181.26/28.95 % ------
% 181.26/28.95 % Current options:
% 181.26/28.95 % ------
% 181.26/28.95
% 181.26/28.95
% 181.26/28.95 %
% 181.26/28.95
% 181.26/28.95 % ------ Proving...
% 181.26/28.95 % Proof_search_loop: time out after: 7493 full_loop iterations
% 181.26/28.95
% 181.26/28.95 % ------ Option_1: Negative Selections Time Limit: 35.
% 181.26/28.95
% 181.26/28.95
% 181.26/28.95 % ------
% 181.26/28.95 % Current options:
% 181.26/28.95 % ------
% 181.26/28.95
% 181.26/28.95
% 181.26/28.95 %
% 181.26/28.95
% 181.26/28.95 % ------ Proving...
% 181.26/28.95 %
% 181.26/28.95
% 181.26/28.95 % SZS status Theorem for theBenchmark.p
% 181.26/28.95
% 181.26/28.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 181.26/28.95
% 181.26/28.95
%------------------------------------------------------------------------------