%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM492+3 : 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 : n006.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 02:25:17 PM UTC 2026
% Result : Theorem 4.40s 6.31s
% Output : CNFRefutation 4.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 16 unt; 0 def)
% Number of atoms : 213 ( 45 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 264 ( 103 ~; 90 |; 64 &)
% ( 0 <=>; 7 =>; 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 52 !; 12 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f33,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X2)
& doDivides0(X0,X1) )
=> doDivides0(X0,sdtpldt0(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivSum) ).
fof(f34,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,sdtpldt0(X1,X2))
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivMin) ).
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))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X0] :
( ( ( doDivides0(X0,xp)
| ? [X1] :
( xp = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xp
| X0 = sz10 ) )
& xp != sz10
& xp != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(f43,axiom,
( xr = sdtmndt0(xn,xp)
& sdtpldt0(xp,xr) = xn
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
fof(f47,axiom,
( sdtasdt0(xr,xm) = sdtmndt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xn,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1978) ).
fof(f48,axiom,
( doDivides0(xp,sdtasdt0(xp,xm))
& ? [X0] :
( sdtasdt0(xp,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2001) ).
fof(f49,conjecture,
( doDivides0(xp,sdtasdt0(xr,xm))
| ? [X0] :
( sdtasdt0(xr,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f50,negated_conjecture,
~ ( doDivides0(xp,sdtasdt0(xr,xm))
| ? [X0] :
( sdtasdt0(xr,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
fof(f54,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X2] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X2)
& aNaturalNumber0(X2) )
& isPrime0(xp)
& ! [X0] :
( ( ( doDivides0(X0,xp)
| ? [X1] :
( xp = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xp
| X0 = sz10 ) )
& xp != sz10
& xp != sz00 ),
inference(rectify,[],[f41]) ).
fof(f55,plain,
( doDivides0(xp,sdtasdt0(xp,xm))
& ? [X1] :
( sdtasdt0(xp,xm) = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) )
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ),
inference(rectify,[],[f48]) ).
fof(f58,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f59,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f58]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,sdtpldt0(X1,X2)) ),
inference(ennf_transformation,[],[f33]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,sdtpldt0(X1,X2)) ),
inference(flattening,[],[f108]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(flattening,[],[f110]) ).
fof(f122,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X2] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X2)
& aNaturalNumber0(X2) )
& isPrime0(xp)
& ! [X0] :
( ( ~ doDivides0(X0,xp)
& ! [X1] :
( sdtasdt0(X0,X1) != xp
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0)
| X0 = xp
| X0 = sz10 )
& xp != sz10
& xp != sz00 ),
inference(ennf_transformation,[],[f54]) ).
fof(f123,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X2] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X2)
& aNaturalNumber0(X2) )
& isPrime0(xp)
& ! [X0] :
( ( ~ doDivides0(X0,xp)
& ! [X1] :
( sdtasdt0(X0,X1) != xp
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0)
| X0 = xp
| X0 = sz10 )
& xp != sz10
& xp != sz00 ),
inference(flattening,[],[f122]) ).
fof(f124,plain,
( ~ doDivides0(xp,sdtasdt0(xr,xm))
& ! [X0] :
( sdtasdt0(xp,X0) != sdtasdt0(xr,xm)
| ~ aNaturalNumber0(X0) ) ),
inference(ennf_transformation,[],[f50]) ).
fof(f151,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK10)
& aNaturalNumber0(sK10)
& isPrime0(xp)
& ! [X0] :
( ( ~ doDivides0(X0,xp)
& ! [X1] :
( sdtasdt0(X0,X1) != xp
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0)
| X0 = xp
| X0 = sz10 )
& xp != sz10
& xp != sz00 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10)],[f123]) ).
fof(f154,plain,
( doDivides0(xp,sdtasdt0(xp,xm))
& sdtasdt0(xp,xm) = sdtasdt0(xp,sK14)
& aNaturalNumber0(sK14)
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK13)
& aNaturalNumber0(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X0,sK13),skolemize(X1,sK14)],[f55]) ).
fof(f159,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f209,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f109]) ).
fof(f210,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(cnf_transformation,[],[f111]) ).
fof(f223,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f224,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f242,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f151]) ).
fof(f255,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f43]) ).
fof(f263,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)),
inference(cnf_transformation,[],[f47]) ).
fof(f264,plain,
doDivides0(xp,sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f154]) ).
fof(f269,plain,
~ doDivides0(xp,sdtasdt0(xr,xm)),
inference(cnf_transformation,[],[f124]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X2)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X0,sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f224]) ).
tcf(c_118,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f223]) ).
tcf(c_142,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f242]) ).
tcf(c_146,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f255]) ).
tcf(c_155,plain,
sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xr,xm)) = sdtasdt0(xn,xm),
inference(cnf_transformation,[],[f263]) ).
tcf(c_161,plain,
doDivides0(xp,sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f264]) ).
tcf(c_163,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xr,xm)),
inference(cnf_transformation,[],[f269]) ).
tcf(c_301,plain,
! [X0: $i] :
( doDivides0(X0,sdtasdt0(xr,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ doDivides0(X0,sdtasdt0(xp,xm))
| ~ doDivides0(X0,sdtasdt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_155,c_103]) ).
tcf(c_317,plain,
! [X0: $i] :
( doDivides0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ doDivides0(X0,sdtasdt0(xr,xm))
| ~ doDivides0(X0,sdtasdt0(xp,xm)) ),
inference(superposition,[status(thm)],[c_155,c_102]) ).
tcf(c_584,plain,
! [X0: $i] :
( doDivides0(X0,sdtasdt0(xr,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ doDivides0(X0,sdtasdt0(xp,xm))
| ~ doDivides0(X0,sdtasdt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_155,c_103]) ).
tcf(c_644,plain,
( doDivides0(xp,sdtasdt0(xr,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ doDivides0(xp,sdtasdt0(xp,xm)) ),
inference(superposition,[status(thm)],[c_142,c_301]) ).
tcf(c_656,plain,
( ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(global_subsumption_just,[status(thm)],[c_317,c_118,c_161,c_163,c_644]) ).
tcf(c_662,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xr,xm)) ),
inference(superposition,[status(thm)],[c_53,c_656]) ).
tcf(c_1150,plain,
~ aNaturalNumber0(sdtasdt0(xr,xm)),
inference(global_subsumption_just,[status(thm)],[c_584,c_118,c_117,c_662]) ).
tcf(c_1152,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_53,c_1150]) ).
tcf(c_1153,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1152,c_117,c_146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM492+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.38 % Computer : n006.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Thu Sep 24 04:15:18 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 4.40/6.31 % SZS status Started for theBenchmark.p
% 4.40/6.31 % SZS status Theorem for theBenchmark.p
% 4.40/6.31
% 4.40/6.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.40/6.31
% 4.40/6.31 % ------ iProver source info
% 4.40/6.31
% 4.40/6.31 % git: date: 2026-07-19 20:42:38 +0200
% 4.40/6.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.40/6.31 % git: non_committed_changes: false
% 4.40/6.31
% 4.40/6.31 % ------ Parsing...
% 4.40/6.31 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.40/6.31 % ------ Proving...
% 4.40/6.31 % ------ Problem Properties
% 4.40/6.31
% 4.40/6.31 %
% 4.40/6.31 % clauses 115
% 4.40/6.31 % conjectures 2
% 4.40/6.31 % EPR 33
% 4.40/6.31 % Horn 75
% 4.40/6.31 % unary 32
% 4.40/6.31 % binary 15
% 4.40/6.31 % lits 409
% 4.40/6.31 % lits eq 122
% 4.40/6.31 % fd_pure 0
% 4.40/6.31 % fd_pseudo 0
% 4.40/6.31 % fd_cond 22
% 4.40/6.31 % fd_pseudo_cond 15
% 4.40/6.31 % AC symbols 0
% 4.40/6.31
% 4.40/6.31 % ------ Input Options Time Limit: Unbounded
% 4.40/6.31
% 4.40/6.31
% 4.40/6.31 % ------
% 4.40/6.31 % Current options:
% 4.40/6.31 % ------
% 4.40/6.31
% 4.40/6.31
% 4.40/6.31 %
% 4.40/6.31
% 4.40/6.31 % ------ Proving...
% 4.40/6.31 %
% 4.40/6.31
% 4.40/6.31 % SZS status Theorem for theBenchmark.p
% 4.40/6.31
% 4.40/6.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.40/6.31
% 4.40/6.31
%------------------------------------------------------------------------------