%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM523+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 : n014.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 02:25:49 PM UTC 2026
% Result : Theorem 3.77s 6.23s
% Output : CNFRefutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 14 unt; 0 def)
% Number of atoms : 189 ( 36 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 236 ( 95 ~; 93 |; 40 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 56 !; 12 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(f39,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X2,sdtasdt0(X0,X1))
& isPrime0(X2) )
=> ( doDivides0(X2,X1)
| doDivides0(X2,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPDP) ).
fof(f40,axiom,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2987) ).
fof(f42,axiom,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3014) ).
fof(f43,axiom,
( isPrime0(xp)
& ! [X0] :
( ( ( doDivides0(X0,xp)
| ? [X1] :
( xp = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xp
| X0 = sz10 ) )
& xp != sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3025) ).
fof(f44,conjecture,
( ( doDivides0(xp,xn)
| ? [X0] :
( xn = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) )
& ( doDivides0(xp,sdtasdt0(xn,xn))
| ? [X0] :
( sdtasdt0(xn,xn) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f45,negated_conjecture,
~ ( ( doDivides0(xp,xn)
| ? [X0] :
( xn = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) )
& ( doDivides0(xp,sdtasdt0(xn,xn))
| ? [X0] :
( sdtasdt0(xn,xn) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f48,plain,
~ ( ( doDivides0(xp,xn)
| ? [X1] :
( xn = sdtasdt0(xp,X1)
& aNaturalNumber0(X1) ) )
& ( doDivides0(xp,sdtasdt0(xn,xn))
| ? [X0] :
( sdtasdt0(xn,xn) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) ) ) ),
inference(rectify,[],[f45]) ).
fof(f51,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f52,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f51]) ).
fof(f95,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f96,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f95]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| doDivides0(X2,X1)
| doDivides0(X2,X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| doDivides0(X2,X1)
| doDivides0(X2,X0) ),
inference(flattening,[],[f113]) ).
fof(f117,plain,
( isPrime0(xp)
& ! [X0] :
( ( ~ doDivides0(X0,xp)
& ! [X1] :
( sdtasdt0(X0,X1) != xp
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0)
| X0 = xp
| X0 = sz10 )
& xp != sz10 ),
inference(ennf_transformation,[],[f43]) ).
fof(f118,plain,
( isPrime0(xp)
& ! [X0] :
( ( ~ doDivides0(X0,xp)
& ! [X1] :
( sdtasdt0(X0,X1) != xp
| ~ aNaturalNumber0(X1) ) )
| ~ aNaturalNumber0(X0)
| X0 = xp
| X0 = sz10 )
& xp != sz10 ),
inference(flattening,[],[f117]) ).
fof(f119,plain,
( ( ~ doDivides0(xp,xn)
& ! [X1] :
( xn != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) ) )
| ( ~ doDivides0(xp,sdtasdt0(xn,xn))
& ! [X0] :
( sdtasdt0(xn,xn) != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) ) ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f125,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,[],[f96]) ).
fof(f126,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,[],[f125]) ).
fof(f127,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))],[f126]) ).
fof(f140,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f185,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f204,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| doDivides0(X2,X1)
| doDivides0(X2,X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f208,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f40]) ).
fof(f209,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f40]) ).
fof(f210,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f40]) ).
fof(f218,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f219,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f118]) ).
fof(f223,plain,
( ~ doDivides0(xp,xn)
| ~ doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f233,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f185]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f233]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X0,X2)
| doDivides0(X0,X1)
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,sdtasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_117,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f210]) ).
tcf(c_118,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f209]) ).
tcf(c_119,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f208]) ).
tcf(c_130,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnf_transformation,[],[f218]) ).
tcf(c_134,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f219]) ).
tcf(c_138,negated_conjecture,
( ~ doDivides0(xp,xn)
| ~ doDivides0(xp,sdtasdt0(xn,xn)) ),
inference(cnf_transformation,[],[f223]) ).
tcf(c_197,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_2613,plain,
( doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(superposition,[status(thm)],[c_130,c_197]) ).
tcf(c_4949,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xm) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_12921,plain,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(global_subsumption_just,[status(thm)],[c_2613,c_119,c_118,c_2613,c_4949]) ).
tcf(c_12929,plain,
( doDivides0(xp,xn)
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_12921,c_116]) ).
tcf(c_12930,plain,
~ doDivides0(xp,xn),
inference(superposition,[status(thm)],[c_12921,c_138]) ).
tcf(c_12931,plain,
( ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12929,c_12930]) ).
tcf(c_12987,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_12931,c_117,c_119,c_134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM523+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/5.40 % Computer : n014.cluster.edu
% 0.12/5.40 % Model : x86_64 x86_64
% 0.12/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.40 % Memory : 8046.5625MB
% 0.12/5.40 % OS : Linux 6.8.0-71-generic
% 0.12/5.40 % CPULimit : 300
% 0.12/5.40 % WCLimit : 300
% 0.12/5.40 % DateTime : Thu Sep 24 04:26:25 UTC 2026
% 0.12/5.41 % CPUTime :
% 0.12/5.41 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/5.44 Running first-order theorem proving
% 0.12/5.44 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
% 0.12/5.45
% 0.12/5.45 % ======== iProver multi-core TPTP/SMT =========
% 0.12/5.45
% 0.12/5.45 % Detected problem language: tptp
% 0.12/5.47 % Proving...
% 3.77/6.23 % SZS status Started for theBenchmark.p
% 3.77/6.23 % SZS status Theorem for theBenchmark.p
% 3.77/6.23
% 3.77/6.23 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.77/6.23
% 3.77/6.23 % ------ iProver source info
% 3.77/6.23
% 3.77/6.23 % git: date: 2026-07-19 20:42:38 +0200
% 3.77/6.23 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.77/6.23 % git: non_committed_changes: false
% 3.77/6.23
% 3.77/6.23 % ------ Parsing...
% 3.77/6.23 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.77/6.23
% 3.77/6.23 % ------ Preprocessing... sup_sim: 0 pe_s pe_e sup_sim: 0 pe_s pe_e %
% 3.77/6.23
% 3.77/6.23 % ------ Preprocessing... gs_s sp: 2 0s gs_e scvd_s sp: 0 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 3.77/6.23
% 3.77/6.23 % ------ Preprocessing...
% 3.77/6.23 % ------ Proving...
% 3.77/6.23 % ------ Problem Properties
% 3.77/6.23
% 3.77/6.23 %
% 3.77/6.23 % clauses 87
% 3.77/6.23 % conjectures 6
% 3.77/6.23 % EPR 24
% 3.77/6.23 % Horn 52
% 3.77/6.23 % unary 14
% 3.77/6.23 % binary 9
% 3.77/6.23 % lits 360
% 3.77/6.23 % lits eq 122
% 3.77/6.23 % fd_pure 0
% 3.77/6.23 % fd_pseudo 0
% 3.77/6.23 % fd_cond 23
% 3.77/6.23 % fd_pseudo_cond 11
% 3.77/6.23 % AC symbols 0
% 3.77/6.23
% 3.77/6.23 % ------ Input Options Time Limit: Unbounded
% 3.77/6.23
% 3.77/6.23
% 3.77/6.23 % ------
% 3.77/6.23 % Current options:
% 3.77/6.23 % ------
% 3.77/6.23
% 3.77/6.23
% 3.77/6.23 %
% 3.77/6.23
% 3.77/6.23 % ------ Proving...
% 3.77/6.23 %
% 3.77/6.23
% 3.77/6.23 % SZS status Theorem for theBenchmark.p
% 3.77/6.23
% 3.77/6.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.77/6.23
% 3.77/6.23
%------------------------------------------------------------------------------