%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM469+2 : 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 : n020.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 02:24:44 PM UTC 2026
% Result : Theorem 4.11s 1.18s
% Output : CNFRefutation 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 20 unt; 1 def)
% Number of atoms : 131 ( 58 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 100 ( 31 ~; 32 |; 33 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 22 !; 6 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(f33,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240) ).
fof(f34,axiom,
( doDivides0(xl,xn)
& ? [X0] :
( xn = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) )
& doDivides0(xl,xm)
& ? [X0] :
( xm = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240_04) ).
fof(f35,axiom,
( xl != sz00
=> ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1298) ).
fof(f36,conjecture,
( doDivides0(xl,sdtpldt0(xm,xn))
| ? [X0] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f37,negated_conjecture,
~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ? [X0] :
( sdtpldt0(xm,xn) = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f40,plain,
( doDivides0(xl,xn)
& ? [X1] :
( xn = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) )
& doDivides0(xl,xm)
& ? [X0] :
( xm = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) ) ),
inference(rectify,[],[f34]) ).
fof(f42,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f43,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f42]) ).
fof(f50,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f56,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f92,plain,
( sz00 = xl
| ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f93,plain,
( ~ doDivides0(xl,sdtpldt0(xm,xn))
& ! [X0] :
( sdtasdt0(xl,X0) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(X0) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f104,plain,
( doDivides0(xl,xn)
& xn = sdtasdt0(xl,sK3)
& aNaturalNumber0(sK3)
& doDivides0(xl,xm)
& xm = sdtasdt0(xl,sK2)
& aNaturalNumber0(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f40]) ).
fof(f108,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f43]) ).
fof(f112,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f50]) ).
fof(f118,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f158,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f33]) ).
fof(f162,plain,
xn = sdtasdt0(xl,sK3),
inference(cnf_transformation,[],[f104]) ).
fof(f163,plain,
aNaturalNumber0(sK3),
inference(cnf_transformation,[],[f104]) ).
fof(f165,plain,
xm = sdtasdt0(xl,sK2),
inference(cnf_transformation,[],[f104]) ).
fof(f166,plain,
aNaturalNumber0(sK2),
inference(cnf_transformation,[],[f104]) ).
fof(f167,plain,
( sz00 = xl
| sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
inference(cnf_transformation,[],[f92]) ).
fof(f169,plain,
( sz00 = xl
| aNaturalNumber0(sdtsldt0(xn,xl)) ),
inference(cnf_transformation,[],[f92]) ).
fof(f171,plain,
( sz00 = xl
| aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(cnf_transformation,[],[f92]) ).
fof(f173,plain,
! [X0] :
( sdtasdt0(xl,X0) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_63,plain,
! [X0: $i] :
( ( sdtasdt0(sz00,X0) = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_103,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f158]) ).
tcf(c_104,plain,
aNaturalNumber0(sK2),
inference(cnf_transformation,[],[f166]) ).
tcf(c_105,plain,
sdtasdt0(xl,sK2) = xm,
inference(cnf_transformation,[],[f165]) ).
tcf(c_107,plain,
aNaturalNumber0(sK3),
inference(cnf_transformation,[],[f163]) ).
tcf(c_108,plain,
sdtasdt0(xl,sK3) = xn,
inference(cnf_transformation,[],[f162]) ).
tcf(c_110,plain,
( aNaturalNumber0(sdtsldt0(xm,xl))
| ( sz00 = xl ) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_112,plain,
( aNaturalNumber0(sdtsldt0(xn,xl))
| ( sz00 = xl ) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_114,plain,
( ( sz00 = xl )
| ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = sdtpldt0(xm,xn) ) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_115,negated_conjecture,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ( sdtasdt0(xl,X0) != sdtpldt0(xm,xn) ) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_1766,definition,
iPr_def_10 = sdtpldt0(xm,xn),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1768,negated_conjecture,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ( sdtasdt0(xl,X0) != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_115]) ).
tcf(c_2720,plain,
( ~ aNaturalNumber0(sK3)
| ( xn != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_108,c_1768]) ).
tcf(c_2721,plain,
xn != iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_2720,c_107]) ).
tcf(c_2755,plain,
sdtpldt0(sz00,xn) = xn,
inference(superposition,[status(thm)],[c_103,c_57]) ).
tcf(c_2830,plain,
sdtasdt0(sz00,sK2) = sz00,
inference(superposition,[status(thm)],[c_104,c_63]) ).
tcf(c_4283,plain,
( ( sz00 = xl )
| ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_114,c_1766]) ).
tcf(c_4293,plain,
( ( sz00 = xl )
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
inference(superposition,[status(thm)],[c_4283,c_1768]) ).
tcf(c_4335,plain,
( ( sz00 = xl )
| ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(superposition,[status(thm)],[c_52,c_4293]) ).
tcf(c_4339,plain,
sz00 = xl,
inference(global_subsumption_just,[status(thm)],[c_4335,c_112,c_110,c_4335]) ).
tcf(c_4364,plain,
sdtasdt0(sz00,sK2) = xm,
inference(demodulation,[status(thm)],[c_105,c_4339]) ).
tcf(c_4370,plain,
sz00 = xm,
inference(light_normalisation,[status(thm)],[c_4364,c_2830]) ).
tcf(c_4388,plain,
sdtpldt0(sz00,xn) = iPr_def_10,
inference(demodulation,[status(thm)],[c_1766,c_4370]) ).
tcf(c_4390,plain,
xn = iPr_def_10,
inference(demodulation,[status(thm)],[c_2755,c_4388]) ).
tcf(c_4391,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4390,c_2721]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM469+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n020.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 04:09:33 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.41
% 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...
% 4.11/1.18 % SZS status Started for theBenchmark.p
% 4.11/1.18 % SZS status Theorem for theBenchmark.p
% 4.11/1.18
% 4.11/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.11/1.18
% 4.11/1.18 % ------ iProver source info
% 4.11/1.18
% 4.11/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 4.11/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.11/1.18 % git: non_committed_changes: false
% 4.11/1.18
% 4.11/1.18 % ------ Parsing...
% 4.11/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.11/1.18
% 4.11/1.18 % ------ 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 %
% 4.11/1.18
% 4.11/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.11/1.18
% 4.11/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.11/1.18 % ------ Proving...
% 4.11/1.18 % ------ Problem Properties
% 4.11/1.18
% 4.11/1.18 %
% 4.11/1.18 % clauses 64
% 4.11/1.18 % conjectures 2
% 4.11/1.18 % EPR 17
% 4.11/1.18 % Horn 46
% 4.11/1.18 % unary 14
% 4.11/1.18 % binary 13
% 4.11/1.18 % lits 205
% 4.11/1.18 % lits eq 61
% 4.11/1.18 % fd_pure 0
% 4.11/1.18 % fd_pseudo 0
% 4.11/1.18 % fd_cond 6
% 4.11/1.18 % fd_pseudo_cond 9
% 4.11/1.18 % AC symbols 0
% 4.11/1.18
% 4.11/1.18 % ------ Schedule dynamic 5 is on
% 4.11/1.18
% 4.11/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.11/1.18
% 4.11/1.18
% 4.11/1.18 % ------
% 4.11/1.18 % Current options:
% 4.11/1.18 % ------
% 4.11/1.18
% 4.11/1.18
% 4.11/1.18 %
% 4.11/1.18
% 4.11/1.18 % ------ Proving...
% 4.11/1.18 %
% 4.11/1.18
% 4.11/1.18 % SZS status Theorem for theBenchmark.p
% 4.11/1.18
% 4.11/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.11/1.18
% 4.11/1.18
%------------------------------------------------------------------------------