%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM472+1 : 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 02:24:57 PM UTC 2026
% Result : Theorem 2.92s 1.17s
% Output : CNFRefutation 2.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 12 unt; 1 def)
% Number of atoms : 91 ( 11 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 105 ( 46 ~; 41 |; 13 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 34 !; 5 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(f34,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324) ).
fof(f39,conjecture,
sdtlseqdt0(xm,sdtpldt0(xm,xn)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f40,negated_conjecture,
~ sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f43,plain,
~ sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(flattening,[],[f40]) ).
fof(f45,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f46,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f45]) ).
fof(f70,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f71,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f70]) ).
fof(f97,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f71]) ).
fof(f98,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(rectify,[],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ( sdtpldt0(X0,sK0(X0,X1)) = X1
& aNaturalNumber0(sK0(X0,X1)) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f98]) ).
fof(f110,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f161,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f34]) ).
fof(f162,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f34]) ).
fof(f169,plain,
~ sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f43]) ).
fof(f170,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f133]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f170]) ).
tcf(c_103,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f162]) ).
tcf(c_104,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f161]) ).
tcf(c_110,negated_conjecture,
~ sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f169]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
tcf(c_1708,definition,
iPr_def_10 = sdtpldt0(xm,xn),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1709,negated_conjecture,
~ sdtlseqdt0(xm,iPr_def_10),
inference(demodulation,[status(thm)],[c_110,c_1708]) ).
tcf(c_2818,plain,
( sdtlseqdt0(xm,iPr_def_10)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_1708,c_147]) ).
tcf(c_2837,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2818,c_1709,c_104,c_103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM472+1 : 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 04:09:48 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.42
% 0.14/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 2.92/1.17 % SZS status Started for theBenchmark.p
% 2.92/1.17 % SZS status Theorem for theBenchmark.p
% 2.92/1.17
% 2.92/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.92/1.17
% 2.92/1.17 % ------ iProver source info
% 2.92/1.17
% 2.92/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 2.92/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.92/1.17 % git: non_committed_changes: false
% 2.92/1.17
% 2.92/1.17 % ------ Parsing...
% 2.92/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.92/1.17
% 2.92/1.17 % ------ 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 %
% 2.92/1.17
% 2.92/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.92/1.17
% 2.92/1.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.92/1.17 % ------ Proving...
% 2.92/1.17 % ------ Problem Properties
% 2.92/1.17
% 2.92/1.17 %
% 2.92/1.17 % clauses 58
% 2.92/1.17 % conjectures 1
% 2.92/1.17 % EPR 15
% 2.92/1.17 % Horn 45
% 2.92/1.17 % unary 13
% 2.92/1.17 % binary 7
% 2.92/1.17 % lits 198
% 2.92/1.17 % lits eq 53
% 2.92/1.17 % fd_pure 0
% 2.92/1.17 % fd_pseudo 0
% 2.92/1.17 % fd_cond 6
% 2.92/1.17 % fd_pseudo_cond 9
% 2.92/1.17 % AC symbols 0
% 2.92/1.17
% 2.92/1.17 % ------ Schedule dynamic 5 is on
% 2.92/1.17
% 2.92/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.92/1.17
% 2.92/1.17
% 2.92/1.17 % ------
% 2.92/1.17 % Current options:
% 2.92/1.17 % ------
% 2.92/1.17
% 2.92/1.17
% 2.92/1.17 %
% 2.92/1.17
% 2.92/1.17 % ------ Proving...
% 2.92/1.17 %
% 2.92/1.17
% 2.92/1.17 % SZS status Theorem for theBenchmark.p
% 2.92/1.17
% 2.92/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.92/1.17
% 2.92/1.17
%------------------------------------------------------------------------------