%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM393+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n002.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 02:24:04 PM UTC 2026
% Result : Theorem 0.35s 6.18s
% Output : CNFRefutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 38 ( 10 unt; 0 def)
% Number of atoms : 111 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 123 ( 50 ~; 52 |; 11 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 52 ( 0 sgn 50 !; 2 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(f8,axiom,
! [X0,X1] :
( inclusion_comparable(X0,X1)
<=> ( subset(X1,X0)
| subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_xboole_0) ).
fof(f24,axiom,
! [X0,X1] :
( ( ordinal(X1)
& ordinal(X0) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f30,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> inclusion_comparable(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_ordinal1) ).
fof(f31,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> inclusion_comparable(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f55,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f56,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f58,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
inference(flattening,[],[f57]) ).
fof(f63,plain,
? [X0] :
( ordinal(X0)
& ? [X1] :
( ordinal(X1)
& ~ inclusion_comparable(X0,X1) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f72,plain,
! [X0,X1] :
( ( ~ inclusion_comparable(X0,X1)
| subset(X1,X0)
| subset(X0,X1) )
& ( ( ~ subset(X1,X0)
& ~ subset(X0,X1) )
| inclusion_comparable(X0,X1) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f73,plain,
! [X0,X1] :
( ( ~ inclusion_comparable(X0,X1)
| subset(X1,X0)
| subset(X0,X1) )
& ( ( ~ subset(X1,X0)
& ~ subset(X0,X1) )
| inclusion_comparable(X0,X1) ) ),
inference(flattening,[],[f72]) ).
fof(f86,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ( ( ~ ordinal_subset(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| ordinal_subset(X0,X1) ) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f87,plain,
( ordinal(sK12)
& ordinal(sK13)
& ~ inclusion_comparable(sK12,sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X0,sK12),skolemize(X1,sK13)],[f63]) ).
fof(f97,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ordinal_subset(X1,X0)
| ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f99,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| inclusion_comparable(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f100,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| inclusion_comparable(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f128,plain,
! [X0,X1] :
( ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal_subset(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f135,plain,
ordinal(sK12),
inference(cnf_transformation,[],[f87]) ).
fof(f136,plain,
ordinal(sK13),
inference(cnf_transformation,[],[f87]) ).
fof(f137,plain,
~ inclusion_comparable(sK12,sK13),
inference(cnf_transformation,[],[f87]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ordinal_subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( inclusion_comparable(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( inclusion_comparable(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0)
| ~ ordinal_subset(X0,X1) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_93,negated_conjecture,
~ inclusion_comparable(sK12,sK13),
inference(cnf_transformation,[],[f137]) ).
tcf(c_94,negated_conjecture,
ordinal(sK13),
inference(cnf_transformation,[],[f136]) ).
tcf(c_95,negated_conjecture,
ordinal(sK12),
inference(cnf_transformation,[],[f135]) ).
tcf(c_1012,negated_conjecture,
ordinal(sK12),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_1013,negated_conjecture,
ordinal(sK13),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_1014,negated_conjecture,
~ inclusion_comparable(sK12,sK13),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_1752,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| ordinal_subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_55,c_87]) ).
tcf(c_1927,plain,
! [X0: $i,X1: $i] :
( subset(X1,X0)
| subset(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_1752,c_87]) ).
tcf(c_2005,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| inclusion_comparable(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(superposition,[status(thm)],[c_1927,c_57]) ).
tcf(c_2098,plain,
! [X0: $i,X1: $i] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| inclusion_comparable(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_2005,c_56,c_2005]) ).
tcf(c_2099,plain,
! [X0: $i,X1: $i] :
( inclusion_comparable(X0,X1)
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(renaming,[status(thm)],[c_2098]) ).
tcf(c_2108,plain,
( ~ ordinal(sK13)
| ~ ordinal(sK12) ),
inference(superposition,[status(thm)],[c_2099,c_1014]) ).
tcf(c_2109,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2108,c_1013,c_1012]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM393+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n002.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 03:52:38 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/5.41 Running first-order theorem proving
% 0.13/5.41 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
% 0.13/5.42
% 0.13/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.42
% 0.13/5.42 % Detected problem language: tptp
% 0.13/5.43 % Proving...
% 0.35/6.18 % SZS status Started for theBenchmark.p
% 0.35/6.18 % SZS status Theorem for theBenchmark.p
% 0.35/6.18
% 0.35/6.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.35/6.18
% 0.35/6.18 % ------ iProver source info
% 0.35/6.18
% 0.35/6.18 % git: date: 2026-07-19 20:42:38 +0200
% 0.35/6.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.35/6.18 % git: non_committed_changes: false
% 0.35/6.18
% 0.35/6.18 % ------ Parsing...
% 0.35/6.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.35/6.18
% 0.35/6.18 % ------ Preprocessing... sup_sim: 0 sf_s rm: 19 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 0.35/6.18
% 0.35/6.18 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.35/6.18
% 0.35/6.18 % ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 0 0s sf_e
% 0.35/6.18 % ------ Proving...
% 0.35/6.18 % ------ Problem Properties
% 0.35/6.18
% 0.35/6.18 %
% 0.35/6.18 % clauses 33
% 0.35/6.18 % conjectures 3
% 0.35/6.18 % EPR 30
% 0.35/6.18 % Horn 29
% 0.35/6.18 % unary 13
% 0.35/6.18 % binary 11
% 0.35/6.18 % lits 65
% 0.35/6.18 % lits eq 2
% 0.35/6.18 % fd_pure 0
% 0.35/6.18 % fd_pseudo 0
% 0.35/6.18 % fd_cond 1
% 0.35/6.18 % fd_pseudo_cond 1
% 0.35/6.18 % AC symbols 0
% 0.35/6.18
% 0.35/6.18 % ------ Schedule dynamic 5 is on
% 0.35/6.18
% 0.35/6.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.35/6.18
% 0.35/6.18
% 0.35/6.18 % ------
% 0.35/6.18 % Current options:
% 0.35/6.18 % ------
% 0.35/6.18
% 0.35/6.18
% 0.35/6.18 %
% 0.35/6.18
% 0.35/6.18 % ------ Proving...
% 0.35/6.18 %
% 0.35/6.18
% 0.35/6.18 % SZS status Theorem for theBenchmark.p
% 0.35/6.18
% 0.35/6.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.35/6.18
% 0.35/6.18
%------------------------------------------------------------------------------