%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU275+2 : TPTP v9.3.1. Released v3.3.0.
% 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 02:56:27 PM UTC 2026
% Result : Theorem 4.67s 2.28s
% Output : CNFRefutation 4.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 26 unt; 1 def)
% Number of atoms : 132 ( 1 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 115 ( 47 ~; 41 |; 20 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 2 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 29 ( 0 sgn 28 !; 1 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
fof(f56,axiom,
! [X0] :
( relation(X0)
=> ( well_ordering(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_wellord1) ).
fof(f86,axiom,
! [X0] : relation(inclusion_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(f262,axiom,
! [X0] : reflexive(inclusion_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_wellord2) ).
fof(f285,axiom,
! [X0] : transitive(inclusion_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_wellord2) ).
fof(f305,axiom,
! [X0] :
( ordinal(X0)
=> connected(inclusion_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_wellord2) ).
fof(f317,axiom,
! [X0] : antisymmetric(inclusion_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord2) ).
fof(f328,axiom,
! [X0] :
( ordinal(X0)
=> well_founded_relation(inclusion_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_wellord2) ).
fof(f337,conjecture,
! [X0] :
( ordinal(X0)
=> well_ordering(inclusion_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_wellord2) ).
fof(f338,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> well_ordering(inclusion_relation(X0)) ),
inference(negated_conjecture,[status(cth)],[f337]) ).
fof(f418,plain,
! [X0] :
( ~ relation(X0)
| ( well_ordering(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) ) ),
inference(ennf_transformation,[],[f56]) ).
fof(f650,plain,
! [X0] :
( ~ ordinal(X0)
| connected(inclusion_relation(X0)) ),
inference(ennf_transformation,[],[f305]) ).
fof(f681,plain,
! [X0] :
( ~ ordinal(X0)
| well_founded_relation(inclusion_relation(X0)) ),
inference(ennf_transformation,[],[f328]) ).
fof(f690,plain,
? [X0] :
( ordinal(X0)
& ~ well_ordering(inclusion_relation(X0)) ),
inference(ennf_transformation,[],[f338]) ).
fof(f831,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_ordering(X0)
| ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) )
& ( ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0) ) ) ),
inference(nnf_transformation,[],[f418]) ).
fof(f832,plain,
! [X0] :
( ~ relation(X0)
| ( ( ~ well_ordering(X0)
| ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) )
& ( ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0) ) ) ),
inference(flattening,[],[f831]) ).
fof(f990,plain,
( ordinal(sK148)
& ~ well_ordering(inclusion_relation(sK148)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(X0,sK148)],[f690]) ).
fof(f1211,plain,
! [X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0) ),
inference(cnf_transformation,[],[f832]) ).
fof(f1293,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f86]) ).
fof(f1576,plain,
! [X0] : reflexive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f262]) ).
fof(f1616,plain,
! [X0] : transitive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f285]) ).
fof(f1644,plain,
! [X0] :
( ~ ordinal(X0)
| connected(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f650]) ).
fof(f1675,plain,
! [X0] : antisymmetric(inclusion_relation(X0)),
inference(cnf_transformation,[],[f317]) ).
fof(f1693,plain,
! [X0] :
( ~ ordinal(X0)
| well_founded_relation(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f681]) ).
fof(f1707,plain,
ordinal(sK148),
inference(cnf_transformation,[],[f990]) ).
fof(f1708,plain,
~ well_ordering(inclusion_relation(sK148)),
inference(cnf_transformation,[],[f990]) ).
tcf(c_254,plain,
! [X0: $i] :
( well_ordering(X0)
| ~ reflexive(X0)
| ~ well_founded_relation(X0)
| ~ transitive(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1211]) ).
tcf(c_340,plain,
! [X0: $i] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f1293]) ).
tcf(c_623,plain,
! [X0: $i] : reflexive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f1576]) ).
tcf(c_663,plain,
! [X0: $i] : transitive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f1616]) ).
tcf(c_690,plain,
! [X0: $i] :
( connected(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1644]) ).
tcf(c_721,plain,
! [X0: $i] : antisymmetric(inclusion_relation(X0)),
inference(cnf_transformation,[],[f1675]) ).
tcf(c_738,plain,
! [X0: $i] :
( well_founded_relation(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1693]) ).
tcf(c_752,negated_conjecture,
~ well_ordering(inclusion_relation(sK148)),
inference(cnf_transformation,[],[f1708]) ).
tcf(c_753,negated_conjecture,
ordinal(sK148),
inference(cnf_transformation,[],[f1707]) ).
tcf(c_31043,definition,
iPr_def_12 = inclusion_relation(sK148),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_31044,negated_conjecture,
ordinal(sK148),
inference(demodulation,[status(thm)],[c_753]) ).
tcf(c_31045,negated_conjecture,
~ well_ordering(iPr_def_12),
inference(demodulation,[status(thm)],[c_752,c_31043]) ).
tcf(c_43081,plain,
relation(iPr_def_12),
inference(superposition,[status(thm)],[c_31043,c_340]) ).
tcf(c_43082,plain,
reflexive(iPr_def_12),
inference(superposition,[status(thm)],[c_31043,c_623]) ).
tcf(c_43083,plain,
transitive(iPr_def_12),
inference(superposition,[status(thm)],[c_31043,c_663]) ).
tcf(c_43084,plain,
antisymmetric(iPr_def_12),
inference(superposition,[status(thm)],[c_31043,c_721]) ).
tcf(c_43364,plain,
( connected(iPr_def_12)
| ~ ordinal(sK148) ),
inference(superposition,[status(thm)],[c_31043,c_690]) ).
tcf(c_43365,plain,
connected(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_43364,c_31044]) ).
tcf(c_43370,plain,
( well_founded_relation(iPr_def_12)
| ~ ordinal(sK148) ),
inference(superposition,[status(thm)],[c_31043,c_738]) ).
tcf(c_43371,plain,
well_founded_relation(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_43370,c_31044]) ).
tcf(c_46897,plain,
( well_ordering(iPr_def_12)
| ~ reflexive(iPr_def_12)
| ~ well_founded_relation(iPr_def_12)
| ~ transitive(iPr_def_12)
| ~ connected(iPr_def_12)
| ~ antisymmetric(iPr_def_12)
| ~ relation(iPr_def_12) ),
inference(instantiation,[status(thm)],[c_254]) ).
tcf(c_46898,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_46897,c_43371,c_43365,c_43084,c_43083,c_43082,c_43081,c_31045]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU275+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 13:30:18 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 4.67/2.28 % SZS status Started for theBenchmark.p
% 4.67/2.28 % SZS status Theorem for theBenchmark.p
% 4.67/2.28
% 4.67/2.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.67/2.28
% 4.67/2.28 % ------ iProver source info
% 4.67/2.28
% 4.67/2.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.67/2.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.67/2.28 % git: non_committed_changes: false
% 4.67/2.28
% 4.67/2.28 % ------ Parsing...
% 4.67/2.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.67/2.28
% 4.67/2.28 % ------ Preprocessing... sup_sim: 69 sf_s rm: 6 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 4.67/2.28
% 4.67/2.28 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.67/2.28
% 4.67/2.28 % ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 0 0s sf_e
% 4.67/2.28 % ------ Proving...
% 4.67/2.28 % ------ Problem Properties
% 4.67/2.28
% 4.67/2.28 %
% 4.67/2.28 % clauses 656
% 4.67/2.28 % conjectures 2
% 4.67/2.28 % EPR 101
% 4.67/2.28 % Horn 512
% 4.67/2.28 % unary 92
% 4.67/2.28 % binary 176
% 4.67/2.28 % lits 1940
% 4.67/2.28 % lits eq 306
% 4.67/2.28 % fd_pure 0
% 4.67/2.28 % fd_pseudo 0
% 4.67/2.28 % fd_cond 21
% 4.67/2.28 % fd_pseudo_cond 103
% 4.67/2.28 % AC symbols 0
% 4.67/2.28
% 4.67/2.28 % ------ Schedule dynamic 5 is on
% 4.67/2.28
% 4.67/2.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.67/2.28
% 4.67/2.28
% 4.67/2.28 % ------
% 4.67/2.28 % Current options:
% 4.67/2.28 % ------
% 4.67/2.28
% 4.67/2.28
% 4.67/2.28 %
% 4.67/2.28
% 4.67/2.28 % ------ Proving...
% 4.67/2.28 %
% 4.67/2.28
% 4.67/2.28 % SZS status Theorem for theBenchmark.p
% 4.67/2.28
% 4.67/2.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.67/2.28
% 4.67/2.28
%------------------------------------------------------------------------------