%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU275+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 02:56:27 PM UTC 2026
% Result : Theorem 1.19s 1.48s
% Output : CNFRefutation 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 19 unt; 0 def)
% Number of atoms : 111 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 118 ( 48 ~; 43 |; 20 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 9 ( 8 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 32 ( 0 sgn 31 !; 1 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( relation(X0)
=> ( well_ordering(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_wellord1) ).
fof(f4,axiom,
! [X0] : relation(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(f6,axiom,
! [X0] : reflexive(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_wellord2) ).
fof(f7,axiom,
! [X0] : transitive(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_wellord2) ).
fof(f8,axiom,
! [X0] :
( ordinal(X0)
=> connected(inclusion_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_wellord2) ).
fof(f9,axiom,
! [X0] : antisymmetric(inclusion_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_wellord2) ).
fof(f10,axiom,
! [X0] :
( ordinal(X0)
=> well_founded_relation(inclusion_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_wellord2) ).
fof(f11,conjecture,
! [X0] :
( ordinal(X0)
=> well_ordering(inclusion_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_wellord2) ).
fof(f12,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> well_ordering(inclusion_relation(X0)) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f16,plain,
! [X0] :
( ~ relation(X0)
| ( well_ordering(X0)
<=> ( well_founded_relation(X0)
& connected(X0)
& antisymmetric(X0)
& transitive(X0)
& reflexive(X0) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f17,plain,
! [X0] :
( ~ ordinal(X0)
| connected(inclusion_relation(X0)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f18,plain,
! [X0] :
( ~ ordinal(X0)
| well_founded_relation(inclusion_relation(X0)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f19,plain,
? [X0] :
( ordinal(X0)
& ~ well_ordering(inclusion_relation(X0)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f20,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,[],[f16]) ).
fof(f21,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,[],[f20]) ).
fof(f23,plain,
( ordinal(sK1)
& ~ well_ordering(inclusion_relation(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f19]) ).
fof(f32,plain,
! [X0] :
( ~ relation(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0)
| well_ordering(X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f33,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f37,plain,
! [X0] : reflexive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f38,plain,
! [X0] : transitive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f39,plain,
! [X0] :
( ~ ordinal(X0)
| connected(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f40,plain,
! [X0] : antisymmetric(inclusion_relation(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f41,plain,
! [X0] :
( ~ ordinal(X0)
| well_founded_relation(inclusion_relation(X0)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f42,plain,
ordinal(sK1),
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
~ well_ordering(inclusion_relation(sK1)),
inference(cnf_transformation,[],[f23]) ).
tcf(c_52,plain,
! [X0: $i] :
( well_ordering(X0)
| ~ relation(X0)
| ~ well_founded_relation(X0)
| ~ connected(X0)
| ~ antisymmetric(X0)
| ~ transitive(X0)
| ~ reflexive(X0) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_58,plain,
! [X0: $i] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f33]) ).
tcf(c_62,plain,
! [X0: $i] : reflexive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f37]) ).
tcf(c_63,plain,
! [X0: $i] : transitive(inclusion_relation(X0)),
inference(cnf_transformation,[],[f38]) ).
tcf(c_64,plain,
! [X0: $i] :
( connected(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_65,plain,
! [X0: $i] : antisymmetric(inclusion_relation(X0)),
inference(cnf_transformation,[],[f40]) ).
tcf(c_66,plain,
! [X0: $i] :
( well_founded_relation(inclusion_relation(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_67,negated_conjecture,
~ well_ordering(inclusion_relation(sK1)),
inference(cnf_transformation,[],[f43]) ).
tcf(c_68,negated_conjecture,
ordinal(sK1),
inference(cnf_transformation,[],[f42]) ).
tcf(c_175,plain,
well_founded_relation(inclusion_relation(sK1)),
inference(resolution,[status(thm)],[c_66,c_68]) ).
tcf(c_179,plain,
connected(inclusion_relation(sK1)),
inference(resolution,[status(thm)],[c_64,c_68]) ).
tcf(c_188,plain,
! [X0: $i] :
( well_ordering(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0))
| ~ well_founded_relation(inclusion_relation(X0))
| ~ connected(inclusion_relation(X0))
| ~ antisymmetric(inclusion_relation(X0))
| ~ transitive(inclusion_relation(X0)) ),
inference(resolution,[status(thm)],[c_52,c_62]) ).
tcf(c_190,plain,
! [X0: $i] :
( well_ordering(inclusion_relation(X0))
| ~ connected(inclusion_relation(X0))
| ~ well_founded_relation(inclusion_relation(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_188,c_65,c_63,c_58,c_188]) ).
tcf(c_191,plain,
! [X0: $i] :
( well_ordering(inclusion_relation(X0))
| ~ well_founded_relation(inclusion_relation(X0))
| ~ connected(inclusion_relation(X0)) ),
inference(renaming,[status(thm)],[c_190]) ).
tcf(c_230,plain,
( well_ordering(inclusion_relation(sK1))
| ~ well_founded_relation(inclusion_relation(sK1)) ),
inference(resolution,[status(thm)],[c_191,c_179]) ).
tcf(c_231,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_230,c_175,c_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU275+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.57 % Computer : n020.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Thu Sep 24 13:31:19 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.61 Running first-order theorem proving
% 0.13/0.61 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.62
% 0.13/0.62 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.62
% 0.13/0.62 % Detected problem language: tptp
% 0.13/0.64 % Proving...
% 1.19/1.48 % SZS status Started for theBenchmark.p
% 1.19/1.48 % SZS status Theorem for theBenchmark.p
% 1.19/1.48
% 1.19/1.48 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.19/1.48
% 1.19/1.48 % ------ iProver source info
% 1.19/1.48
% 1.19/1.48 % git: date: 2026-07-19 20:42:38 +0200
% 1.19/1.48 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.19/1.48 % git: non_committed_changes: false
% 1.19/1.48
% 1.19/1.48 % ------ Parsing...
% 1.19/1.48 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.19/1.48
% 1.19/1.48 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s%
% 1.19/1.48
% 1.19/1.48 % SZS status Theorem for theBenchmark.p
% 1.19/1.48
% 1.19/1.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.19/1.48
% 1.19/1.48
%------------------------------------------------------------------------------