%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU234+2 : 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 : 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 02:56:16 PM UTC 2026
% Result : Theorem 10.85s 7.30s
% Output : CNFRefutation 10.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 60 ( 8 unt; 0 def)
% Number of atoms : 201 ( 17 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 226 ( 85 ~; 91 |; 38 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 73 ( 0 sgn 66 !; 7 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f27,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f33,axiom,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
~ ( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).
fof(f38,axiom,
! [X0] :
( ordinal(X0)
<=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_ordinal1) ).
fof(f191,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ~ ( ~ in(X1,X0)
& X0 != X1
& ~ in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(f200,conjecture,
! [X0] :
( ! [X1] :
( in(X1,X0)
=> ( subset(X1,X0)
& ordinal(X1) ) )
=> ordinal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_ordinal1) ).
fof(f201,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( in(X1,X0)
=> ( subset(X1,X0)
& ordinal(X1) ) )
=> ordinal(X0) ),
inference(negated_conjecture,[status(cth)],[f200]) ).
fof(f305,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f308,plain,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f437,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ) ),
inference(ennf_transformation,[],[f191]) ).
fof(f438,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ) ),
inference(flattening,[],[f437]) ).
fof(f448,plain,
? [X0] :
( ! [X1] :
( ~ in(X1,X0)
| ( subset(X1,X0)
& ordinal(X1) ) )
& ~ ordinal(X0) ),
inference(ennf_transformation,[],[f201]) ).
fof(f571,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f305]) ).
fof(f572,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(rectify,[],[f571]) ).
fof(f573,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ( in(sK27(X0),X0)
& ~ subset(sK27(X0),X0) )
| epsilon_transitive(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(X1,sK27(X0))],[f572]) ).
fof(f589,plain,
! [X0] :
( ( ~ epsilon_connected(X0)
| ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) )
& ( ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) )
| epsilon_connected(X0) ) ),
inference(nnf_transformation,[],[f308]) ).
fof(f590,plain,
! [X0] :
( ( ~ epsilon_connected(X0)
| ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) ) )
& ( ? [X1,X2] :
( ~ in(X2,X1)
& X1 != X2
& ~ in(X1,X2)
& in(X2,X0)
& in(X1,X0) )
| epsilon_connected(X0) ) ),
inference(rectify,[],[f589]) ).
fof(f591,plain,
! [X0] :
( ( ~ epsilon_connected(X0)
| ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) ) )
& ( ( ~ in(sK38(X0),sK37(X0))
& sK37(X0) != sK38(X0)
& ~ in(sK37(X0),sK38(X0))
& in(sK38(X0),X0)
& in(sK37(X0),X0) )
| epsilon_connected(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37,sK38]),skolemize(X1,sK37(X0)),skolemize(X2,sK38(X0))],[f590]) ).
fof(f603,plain,
! [X0] :
( ( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) )
& ( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f604,plain,
! [X0] :
( ( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) )
& ( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ) ),
inference(flattening,[],[f603]) ).
fof(f674,plain,
( ! [X1] :
( ~ in(X1,sK85)
| ( subset(X1,sK85)
& ordinal(X1) ) )
& ~ ordinal(sK85) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(X0,sK85)],[f448]) ).
fof(f806,plain,
! [X0] :
( in(sK27(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f573]) ).
fof(f807,plain,
! [X0] :
( ~ subset(sK27(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f573]) ).
fof(f837,plain,
! [X0] :
( ~ in(sK38(X0),sK37(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f591]) ).
fof(f838,plain,
! [X0] :
( sK37(X0) != sK38(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f591]) ).
fof(f839,plain,
! [X0] :
( ~ in(sK37(X0),sK38(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f591]) ).
fof(f840,plain,
! [X0] :
( in(sK38(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f591]) ).
fof(f841,plain,
! [X0] :
( in(sK37(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f591]) ).
fof(f860,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f604]) ).
fof(f1100,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ),
inference(cnf_transformation,[],[f438]) ).
fof(f1112,plain,
! [X1] :
( ~ in(X1,sK85)
| subset(X1,sK85) ),
inference(cnf_transformation,[],[f674]) ).
fof(f1113,plain,
! [X1] :
( ~ in(X1,sK85)
| ordinal(X1) ),
inference(cnf_transformation,[],[f674]) ).
fof(f1114,plain,
~ ordinal(sK85),
inference(cnf_transformation,[],[f674]) ).
tcf(c_139,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ subset(sK27(X0),X0) ),
inference(cnf_transformation,[],[f807]) ).
tcf(c_140,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK27(X0),X0) ),
inference(cnf_transformation,[],[f806]) ).
tcf(c_170,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK37(X0),X0) ),
inference(cnf_transformation,[],[f841]) ).
tcf(c_171,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK38(X0),X0) ),
inference(cnf_transformation,[],[f840]) ).
tcf(c_172,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK37(X0),sK38(X0)) ),
inference(cnf_transformation,[],[f839]) ).
tcf(c_173,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK37(X0) != sK38(X0) ) ),
inference(cnf_transformation,[],[f838]) ).
tcf(c_174,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK38(X0),sK37(X0)) ),
inference(cnf_transformation,[],[f837]) ).
tcf(c_192,plain,
! [X0: $i] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f860]) ).
tcf(c_433,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| ( X0 = X1 )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f1100]) ).
tcf(c_445,negated_conjecture,
~ ordinal(sK85),
inference(cnf_transformation,[],[f1114]) ).
tcf(c_446,negated_conjecture,
! [X0: $i] :
( ordinal(X0)
| ~ in(X0,sK85) ),
inference(cnf_transformation,[],[f1113]) ).
tcf(c_447,negated_conjecture,
! [X0: $i] :
( subset(X0,sK85)
| ~ in(X0,sK85) ),
inference(cnf_transformation,[],[f1112]) ).
tcf(c_14960,negated_conjecture,
! [X0: $i] :
( subset(X0,sK85)
| ~ in(X0,sK85) ),
inference(demodulation,[status(thm)],[c_447]) ).
tcf(c_14961,negated_conjecture,
! [X0: $i] :
( ordinal(X0)
| ~ in(X0,sK85) ),
inference(demodulation,[status(thm)],[c_446]) ).
tcf(c_14962,negated_conjecture,
~ ordinal(sK85),
inference(demodulation,[status(thm)],[c_445]) ).
tcf(c_23100,plain,
( epsilon_transitive(sK85)
| subset(sK27(sK85),sK85) ),
inference(superposition,[status(thm)],[c_140,c_14960]) ).
tcf(c_23123,plain,
( epsilon_connected(sK85)
| ordinal(sK37(sK85)) ),
inference(superposition,[status(thm)],[c_170,c_14961]) ).
tcf(c_23134,plain,
( epsilon_connected(sK85)
| ordinal(sK38(sK85)) ),
inference(superposition,[status(thm)],[c_171,c_14961]) ).
tcf(c_23349,plain,
epsilon_transitive(sK85),
inference(backward_subsumption_resolution,[status(thm)],[c_23100,c_139]) ).
tcf(c_23926,plain,
( ordinal(sK85)
| ~ epsilon_connected(sK85) ),
inference(superposition,[status(thm)],[c_23349,c_192]) ).
tcf(c_23933,plain,
~ epsilon_connected(sK85),
inference(forward_subsumption_resolution,[status(thm)],[c_23926,c_14962]) ).
tcf(c_23938,plain,
ordinal(sK38(sK85)),
inference(backward_subsumption_resolution,[status(thm)],[c_23134,c_23933]) ).
tcf(c_23940,plain,
ordinal(sK37(sK85)),
inference(backward_subsumption_resolution,[status(thm)],[c_23123,c_23933]) ).
tcf(c_33824,plain,
( epsilon_connected(sK85)
| ( sK37(sK85) != sK38(sK85) ) ),
inference(instantiation,[status(thm)],[c_173]) ).
tcf(c_33826,plain,
( epsilon_connected(sK85)
| ~ in(sK38(sK85),sK37(sK85)) ),
inference(instantiation,[status(thm)],[c_174]) ).
tcf(c_33827,plain,
( epsilon_connected(sK85)
| ~ in(sK37(sK85),sK38(sK85)) ),
inference(instantiation,[status(thm)],[c_172]) ).
tcf(c_47046,plain,
( in(sK38(sK85),sK37(sK85))
| in(sK37(sK85),sK38(sK85))
| ( sK37(sK85) = sK38(sK85) )
| ~ ordinal(sK38(sK85))
| ~ ordinal(sK37(sK85)) ),
inference(instantiation,[status(thm)],[c_433]) ).
tcf(c_47055,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_47046,c_33824,c_33826,c_33827,c_23933,c_23938,c_23940]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU234+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.38 % Computer : n014.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Thu Sep 24 13:20:10 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 10.85/7.30 % SZS status Started for theBenchmark.p
% 10.85/7.30 % SZS status Theorem for theBenchmark.p
% 10.85/7.30
% 10.85/7.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.85/7.30
% 10.85/7.30 % ------ iProver source info
% 10.85/7.30
% 10.85/7.30 % git: date: 2026-07-19 20:42:38 +0200
% 10.85/7.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.85/7.30 % git: non_committed_changes: false
% 10.85/7.30
% 10.85/7.30 % ------ Parsing...
% 10.85/7.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.85/7.30
% 10.85/7.30 % ------ Preprocessing... sup_sim: 41 sf_s rm: 6 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 10.85/7.30
% 10.85/7.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.85/7.30
% 10.85/7.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.85/7.30 % ------ Proving...
% 10.85/7.30 % ------ Problem Properties
% 10.85/7.30
% 10.85/7.30 %
% 10.85/7.30 % clauses 448
% 10.85/7.30 % conjectures 3
% 10.85/7.30 % EPR 80
% 10.85/7.30 % Horn 361
% 10.85/7.30 % unary 81
% 10.85/7.30 % binary 129
% 10.85/7.30 % lits 1260
% 10.85/7.30 % lits eq 234
% 10.85/7.30 % fd_pure 0
% 10.85/7.30 % fd_pseudo 0
% 10.85/7.30 % fd_cond 14
% 10.85/7.30 % fd_pseudo_cond 92
% 10.85/7.30 % AC symbols 0
% 10.85/7.30
% 10.85/7.30 % ------ Schedule dynamic 5 is on
% 10.85/7.30
% 10.85/7.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.85/7.30
% 10.85/7.30
% 10.85/7.30 % ------
% 10.85/7.30 % Current options:
% 10.85/7.30 % ------
% 10.85/7.30
% 10.85/7.30
% 10.85/7.30 %
% 10.85/7.30
% 10.85/7.30 % ------ Proving...
% 10.85/7.30 %
% 10.85/7.30
% 10.85/7.30 % SZS status Theorem for theBenchmark.p
% 10.85/7.30
% 10.85/7.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.85/7.30
% 10.85/7.30
%------------------------------------------------------------------------------