%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU234+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n005.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 02:56:17 PM UTC 2026
% Result : Theorem 2.77s 1.27s
% Output : CNFRefutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 67 ( 9 unt; 0 def)
% Number of atoms : 216 ( 19 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 240 ( 91 ~; 99 |; 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 : 79 ( 0 sgn 72 !; 7 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f9,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(f10,axiom,
! [X0] :
( ordinal(X0)
<=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_ordinal1) ).
fof(f31,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(f33,conjecture,
! [X0] :
( ! [X1] :
( in(X1,X0)
=> ( subset(X1,X0)
& ordinal(X1) ) )
=> ordinal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_ordinal1) ).
fof(f34,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( in(X1,X0)
=> ( subset(X1,X0)
& ordinal(X1) ) )
=> ordinal(X0) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f60,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f61,plain,
! [X0] :
( epsilon_connected(X0)
<=> ! [X1,X2] :
( in(X2,X1)
| X1 = X2
| in(X1,X2)
| ~ in(X2,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f63,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f64,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ) ),
inference(flattening,[],[f63]) ).
fof(f67,plain,
? [X0] :
( ! [X1] :
( ~ in(X1,X0)
| ( subset(X1,X0)
& ordinal(X1) ) )
& ~ ordinal(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f74,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,[],[f60]) ).
fof(f75,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ( in(sK0(X0),X0)
& ~ subset(sK0(X0),X0) )
| epsilon_transitive(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f75]) ).
fof(f77,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,[],[f61]) ).
fof(f78,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,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ( ~ epsilon_connected(X0)
| ! [X3,X4] :
( in(X4,X3)
| X3 = X4
| in(X3,X4)
| ~ in(X4,X0)
| ~ in(X3,X0) ) )
& ( ( ~ in(sK2(X0),sK1(X0))
& sK1(X0) != sK2(X0)
& ~ in(sK1(X0),sK2(X0))
& in(sK2(X0),X0)
& in(sK1(X0),X0) )
| epsilon_connected(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f78]) ).
fof(f80,plain,
! [X0] :
( ( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) )
& ( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f81,plain,
! [X0] :
( ( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) )
& ( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ) ),
inference(flattening,[],[f80]) ).
fof(f96,plain,
( ! [X1] :
( ~ in(X1,sK17)
| ( subset(X1,sK17)
& ordinal(X1) ) )
& ~ ordinal(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X0,sK17)],[f67]) ).
fof(f110,plain,
! [X0] :
( in(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f111,plain,
! [X0] :
( ~ subset(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f113,plain,
! [X0] :
( ~ in(sK2(X0),sK1(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f114,plain,
! [X0] :
( sK1(X0) != sK2(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f115,plain,
! [X0] :
( ~ in(sK1(X0),sK2(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f116,plain,
! [X0] :
( in(sK2(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f117,plain,
! [X0] :
( in(sK1(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f120,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f166,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f168,plain,
! [X1] :
( ~ in(X1,sK17)
| subset(X1,sK17) ),
inference(cnf_transformation,[],[f96]) ).
fof(f169,plain,
! [X1] :
( ~ in(X1,sK17)
| ordinal(X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f170,plain,
~ ordinal(sK17),
inference(cnf_transformation,[],[f96]) ).
tcf(c_58,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ subset(sK0(X0),X0) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_59,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK0(X0),X0) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_61,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK1(X0),X0) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_62,plain,
! [X0: $i] :
( epsilon_connected(X0)
| in(sK2(X0),X0) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_63,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK1(X0),sK2(X0)) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_64,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ( sK1(X0) != sK2(X0) ) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_65,plain,
! [X0: $i] :
( epsilon_connected(X0)
| ~ in(sK2(X0),sK1(X0)) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_67,plain,
! [X0: $i] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| ( X0 = X1 )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_117,negated_conjecture,
~ ordinal(sK17),
inference(cnf_transformation,[],[f170]) ).
tcf(c_118,negated_conjecture,
! [X0: $i] :
( ordinal(X0)
| ~ in(X0,sK17) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_119,negated_conjecture,
! [X0: $i] :
( subset(X0,sK17)
| ~ in(X0,sK17) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_174,plain,
! [X0: $i] :
( ~ subset(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(prop_impl_just,[status(thm)],[c_58]) ).
tcf(c_175,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ subset(sK0(X0),X0) ),
inference(renaming,[status(thm)],[c_174]) ).
tcf(c_176,plain,
! [X0: $i] :
( in(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(prop_impl_just,[status(thm)],[c_59]) ).
tcf(c_177,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK0(X0),X0) ),
inference(renaming,[status(thm)],[c_176]) ).
tcf(c_204,plain,
! [X0: $i] :
( subset(X0,sK17)
| ~ in(X0,sK17) ),
inference(prop_impl_just,[status(thm)],[c_119]) ).
tcf(c_935,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| ~ in(X1,sK17)
| ( X0 != sK17 )
| ( sK0(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_175,c_204]) ).
tcf(c_936,plain,
( epsilon_transitive(sK17)
| ~ in(sK0(sK17),sK17) ),
inference(unflattening,[status(thm)],[c_935]) ).
tcf(c_941,plain,
epsilon_transitive(sK17),
inference(forward_subsumption_resolution,[status(thm)],[c_936,c_177]) ).
tcf(c_2522,negated_conjecture,
! [X0: $i] :
( ordinal(X0)
| ~ in(X0,sK17) ),
inference(demodulation,[status(thm)],[c_118]) ).
tcf(c_2523,negated_conjecture,
~ ordinal(sK17),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_3337,plain,
( epsilon_connected(sK17)
| ordinal(sK1(sK17)) ),
inference(superposition,[status(thm)],[c_61,c_2522]) ).
tcf(c_3399,plain,
( epsilon_connected(sK17)
| ordinal(sK2(sK17)) ),
inference(superposition,[status(thm)],[c_62,c_2522]) ).
tcf(c_3426,plain,
( epsilon_transitive(sK17)
| ordinal(sK0(sK17)) ),
inference(superposition,[status(thm)],[c_59,c_2522]) ).
tcf(c_3468,plain,
epsilon_transitive(sK17),
inference(global_subsumption_just,[status(thm)],[c_3426,c_941]) ).
tcf(c_3545,plain,
( ordinal(sK17)
| ~ epsilon_connected(sK17) ),
inference(superposition,[status(thm)],[c_3468,c_67]) ).
tcf(c_3548,plain,
~ epsilon_connected(sK17),
inference(forward_subsumption_resolution,[status(thm)],[c_3545,c_2523]) ).
tcf(c_3552,plain,
ordinal(sK2(sK17)),
inference(backward_subsumption_resolution,[status(thm)],[c_3399,c_3548]) ).
tcf(c_3555,plain,
ordinal(sK1(sK17)),
inference(backward_subsumption_resolution,[status(thm)],[c_3337,c_3548]) ).
tcf(c_4176,plain,
( epsilon_connected(sK17)
| ( sK1(sK17) != sK2(sK17) ) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_4178,plain,
( epsilon_connected(sK17)
| ~ in(sK2(sK17),sK1(sK17)) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_4179,plain,
( epsilon_connected(sK17)
| ~ in(sK1(sK17),sK2(sK17)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_4714,plain,
( in(sK2(sK17),sK1(sK17))
| in(sK1(sK17),sK2(sK17))
| ( sK1(sK17) = sK2(sK17) )
| ~ ordinal(sK2(sK17))
| ~ ordinal(sK1(sK17)) ),
inference(instantiation,[status(thm)],[c_115]) ).
tcf(c_4715,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4714,c_4176,c_4178,c_4179,c_3548,c_3552,c_3555]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU234+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 13:20:18 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 2.77/1.27 % SZS status Started for theBenchmark.p
% 2.77/1.27 % SZS status Theorem for theBenchmark.p
% 2.77/1.27
% 2.77/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.77/1.27
% 2.77/1.27 % ------ iProver source info
% 2.77/1.27
% 2.77/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.77/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.77/1.27 % git: non_committed_changes: false
% 2.77/1.27
% 2.77/1.27 % ------ Parsing...
% 2.77/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.77/1.27
% 2.77/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 22 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 2.77/1.27
% 2.77/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.77/1.27
% 2.77/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.77/1.27 % ------ Proving...
% 2.77/1.27 % ------ Problem Properties
% 2.77/1.27
% 2.77/1.27 %
% 2.77/1.27 % clauses 51
% 2.77/1.27 % conjectures 3
% 2.77/1.27 % EPR 41
% 2.77/1.27 % Horn 45
% 2.77/1.27 % unary 23
% 2.77/1.27 % binary 20
% 2.77/1.27 % lits 92
% 2.77/1.27 % lits eq 5
% 2.77/1.27 % fd_pure 0
% 2.77/1.27 % fd_pseudo 0
% 2.77/1.27 % fd_cond 1
% 2.77/1.27 % fd_pseudo_cond 3
% 2.77/1.27 % AC symbols 0
% 2.77/1.27
% 2.77/1.27 % ------ Schedule dynamic 5 is on
% 2.77/1.27
% 2.77/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.77/1.27
% 2.77/1.27
% 2.77/1.27 % ------
% 2.77/1.27 % Current options:
% 2.77/1.27 % ------
% 2.77/1.27
% 2.77/1.27
% 2.77/1.27 %
% 2.77/1.27
% 2.77/1.27 % ------ Proving...
% 2.77/1.27 %
% 2.77/1.27
% 2.77/1.27 % SZS status Theorem for theBenchmark.p
% 2.77/1.27
% 2.77/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.77/1.28
% 2.77/1.28
%------------------------------------------------------------------------------