%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU234+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 : n008.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 2.58s 11.32s
% Output : CNFRefutation 2.58s
% 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(f33,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(f35,conjecture,
! [X0] :
( ! [X1] :
( in(X1,X0)
=> ( subset(X1,X0)
& ordinal(X1) ) )
=> ordinal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t31_ordinal1) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ! [X1] :
( in(X1,X0)
=> ( subset(X1,X0)
& ordinal(X1) ) )
=> ordinal(X0) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f61,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( ~ in(X1,X0)
| subset(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f62,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(f64,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f65,plain,
! [X0] :
( ~ ordinal(X0)
| ! [X1] :
( ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ) ),
inference(flattening,[],[f64]) ).
fof(f68,plain,
? [X0] :
( ! [X1] :
( ~ in(X1,X0)
| ( subset(X1,X0)
& ordinal(X1) ) )
& ~ ordinal(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f75,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,[],[f61]) ).
fof(f76,plain,
! [X0] :
( ( ~ epsilon_transitive(X0)
| ! [X2] :
( ~ in(X2,X0)
| subset(X2,X0) ) )
& ( ? [X1] :
( in(X1,X0)
& ~ subset(X1,X0) )
| epsilon_transitive(X0) ) ),
inference(rectify,[],[f75]) ).
fof(f77,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))],[f76]) ).
fof(f78,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,[],[f62]) ).
fof(f79,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,[],[f78]) ).
fof(f80,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))],[f79]) ).
fof(f81,plain,
! [X0] :
( ( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) )
& ( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f82,plain,
! [X0] :
( ( ~ ordinal(X0)
| ( epsilon_connected(X0)
& epsilon_transitive(X0) ) )
& ( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ) ),
inference(flattening,[],[f81]) ).
fof(f96,plain,
( ! [X1] :
( ~ in(X1,sK16)
| ( subset(X1,sK16)
& ordinal(X1) ) )
& ~ ordinal(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X0,sK16)],[f68]) ).
fof(f110,plain,
! [X0] :
( in(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f111,plain,
! [X0] :
( ~ subset(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f113,plain,
! [X0] :
( ~ in(sK2(X0),sK1(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f114,plain,
! [X0] :
( sK1(X0) != sK2(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f115,plain,
! [X0] :
( ~ in(sK1(X0),sK2(X0))
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f116,plain,
! [X0] :
( in(sK2(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f117,plain,
! [X0] :
( in(sK1(X0),X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f120,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f164,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ ordinal(X1)
| in(X1,X0)
| X0 = X1
| in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f166,plain,
! [X1] :
( ~ in(X1,sK16)
| subset(X1,sK16) ),
inference(cnf_transformation,[],[f96]) ).
fof(f167,plain,
! [X1] :
( ~ in(X1,sK16)
| ordinal(X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f168,plain,
~ ordinal(sK16),
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_113,plain,
! [X0: $i,X1: $i] :
( in(X1,X0)
| in(X0,X1)
| ( X0 = X1 )
| ~ ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_115,negated_conjecture,
~ ordinal(sK16),
inference(cnf_transformation,[],[f168]) ).
tcf(c_116,negated_conjecture,
! [X0: $i] :
( ordinal(X0)
| ~ in(X0,sK16) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_117,negated_conjecture,
! [X0: $i] :
( subset(X0,sK16)
| ~ in(X0,sK16) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_172,plain,
! [X0: $i] :
( ~ subset(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(prop_impl_just,[status(thm)],[c_58]) ).
tcf(c_173,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| ~ subset(sK0(X0),X0) ),
inference(renaming,[status(thm)],[c_172]) ).
tcf(c_174,plain,
! [X0: $i] :
( in(sK0(X0),X0)
| epsilon_transitive(X0) ),
inference(prop_impl_just,[status(thm)],[c_59]) ).
tcf(c_175,plain,
! [X0: $i] :
( epsilon_transitive(X0)
| in(sK0(X0),X0) ),
inference(renaming,[status(thm)],[c_174]) ).
tcf(c_202,plain,
! [X0: $i] :
( subset(X0,sK16)
| ~ in(X0,sK16) ),
inference(prop_impl_just,[status(thm)],[c_117]) ).
tcf(c_927,plain,
! [X0: $i,X1: $i] :
( epsilon_transitive(X0)
| ~ in(X1,sK16)
| ( X0 != sK16 )
| ( sK0(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_173,c_202]) ).
tcf(c_928,plain,
( epsilon_transitive(sK16)
| ~ in(sK0(sK16),sK16) ),
inference(unflattening,[status(thm)],[c_927]) ).
tcf(c_933,plain,
epsilon_transitive(sK16),
inference(forward_subsumption_resolution,[status(thm)],[c_928,c_175]) ).
tcf(c_2514,negated_conjecture,
! [X0: $i] :
( ordinal(X0)
| ~ in(X0,sK16) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_2515,negated_conjecture,
~ ordinal(sK16),
inference(demodulation,[status(thm)],[c_115]) ).
tcf(c_3329,plain,
( epsilon_connected(sK16)
| ordinal(sK1(sK16)) ),
inference(superposition,[status(thm)],[c_61,c_2514]) ).
tcf(c_3391,plain,
( epsilon_connected(sK16)
| ordinal(sK2(sK16)) ),
inference(superposition,[status(thm)],[c_62,c_2514]) ).
tcf(c_3418,plain,
( epsilon_transitive(sK16)
| ordinal(sK0(sK16)) ),
inference(superposition,[status(thm)],[c_59,c_2514]) ).
tcf(c_3460,plain,
epsilon_transitive(sK16),
inference(global_subsumption_just,[status(thm)],[c_3418,c_933]) ).
tcf(c_3537,plain,
( ordinal(sK16)
| ~ epsilon_connected(sK16) ),
inference(superposition,[status(thm)],[c_3460,c_67]) ).
tcf(c_3540,plain,
~ epsilon_connected(sK16),
inference(forward_subsumption_resolution,[status(thm)],[c_3537,c_2515]) ).
tcf(c_3544,plain,
ordinal(sK2(sK16)),
inference(backward_subsumption_resolution,[status(thm)],[c_3391,c_3540]) ).
tcf(c_3547,plain,
ordinal(sK1(sK16)),
inference(backward_subsumption_resolution,[status(thm)],[c_3329,c_3540]) ).
tcf(c_4168,plain,
( epsilon_connected(sK16)
| ( sK1(sK16) != sK2(sK16) ) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_4170,plain,
( epsilon_connected(sK16)
| ~ in(sK2(sK16),sK1(sK16)) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_4171,plain,
( epsilon_connected(sK16)
| ~ in(sK1(sK16),sK2(sK16)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_4706,plain,
( in(sK2(sK16),sK1(sK16))
| in(sK1(sK16),sK2(sK16))
| ( sK1(sK16) = sK2(sK16) )
| ~ ordinal(sK2(sK16))
| ~ ordinal(sK1(sK16)) ),
inference(instantiation,[status(thm)],[c_113]) ).
tcf(c_4707,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4706,c_4168,c_4170,c_4171,c_3540,c_3544,c_3547]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU234+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/10.41 % Computer : n008.cluster.edu
% 0.14/10.41 % Model : x86_64 x86_64
% 0.14/10.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/10.41 % Memory : 8046.5625MB
% 0.14/10.41 % OS : Linux 6.8.0-71-generic
% 0.14/10.41 % CPULimit : 300
% 0.14/10.41 % WCLimit : 300
% 0.14/10.41 % DateTime : Thu Sep 24 13:20:55 UTC 2026
% 0.14/10.41 % CPUTime :
% 0.14/10.41 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/10.45 Running first-order theorem proving
% 0.14/10.45 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
% 0.14/10.46
% 0.14/10.46 % ======== iProver multi-core TPTP/SMT =========
% 0.14/10.46
% 0.14/10.46 % Detected problem language: tptp
% 0.14/10.48 % Proving...
% 2.58/11.32 % SZS status Started for theBenchmark.p
% 2.58/11.32 % SZS status Theorem for theBenchmark.p
% 2.58/11.32
% 2.58/11.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.58/11.32
% 2.58/11.32 % ------ iProver source info
% 2.58/11.32
% 2.58/11.32 % git: date: 2026-07-19 20:42:38 +0200
% 2.58/11.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.58/11.32 % git: non_committed_changes: false
% 2.58/11.32
% 2.58/11.32 % ------ Parsing...
% 2.58/11.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.58/11.32
% 2.58/11.32 % ------ Preprocessing... sup_sim: 0 sf_s rm: 20 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 2.58/11.32
% 2.58/11.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.58/11.32
% 2.58/11.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.58/11.32 % ------ Proving...
% 2.58/11.32 % ------ Problem Properties
% 2.58/11.32
% 2.58/11.32 %
% 2.58/11.32 % clauses 51
% 2.58/11.32 % conjectures 3
% 2.58/11.32 % EPR 41
% 2.58/11.32 % Horn 45
% 2.58/11.32 % unary 23
% 2.58/11.32 % binary 20
% 2.58/11.32 % lits 92
% 2.58/11.32 % lits eq 5
% 2.58/11.32 % fd_pure 0
% 2.58/11.32 % fd_pseudo 0
% 2.58/11.32 % fd_cond 1
% 2.58/11.32 % fd_pseudo_cond 3
% 2.58/11.32 % AC symbols 0
% 2.58/11.32
% 2.58/11.32 % ------ Schedule dynamic 5 is on
% 2.58/11.32
% 2.58/11.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.58/11.32
% 2.58/11.32
% 2.58/11.32 % ------
% 2.58/11.32 % Current options:
% 2.58/11.32 % ------
% 2.58/11.32
% 2.58/11.32
% 2.58/11.32 %
% 2.58/11.32
% 2.58/11.32 % ------ Proving...
% 2.58/11.32 %
% 2.58/11.32
% 2.58/11.32 % SZS status Theorem for theBenchmark.p
% 2.58/11.32
% 2.58/11.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.58/11.32
% 2.58/11.32
%------------------------------------------------------------------------------