%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU165+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 : n011.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 02:55:42 PM UTC 2026
% Result : Theorem 1.19s 31.29s
% Output : CNFRefutation 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 8 unt; 0 def)
% Number of atoms : 180 ( 30 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 210 ( 79 ~; 88 |; 37 &)
% ( 5 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 139 ( 0 sgn 115 !; 24 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0,X1,X2] :
( X2 = cartesian_product2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( X3 = ordered_pair(X4,X5)
& in(X5,X1)
& in(X4,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f17,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f46,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f51,conjecture,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f52,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f85,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f110,plain,
? [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<~> ( in(X1,X3)
& in(X0,X2) ) ),
inference(ennf_transformation,[],[f52]) ).
fof(f151,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f152,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f151]) ).
fof(f153,plain,
? [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ) ),
inference(nnf_transformation,[],[f110]) ).
fof(f154,plain,
? [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ) ),
inference(flattening,[],[f153]) ).
fof(f155,plain,
( ( in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3))
| ( in(sK1,sK3)
& in(sK0,sK2) ) )
& ( ~ in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3))
| ~ in(sK1,sK3)
| ~ in(sK0,sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f154]) ).
fof(f191,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4,X5] :
( X3 = ordered_pair(X4,X5)
& in(X5,X1)
& in(X4,X0) ) )
& ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4,X5] :
( X3 = ordered_pair(X4,X5)
& in(X5,X1)
& in(X4,X0) ) )
& ( ~ in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) ) )
| X2 = cartesian_product2(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f192,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) != X2
| ! [X8] :
( ( ~ in(X8,X2)
| ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X1)
& in(X11,X0) ) )
& ( ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) )
| in(X8,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X1)
& in(X6,X0) ) )
& ( ~ in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) ) )
| X2 = cartesian_product2(X0,X1) ) ),
inference(rectify,[],[f191]) ).
fof(f193,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) != X2
| ! [X8] :
( ( ~ in(X8,X2)
| ( ordered_pair(sK18(X0,X1,X8),sK19(X0,X1,X8)) = X8
& in(sK19(X0,X1,X8),X1)
& in(sK18(X0,X1,X8),X0) ) )
& ( ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) )
| in(X8,X2) ) ) )
& ( ( ( in(sK15(X0,X1,X2),X2)
| ( sK15(X0,X1,X2) = ordered_pair(sK16(X0,X1,X2),sK17(X0,X1,X2))
& in(sK17(X0,X1,X2),X1)
& in(sK16(X0,X1,X2),X0) ) )
& ( ~ in(sK15(X0,X1,X2),X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != sK15(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) ) ) )
| X2 = cartesian_product2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17,sK18,sK19]),skolemize(X3,sK15(X0,X1,X2)),skolemize(X6,sK16(X0,X1,X2)),skolemize(X7,sK17(X0,X1,X2)),skolemize(X11,sK18(X0,X1,X8)),skolemize(X12,sK19(X0,X1,X8))],[f192]) ).
fof(f220,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f152]) ).
fof(f221,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f152]) ).
fof(f223,plain,
( in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3))
| in(sK1,sK3) ),
inference(cnf_transformation,[],[f155]) ).
fof(f224,plain,
( in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3))
| in(sK0,sK2) ),
inference(cnf_transformation,[],[f155]) ).
fof(f225,plain,
( ~ in(ordered_pair(sK0,sK1),cartesian_product2(sK2,sK3))
| ~ in(sK1,sK3)
| ~ in(sK0,sK2) ),
inference(cnf_transformation,[],[f155]) ).
fof(f264,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f85]) ).
fof(f320,plain,
! [X2,X10,X0,X1,X8,X9] :
( cartesian_product2(X0,X1) != X2
| ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0)
| in(X8,X2) ),
inference(cnf_transformation,[],[f193]) ).
fof(f326,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f357,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f326,f264]) ).
fof(f369,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f221,f357]) ).
fof(f370,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f220,f357]) ).
fof(f371,plain,
( ~ in(unordered_pair(unordered_pair(sK0,sK1),unordered_pair(sK0,sK0)),cartesian_product2(sK2,sK3))
| ~ in(sK1,sK3)
| ~ in(sK0,sK2) ),
inference(definition_unfolding,[],[f225,f357]) ).
fof(f372,plain,
( in(unordered_pair(unordered_pair(sK0,sK1),unordered_pair(sK0,sK0)),cartesian_product2(sK2,sK3))
| in(sK0,sK2) ),
inference(definition_unfolding,[],[f224,f357]) ).
fof(f373,plain,
( in(unordered_pair(unordered_pair(sK0,sK1),unordered_pair(sK0,sK0)),cartesian_product2(sK2,sK3))
| in(sK1,sK3) ),
inference(definition_unfolding,[],[f223,f357]) ).
fof(f403,plain,
! [X2,X10,X0,X1,X8,X9] :
( cartesian_product2(X0,X1) != X2
| unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)) != X8
| ~ in(X10,X1)
| ~ in(X9,X0)
| in(X8,X2) ),
inference(definition_unfolding,[],[f320,f357]) ).
fof(f433,plain,
! [X2,X10,X0,X1,X9] :
( cartesian_product2(X0,X1) != X2
| ~ in(X10,X1)
| ~ in(X9,X0)
| in(unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)),X2) ),
inference(equality_resolution,[],[f403]) ).
fof(f434,plain,
! [X10,X0,X1,X9] :
( ~ in(X10,X1)
| ~ in(X9,X0)
| in(unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)),cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f433]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f369]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f370]) ).
tcf(c_65,negated_conjecture,
( ~ in(sK1,sK3)
| ~ in(sK0,sK2)
| ~ in(unordered_pair(unordered_pair(sK0,sK1),unordered_pair(sK0,sK0)),cartesian_product2(sK2,sK3)) ),
inference(cnf_transformation,[],[f371]) ).
tcf(c_66,negated_conjecture,
( in(sK0,sK2)
| in(unordered_pair(unordered_pair(sK0,sK1),unordered_pair(sK0,sK0)),cartesian_product2(sK2,sK3)) ),
inference(cnf_transformation,[],[f372]) ).
tcf(c_67,negated_conjecture,
( in(sK1,sK3)
| in(unordered_pair(unordered_pair(sK0,sK1),unordered_pair(sK0,sK0)),cartesian_product2(sK2,sK3)) ),
inference(cnf_transformation,[],[f373]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),cartesian_product2(X1,X3))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f434]) ).
tcf(c_322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(prop_impl_just,[status(thm)],[c_63]) ).
tcf(c_324,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(prop_impl_just,[status(thm)],[c_64]) ).
tcf(c_336,plain,
( in(unordered_pair(unordered_pair(sK0,sK1),unordered_pair(sK0,sK0)),cartesian_product2(sK2,sK3))
| in(sK0,sK2) ),
inference(prop_impl_just,[status(thm)],[c_66]) ).
tcf(c_337,plain,
( in(sK0,sK2)
| in(unordered_pair(unordered_pair(sK0,sK1),unordered_pair(sK0,sK0)),cartesian_product2(sK2,sK3)) ),
inference(renaming,[status(thm)],[c_336]) ).
tcf(c_338,plain,
( in(unordered_pair(unordered_pair(sK0,sK1),unordered_pair(sK0,sK0)),cartesian_product2(sK2,sK3))
| in(sK1,sK3) ),
inference(prop_impl_just,[status(thm)],[c_67]) ).
tcf(c_339,plain,
( in(sK1,sK3)
| in(unordered_pair(unordered_pair(sK0,sK1),unordered_pair(sK0,sK0)),cartesian_product2(sK2,sK3)) ),
inference(renaming,[status(thm)],[c_338]) ).
tcf(c_933,plain,
in(sK0,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_337,c_322]) ).
tcf(c_940,plain,
in(sK1,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_339,c_324]) ).
tcf(c_7396,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(unordered_pair(sK0,X0),unordered_pair(sK0,sK0)),cartesian_product2(sK2,X1))
| ~ in(sK0,sK2)
| ~ in(X0,X1) ),
inference(instantiation,[status(thm)],[c_161]) ).
tcf(c_11577,plain,
( in(unordered_pair(unordered_pair(sK0,sK1),unordered_pair(sK0,sK0)),cartesian_product2(sK2,sK3))
| ~ in(sK1,sK3)
| ~ in(sK0,sK2) ),
inference(instantiation,[status(thm)],[c_7396]) ).
tcf(c_11578,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11577,c_940,c_933,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU165+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/30.46 % CPULimit : 300
% 0.10/30.46 % WCLimit : 300
% 0.10/30.46 % DateTime : Thu Sep 24 13:00:29 UTC 2026
% 0.10/30.46 % CPUTime :
% 0.10/30.46 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/30.50 Running first-order theorem proving
% 0.36/30.50 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
% 0.36/30.51
% 0.36/30.51 % ======== iProver multi-core TPTP/SMT =========
% 0.36/30.51
% 0.36/30.51 % Detected problem language: tptp
% 0.36/30.52 % Proving...
% 1.19/31.29 % SZS status Started for theBenchmark.p
% 1.19/31.29 % SZS status Theorem for theBenchmark.p
% 1.19/31.29
% 1.19/31.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.19/31.29
% 1.19/31.29 % ------ iProver source info
% 1.19/31.29
% 1.19/31.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.19/31.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.19/31.29 % git: non_committed_changes: false
% 1.19/31.29
% 1.19/31.29 % ------ Parsing...
% 1.19/31.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.19/31.29
% 1.19/31.29 % ------ Preprocessing... sup_sim: 7 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.19/31.29
% 1.19/31.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.19/31.29
% 1.19/31.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.19/31.29 % ------ Proving...
% 1.19/31.29 % ------ Problem Properties
% 1.19/31.29
% 1.19/31.29 %
% 1.19/31.29 % clauses 127
% 1.19/31.29 % conjectures 0
% 1.19/31.29 % EPR 23
% 1.19/31.29 % Horn 98
% 1.19/31.29 % unary 28
% 1.19/31.29 % binary 55
% 1.19/31.29 % lits 277
% 1.19/31.29 % lits eq 81
% 1.19/31.29 % fd_pure 0
% 1.19/31.29 % fd_pseudo 0
% 1.19/31.29 % fd_cond 3
% 1.19/31.29 % fd_pseudo_cond 35
% 1.19/31.29 % AC symbols 0
% 1.19/31.29
% 1.19/31.29 % ------ Schedule dynamic 5 is on
% 1.19/31.29
% 1.19/31.29 % ------ no conjectures: strip conj schedule
% 1.19/31.29
% 1.19/31.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.19/31.29
% 1.19/31.29
% 1.19/31.29 % ------
% 1.19/31.29 % Current options:
% 1.19/31.29 % ------
% 1.19/31.29
% 1.19/31.29
% 1.19/31.29 %
% 1.19/31.29
% 1.19/31.29 % ------ Proving...
% 1.19/31.29 %
% 1.19/31.29
% 1.19/31.29 % SZS status Theorem for theBenchmark.p
% 1.19/31.29
% 1.19/31.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.19/31.29
% 1.19/31.29
%------------------------------------------------------------------------------