%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU165+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 : n007.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 1.78s 6.27s
% Output : CNFRefutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 17 unt; 4 def)
% Number of atoms : 127 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 116 ( 50 ~; 48 |; 14 &)
% ( 3 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 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 : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 74 !; 12 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f6,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(f7,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(f8,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)],[f7]) ).
fof(f9,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(f11,plain,
? [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<~> ( in(X1,X3)
& in(X0,X2) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f14,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,[],[f11]) ).
fof(f15,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,[],[f14]) ).
fof(f16,plain,
( ( in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5))
| ( in(sK3,sK5)
& in(sK2,sK4) ) )
& ( ~ in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5))
| ~ in(sK3,sK5)
| ~ in(sK2,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f15]) ).
fof(f17,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,[],[f9]) ).
fof(f18,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,[],[f17]) ).
fof(f19,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f24,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f25,plain,
( in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5))
| in(sK3,sK5) ),
inference(cnf_transformation,[],[f16]) ).
fof(f26,plain,
( in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5))
| in(sK2,sK4) ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
( ~ in(ordered_pair(sK2,sK3),cartesian_product2(sK4,sK5))
| ~ in(sK3,sK5)
| ~ in(sK2,sK4) ),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
( ~ in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5))
| ~ in(sK3,sK5)
| ~ in(sK2,sK4) ),
inference(definition_unfolding,[],[f27,f24]) ).
fof(f33,plain,
( in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5))
| in(sK2,sK4) ),
inference(definition_unfolding,[],[f26,f24]) ).
fof(f34,plain,
( in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5))
| in(sK3,sK5) ),
inference(definition_unfolding,[],[f25,f24]) ).
fof(f35,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f30,f24]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f29,f24]) ).
fof(f37,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f28,f24]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f19]) ).
tcf(c_54,negated_conjecture,
( ~ in(sK3,sK5)
| ~ in(sK2,sK4)
| ~ in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_55,negated_conjecture,
( in(sK2,sK4)
| in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_56,negated_conjecture,
( in(sK3,sK5)
| in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),cartesian_product2(X1,X3))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_78,plain,
in(sK2,sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_55,c_58]) ).
tcf(c_82,plain,
( ~ in(sK3,sK5)
| ~ in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_54,c_78]) ).
tcf(c_85,plain,
in(sK3,sK5),
inference(forward_subsumption_resolution,[status(thm)],[c_56,c_59]) ).
tcf(c_89,plain,
~ in(unordered_pair(unordered_pair(sK2,sK3),singleton(sK2)),cartesian_product2(sK4,sK5)),
inference(backward_subsumption_resolution,[status(thm)],[c_82,c_85]) ).
tcf(c_109,plain,
~ in(unordered_pair(singleton(sK2),unordered_pair(sK2,sK3)),cartesian_product2(sK4,sK5)),
inference(demodulation,[status(thm)],[c_89,c_49]) ).
tcf(c_124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X2)),cartesian_product2(X1,X3))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_57,c_49]) ).
tcf(c_155,definition,
iPr_def_10 = singleton(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_156,definition,
iPr_def_11 = unordered_pair(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_157,definition,
iPr_def_12 = unordered_pair(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_158,definition,
iPr_def_13 = cartesian_product2(sK4,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_159,plain,
~ in(iPr_def_12,iPr_def_13),
inference(demodulation,[status(thm)],[c_109,c_158,c_156,c_155,c_157]) ).
tcf(c_160,plain,
in(sK3,sK5),
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_161,plain,
in(sK2,sK4),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_433,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(sK2),iPr_def_11),cartesian_product2(X0,X1))
| ~ in(sK3,X1)
| ~ in(sK2,X0) ),
inference(superposition,[status(thm)],[c_156,c_124]) ).
tcf(c_445,plain,
! [X0: $i,X1: $i] :
( in(iPr_def_12,cartesian_product2(X0,X1))
| ~ in(sK3,X1)
| ~ in(sK2,X0) ),
inference(light_normalisation,[status(thm)],[c_433,c_155,c_157]) ).
tcf(c_624,plain,
( in(iPr_def_12,iPr_def_13)
| ~ in(sK3,sK5)
| ~ in(sK2,sK4) ),
inference(superposition,[status(thm)],[c_158,c_445]) ).
tcf(c_628,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_624,c_159,c_160,c_161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU165+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.37 % Computer : n007.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Thu Sep 24 12:58:12 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.40 Running first-order theorem proving
% 0.15/5.40 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
% 0.15/5.41
% 0.15/5.41 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.41
% 0.15/5.42 % Detected problem language: tptp
% 0.15/5.43 % Proving...
% 1.78/6.27 % SZS status Started for theBenchmark.p
% 1.78/6.27 % SZS status Theorem for theBenchmark.p
% 1.78/6.27
% 1.78/6.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.78/6.27
% 1.78/6.27 % ------ iProver source info
% 1.78/6.27
% 1.78/6.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.78/6.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.78/6.27 % git: non_committed_changes: false
% 1.78/6.27
% 1.78/6.27 % ------ Parsing...
% 1.78/6.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.78/6.27
% 1.78/6.27 % ------ Preprocessing... sup_sim: 5 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.78/6.27
% 1.78/6.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.78/6.27
% 1.78/6.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.78/6.27 % ------ Proving...
% 1.78/6.27 % ------ Problem Properties
% 1.78/6.27
% 1.78/6.27 %
% 1.78/6.27 % clauses 15
% 1.78/6.27 % conjectures 0
% 1.78/6.27 % EPR 6
% 1.78/6.27 % Horn 15
% 1.78/6.27 % unary 11
% 1.78/6.27 % binary 3
% 1.78/6.27 % lits 20
% 1.78/6.27 % lits eq 5
% 1.78/6.27 % fd_pure 0
% 1.78/6.27 % fd_pseudo 0
% 1.78/6.27 % fd_cond 0
% 1.78/6.27 % fd_pseudo_cond 0
% 1.78/6.27 % AC symbols 0
% 1.78/6.27
% 1.78/6.27 % ------ Schedule dynamic 5 is on
% 1.78/6.27
% 1.78/6.27 % ------ no conjectures: strip conj schedule
% 1.78/6.27
% 1.78/6.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.78/6.27
% 1.78/6.27
% 1.78/6.27 % ------
% 1.78/6.27 % Current options:
% 1.78/6.27 % ------
% 1.78/6.27
% 1.78/6.27
% 1.78/6.27 %
% 1.78/6.27
% 1.78/6.27 % ------ Proving...
% 1.78/6.27 %
% 1.78/6.27
% 1.78/6.27 % SZS status Theorem for theBenchmark.p
% 1.78/6.27
% 1.78/6.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.78/6.27
% 1.78/6.27
%------------------------------------------------------------------------------