%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU180+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 : n009.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 02:55:46 PM UTC 2026
% Result : Theorem 120.93s 35.78s
% Output : CNFRefutation 120.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 72 ( 21 unt; 0 def)
% Number of atoms : 210 ( 24 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 227 ( 89 ~; 87 |; 39 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 151 ( 0 sgn 140 !; 11 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f14,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f16,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f24,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(f25,axiom,
! [X0] :
( relation(X0)
=> relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
fof(f87,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',t106_zfmisc_1) ).
fof(f100,axiom,
! [X0] :
( relation(X0)
=> subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
fof(f108,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f109,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f108]) ).
fof(f139,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f168,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f172,plain,
! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
inference(ennf_transformation,[],[f25]) ).
fof(f218,plain,
! [X0] :
( ~ relation(X0)
| subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
inference(ennf_transformation,[],[f100]) ).
fof(f226,plain,
? [X0,X1,X2] :
( relation(X2)
& in(ordered_pair(X0,X1),X2)
& ( ~ in(X1,relation_field(X2))
| ~ in(X0,relation_field(X2)) ) ),
inference(ennf_transformation,[],[f109]) ).
fof(f227,plain,
? [X0,X1,X2] :
( relation(X2)
& in(ordered_pair(X0,X1),X2)
& ( ~ in(X1,relation_field(X2))
| ~ in(X0,relation_field(X2)) ) ),
inference(flattening,[],[f226]) ).
fof(f285,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f286,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(flattening,[],[f285]) ).
fof(f287,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(rectify,[],[f286]) ).
fof(f288,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ( ( in(sK10(X0,X1,X2),X2)
| in(sK10(X0,X1,X2),X1)
| in(sK10(X0,X1,X2),X0) )
& ( ~ in(sK10(X0,X1,X2),X2)
| ( ~ in(sK10(X0,X1,X2),X1)
& ~ in(sK10(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X3,sK10(X0,X1,X2))],[f287]) ).
fof(f292,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f168]) ).
fof(f293,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f292]) ).
fof(f294,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK16(X0,X1),X0)
& ~ in(sK16(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X2,sK16(X0,X1))],[f293]) ).
fof(f330,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,[],[f87]) ).
fof(f331,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,[],[f330]) ).
fof(f335,plain,
( relation(sK40)
& in(ordered_pair(sK38,sK39),sK40)
& ( ~ in(sK39,relation_field(sK40))
| ~ in(sK38,relation_field(sK40)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38,sK39,sK40]),skolemize(X0,sK38),skolemize(X1,sK39),skolemize(X2,sK40)],[f227]) ).
fof(f351,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f389,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f288]) ).
fof(f390,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f288]) ).
fof(f402,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f294]) ).
fof(f433,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f434,plain,
! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
inference(cnf_transformation,[],[f172]) ).
fof(f496,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f331]) ).
fof(f497,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f331]) ).
fof(f515,plain,
! [X0] :
( ~ relation(X0)
| subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
inference(cnf_transformation,[],[f218]) ).
fof(f525,plain,
relation(sK40),
inference(cnf_transformation,[],[f335]) ).
fof(f526,plain,
in(ordered_pair(sK38,sK39),sK40),
inference(cnf_transformation,[],[f335]) ).
fof(f527,plain,
( ~ in(sK39,relation_field(sK40))
| ~ in(sK38,relation_field(sK40)) ),
inference(cnf_transformation,[],[f335]) ).
fof(f570,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f139]) ).
fof(f587,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f433,f570]) ).
fof(f632,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,[],[f497,f587]) ).
fof(f633,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,[],[f496,f587]) ).
fof(f642,plain,
in(unordered_pair(unordered_pair(sK38,sK39),unordered_pair(sK38,sK38)),sK40),
inference(definition_unfolding,[],[f526,f587]) ).
fof(f678,plain,
! [X0,X1,X4] :
( ~ in(X4,X0)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f390]) ).
fof(f679,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f389]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f351]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f678]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f679]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f402]) ).
tcf(c_133,plain,
! [X0: $i] :
( ( set_union2(relation_dom(X0),relation_rng(X0)) = relation_field(X0) )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f434]) ).
tcf(c_196,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,[],[f632]) ).
tcf(c_197,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,[],[f633]) ).
tcf(c_214,plain,
! [X0: $i] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f515]) ).
tcf(c_224,negated_conjecture,
( ~ in(sK39,relation_field(sK40))
| ~ in(sK38,relation_field(sK40)) ),
inference(cnf_transformation,[],[f527]) ).
tcf(c_225,negated_conjecture,
in(unordered_pair(unordered_pair(sK38,sK39),unordered_pair(sK38,sK38)),sK40),
inference(cnf_transformation,[],[f642]) ).
tcf(c_226,negated_conjecture,
relation(sK40),
inference(cnf_transformation,[],[f525]) ).
tcf(c_2027,plain,
in(unordered_pair(unordered_pair(sK38,sK38),unordered_pair(sK38,sK39)),sK40),
inference(demodulation,[status(thm)],[c_225,c_51]) ).
tcf(c_35644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_51,c_196]) ).
tcf(c_35651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3)) ),
inference(superposition,[status(thm)],[c_51,c_197]) ).
tcf(c_35992,plain,
set_union2(relation_dom(sK40),relation_rng(sK40)) = relation_field(sK40),
inference(superposition,[status(thm)],[c_226,c_133]) ).
tcf(c_36036,plain,
! [X0: $i] :
( in(X0,relation_field(sK40))
| ~ in(X0,relation_dom(sK40)) ),
inference(superposition,[status(thm)],[c_35992,c_91]) ).
tcf(c_36065,plain,
! [X0: $i] :
( in(X0,relation_field(sK40))
| ~ in(X0,relation_rng(sK40)) ),
inference(superposition,[status(thm)],[c_35992,c_92]) ).
tcf(c_38802,plain,
! [X0: $i] :
( in(unordered_pair(unordered_pair(sK38,sK38),unordered_pair(sK38,sK39)),X0)
| ~ subset(sK40,X0) ),
inference(superposition,[status(thm)],[c_2027,c_104]) ).
tcf(c_38891,plain,
! [X0: $i,X1: $i] :
( in(sK39,X1)
| ~ subset(sK40,cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_38802,c_35651]) ).
tcf(c_38892,plain,
! [X0: $i,X1: $i] :
( in(sK38,X0)
| ~ subset(sK40,cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_38802,c_35644]) ).
tcf(c_41043,plain,
( in(sK39,relation_rng(sK40))
| ~ relation(sK40) ),
inference(superposition,[status(thm)],[c_214,c_38891]) ).
tcf(c_41044,plain,
in(sK39,relation_rng(sK40)),
inference(forward_subsumption_resolution,[status(thm)],[c_41043,c_226]) ).
tcf(c_41053,plain,
in(sK39,relation_field(sK40)),
inference(superposition,[status(thm)],[c_41044,c_36065]) ).
tcf(c_41058,plain,
~ in(sK38,relation_field(sK40)),
inference(backward_subsumption_resolution,[status(thm)],[c_224,c_41053]) ).
tcf(c_42204,plain,
( in(sK38,relation_dom(sK40))
| ~ relation(sK40) ),
inference(superposition,[status(thm)],[c_214,c_38892]) ).
tcf(c_42205,plain,
in(sK38,relation_dom(sK40)),
inference(forward_subsumption_resolution,[status(thm)],[c_42204,c_226]) ).
tcf(c_42214,plain,
in(sK38,relation_field(sK40)),
inference(superposition,[status(thm)],[c_42205,c_36036]) ).
tcf(c_42215,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_42214,c_41058]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU180+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n009.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 13:04:28 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 120.93/35.78 % SZS status Started for theBenchmark.p
% 120.93/35.78 % SZS status Theorem for theBenchmark.p
% 120.93/35.78
% 120.93/35.78 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 120.93/35.78
% 120.93/35.78 % ------ iProver source info
% 120.93/35.78
% 120.93/35.78 % git: date: 2026-07-19 20:42:38 +0200
% 120.93/35.78 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 120.93/35.78 % git: non_committed_changes: false
% 120.93/35.78
% 120.93/35.78 % ------ Parsing...
% 120.93/35.78 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 120.93/35.78
% 120.93/35.78 % ------ Preprocessing... sup_sim: 14 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 %
% 120.93/35.78
% 120.93/35.78 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 120.93/35.78
% 120.93/35.78 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 120.93/35.78 % ------ Proving...
% 120.93/35.78 % ------ Problem Properties
% 120.93/35.78
% 120.93/35.78 %
% 120.93/35.78 % clauses 204
% 120.93/35.78 % conjectures 2
% 120.93/35.78 % EPR 30
% 120.93/35.78 % Horn 157
% 120.93/35.78 % unary 38
% 120.93/35.78 % binary 80
% 120.93/35.78 % lits 485
% 120.93/35.78 % lits eq 115
% 120.93/35.78 % fd_pure 0
% 120.93/35.78 % fd_pseudo 0
% 120.93/35.78 % fd_cond 10
% 120.93/35.78 % fd_pseudo_cond 45
% 120.93/35.78 % AC symbols 0
% 120.93/35.78
% 120.93/35.78 % ------ Input Options Time Limit: Unbounded
% 120.93/35.78
% 120.93/35.78
% 120.93/35.78 % ------
% 120.93/35.78 % Current options:
% 120.93/35.78 % ------
% 120.93/35.78
% 120.93/35.78
% 120.93/35.78 %
% 120.93/35.78
% 120.93/35.78 % ------ Proving...
% 120.93/35.78 %
% 120.93/35.78
% 120.93/35.78 % SZS status Theorem for theBenchmark.p
% 120.93/35.78
% 120.93/35.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 120.93/35.79
% 120.93/35.79
%------------------------------------------------------------------------------