%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU263+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n004.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 02:56:24 PM UTC 2026
% Result : Theorem 212.44s 32.28s
% Output : CNFRefutation 212.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 62 ( 11 unt; 0 def)
% Number of atoms : 143 ( 9 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 146 ( 65 ~; 57 |; 12 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 140 ( 0 sgn 132 !; 8 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f29,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
<=> subset(X2,cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relset_1) ).
fof(f109,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f184,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f198,axiom,
! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(f199,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( subset(relation_rng(X2),X1)
& subset(relation_dom(X2),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).
fof(f210,conjecture,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(relation_rng(X3),X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_relset_1) ).
fof(f211,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(relation_rng(X3),X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f210]) ).
fof(f225,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f231,axiom,
! [X0] :
( relation(X0)
=> subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
fof(f349,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f424,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f109]) ).
fof(f495,plain,
! [X0,X1,X2,X3] :
( ~ subset(X2,X3)
| ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(ennf_transformation,[],[f198]) ).
fof(f496,plain,
! [X0,X1,X2,X3] :
( ~ subset(X2,X3)
| ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(flattening,[],[f495]) ).
fof(f497,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ( subset(relation_rng(X2),X1)
& subset(relation_dom(X2),X0) ) ),
inference(ennf_transformation,[],[f199]) ).
fof(f512,plain,
? [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
& subset(relation_rng(X3),X1)
& ~ relation_of2_as_subset(X3,X2,X1) ),
inference(ennf_transformation,[],[f211]) ).
fof(f513,plain,
? [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
& subset(relation_rng(X3),X1)
& ~ relation_of2_as_subset(X3,X2,X1) ),
inference(flattening,[],[f512]) ).
fof(f529,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(ennf_transformation,[],[f225]) ).
fof(f530,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(flattening,[],[f529]) ).
fof(f538,plain,
! [X0] :
( ~ relation(X0)
| subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
inference(ennf_transformation,[],[f231]) ).
fof(f705,plain,
! [X0,X1,X2] :
( ( ~ relation_of2(X2,X0,X1)
| subset(X2,cartesian_product2(X0,X1)) )
& ( ~ subset(X2,cartesian_product2(X0,X1))
| relation_of2(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f851,plain,
! [X0,X1,X2] :
( ( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) )
& ( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f184]) ).
fof(f861,plain,
( relation_of2_as_subset(sK113,sK112,sK110)
& subset(relation_rng(sK113),sK111)
& ~ relation_of2_as_subset(sK113,sK112,sK111) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110,sK111,sK112,sK113]),skolemize(X0,sK110),skolemize(X1,sK111),skolemize(X2,sK112),skolemize(X3,sK113)],[f513]) ).
fof(f923,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f349]) ).
fof(f1004,plain,
! [X2,X0,X1] :
( ~ subset(X2,cartesian_product2(X0,X1))
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f705]) ).
fof(f1213,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f424]) ).
fof(f1360,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f851]) ).
fof(f1380,plain,
! [X2,X3,X0,X1] :
( ~ subset(X2,X3)
| ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(cnf_transformation,[],[f496]) ).
fof(f1382,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| subset(relation_dom(X2),X0) ),
inference(cnf_transformation,[],[f497]) ).
fof(f1398,plain,
relation_of2_as_subset(sK113,sK112,sK110),
inference(cnf_transformation,[],[f861]) ).
fof(f1399,plain,
subset(relation_rng(sK113),sK111),
inference(cnf_transformation,[],[f861]) ).
fof(f1400,plain,
~ relation_of2_as_subset(sK113,sK112,sK111),
inference(cnf_transformation,[],[f861]) ).
fof(f1420,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f530]) ).
fof(f1430,plain,
! [X0] :
( ~ relation(X0)
| subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
inference(cnf_transformation,[],[f538]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X0)
| ~ element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[],[f923]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X0,X1,X2)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f1004]) ).
tcf(c_341,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f1213]) ).
tcf(c_487,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2_as_subset(X0,X1,X2)
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f1360]) ).
tcf(c_508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1380]) ).
tcf(c_509,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(X0),X1)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f1382]) ).
tcf(c_526,negated_conjecture,
~ relation_of2_as_subset(sK113,sK112,sK111),
inference(cnf_transformation,[],[f1400]) ).
tcf(c_527,negated_conjecture,
subset(relation_rng(sK113),sK111),
inference(cnf_transformation,[],[f1399]) ).
tcf(c_528,negated_conjecture,
relation_of2_as_subset(sK113,sK112,sK110),
inference(cnf_transformation,[],[f1398]) ).
tcf(c_548,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X2,X1)
| ~ subset(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1420]) ).
tcf(c_558,plain,
! [X0: $i] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f1430]) ).
tcf(c_1187,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(X0,cartesian_product2(X1,X2))
| relation_of2_as_subset(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_487,c_132]) ).
tcf(c_1188,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2_as_subset(X0,X1,X2)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(renaming,[status(thm)],[c_1187]) ).
tcf(c_1381,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation_of2_as_subset(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(prop_impl_just,[status(thm)],[c_341]) ).
tcf(c_1382,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_1381]) ).
tcf(c_1543,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(X0),X1)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_509]) ).
tcf(c_10258,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(X0,cartesian_product2(X1,X2))
| ( X2 != sK111 )
| ( X1 != sK112 )
| ( X0 != sK113 ) ),
inference(resolution_lifted,[status(thm)],[c_1188,c_526]) ).
tcf(c_10259,plain,
~ subset(sK113,cartesian_product2(sK112,sK111)),
inference(unflattening,[status(thm)],[c_10258]) ).
tcf(c_10273,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(X0),X1)
| ( X2 != sK110 )
| ( X1 != sK112 )
| ( X0 != sK113 ) ),
inference(resolution_lifted,[status(thm)],[c_1543,c_528]) ).
tcf(c_10274,plain,
subset(relation_dom(sK113),sK112),
inference(unflattening,[status(thm)],[c_10273]) ).
tcf(c_10278,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ( X2 != sK110 )
| ( X1 != sK112 )
| ( X0 != sK113 ) ),
inference(resolution_lifted,[status(thm)],[c_1382,c_528]) ).
tcf(c_10279,plain,
element(sK113,powerset(cartesian_product2(sK112,sK110))),
inference(unflattening,[status(thm)],[c_10278]) ).
tcf(c_40571,plain,
relation(sK113),
inference(superposition,[status(thm)],[c_10279,c_55]) ).
tcf(c_62349,plain,
( subset(sK113,cartesian_product2(relation_dom(sK113),relation_rng(sK113)))
| ~ relation(sK113) ),
inference(instantiation,[status(thm)],[c_558]) ).
tcf(c_162911,plain,
! [X0: $i] :
( subset(sK113,cartesian_product2(sK112,sK111))
| ~ subset(sK113,X0)
| ~ subset(X0,cartesian_product2(sK112,sK111)) ),
inference(instantiation,[status(thm)],[c_548]) ).
tcf(c_164403,plain,
( subset(sK113,cartesian_product2(sK112,sK111))
| ~ subset(sK113,cartesian_product2(relation_dom(sK113),relation_rng(sK113)))
| ~ subset(cartesian_product2(relation_dom(sK113),relation_rng(sK113)),cartesian_product2(sK112,sK111)) ),
inference(instantiation,[status(thm)],[c_162911]) ).
tcf(c_167213,plain,
( subset(cartesian_product2(relation_dom(sK113),relation_rng(sK113)),cartesian_product2(sK112,sK111))
| ~ subset(relation_rng(sK113),sK111)
| ~ subset(relation_dom(sK113),sK112) ),
inference(instantiation,[status(thm)],[c_508]) ).
tcf(c_167214,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_167213,c_164403,c_62349,c_40571,c_10274,c_10259,c_527]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU263+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.43 % Computer : n004.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Thu Sep 24 13:27:06 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.51
% 0.22/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.22/0.51
% 0.22/0.51 % Detected problem language: tptp
% 0.22/0.53 % Proving...
% 212.44/32.28 % SZS status Started for theBenchmark.p
% 212.44/32.28 % SZS status Theorem for theBenchmark.p
% 212.44/32.28
% 212.44/32.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 212.44/32.28
% 212.44/32.28 % ------ iProver source info
% 212.44/32.28
% 212.44/32.28 % git: date: 2026-07-19 20:42:38 +0200
% 212.44/32.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 212.44/32.28 % git: non_committed_changes: false
% 212.44/32.28
% 212.44/32.28 % ------ Parsing...
% 212.44/32.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 212.44/32.28
% 212.44/32.28 % ------ Preprocessing... sup_sim: 61 sf_s rm: 6 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 212.44/32.28
% 212.44/32.28 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 212.44/32.28
% 212.44/32.28 % ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 0 0s sf_e
% 212.44/32.28 % ------ Proving...
% 212.44/32.28 % ------ Problem Properties
% 212.44/32.28
% 212.44/32.28 %
% 212.44/32.28 % clauses 611
% 212.44/32.28 % conjectures 1
% 212.44/32.28 % EPR 99
% 212.44/32.28 % Horn 480
% 212.44/32.28 % unary 97
% 212.44/32.28 % binary 154
% 212.44/32.28 % lits 1799
% 212.44/32.28 % lits eq 277
% 212.44/32.28 % fd_pure 0
% 212.44/32.28 % fd_pseudo 0
% 212.44/32.28 % fd_cond 21
% 212.44/32.28 % fd_pseudo_cond 99
% 212.44/32.28 % AC symbols 0
% 212.44/32.28
% 212.44/32.28 % ------ Input Options Time Limit: Unbounded
% 212.44/32.28
% 212.44/32.28
% 212.44/32.28 % ------
% 212.44/32.28 % Current options:
% 212.44/32.28 % ------
% 212.44/32.28
% 212.44/32.28
% 212.44/32.28 %
% 212.44/32.28
% 212.44/32.28 % ------ Proving...
% 212.44/32.28 %
% 212.44/32.28
% 212.44/32.28 % SZS status Theorem for theBenchmark.p
% 212.44/32.28
% 212.44/32.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 212.44/32.28
% 212.44/32.28
%------------------------------------------------------------------------------