%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU053+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n003.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 : Sun Sep 27 08:37:31 AM UTC 2026
% Result : Theorem 7.16s 3.49s
% Output : Refutation 7.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 56
% Syntax : Number of formulae : 169 ( 73 unt; 0 typ; 10 def)
% Number of atoms : 408 ( 74 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 873 ( 90 ~; 15 |; 105 &; 586 @)
% ( 6 <=>; 71 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 12 con; 0-2 aty)
% Number of variables : 187 ( 1 ^; 154 !; 22 ?; 187 :)
% ( 0 !>; 0 ?*; 0 @-; 10 @+)
% Comments :
%------------------------------------------------------------------------------
thf(relation_decl,type,
relation: $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(relation_image_decl,type,
relation_image: $i > $i > $i ).
thf(set_intersection2_decl,type,
set_intersection2: $i > $i > $i ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(disjoint_nonempty_decl,type,
disjoint_nonempty: $i > $i > $o ).
thf(disjoint_decl,type,
disjoint: $i > $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(relation_dom_decl,type,
relation_dom: $i > $i ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(relation_empty_yielding_decl,type,
relation_empty_yielding: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk13_decl,type,
sk13: $i ).
thf(sk14_decl,type,
sk14: $i ).
thf(sk15_decl,type,
sk15: $i ).
thf(sk16_decl,type,
sk16: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( ( A @ function )
& ( A @ relation ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ set_intersection2 ) @ ( A @ relation_image ) )
= ( C @ ( A @ relation_image ) @ ( B @ ( A @ relation_image ) @ set_intersection2 ) ) )
=> ( A @ one_to_one ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i] :
( ( A @ relation )
& ( A @ empty ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( @+[A: $i] :
( ( A @ function )
& ( A @ relation ) ) ) ) ).
thf(37,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(183,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(184,plain,
( ( sk13 @ relation_empty_yielding )
& ( sk13 @ relation ) ),
inference(cnf,[status(esa)],[183]) ).
thf(185,plain,
sk13 @ relation,
inference(cnfConj,[status(thm)],[184]) ).
thf(39,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(195,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(196,plain,
( ( sk14 @ relation )
& ( sk14 @ empty ) ),
inference(cnf,[status(esa)],[195]) ).
thf(197,plain,
sk14 @ empty,
inference(cnfConj,[status(thm)],[196]) ).
thf(36,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
<=> ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ apply ) )
= ( C @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( C @ in ) )
& ( A @ relation_dom @ ( B @ in ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
thf(173,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ apply ) )
= ( C @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( C @ in ) )
& ( A @ relation_dom @ ( B @ in ) ) )
=> ( B = C ) )
=> ( A @ one_to_one ) )
& ( ( A @ one_to_one )
=> ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ apply ) )
= ( C @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( C @ in ) )
& ( A @ relation_dom @ ( B @ in ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_intersection2 ) @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
thf(204,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_intersection2 ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( B @ singleton @ ( A @ singleton @ disjoint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_zfmisc_1) ).
thf(138,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( B @ singleton @ ( A @ singleton @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(15,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(93,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(94,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[93]) ).
thf(95,plain,
~ ( sk6 @ empty ),
inference(cnf,[status(esa)],[94]) ).
thf(245,plain,
( ( ( sk14 @ empty )
!= ( sk6 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[197,95]) ).
thf(246,plain,
( ( sk14 @ empty )
!= ( sk6 @ empty ) ),
inference(simp,[status(thm)],[245]) ).
thf(249,plain,
sk14 != sk6,
inference(simp,[status(thm)],[246]) ).
thf(34,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(167,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(168,plain,
( ( sk10 @ relation )
& ~ ( sk10 @ empty ) ),
inference(cnf,[status(esa)],[167]) ).
thf(170,plain,
sk10 @ relation,
inference(cnfConj,[status(thm)],[168]) ).
thf(40,axiom,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(199,plain,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(200,plain,
( ( sk15 @ one_to_one )
& ( sk15 @ function )
& ( sk15 @ relation ) ),
inference(cnf,[status(esa)],[199]) ).
thf(202,plain,
sk15 @ function,
inference(cnfConj,[status(thm)],[200]) ).
thf(3,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(55,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(56,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(cnf,[status(esa)],[55]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(153,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(110,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ( ( B
= ( A @ singleton ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ relation )
=> ( ( empty_set @ ( A @ relation_image ) )
= empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t149_relat_1) ).
thf(157,plain,
! [A: $i] :
( ( A @ relation )
=> ( ( empty_set @ ( A @ relation_image ) )
= empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(10,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(81,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(82,plain,
sk5 @ empty,
inference(cnf,[status(esa)],[81]) ).
thf(226,plain,
( ( ( sk6 @ empty )
!= ( sk5 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,95]) ).
thf(227,plain,
( ( sk6 @ empty )
!= ( sk5 @ empty ) ),
inference(simp,[status(thm)],[226]) ).
thf(228,plain,
sk6 != sk5,
inference(simp,[status(thm)],[227]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( B @ powerset @ ( A @ element ) ) )
& ( ( B @ powerset @ ( A @ element ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(33,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(162,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(163,plain,
( ( sk9 @ function )
& ( sk9 @ empty )
& ( sk9 @ relation ) ),
inference(cnf,[status(esa)],[162]) ).
thf(164,plain,
sk9 @ relation,
inference(cnfConj,[status(thm)],[163]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( B @ relation_dom @ ( A @ in ) )
=> ( ( A @ singleton @ ( B @ relation_image ) )
= ( A @ ( B @ apply ) @ singleton ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_funct_1) ).
thf(211,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( B @ relation_dom @ ( A @ in ) )
=> ( ( A @ singleton @ ( B @ relation_image ) )
= ( A @ ( B @ apply ) @ singleton ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(203,plain,
sk15 @ one_to_one,
inference(cnfConj,[status(thm)],[200]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ set_intersection2 ) @ ( A @ relation_image ) )
= ( C @ ( A @ relation_image ) @ ( B @ ( A @ relation_image ) @ set_intersection2 ) ) )
=> ( A @ one_to_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t122_funct_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ set_intersection2 ) @ ( A @ relation_image ) )
= ( C @ ( A @ relation_image ) @ ( B @ ( A @ relation_image ) @ set_intersection2 ) ) )
=> ( A @ one_to_one ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(48,plain,
~ ! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ set_intersection2 ) @ ( A @ relation_image ) )
= ( C @ ( A @ relation_image ) @ ( B @ ( A @ relation_image ) @ set_intersection2 ) ) )
=> ( A @ one_to_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ one_to_one )
& ( ( B @ ( A @ set_intersection2 ) @ ( sk1 @ relation_image ) )
= ( B @ ( sk1 @ relation_image ) @ ( A @ ( sk1 @ relation_image ) @ set_intersection2 ) ) )
& ( sk1 @ function )
& ( sk1 @ relation ) ),
inference(cnf,[status(esa)],[48]) ).
thf(53,plain,
~ ( sk1 @ one_to_one ),
inference(cnfConj,[status(thm)],[49]) ).
thf(251,plain,
( ( ( sk15 @ one_to_one )
!= ( sk1 @ one_to_one ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[203,53]) ).
thf(252,plain,
( ( sk15 @ one_to_one )
!= ( sk1 @ one_to_one ) ),
inference(simp,[status(thm)],[251]) ).
thf(253,plain,
sk15 != sk1,
inference(simp,[status(thm)],[252]) ).
thf(46,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(219,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(220,plain,
( ( sk16 @ function )
& ( sk16 @ relation ) ),
inference(cnf,[status(esa)],[219]) ).
thf(221,plain,
sk16 @ relation,
inference(cnfConj,[status(thm)],[220]) ).
thf(165,plain,
sk9 @ empty,
inference(cnfConj,[status(thm)],[163]) ).
thf(239,plain,
( ( ( sk9 @ empty )
!= ( sk6 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[165,95]) ).
thf(240,plain,
( ( sk9 @ empty )
!= ( sk6 @ empty ) ),
inference(simp,[status(thm)],[239]) ).
thf(243,plain,
sk9 != sk6,
inference(simp,[status(thm)],[240]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(206,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(89,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(24,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(133,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(58,plain,
( ! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( B @ powerset @ ( A @ element ) ) )
& ! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(miniscope,[status(thm)],[57]) ).
thf(59,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ powerset @ ( C @ element ) )
| ~ ( D @ ( C @ subset ) ) )
& ( ( B @ ( A @ subset ) )
| ~ ( B @ powerset @ ( A @ element ) ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ powerset @ ( A @ element ) ) ),
inference(cnfConj,[status(thm)],[59]) ).
thf(201,plain,
sk15 @ relation,
inference(cnfConj,[status(thm)],[200]) ).
thf(32,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(160,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(6,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(67,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(68,plain,
! [A: $i] :
( ( A @ sk3 @ empty )
& ( A @ powerset @ ( A @ sk3 @ element ) ) ),
inference(cnf,[status(esa)],[67]) ).
thf(70,plain,
! [A: $i] : ( A @ sk3 @ empty ),
inference(cnfConj,[status(thm)],[68]) ).
thf(169,plain,
~ ( sk10 @ empty ),
inference(cnfConj,[status(thm)],[168]) ).
thf(27,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(141,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(9,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(77,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(16,axiom,
! [A: $i] :
~ ( A @ singleton @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(96,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( ( B @ ( A @ disjoint_nonempty ) )
<=> ( B @ ( A @ disjoint ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_subset_1) ).
thf(73,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( ( ( B @ ( A @ disjoint ) )
=> ( B @ ( A @ disjoint_nonempty ) ) )
& ( ( B @ ( A @ disjoint_nonempty ) )
=> ( B @ ( A @ disjoint ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(99,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(234,plain,
( ( ( sk10 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[99,169]) ).
thf(235,plain,
( ( sk10 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[234]) ).
thf(237,plain,
sk10 != empty_set,
inference(simp,[status(thm)],[235]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( A @ ( A @ disjoint_nonempty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r1_subset_1) ).
thf(105,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( A @ ( A @ disjoint_nonempty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(241,plain,
( ( ( sk10 @ empty )
!= ( sk9 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[165,169]) ).
thf(242,plain,
( ( sk10 @ empty )
!= ( sk9 @ empty ) ),
inference(simp,[status(thm)],[241]) ).
thf(244,plain,
sk10 != sk9,
inference(simp,[status(thm)],[242]) ).
thf(166,plain,
sk9 @ function,
inference(cnfConj,[status(thm)],[163]) ).
thf(28,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(146,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(147,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(cnf,[status(esa)],[146]) ).
thf(149,plain,
empty_set @ relation,
inference(cnfConj,[status(thm)],[147]) ).
thf(7,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(71,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_intersection2 ) @ ( sk1 @ relation_image ) )
= ( B @ ( sk1 @ relation_image ) @ ( A @ ( sk1 @ relation_image ) @ set_intersection2 ) ) ),
inference(cnfConj,[status(thm)],[49]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( B @ ( sk1 @ relation_image ) @ ( A @ ( sk1 @ relation_image ) @ set_intersection2 ) )
= ( B @ ( A @ set_intersection2 ) @ ( sk1 @ relation_image ) ) ),
inference(lifteq,[status(thm)],[52]) ).
thf(232,plain,
( ( ( sk6 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[99,95]) ).
thf(233,plain,
( ( sk6 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[232]) ).
thf(236,plain,
sk6 != empty_set,
inference(simp,[status(thm)],[233]) ).
thf(12,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(86,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
<=> ( ( B @ ( A @ set_intersection2 ) )
= empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(187,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ set_intersection2 ) )
= empty_set )
=> ( B @ ( A @ disjoint ) ) )
& ( ( B @ ( A @ disjoint ) )
=> ( ( B @ ( A @ set_intersection2 ) )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(103,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( ( B @ ( A @ disjoint_nonempty ) )
=> ( A @ ( B @ disjoint_nonempty ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_subset_1) ).
thf(91,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ( ( B @ ( A @ disjoint_nonempty ) )
=> ( A @ ( B @ disjoint_nonempty ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(198,plain,
sk14 @ relation,
inference(cnfConj,[status(thm)],[196]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(108,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(47,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(223,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(209,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(5,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(63,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(150,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(50,plain,
sk1 @ relation,
inference(cnfConj,[status(thm)],[49]) ).
thf(229,plain,
( ( ( sk10 @ empty )
!= ( sk5 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,169]) ).
thf(230,plain,
( ( sk10 @ empty )
!= ( sk5 @ empty ) ),
inference(simp,[status(thm)],[229]) ).
thf(231,plain,
sk10 != sk5,
inference(simp,[status(thm)],[230]) ).
thf(45,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(214,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(215,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(cnf,[status(esa)],[214]) ).
thf(218,plain,
empty_set @ relation_empty_yielding,
inference(cnfConj,[status(thm)],[215]) ).
thf(186,plain,
sk13 @ relation_empty_yielding,
inference(cnfConj,[status(thm)],[184]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(171,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(51,plain,
sk1 @ function,
inference(cnfConj,[status(thm)],[49]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(136,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(131,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( B @ powerset @ ( A @ element ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[59]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( B @ powerset @ ( A @ element ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[61]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(83,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(222,plain,
sk16 @ function,
inference(cnfConj,[status(thm)],[220]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(100,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(338,plain,
$false,
inference(e,[status(thm)],[185,197,173,204,138,249,170,202,56,153,110,157,93,228,57,164,211,253,221,243,206,89,133,60,201,160,70,165,53,169,141,77,96,73,237,105,244,166,149,71,54,236,86,187,219,81,103,91,198,108,223,167,162,209,48,63,150,95,50,67,199,231,99,203,218,186,55,171,82,214,146,51,183,136,195,131,62,83,222,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU053+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.42 % Computer : n003.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sat Sep 26 08:34:54 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.43 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.82/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.34/1.21 % [INFO] Parsing done (207ms).
% 1.34/1.23 % [INFO] Running in sequential loop mode.
% 1.97/1.63 % [INFO] eprover registered as external prover.
% 1.97/1.64 % [INFO] Scanning for conjecture ...
% 2.17/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 45 axioms. Running axiom selection ...
% 2.31/1.84 % [INFO] Axiom selection finished. Selected 45 axioms (removed 0 axioms).
% 2.53/1.90 % [INFO] Problem is first-order (TPTP FOF).
% 2.53/1.91 % [INFO] Type checking passed.
% 2.53/1.92 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 7.16/3.48 % External prover 'e' found a proof!
% 7.16/3.48 % [INFO] Killing All external provers ...
% 7.16/3.48 % Time passed: 2916ms (effective reasoning time: 2251ms)
% 7.16/3.48 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 7.16/3.49 % Axioms used in derivation (45): d8_funct_1, rc3_funct_1, rc1_funct_1, t5_subset, fc2_subset_1, t4_subset, rc2_relat_1, t149_relat_1, rc2_xboole_0, antisymmetry_r2_hidden, d1_tarski, t17_zfmisc_1, idempotence_k3_xboole_0, irreflexivity_r1_subset_1, fc1_xboole_0, fc4_relat_1, t1_subset, t2_boole, t117_funct_1, cc1_relat_1, commutativity_k3_xboole_0, rc3_relat_1, t6_boole, rc2_subset_1, t7_boole, cc1_funct_1, symmetry_r1_subset_1, fc1_subset_1, rc2_funct_1, rc1_subset_1, redefinition_r1_subset_1, d7_xboole_0, fc5_relat_1, cc2_funct_1, t3_subset, existence_m1_subset_1, rc1_relat_1, reflexivity_r1_tarski, fc1_relat_1, t8_boole, rc1_xboole_0, t2_subset, fc7_relat_1, fc12_relat_1, symmetry_r1_xboole_0
% 7.16/3.49 % No. of inferences in proof: 159
% 7.16/3.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2916 ms resp. 2251 ms w/o parsing
% 7.55/3.60 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.55/3.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------