%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU226+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n001.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 08:38:07 AM UTC 2026
% Result : Theorem 35.45s 10.13s
% Output : Refutation 36.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 44
% Syntax : Number of formulae : 145 ( 59 unt; 0 typ; 10 def)
% Number of atoms : 379 ( 52 equ; 0 cnn)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 782 ( 89 ~; 28 |; 108 &; 501 @)
% ( 6 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 13 con; 0-2 aty)
% Number of variables : 152 ( 0 ^; 108 !; 34 ?; 152 :)
% ( 0 !>; 0 ?*; 0 @-; 10 @+)
% Comments :
%------------------------------------------------------------------------------
thf(relation_decl,type,
relation: $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(relation_image_decl,type,
relation_image: $i > $i > $i ).
thf(relation_inverse_image_decl,type,
relation_inverse_image: $i > $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
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(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk14_decl,type,
sk14: $i ).
thf(sk15_decl,type,
sk15: $i ).
thf(sk16_decl,type,
sk16: $i ).
thf(sk17_decl,type,
sk17: $i ).
thf(sk22_decl,type,
sk22: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( A @ ( A @ ( B @ relation_inverse_image ) @ ( B @ relation_image ) @ subset ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( A @ function )
& ( A @ relation ) )
=> ( sk1 @ ( sk1 @ ( A @ relation_inverse_image ) @ ( A @ relation_image ) @ subset ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( @+[A: $i] :
( ( A @ relation )
& ( A @ empty ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( @+[A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( @+[A: $i] :
( ( A @ function )
& ( A @ relation ) ) ) ) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(138,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)],[26]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(41,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(45,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(46,plain,
sk3 @ empty,
inference(cnf,[status(esa)],[45]) ).
thf(8,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(55,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(56,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[55]) ).
thf(57,plain,
~ ( sk4 @ empty ),
inference(cnf,[status(esa)],[56]) ).
thf(207,plain,
( ( ( sk4 @ empty )
!= ( sk3 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,57]) ).
thf(208,plain,
( ( sk4 @ empty )
!= ( sk3 @ empty ) ),
inference(simp,[status(thm)],[207]) ).
thf(209,plain,
sk4 != sk3,
inference(simp,[status(thm)],[208]) ).
thf(6,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(50,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(90,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(9,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(58,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(25,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(134,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(135,plain,
( ( sk14 @ relation )
& ~ ( sk14 @ empty ) ),
inference(cnf,[status(esa)],[134]) ).
thf(136,plain,
~ ( sk14 @ empty ),
inference(cnfConj,[status(thm)],[135]) ).
thf(213,plain,
( ( ( sk14 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[58,136]) ).
thf(214,plain,
( ( sk14 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[213]) ).
thf(217,plain,
sk14 != empty_set,
inference(simp,[status(thm)],[214]) ).
thf(34,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(198,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(199,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(cnf,[status(esa)],[198]) ).
thf(202,plain,
empty_set @ relation_empty_yielding,
inference(cnfConj,[status(thm)],[199]) ).
thf(51,plain,
~ ? [A: $i,B: $i] :
( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(miniscope,[status(thm)],[50]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[51]) ).
thf(42,plain,
~ ? [A: $i] :
( ? [B: $i] :
( ( B @ empty )
& ( A != B ) )
& ( A @ empty ) ),
inference(miniscope,[status(thm)],[41]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ( A = B )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[42]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( A @ empty )
| ( A = B ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( A @ ( A @ ( B @ relation_inverse_image ) @ ( B @ relation_image ) @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t145_funct_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( A @ ( A @ ( B @ relation_inverse_image ) @ ( B @ relation_image ) @ subset ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(36,plain,
~ ! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( A @ ( A @ ( B @ relation_inverse_image ) @ ( B @ relation_image ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(37,plain,
( ~ ( sk1 @ ( sk1 @ ( sk2 @ relation_inverse_image ) @ ( sk2 @ relation_image ) @ subset ) )
& ( sk2 @ function )
& ( sk2 @ relation ) ),
inference(cnf,[status(esa)],[36]) ).
thf(38,plain,
sk2 @ relation,
inference(cnfConj,[status(thm)],[37]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( A @ relation )
| ~ ( B @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[44,38]) ).
thf(223,plain,
! [A: $i] :
( ( A @ relation )
| ~ ( sk2 @ empty )
| ~ ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[222:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(370,plain,
! [A: $i] :
( ( ( sk3 @ empty )
!= ( A @ empty ) )
| ( A @ relation )
| ~ ( sk2 @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,223]) ).
thf(371,plain,
! [A: $i] :
( ( ( sk3 @ empty )
!= ( A @ empty ) )
| ( A @ relation )
| ~ ( sk2 @ empty ) ),
inference(simp,[status(thm)],[370]) ).
thf(372,plain,
( ( sk3 @ relation )
| ~ ( sk2 @ empty ) ),
inference(pattern_uni,[status(thm)],[371:[bind(A,$thf( sk3 ))]]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(157,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(29,axiom,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(152,plain,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(27,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(144,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(145,plain,
( ( sk15 @ relation_empty_yielding )
& ( sk15 @ relation ) ),
inference(cnf,[status(esa)],[144]) ).
thf(147,plain,
sk15 @ relation_empty_yielding,
inference(cnfConj,[status(thm)],[145]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(61,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(132,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(19,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(86,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(87,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(cnf,[status(esa)],[86]) ).
thf(89,plain,
empty_set @ relation,
inference(cnfConj,[status(thm)],[87]) ).
thf(35,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(203,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(204,plain,
( ( sk22 @ function )
& ( sk22 @ relation ) ),
inference(cnf,[status(esa)],[203]) ).
thf(206,plain,
sk22 @ function,
inference(cnfConj,[status(thm)],[204]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(137,plain,
sk14 @ relation,
inference(cnfConj,[status(thm)],[135]) ).
thf(21,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(92,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(65,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(22,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ relation_image ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ? [E: $i] :
( ( D
= ( E @ ( A @ apply ) ) )
& ( B @ ( E @ in ) )
& ( A @ relation_dom @ ( E @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
thf(97,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ? [E: $i] :
( ( D
= ( E @ ( A @ apply ) ) )
& ( B @ ( E @ in ) )
& ( A @ relation_dom @ ( E @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ( D
= ( E @ ( A @ apply ) ) )
& ( B @ ( E @ in ) )
& ( A @ relation_dom @ ( E @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_image ) ) ) )
& ( ( C
= ( B @ ( A @ relation_image ) ) )
=> ! [D: $i] :
( ( ? [E: $i] :
( ( D
= ( E @ ( A @ apply ) ) )
& ( B @ ( E @ in ) )
& ( A @ relation_dom @ ( E @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ? [E: $i] :
( ( D
= ( E @ ( A @ apply ) ) )
& ( B @ ( E @ in ) )
& ( A @ relation_dom @ ( E @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(93,plain,
( ( sk8 @ function )
& ( sk8 @ empty )
& ( sk8 @ relation ) ),
inference(cnf,[status(esa)],[92]) ).
thf(95,plain,
sk8 @ empty,
inference(cnfConj,[status(thm)],[93]) ).
thf(327,plain,
( ( ( sk14 @ empty )
!= ( sk8 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[95,136]) ).
thf(328,plain,
( ( sk14 @ empty )
!= ( sk8 @ empty ) ),
inference(simp,[status(thm)],[327]) ).
thf(329,plain,
sk14 != sk8,
inference(simp,[status(thm)],[328]) ).
thf(153,plain,
( ( sk17 @ one_to_one )
& ( sk17 @ function )
& ( sk17 @ relation ) ),
inference(cnf,[status(esa)],[152]) ).
thf(156,plain,
sk17 @ one_to_one,
inference(cnfConj,[status(thm)],[153]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(53,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(169,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(210,plain,
( ( ( sk14 @ empty )
!= ( sk3 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,136]) ).
thf(211,plain,
( ( sk14 @ empty )
!= ( sk3 @ empty ) ),
inference(simp,[status(thm)],[210]) ).
thf(212,plain,
sk14 != sk3,
inference(simp,[status(thm)],[211]) ).
thf(96,plain,
sk8 @ function,
inference(cnfConj,[status(thm)],[93]) ).
thf(205,plain,
sk22 @ relation,
inference(cnfConj,[status(thm)],[204]) ).
thf(28,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(148,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(149,plain,
( ( sk16 @ relation )
& ( sk16 @ empty ) ),
inference(cnf,[status(esa)],[148]) ).
thf(150,plain,
sk16 @ empty,
inference(cnfConj,[status(thm)],[149]) ).
thf(428,plain,
( ( ( sk16 @ empty )
!= ( sk14 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[150,136]) ).
thf(429,plain,
( ( sk16 @ empty )
!= ( sk14 @ empty ) ),
inference(simp,[status(thm)],[428]) ).
thf(430,plain,
sk16 != sk14,
inference(simp,[status(thm)],[429]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(161,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(59,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ element ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(47,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(48,plain,
~ ? [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ empty )
& ( C @ powerset @ ( B @ element ) ) )
& ( B @ ( A @ in ) ) ),
inference(miniscope,[status(thm)],[47]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ empty )
| ~ ( C @ powerset @ ( B @ element ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[48]) ).
thf(18,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(81,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)],[18]) ).
thf(39,plain,
sk2 @ function,
inference(cnfConj,[status(thm)],[37]) ).
thf(155,plain,
sk17 @ function,
inference(cnfConj,[status(thm)],[153]) ).
thf(325,plain,
( ( ( sk8 @ empty )
!= ( sk4 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[95,57]) ).
thf(326,plain,
( ( sk8 @ empty )
!= ( sk4 @ empty ) ),
inference(simp,[status(thm)],[325]) ).
thf(330,plain,
sk8 != sk4,
inference(simp,[status(thm)],[326]) ).
thf(23,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(130,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(154,plain,
sk17 @ relation,
inference(cnfConj,[status(thm)],[153]) ).
thf(15,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(72,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(215,plain,
( ( ( sk4 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[58,57]) ).
thf(216,plain,
( ( sk4 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[215]) ).
thf(218,plain,
sk4 != empty_set,
inference(simp,[status(thm)],[216]) ).
thf(40,plain,
~ ( sk1 @ ( sk1 @ ( sk2 @ relation_inverse_image ) @ ( sk2 @ relation_image ) @ subset ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(33,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( C
= ( B @ ( A @ relation_inverse_image ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( B @ ( D @ ( A @ apply ) @ in ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_funct_1) ).
thf(171,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ ( A @ apply ) @ in ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ ( A @ apply ) @ in ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_inverse_image ) ) ) )
& ( ( C
= ( B @ ( A @ relation_inverse_image ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ ( A @ apply ) @ in ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ ( A @ apply ) @ in ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(16,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(75,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(151,plain,
sk16 @ relation,
inference(cnfConj,[status(thm)],[149]) ).
thf(146,plain,
sk15 @ relation,
inference(cnfConj,[status(thm)],[145]) ).
thf(17,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(79,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(94,plain,
sk8 @ relation,
inference(cnfConj,[status(thm)],[93]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(68,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)],[13]) ).
thf(9697,plain,
$false,
inference(e,[status(thm)],[138,41,209,50,90,217,202,52,372,157,46,152,57,147,61,132,89,206,38,70,137,92,65,97,329,156,53,169,212,96,134,205,430,148,45,161,44,59,54,144,49,86,81,39,155,198,330,130,223,150,95,154,72,203,218,40,55,171,75,58,151,36,146,136,79,94,47,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU226+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.46 % Computer : n001.cluster.edu
% 0.14/0.46 % Model : x86_64 x86_64
% 0.14/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.46 % Memory : 8046.5625MB
% 0.14/0.46 % OS : Linux 6.8.0-71-generic
% 0.14/0.46 % CPULimit : 300
% 0.14/0.46 % WCLimit : 300
% 0.14/0.46 % DateTime : Sat Sep 26 08:59:42 UTC 2026
% 0.14/0.46 % CPUTime :
% 0.14/0.46 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.00/1.31 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/1.59 % [INFO] Parsing done (276ms).
% 1.45/1.62 % [INFO] Running in sequential loop mode.
% 2.19/2.16 % [INFO] eprover registered as external prover.
% 2.19/2.17 % [INFO] Scanning for conjecture ...
% 2.39/2.31 % [INFO] Found a conjecture (or negated_conjecture) and 33 axioms. Running axiom selection ...
% 2.54/2.42 % [INFO] Axiom selection finished. Selected 33 axioms (removed 0 axioms).
% 2.54/2.49 % [INFO] Problem is first-order (TPTP FOF).
% 2.72/2.50 % [INFO] Type checking passed.
% 2.72/2.51 % [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 ...
% 35.45/10.12 % External prover 'e' found a proof!
% 35.45/10.12 % [INFO] Killing All external provers ...
% 35.45/10.12 % Time passed: 9428ms (effective reasoning time: 8501ms)
% 35.45/10.12 % 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)>
% 35.45/10.13 % Axioms used in derivation (33): rc3_funct_1, cc1_relat_1, rc1_funct_1, t5_subset, fc5_relat_1, rc2_relat_1, d12_funct_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, fc4_relat_1, t1_subset, rc3_relat_1, t6_boole, rc2_subset_1, d13_funct_1, t4_subset, t7_boole, cc1_funct_1, fc1_subset_1, rc2_funct_1, rc1_subset_1, cc2_funct_1, t3_subset, existence_m1_subset_1, d3_tarski, rc1_relat_1, reflexivity_r1_tarski, t8_boole, rc1_xboole_0, t2_subset, fc7_relat_1, fc12_relat_1
% 35.45/10.13 % No. of inferences in proof: 135
% 35.45/10.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9428 ms resp. 8501 ms w/o parsing
% 36.07/10.20 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 36.07/10.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------