%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU105+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 : n019.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 08:37:35 AM UTC 2026
% Result : Theorem 25.55s 7.11s
% Output : Refutation 23.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 55
% Syntax : Number of formulae : 171 ( 92 unt; 0 typ; 7 def)
% Number of atoms : 420 ( 75 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 958 ( 118 ~; 24 |; 105 &; 646 @)
% ( 2 <=>; 63 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 8 con; 0-2 aty)
% Number of variables : 213 ( 2 ^; 183 !; 21 ?; 213 :)
% ( 0 !>; 0 ?*; 0 @-; 7 @+)
% Comments :
%------------------------------------------------------------------------------
thf(empty_decl,type,
empty: $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(symmetric_difference_decl,type,
symmetric_difference: $i > $i > $i ).
thf(set_intersection2_decl,type,
set_intersection2: $i > $i > $i ).
thf(preboolean_decl,type,
preboolean: $i > $o ).
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(finite_decl,type,
finite: $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(cup_closed_decl,type,
cup_closed: $i > $o ).
thf(diff_closed_decl,type,
diff_closed: $i > $o ).
thf(cap_closed_decl,type,
cap_closed: $i > $o ).
thf(relation_decl,type,
relation: $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
thf(epsilon_transitive_decl,type,
epsilon_transitive: $i > $o ).
thf(epsilon_connected_decl,type,
epsilon_connected: $i > $o ).
thf(ordinal_decl,type,
ordinal: $i > $o ).
thf(natural_decl,type,
natural: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk8_decl,type,
sk8: $i > $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk13_decl,type,
sk13: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ~ ( A @ empty )
=> ( ! [B: $i] :
( ( A @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ ( C @ element ) )
=> ( ( A @ ( C @ ( B @ set_intersection2 ) @ in ) )
& ( A @ ( C @ ( B @ symmetric_difference ) @ in ) ) ) ) )
=> ( A @ preboolean ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
( ( A @ preboolean )
& ( A @ diff_closed )
& ( A @ cap_closed )
& ( A @ cup_closed )
& ~ ( A @ empty ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ finite )
& ( B @ natural )
& ( B @ ordinal )
& ( B @ epsilon_connected )
& ( B @ epsilon_transitive )
& ( B @ one_to_one )
& ( B @ function )
& ( B @ relation )
& ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ) ) ).
thf(14,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(88,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A @ finite )
=> ( B @ ( A @ set_difference ) @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( A @ finite )
=> ( B @ ( A @ set_difference ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(30,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(129,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)],[30]) ).
thf(44,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(187,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(36,axiom,
? [A: $i] :
( ( A @ preboolean )
& ( A @ diff_closed )
& ( A @ cap_closed )
& ( A @ cup_closed )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finsub_1) ).
thf(149,plain,
? [A: $i] :
( ( A @ preboolean )
& ( A @ diff_closed )
& ( A @ cap_closed )
& ( A @ cup_closed )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(150,plain,
( ( sk9 @ preboolean )
& ( sk9 @ diff_closed )
& ( sk9 @ cap_closed )
& ( sk9 @ cup_closed )
& ~ ( sk9 @ empty ) ),
inference(cnf,[status(esa)],[149]) ).
thf(154,plain,
~ ( sk9 @ empty ),
inference(cnfConj,[status(thm)],[150]) ).
thf(47,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ finite )
& ( B @ natural )
& ( B @ ordinal )
& ( B @ epsilon_connected )
& ( B @ epsilon_transitive )
& ( B @ one_to_one )
& ( B @ function )
& ( B @ relation )
& ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_finset_1) ).
thf(197,plain,
! [A: $i] :
? [B: $i] :
( ( B @ finite )
& ( B @ natural )
& ( B @ ordinal )
& ( B @ epsilon_connected )
& ( B @ epsilon_transitive )
& ( B @ one_to_one )
& ( B @ function )
& ( B @ relation )
& ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(198,plain,
! [A: $i] :
( ( A @ sk13 @ finite )
& ( A @ sk13 @ natural )
& ( A @ sk13 @ ordinal )
& ( A @ sk13 @ epsilon_connected )
& ( A @ sk13 @ epsilon_transitive )
& ( A @ sk13 @ one_to_one )
& ( A @ sk13 @ function )
& ( A @ sk13 @ relation )
& ( A @ sk13 @ empty )
& ( A @ powerset @ ( A @ sk13 @ element ) ) ),
inference(cnf,[status(esa)],[197]) ).
thf(203,plain,
! [A: $i] : ( A @ sk13 @ epsilon_transitive ),
inference(cnfConj,[status(thm)],[198]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ preboolean )
<=> ! [B: $i,C: $i] :
( ( ( A @ ( C @ in ) )
& ( A @ ( B @ in ) ) )
=> ( ( A @ ( C @ ( B @ set_difference ) @ in ) )
& ( A @ ( C @ ( B @ set_union2 ) @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_finsub_1) ).
thf(170,plain,
! [A: $i] :
( ( ! [B: $i,C: $i] :
( ( ( A @ ( C @ in ) )
& ( A @ ( B @ in ) ) )
=> ( ( A @ ( C @ ( B @ set_difference ) @ in ) )
& ( A @ ( C @ ( B @ set_union2 ) @ in ) ) ) )
=> ( A @ preboolean ) )
& ( ( A @ preboolean )
=> ! [B: $i,C: $i] :
( ( ( A @ ( C @ in ) )
& ( A @ ( B @ in ) ) )
=> ( ( A @ ( C @ ( B @ set_difference ) @ in ) )
& ( A @ ( C @ ( B @ set_union2 ) @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(25,axiom,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(115,plain,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(89,plain,
sk2 @ empty,
inference(cnf,[status(esa)],[88]) ).
thf(1,conjecture,
! [A: $i] :
( ~ ( A @ empty )
=> ( ! [B: $i] :
( ( A @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ ( C @ element ) )
=> ( ( A @ ( C @ ( B @ set_intersection2 ) @ in ) )
& ( A @ ( C @ ( B @ symmetric_difference ) @ in ) ) ) ) )
=> ( A @ preboolean ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_finsub_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ~ ( A @ empty )
=> ( ! [B: $i] :
( ( A @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ ( C @ element ) )
=> ( ( A @ ( C @ ( B @ set_intersection2 ) @ in ) )
& ( A @ ( C @ ( B @ symmetric_difference ) @ in ) ) ) ) )
=> ( A @ preboolean ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(50,plain,
~ ! [A: $i] :
( ~ ( A @ empty )
=> ( ! [B: $i] :
( ( A @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ ( C @ element ) )
=> ( ( A @ ( C @ ( B @ set_intersection2 ) @ in ) )
& ( A @ ( C @ ( B @ symmetric_difference ) @ in ) ) ) ) )
=> ( A @ preboolean ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ preboolean )
& ( ( sk1 @ ( B @ ( A @ set_intersection2 ) @ in ) )
| ~ ( sk1 @ ( B @ element ) )
| ~ ( sk1 @ ( A @ element ) ) )
& ( ( sk1 @ ( B @ ( A @ symmetric_difference ) @ in ) )
| ~ ( sk1 @ ( B @ element ) )
| ~ ( sk1 @ ( A @ element ) ) )
& ~ ( sk1 @ empty ) ),
inference(cnf,[status(esa)],[50]) ).
thf(52,plain,
~ ( sk1 @ empty ),
inference(cnfConj,[status(thm)],[51]) ).
thf(215,plain,
( ( ( sk2 @ empty )
!= ( sk1 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[89,52]) ).
thf(216,plain,
( ( sk2 @ empty )
!= ( sk1 @ empty ) ),
inference(simp,[status(thm)],[215]) ).
thf(217,plain,
sk2 != sk1,
inference(simp,[status(thm)],[216]) ).
thf(22,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(108,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(43,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(184,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(185,plain,
~ ? [A: $i] : ( A @ powerset @ empty ),
inference(miniscope,[status(thm)],[184]) ).
thf(186,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(cnf,[status(esa)],[185]) ).
thf(244,plain,
! [A: $i] :
( ( ( A @ powerset @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,186]) ).
thf(245,plain,
! [A: $i] :
( ( A @ powerset @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[244]) ).
thf(247,plain,
! [A: $i] :
( ( A @ powerset )
!= empty_set ),
inference(simp,[status(thm)],[245]) ).
thf(202,plain,
! [A: $i] : ( A @ sk13 @ function ),
inference(cnfConj,[status(thm)],[198]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(56,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(153,plain,
sk9 @ diff_closed,
inference(cnfConj,[status(thm)],[150]) ).
thf(152,plain,
sk9 @ cup_closed,
inference(cnfConj,[status(thm)],[150]) ).
thf(11,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(78,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(164,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)],[40]) ).
thf(21,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(105,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(106,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[105]) ).
thf(107,plain,
~ ( sk3 @ empty ),
inference(cnf,[status(esa)],[106]) ).
thf(233,plain,
( ( ( sk3 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,107]) ).
thf(234,plain,
( ( sk3 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[233]) ).
thf(238,plain,
sk3 != empty_set,
inference(simp,[status(thm)],[234]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(121,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(5,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(61,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( B @ finite )
=> ( B @ ( A @ set_intersection2 ) @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(133,plain,
! [A: $i,B: $i] :
( ( B @ finite )
=> ( B @ ( A @ set_intersection2 ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(218,plain,
( ( ( sk3 @ empty )
!= ( sk2 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[89,107]) ).
thf(219,plain,
( ( sk3 @ empty )
!= ( sk2 @ empty ) ),
inference(simp,[status(thm)],[218]) ).
thf(220,plain,
sk3 != sk2,
inference(simp,[status(thm)],[219]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(102,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ set_union2 ) @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(59,plain,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ set_union2 ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_union2 ) @ finite )
| ~ ( B @ finite )
| ~ ( A @ finite ) ),
inference(cnf,[status(esa)],[59]) ).
thf(116,plain,
( ( sk5 @ finite )
& ~ ( sk5 @ empty ) ),
inference(cnf,[status(esa)],[115]) ).
thf(117,plain,
~ ( sk5 @ empty ),
inference(cnfConj,[status(thm)],[116]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( A @ finite )
=> ( B @ ( A @ set_intersection2 ) @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(85,plain,
! [A: $i,B: $i] :
( ( A @ finite )
=> ( B @ ( A @ set_intersection2 ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(201,plain,
! [A: $i] : ( A @ sk13 @ relation ),
inference(cnfConj,[status(thm)],[198]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ symmetric_difference ) @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc17_finset_1) ).
thf(92,plain,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ symmetric_difference ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(18,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(97,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( B @ ( A @ set_intersection2 ) @ ( B @ ( A @ symmetric_difference ) @ symmetric_difference ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_xboole_1) ).
thf(156,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( B @ ( A @ set_intersection2 ) @ ( B @ ( A @ symmetric_difference ) @ symmetric_difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( sk1 @ ( B @ ( A @ symmetric_difference ) @ in ) )
| ~ ( sk1 @ ( B @ element ) )
| ~ ( sk1 @ ( A @ element ) ) ),
inference(cnfConj,[status(thm)],[51]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(109,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(49,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(212,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(9,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(73,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(231,plain,
( ( ( sk9 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,154]) ).
thf(232,plain,
( ( sk9 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[231]) ).
thf(237,plain,
sk9 != empty_set,
inference(simp,[status(thm)],[232]) ).
thf(35,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(145,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(146,plain,
! [A: $i] :
( ( A @ sk8 @ empty )
& ( A @ powerset @ ( A @ sk8 @ element ) ) ),
inference(cnf,[status(esa)],[145]) ).
thf(148,plain,
! [A: $i] : ( A @ sk8 @ empty ),
inference(cnfConj,[status(thm)],[146]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ symmetric_difference ) )
= ( A @ ( B @ symmetric_difference ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).
thf(161,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ symmetric_difference ) )
= ( A @ ( B @ symmetric_difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(64,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(118,plain,
sk5 @ finite,
inference(cnfConj,[status(thm)],[116]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( sk1 @ ( B @ ( A @ set_intersection2 ) @ in ) )
| ~ ( sk1 @ ( B @ element ) )
| ~ ( sk1 @ ( A @ element ) ) ),
inference(cnfConj,[status(thm)],[51]) ).
thf(229,plain,
( ( ( sk5 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,117]) ).
thf(230,plain,
( ( sk5 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[229]) ).
thf(236,plain,
sk5 != empty_set,
inference(simp,[status(thm)],[230]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ symmetric_difference ) )
= ( A @ ( B @ set_difference ) @ ( B @ ( A @ set_difference ) @ set_union2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).
thf(181,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ symmetric_difference ) )
= ( A @ ( B @ set_difference ) @ ( B @ ( A @ set_difference ) @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(38,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(159,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(34,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(140,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(155,plain,
sk9 @ preboolean,
inference(cnfConj,[status(thm)],[150]) ).
thf(221,plain,
( ( ( sk5 @ empty )
!= ( sk2 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[89,117]) ).
thf(222,plain,
( ( sk5 @ empty )
!= ( sk2 @ empty ) ),
inference(simp,[status(thm)],[221]) ).
thf(223,plain,
sk5 != sk2,
inference(simp,[status(thm)],[222]) ).
thf(33,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(135,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(224,plain,
( ( ( sk9 @ empty )
!= ( sk2 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[89,154]) ).
thf(225,plain,
( ( sk9 @ empty )
!= ( sk2 @ empty ) ),
inference(simp,[status(thm)],[224]) ).
thf(226,plain,
sk9 != sk2,
inference(simp,[status(thm)],[225]) ).
thf(55,plain,
~ ( sk1 @ preboolean ),
inference(cnfConj,[status(thm)],[51]) ).
thf(239,plain,
( ( ( sk9 @ preboolean )
!= ( sk1 @ preboolean ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[155,55]) ).
thf(240,plain,
( ( sk9 @ preboolean )
!= ( sk1 @ preboolean ) ),
inference(simp,[status(thm)],[239]) ).
thf(241,plain,
sk9 != sk1,
inference(simp,[status(thm)],[240]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(209,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(123,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(46,axiom,
! [A: $i] :
( ( empty_set @ ( A @ symmetric_difference ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_boole) ).
thf(194,plain,
! [A: $i] :
( ( empty_set @ ( A @ symmetric_difference ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(7,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(67,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(199,plain,
! [A: $i] : ( A @ sk13 @ natural ),
inference(cnfConj,[status(thm)],[198]) ).
thf(248,plain,
! [A: $i] :
( ( ( A @ sk8 @ empty )
!= ( sk1 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[148,52]) ).
thf(249,plain,
! [A: $i] :
( ( A @ sk8 @ empty )
!= ( sk1 @ empty ) ),
inference(simp,[status(thm)],[248]) ).
thf(258,plain,
! [A: $i] :
( ( A @ sk8 )
!= sk1 ),
inference(simp,[status(thm)],[249]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(75,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_difference ) )
= ( B @ ( A @ set_intersection2 ) @ ( A @ symmetric_difference ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_xboole_1) ).
thf(82,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_difference ) )
= ( B @ ( A @ set_intersection2 ) @ ( A @ symmetric_difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(26,axiom,
! [A: $i] :
( ( ( A @ diff_closed )
& ( A @ cup_closed ) )
=> ( A @ preboolean ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finsub_1) ).
thf(119,plain,
! [A: $i] :
( ( ( A @ diff_closed )
& ( A @ cup_closed ) )
=> ( A @ preboolean ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(cnf,[status(esa)],[56]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(227,plain,
( ( ( sk1 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[108,52]) ).
thf(228,plain,
( ( sk1 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[227]) ).
thf(235,plain,
sk1 != empty_set,
inference(simp,[status(thm)],[228]) ).
thf(242,plain,
! [A: $i] :
( ( ( A @ powerset @ empty )
!= ( sk2 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[89,186]) ).
thf(243,plain,
! [A: $i] :
( ( A @ powerset @ empty )
!= ( sk2 @ empty ) ),
inference(simp,[status(thm)],[242]) ).
thf(246,plain,
! [A: $i] :
( ( A @ powerset )
!= sk2 ),
inference(simp,[status(thm)],[243]) ).
thf(151,plain,
sk9 @ cap_closed,
inference(cnfConj,[status(thm)],[150]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ preboolean )
=> ( ( A @ diff_closed )
& ( A @ cup_closed ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finsub_1) ).
thf(190,plain,
! [A: $i] :
( ( A @ preboolean )
=> ( ( A @ diff_closed )
& ( A @ cup_closed ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(126,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(17,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(94,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(131,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(200,plain,
! [A: $i] : ( A @ sk13 @ finite ),
inference(cnfConj,[status(thm)],[198]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(100,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(90,plain,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(24,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(111,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1817,plain,
$false,
inference(e,[status(thm)],[88,70,129,187,154,203,170,115,217,247,202,56,153,52,184,152,78,164,238,121,61,89,133,220,102,60,117,85,201,92,197,97,156,53,109,212,73,237,105,148,161,64,149,59,118,54,236,181,159,140,155,108,223,135,226,241,209,123,194,145,50,67,199,258,186,55,75,82,119,58,235,246,151,190,107,126,94,131,200,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU105+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
% 0.14/0.39 % Computer : n019.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 08:36:18 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 1.31/1.23 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.81/1.55 % [INFO] Parsing done (316ms).
% 1.81/1.57 % [INFO] Running in sequential loop mode.
% 2.93/2.17 % [INFO] eprover registered as external prover.
% 2.93/2.18 % [INFO] Scanning for conjecture ...
% 3.19/2.33 % [INFO] Found a conjecture (or negated_conjecture) and 47 axioms. Running axiom selection ...
% 3.35/2.46 % [INFO] Axiom selection finished. Selected 47 axioms (removed 0 axioms).
% 3.57/2.57 % [INFO] Problem is first-order (TPTP FOF).
% 3.57/2.58 % [INFO] Type checking passed.
% 3.57/2.59 % [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 ...
% 25.55/7.11 % External prover 'e' found a proof!
% 25.55/7.11 % [INFO] Killing All external provers ...
% 25.55/7.11 % Time passed: 6505ms (effective reasoning time: 5525ms)
% 25.55/7.11 % 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)>
% 25.55/7.11 % Axioms used in derivation (47): t5_boole, cc2_finset_1, t2_boole, commutativity_k3_xboole_0, commutativity_k5_xboole_0, rc1_subset_1, d6_xboole_0, t2_subset, idempotence_k2_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, idempotence_k3_xboole_0, rc4_finset_1, t1_boole, rc1_finsub_1, fc1_xboole_0, t1_subset, fc11_finset_1, cc2_finsub_1, fc2_xboole_0, fc10_finset_1, t6_boole, rc2_subset_1, fc9_finset_1, fc17_finset_1, commutativity_k2_xboole_0, t5_subset, t4_boole, t4_subset, fc3_xboole_0, t7_boole, fc1_subset_1, t3_subset, existence_m1_subset_1, t100_xboole_1, cc1_finsub_1, rc2_finset_1, reflexivity_r1_tarski, rc3_finset_1, t94_xboole_1, rc1_finset_1, cc1_finset_1, fc12_finset_1, t8_boole, rc1_xboole_0, t3_boole, t10_finsub_1
% 25.55/7.11 % No. of inferences in proof: 164
% 25.55/7.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6505 ms resp. 5525 ms w/o parsing
% 23.13/7.25 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 23.13/7.26 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------