%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU055+1 : 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 : n016.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 17.35s 4.92s
% Output : Refutation 18.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 51
% Syntax : Number of formulae : 156 ( 72 unt; 0 typ; 11 def)
% Number of atoms : 373 ( 75 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 771 ( 75 ~; 14 |; 99 &; 522 @)
% ( 6 <=>; 55 =>; 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 : 29 ( 26 usr; 12 con; 0-2 aty)
% Number of variables : 155 ( 2 ^; 120 !; 22 ?; 155 :)
% ( 0 !>; 0 ?*; 0 @-; 11 @+)
% 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_difference_decl,type,
set_difference: $i > $i > $i ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(subset_decl,type,
subset: $i > $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 > $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_difference ) @ ( A @ relation_image ) )
= ( C @ ( A @ relation_image ) @ ( B @ ( A @ relation_image ) @ set_difference ) ) )
=> ( A @ one_to_one ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i] :
@+[B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ) ) ).
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(33,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(168,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(169,plain,
( ( sk13 @ relation_empty_yielding )
& ( sk13 @ relation ) ),
inference(cnf,[status(esa)],[168]) ).
thf(170,plain,
sk13 @ relation,
inference(cnfConj,[status(thm)],[169]) ).
thf(4,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(53,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(54,plain,
! [A: $i] :
( ( A @ sk3 @ empty )
& ( A @ powerset @ ( A @ sk3 @ element ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(56,plain,
! [A: $i] : ( A @ sk3 @ empty ),
inference(cnfConj,[status(thm)],[54]) ).
thf(3,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(49,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(50,plain,
! [A: $i] :
( ( ~ ( A @ sk2 @ empty )
| ( A @ empty ) )
& ( ( A @ powerset @ ( A @ sk2 @ element ) )
| ( A @ empty ) ) ),
inference(cnf,[status(esa)],[49]) ).
thf(52,plain,
! [A: $i] :
( ~ ( A @ sk2 @ empty )
| ( A @ empty ) ),
inference(cnfConj,[status(thm)],[50]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(137,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_difference ) )
= empty_set ) )
& ( ( ( B @ ( A @ set_difference ) )
= empty_set )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(23,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(126,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(127,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(cnf,[status(esa)],[126]) ).
thf(129,plain,
empty_set @ relation,
inference(cnfConj,[status(thm)],[127]) ).
thf(34,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(172,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(173,plain,
( ( sk14 @ relation )
& ( sk14 @ empty ) ),
inference(cnf,[status(esa)],[172]) ).
thf(174,plain,
sk14 @ empty,
inference(cnfConj,[status(thm)],[173]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( ( B @ singleton @ ( A @ singleton @ set_difference ) )
= ( A @ singleton ) )
<=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_zfmisc_1) ).
thf(185,plain,
! [A: $i,B: $i] :
( ( ( A != B )
=> ( ( B @ singleton @ ( A @ singleton @ set_difference ) )
= ( A @ singleton ) ) )
& ( ( ( B @ singleton @ ( A @ singleton @ set_difference ) )
= ( A @ singleton ) )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ set_difference ) @ ( A @ relation_image ) )
= ( C @ ( A @ relation_image ) @ ( B @ ( A @ relation_image ) @ set_difference ) ) )
=> ( A @ one_to_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_funct_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ set_difference ) @ ( A @ relation_image ) )
= ( C @ ( A @ relation_image ) @ ( B @ ( A @ relation_image ) @ set_difference ) ) )
=> ( A @ one_to_one ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(42,plain,
~ ! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ! [B: $i,C: $i] :
( ( C @ ( B @ set_difference ) @ ( A @ relation_image ) )
= ( C @ ( A @ relation_image ) @ ( B @ ( A @ relation_image ) @ set_difference ) ) )
=> ( A @ one_to_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(93,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)],[18]) ).
thf(30,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(152,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(5,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(57,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(35,axiom,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(176,plain,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(177,plain,
( ( sk15 @ one_to_one )
& ( sk15 @ function )
& ( sk15 @ relation ) ),
inference(cnf,[status(esa)],[176]) ).
thf(179,plain,
sk15 @ function,
inference(cnfConj,[status(thm)],[177]) ).
thf(7,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(63,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(64,plain,
sk5 @ empty,
inference(cnf,[status(esa)],[63]) ).
thf(11,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(73,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(74,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[73]) ).
thf(75,plain,
~ ( sk6 @ empty ),
inference(cnf,[status(esa)],[74]) ).
thf(209,plain,
( ( ( sk6 @ empty )
!= ( sk5 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[64,75]) ).
thf(210,plain,
( ( sk6 @ empty )
!= ( sk5 @ empty ) ),
inference(simp,[status(thm)],[209]) ).
thf(211,plain,
sk6 != sk5,
inference(simp,[status(thm)],[210]) ).
thf(22,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(121,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)],[22]) ).
thf(29,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(147,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_difference ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_relat_1) ).
thf(133,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ set_difference ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(20,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(116,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(180,plain,
sk15 @ one_to_one,
inference(cnfConj,[status(thm)],[177]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ one_to_one )
& ( ( B @ ( A @ set_difference ) @ ( sk1 @ relation_image ) )
= ( B @ ( sk1 @ relation_image ) @ ( A @ ( sk1 @ relation_image ) @ set_difference ) ) )
& ( sk1 @ function )
& ( sk1 @ relation ) ),
inference(cnf,[status(esa)],[42]) ).
thf(47,plain,
~ ( sk1 @ one_to_one ),
inference(cnfConj,[status(thm)],[43]) ).
thf(246,plain,
( ( ( sk15 @ one_to_one )
!= ( sk1 @ one_to_one ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[180,47]) ).
thf(247,plain,
( ( sk15 @ one_to_one )
!= ( sk1 @ one_to_one ) ),
inference(simp,[status(thm)],[246]) ).
thf(248,plain,
sk15 != sk1,
inference(simp,[status(thm)],[247]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(85,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)],[16]) ).
thf(13,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(79,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(217,plain,
( ( ( sk6 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,75]) ).
thf(218,plain,
( ( sk6 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[217]) ).
thf(220,plain,
sk6 != empty_set,
inference(simp,[status(thm)],[218]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(197,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(8,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(65,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(156,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(153,plain,
( ( sk10 @ relation )
& ~ ( sk10 @ empty ) ),
inference(cnf,[status(esa)],[152]) ).
thf(154,plain,
~ ( sk10 @ empty ),
inference(cnfConj,[status(thm)],[153]) ).
thf(239,plain,
( ( ( sk14 @ empty )
!= ( sk10 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[174,154]) ).
thf(240,plain,
( ( sk14 @ empty )
!= ( sk10 @ empty ) ),
inference(simp,[status(thm)],[239]) ).
thf(244,plain,
sk14 != sk10,
inference(simp,[status(thm)],[240]) ).
thf(41,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(205,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(45,plain,
sk1 @ function,
inference(cnfConj,[status(thm)],[43]) ).
thf(148,plain,
( ( sk9 @ function )
& ( sk9 @ empty )
& ( sk9 @ relation ) ),
inference(cnf,[status(esa)],[147]) ).
thf(149,plain,
sk9 @ relation,
inference(cnfConj,[status(thm)],[148]) ).
thf(44,plain,
sk1 @ relation,
inference(cnfConj,[status(thm)],[43]) ).
thf(6,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(59,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(40,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(200,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(201,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(cnf,[status(esa)],[200]) ).
thf(204,plain,
empty_set @ relation_empty_yielding,
inference(cnfConj,[status(thm)],[201]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(181,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(215,plain,
( ( ( sk10 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,154]) ).
thf(216,plain,
( ( sk10 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[215]) ).
thf(219,plain,
sk10 != empty_set,
inference(simp,[status(thm)],[216]) ).
thf(12,axiom,
! [A: $i] :
~ ( A @ singleton @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(76,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(206,plain,
( ( sk16 @ function )
& ( sk16 @ relation ) ),
inference(cnf,[status(esa)],[205]) ).
thf(208,plain,
sk16 @ function,
inference(cnfConj,[status(thm)],[206]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(91,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(155,plain,
sk10 @ relation,
inference(cnfConj,[status(thm)],[153]) ).
thf(24,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(130,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(135,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(150,plain,
sk9 @ empty,
inference(cnfConj,[status(thm)],[148]) ).
thf(222,plain,
( ( ( sk10 @ empty )
!= ( sk9 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[150,154]) ).
thf(223,plain,
( ( sk10 @ empty )
!= ( sk9 @ empty ) ),
inference(simp,[status(thm)],[222]) ).
thf(226,plain,
sk10 != sk9,
inference(simp,[status(thm)],[223]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(80,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',t117_funct_1) ).
thf(194,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)],[38]) ).
thf(28,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(145,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_difference ) @ ( sk1 @ relation_image ) )
= ( B @ ( sk1 @ relation_image ) @ ( A @ ( sk1 @ relation_image ) @ set_difference ) ) ),
inference(cnfConj,[status(thm)],[43]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( B @ ( sk1 @ relation_image ) @ ( A @ ( sk1 @ relation_image ) @ set_difference ) )
= ( B @ ( A @ set_difference ) @ ( sk1 @ relation_image ) ) ),
inference(lifteq,[status(thm)],[46]) ).
thf(175,plain,
sk14 @ relation,
inference(cnfConj,[status(thm)],[173]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
thf(158,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)],[32]) ).
thf(171,plain,
sk13 @ relation_empty_yielding,
inference(cnfConj,[status(thm)],[169]) ).
thf(55,plain,
! [A: $i] : ( A @ powerset @ ( A @ sk3 @ element ) ),
inference(cnfConj,[status(thm)],[54]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(114,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(21,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(119,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(207,plain,
sk16 @ relation,
inference(cnfConj,[status(thm)],[206]) ).
thf(212,plain,
( ( ( sk10 @ empty )
!= ( sk5 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[64,154]) ).
thf(213,plain,
( ( sk10 @ empty )
!= ( sk5 @ empty ) ),
inference(simp,[status(thm)],[212]) ).
thf(214,plain,
sk10 != sk5,
inference(simp,[status(thm)],[213]) ).
thf(151,plain,
sk9 @ function,
inference(cnfConj,[status(thm)],[148]) ).
thf(51,plain,
! [A: $i] :
( ( A @ powerset @ ( A @ sk2 @ element ) )
| ( A @ empty ) ),
inference(cnfConj,[status(thm)],[50]) ).
thf(9,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(68,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(178,plain,
sk15 @ relation,
inference(cnfConj,[status(thm)],[177]) ).
thf(224,plain,
( ( ( sk9 @ empty )
!= ( sk6 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[150,75]) ).
thf(225,plain,
( ( sk9 @ empty )
!= ( sk6 @ empty ) ),
inference(simp,[status(thm)],[224]) ).
thf(227,plain,
sk9 != sk6,
inference(simp,[status(thm)],[225]) ).
thf(15,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(83,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)],[15]) ).
thf(1804,plain,
$false,
inference(e,[status(thm)],[170,56,52,137,129,174,185,42,93,152,57,179,211,121,147,133,116,248,85,220,197,65,156,53,73,244,205,45,64,180,149,176,44,59,204,71,49,181,172,219,76,208,91,155,130,135,226,80,194,145,48,63,150,154,175,158,171,55,114,75,119,207,214,151,168,51,126,79,47,200,68,178,227,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU055+1 : 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
% 0.17/0.42 % Computer : n016.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 08:37:44 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 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
% 0.93/1.02 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.47/1.23 % [INFO] Parsing done (206ms).
% 1.47/1.25 % [INFO] Running in sequential loop mode.
% 2.18/1.64 % [INFO] eprover registered as external prover.
% 2.18/1.65 % [INFO] Scanning for conjecture ...
% 2.39/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 39 axioms. Running axiom selection ...
% 2.53/1.84 % [INFO] Axiom selection finished. Selected 39 axioms (removed 0 axioms).
% 2.53/1.89 % [INFO] Problem is first-order (TPTP FOF).
% 2.75/1.90 % [INFO] Type checking passed.
% 2.75/1.90 % [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 ...
% 17.35/4.91 % External prover 'e' found a proof!
% 17.35/4.91 % [INFO] Killing All external provers ...
% 17.35/4.92 % Time passed: 4351ms (effective reasoning time: 3662ms)
% 17.35/4.92 % 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)>
% 17.35/4.92 % Axioms used in derivation (39): t117_funct_1, rc3_funct_1, rc1_funct_1, t5_subset, fc2_subset_1, fc5_relat_1, rc2_relat_1, t3_boole, rc2_xboole_0, antisymmetry_r2_hidden, t20_zfmisc_1, d1_tarski, fc1_xboole_0, fc4_relat_1, t1_subset, fc3_relat_1, d8_funct_1, t37_xboole_1, cc1_relat_1, rc3_relat_1, t6_boole, rc2_subset_1, t4_boole, 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, rc1_relat_1, reflexivity_r1_tarski, t8_boole, rc1_xboole_0, t2_subset, fc7_relat_1, fc12_relat_1
% 17.35/4.92 % No. of inferences in proof: 145
% 17.35/4.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4351 ms resp. 3662 ms w/o parsing
% 18.17/5.05 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.17/5.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------