%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU339+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:38:30 AM UTC 2026
% Result : Theorem 59.65s 11.66s
% Output : Refutation 50.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 46
% Syntax : Number of formulae : 139 ( 78 unt; 0 typ; 10 def)
% Number of atoms : 321 ( 62 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 811 ( 78 ~; 20 |; 54 &; 585 @)
% ( 6 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 30 usr; 10 con; 0-3 aty)
% Number of variables : 213 ( 4 ^; 177 !; 22 ?; 213 :)
% ( 0 !>; 0 ?*; 0 @-; 10 @+)
% Comments :
%------------------------------------------------------------------------------
thf(antisymmetric_relstr_decl,type,
antisymmetric_relstr: $i > $o ).
thf(rel_str_decl,type,
rel_str: $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(the_carrier_decl,type,
the_carrier: $i > $i ).
thf(related_decl,type,
related: $i > $i > $i > $o ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(relation_of2_decl,type,
relation_of2: $i > $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(relation_decl,type,
relation: $i > $o ).
thf(is_antisymmetric_in_decl,type,
is_antisymmetric_in: $i > $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(relation_of2_as_subset_decl,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(the_InternalRel_decl,type,
the_InternalRel: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk12_decl,type,
sk12: $i ).
thf(sk13_decl,type,
sk13: $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ related ) ) )
& ( C @ ( B @ ( A @ related ) ) ) )
=> ( B = C ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( sk1 @ the_carrier @ ( A @ element ) )
=> ! [B: $i] :
( ( sk1 @ the_carrier @ ( B @ element ) )
=> ( ( ( A @ ( B @ ( sk1 @ related ) ) )
& ( B @ ( A @ ( sk1 @ related ) ) ) )
=> ( A = B ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( sk1 @ the_carrier @ ( A @ element ) )
=> ( ( ( sk2 @ ( A @ ( sk1 @ related ) ) )
& ( A @ ( sk2 @ ( sk1 @ related ) ) ) )
=> ( sk2 = A ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( A @ ( B @ ( C @ relation_of2 ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] : ( A @ one_sorted_str ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i] : ( A @ rel_str ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ element ) ) ) ) ).
thf(29,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(138,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(120,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(35,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(153,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(12,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(85,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ related ) ) )
& ( C @ ( B @ ( A @ related ) ) ) )
=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_orders_2) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ related ) ) )
& ( C @ ( B @ ( A @ related ) ) ) )
=> ( B = C ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(38,plain,
~ ! [A: $i] :
( ( ( A @ rel_str )
& ( A @ antisymmetric_relstr ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( B @ ( C @ ( A @ related ) ) )
& ( C @ ( B @ ( A @ related ) ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(26,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(128,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)],[26]) ).
thf(10,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(81,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(154,plain,
! [A: $i] :
( ( A @ sk13 @ empty )
& ( A @ powerset @ ( A @ sk13 @ element ) ) ),
inference(cnf,[status(esa)],[153]) ).
thf(155,plain,
! [A: $i] : ( A @ powerset @ ( A @ sk13 @ element ) ),
inference(cnfConj,[status(thm)],[154]) ).
thf(156,plain,
! [A: $i] : ( A @ sk13 @ empty ),
inference(cnfConj,[status(thm)],[154]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(107,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(108,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[107]) ).
thf(109,plain,
! [A: $i] :
( ~ ( A @ empty )
| ( A = empty_set ) ),
inference(lifteq,[status(thm)],[108]) ).
thf(255,plain,
! [B: $i,A: $i] :
( ( ( A @ sk13 @ empty )
!= ( B @ empty ) )
| ~ $true
| ( B = empty_set ) ),
inference(paramod_ordered,[status(thm)],[156,109]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ( ( A @ sk13 @ empty )
!= ( B @ empty ) )
| ( B = empty_set ) ),
inference(simp,[status(thm)],[255]) ).
thf(257,plain,
! [A: $i] :
( ( A @ sk13 )
= empty_set ),
inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( C )),bind(B,$thf( C @ sk13 ))]]) ).
thf(289,plain,
! [A: $i] :
( ( A @ sk13 )
= empty_set ),
inference(simp,[status(thm)],[257]) ).
thf(345,plain,
! [A: $i] : ( A @ powerset @ ( empty_set @ element ) ),
inference(rewrite,[status(thm)],[155,289]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(cnf,[status(esa)],[48]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(lifteq,[status(thm)],[49]) ).
thf(39,plain,
( ( sk2 != sk3 )
& ( sk2 @ ( sk3 @ ( sk1 @ related ) ) )
& ( sk3 @ ( sk2 @ ( sk1 @ related ) ) )
& ( sk1 @ the_carrier @ ( sk3 @ element ) )
& ( sk1 @ the_carrier @ ( sk2 @ element ) )
& ( sk1 @ rel_str )
& ( sk1 @ antisymmetric_relstr ) ),
inference(cnf,[status(esa)],[38]) ).
thf(40,plain,
sk2 != sk3,
inference(cnfConj,[status(thm)],[39]) ).
thf(47,plain,
sk3 != sk2,
inference(lifteq,[status(thm)],[40]) ).
thf(42,plain,
sk1 @ the_carrier @ ( sk2 @ element ),
inference(cnfConj,[status(thm)],[39]) ).
thf(6,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(57,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(58,plain,
sk5 @ empty,
inference(cnf,[status(esa)],[57]) ).
thf(286,plain,
! [A: $i] :
( ( ( sk5 @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[58,109]) ).
thf(287,plain,
! [A: $i] :
( ( ( sk5 @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[286]) ).
thf(288,plain,
sk5 = empty_set,
inference(pattern_uni,[status(thm)],[287:[bind(A,$thf( sk5 ))]]) ).
thf(4,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(51,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(52,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ ( B @ sk4 ) @ relation_of2 ) ) ),
inference(cnf,[status(esa)],[51]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(110,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ related ) ) )
<=> ( A @ the_InternalRel @ ( C @ ( B @ ordered_pair ) @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_orders_2) ).
thf(157,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( A @ the_InternalRel @ ( C @ ( B @ ordered_pair ) @ in ) )
=> ( C @ ( B @ ( A @ related ) ) ) )
& ( ( C @ ( B @ ( A @ related ) ) )
=> ( A @ the_InternalRel @ ( C @ ( B @ ordered_pair ) @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(46,plain,
sk2 @ ( sk3 @ ( sk1 @ related ) ),
inference(cnfConj,[status(thm)],[39]) ).
thf(15,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(92,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(93,plain,
sk10 @ one_sorted_str,
inference(cnf,[status(esa)],[92]) ).
thf(9,axiom,
! [A: $i] :
~ ( A @ singleton @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(78,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(16,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(94,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(95,plain,
~ ? [A: $i] : ( A @ powerset @ empty ),
inference(miniscope,[status(thm)],[94]) ).
thf(96,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(cnf,[status(esa)],[95]) ).
thf(175,plain,
! [A: $i] :
( ( ( A @ powerset @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,96]) ).
thf(176,plain,
! [A: $i] :
( ( A @ powerset @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[175]) ).
thf(179,plain,
! [A: $i] :
( ( A @ powerset )
!= empty_set ),
inference(simp,[status(thm)],[176]) ).
thf(18,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(104,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(105,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ unordered_pair ) @ empty ),
inference(miniscope,[status(thm)],[104]) ).
thf(106,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
inference(cnf,[status(esa)],[105]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
<=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(97,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) )
=> ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
& ( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(53,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(141,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(8,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(75,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(76,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[75]) ).
thf(77,plain,
~ ( sk8 @ empty ),
inference(cnf,[status(esa)],[76]) ).
thf(79,plain,
~ ? [A: $i] : ( A @ singleton @ empty ),
inference(miniscope,[status(thm)],[78]) ).
thf(80,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(cnf,[status(esa)],[79]) ).
thf(169,plain,
! [A: $i] :
( ( ( A @ singleton @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,80]) ).
thf(170,plain,
! [A: $i] :
( ( A @ singleton @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[169]) ).
thf(173,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(simp,[status(thm)],[170]) ).
thf(41,plain,
sk1 @ rel_str,
inference(cnfConj,[status(thm)],[39]) ).
thf(45,plain,
sk1 @ antisymmetric_relstr,
inference(cnfConj,[status(thm)],[39]) ).
thf(37,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(161,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(149,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(44,plain,
sk3 @ ( sk2 @ ( sk1 @ related ) ),
inference(cnfConj,[status(thm)],[39]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ ( A @ is_antisymmetric_in ) )
<=> ! [C: $i,D: $i] :
( ( ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_2) ).
thf(59,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( ! [C: $i,D: $i] :
( ( ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) )
=> ( C = D ) )
=> ( B @ ( A @ is_antisymmetric_in ) ) )
& ( ( B @ ( A @ is_antisymmetric_in ) )
=> ! [C: $i,D: $i] :
( ( ( A @ ( C @ ( D @ ordered_pair ) @ in ) )
& ( A @ ( D @ ( C @ ordered_pair ) @ in ) )
& ( B @ ( D @ in ) )
& ( B @ ( C @ in ) ) )
=> ( C = D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(22,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(118,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(31,axiom,
? [A: $i] : ( A @ rel_str ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(143,plain,
? [A: $i] : ( A @ rel_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(144,plain,
sk12 @ rel_str,
inference(cnf,[status(esa)],[143]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ( ( A @ sk13 @ empty )
!= ( B @ powerset @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[156,96]) ).
thf(186,plain,
! [B: $i,A: $i] :
( ( A @ sk13 @ empty )
!= ( B @ powerset @ empty ) ),
inference(simp,[status(thm)],[185]) ).
thf(189,plain,
! [B: $i,A: $i] :
( ( A @ sk13 )
!= ( B @ powerset ) ),
inference(simp,[status(thm)],[186]) ).
thf(335,plain,
! [A: $i] :
( ( A @ powerset )
!= empty_set ),
inference(rewrite,[status(thm)],[189,289]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(130,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)],[27]) ).
thf(162,plain,
! [A: $i] : ( A @ ( A @ sk14 @ element ) ),
inference(cnf,[status(esa)],[161]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
<=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(112,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ) )
& ( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ antisymmetric_relstr )
<=> ( A @ the_carrier @ ( A @ the_InternalRel @ is_antisymmetric_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_orders_2) ).
thf(145,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ the_carrier @ ( A @ the_InternalRel @ is_antisymmetric_in ) )
=> ( A @ antisymmetric_relstr ) )
& ( ( A @ antisymmetric_relstr )
=> ( A @ the_carrier @ ( A @ the_InternalRel @ is_antisymmetric_in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(43,plain,
sk1 @ the_carrier @ ( sk3 @ element ),
inference(cnfConj,[status(thm)],[39]) ).
thf(230,plain,
! [A: $i] :
( ( A != sk3 )
| ( sk2 != empty_set )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[109,47]) ).
thf(231,plain,
( ( sk2 != empty_set )
| ~ ( sk3 @ empty ) ),
inference(pattern_uni,[status(thm)],[230:[bind(A,$thf( sk3 ))]]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(87,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(119,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(cnf,[status(esa)],[118]) ).
thf(11,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(82,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(151,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(166,plain,
( ( ( sk8 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,77]) ).
thf(167,plain,
( ( sk8 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[166]) ).
thf(168,plain,
sk8 != empty_set,
inference(simp,[status(thm)],[167]) ).
thf(267,plain,
! [A: $i] :
( ( A != sk1 )
| ( empty_set @ rel_str )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[109,41]) ).
thf(268,plain,
( ( empty_set @ rel_str )
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[267:[bind(A,$thf( sk1 ))]]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ relation_of2_as_subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(126,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ relation_of2_as_subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(136,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(90,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(24,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(122,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(11126,plain,
$false,
inference(e,[status(thm)],[138,120,153,85,38,128,81,345,48,50,47,42,288,52,110,157,46,93,289,57,78,179,106,92,97,53,141,109,77,96,173,41,45,161,149,44,59,118,144,335,130,80,162,112,145,143,43,231,87,104,75,119,82,151,168,51,107,268,94,126,136,90,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU339+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % 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
% 0.14/0.40 % Computer : n004.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % 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 09:15:22 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.69/0.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.92/0.84 % [INFO] Parsing done (126ms).
% 0.92/0.85 % [INFO] Running in sequential loop mode.
% 1.59/1.07 % [INFO] eprover registered as external prover.
% 1.59/1.07 % [INFO] Scanning for conjecture ...
% 1.59/1.13 % [INFO] Found a conjecture (or negated_conjecture) and 45 axioms. Running axiom selection ...
% 1.87/1.19 % [INFO] Axiom selection finished. Selected 35 axioms (removed 10 axioms).
% 1.99/1.22 % [INFO] Problem is first-order (TPTP FOF).
% 1.99/1.23 % [INFO] Type checking passed.
% 1.99/1.23 % [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 ...
% 59.65/11.65 % External prover 'e' found a proof!
% 59.65/11.65 % [INFO] Killing All external provers ...
% 59.65/11.65 % Time passed: 11156ms (effective reasoning time: 10795ms)
% 59.65/11.65 % 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)>
% 59.65/11.66 % Axioms used in derivation (35): redefinition_m2_relset_1, dt_m2_relset_1, dt_u1_orders_2, d9_orders_2, t4_subset, rc1_subset_1, t106_zfmisc_1, existence_m2_relset_1, dt_l1_orders_2, reflexivity_r1_tarski, t2_subset, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, d5_tarski, t1_subset, fc4_subset_1, d6_orders_2, t6_boole, rc2_subset_1, fc3_subset_1, t5_subset, existence_m1_relset_1, fc2_subset_1, t7_boole, existence_l1_orders_2, fc1_subset_1, t3_subset, cc1_relset_1, existence_m1_subset_1, commutativity_k2_tarski, t8_boole, rc1_xboole_0, existence_l1_struct_0, d4_relat_2
% 59.65/11.66 % No. of inferences in proof: 129
% 59.65/11.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 11156 ms resp. 10795 ms w/o parsing
% 50.22/11.77 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 50.22/11.77 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------