%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU362+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : 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 08:38:34 AM UTC 2026
% Result : Theorem 5.94s 17.36s
% Output : Refutation 6.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 50
% Syntax : Number of formulae : 143 ( 69 unt; 0 typ; 16 def)
% Number of atoms : 385 ( 70 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 929 ( 78 ~; 31 |; 69 &; 645 @)
% ( 4 <=>; 102 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 34 usr; 14 con; 0-3 aty)
% Number of variables : 207 ( 7 ^; 160 !; 24 ?; 207 :)
% ( 0 !>; 0 ?*; 0 @-; 16 @+)
% Comments :
%------------------------------------------------------------------------------
thf(rel_str_decl,type,
rel_str: $i > $o ).
thf(subrelstr_decl,type,
subrelstr: $i > $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(relation_of2_decl,type,
relation_of2: $i > $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(relation_of2_as_subset_decl,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(finite_decl,type,
finite: $i > $o ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(the_InternalRel_decl,type,
the_InternalRel: $i > $i ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(relation_decl,type,
relation: $i > $o ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $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 ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i > $i > $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk12_decl,type,
sk12: $i ).
thf(sk14_decl,type,
sk14: $i ).
thf(sk15_decl,type,
sk15: $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ ( B @ subrelstr ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ! [F: $i] :
( ( B @ the_carrier @ ( F @ element ) )
=> ( ( ( F @ ( E @ ( B @ related ) ) )
& ( F = D )
& ( E = C ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( sk1 @ ( A @ subrelstr ) )
=> ! [B: $i] :
( ( sk1 @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( sk1 @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ! [E: $i] :
( ( A @ the_carrier @ ( E @ element ) )
=> ( ( ( E @ ( D @ ( A @ related ) ) )
& ( E = C )
& ( D = B ) )
=> ( C @ ( B @ ( sk1 @ related ) ) ) ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( sk1 @ the_carrier @ ( A @ element ) )
=> ! [B: $i] :
( ( sk1 @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( sk2 @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( sk2 @ the_carrier @ ( D @ element ) )
=> ( ( ( D @ ( C @ ( sk2 @ related ) ) )
& ( D = B )
& ( C = A ) )
=> ( B @ ( A @ ( sk1 @ related ) ) ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( sk1 @ the_carrier @ ( A @ element ) )
=> ! [B: $i] :
( ( sk2 @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( sk2 @ the_carrier @ ( C @ element ) )
=> ( ( ( C @ ( B @ ( sk2 @ related ) ) )
& ( C = A )
& ( B = sk3 ) )
=> ( A @ ( sk3 @ ( sk1 @ related ) ) ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( sk2 @ the_carrier @ ( A @ element ) )
=> ! [B: $i] :
( ( sk2 @ the_carrier @ ( B @ element ) )
=> ( ( ( B @ ( A @ ( sk2 @ related ) ) )
& ( B = sk4 )
& ( A = sk3 ) )
=> ( sk4 @ ( sk3 @ ( sk1 @ related ) ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( ( sk2 @ the_carrier @ ( A @ element ) )
=> ( ( ( A @ ( sk5 @ ( sk2 @ related ) ) )
& ( A = sk4 )
& ( sk5 = sk3 ) )
=> ( sk4 @ ( sk3 @ ( sk1 @ related ) ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( A @ ( B @ ( C @ relation_of2 ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( A @ ( B @ ( C @ relation_of2_as_subset ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i] : ( A @ one_sorted_str ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i] : ( A @ rel_str ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ element ) ) ) ) ).
thf(17,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(88,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(115,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(92,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(35,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(140,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(141,plain,
! [A: $i] : ( A @ ( A @ sk17 @ element ) ),
inference(cnf,[status(esa)],[140]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(129,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)],[32]) ).
thf(29,axiom,
? [A: $i] : ( A @ rel_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(117,plain,
? [A: $i] : ( A @ rel_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(118,plain,
sk14 @ rel_str,
inference(cnf,[status(esa)],[117]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(104,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ ( B @ subrelstr ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ! [F: $i] :
( ( B @ the_carrier @ ( F @ element ) )
=> ( ( ( F @ ( E @ ( B @ related ) ) )
& ( F = D )
& ( E = C ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_yellow_0) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ ( B @ subrelstr ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ! [F: $i] :
( ( B @ the_carrier @ ( F @ element ) )
=> ( ( ( F @ ( E @ ( B @ related ) ) )
& ( F = D )
& ( E = C ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(36,plain,
~ ! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ ( B @ subrelstr ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ! [F: $i] :
( ( B @ the_carrier @ ( F @ element ) )
=> ( ( ( F @ ( E @ ( B @ related ) ) )
& ( F = D )
& ( E = C ) )
=> ( D @ ( C @ ( A @ related ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(37,plain,
( ~ ( sk4 @ ( sk3 @ ( sk1 @ related ) ) )
& ( sk6 @ ( sk5 @ ( sk2 @ related ) ) )
& ( sk6 = sk4 )
& ( sk5 = sk3 )
& ( sk2 @ the_carrier @ ( sk6 @ element ) )
& ( sk2 @ the_carrier @ ( sk5 @ element ) )
& ( sk1 @ the_carrier @ ( sk4 @ element ) )
& ( sk1 @ the_carrier @ ( sk3 @ element ) )
& ( sk1 @ ( sk2 @ subrelstr ) )
& ( sk1 @ rel_str ) ),
inference(cnf,[status(esa)],[36]) ).
thf(40,plain,
sk1 @ the_carrier @ ( sk4 @ element ),
inference(cnfConj,[status(thm)],[37]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ ( B @ subrelstr ) )
=> ( B @ rel_str ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow_0) ).
thf(90,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ ( B @ subrelstr ) )
=> ( B @ rel_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(5,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(56,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(61,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(64,plain,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(65,plain,
( ( sk11 @ finite )
& ~ ( sk11 @ empty ) ),
inference(cnf,[status(esa)],[64]) ).
thf(66,plain,
~ ( sk11 @ empty ),
inference(cnfConj,[status(thm)],[65]) ).
thf(150,plain,
( ( ( sk11 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[61,66]) ).
thf(151,plain,
( ( sk11 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[150]) ).
thf(153,plain,
sk11 != empty_set,
inference(simp,[status(thm)],[151]) ).
thf(42,plain,
sk1 @ the_carrier @ ( sk3 @ element ),
inference(cnfConj,[status(thm)],[37]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(77,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(78,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[77]) ).
thf(79,plain,
! [A: $i] :
( ~ ( A @ empty )
| ( A = empty_set ) ),
inference(lifteq,[status(thm)],[78]) ).
thf(43,plain,
sk6 = sk4,
inference(cnfConj,[status(thm)],[37]) ).
thf(48,plain,
sk6 = sk4,
inference(lifteq,[status(thm)],[43]) ).
thf(190,plain,
! [A: $i] :
( ( A != sk6 )
| ( sk4 = empty_set )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[79,48]) ).
thf(191,plain,
( ( sk4 = empty_set )
| ~ ( sk6 @ empty ) ),
inference(pattern_uni,[status(thm)],[190:[bind(A,$thf( sk6 ))]]) ).
thf(288,plain,
( ( sk4 = empty_set )
| ~ ( sk4 @ empty ) ),
inference(rewrite,[status(thm)],[191,48]) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(52,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(26,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(110,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(188,plain,
! [A: $i] :
( ( A != sk14 )
| ( empty_set @ rel_str )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[79,118]) ).
thf(189,plain,
( ( empty_set @ rel_str )
| ~ ( sk14 @ empty ) ),
inference(pattern_uni,[status(thm)],[188:[bind(A,$thf( sk14 ))]]) ).
thf(46,plain,
sk1 @ rel_str,
inference(cnfConj,[status(thm)],[37]) ).
thf(6,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(58,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(59,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[58]) ).
thf(60,plain,
~ ( sk9 @ empty ),
inference(cnf,[status(esa)],[59]) ).
thf(148,plain,
( ( ( sk9 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[61,60]) ).
thf(149,plain,
( ( sk9 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[148]) ).
thf(152,plain,
sk9 != empty_set,
inference(simp,[status(thm)],[149]) ).
thf(57,plain,
sk8 @ empty,
inference(cnf,[status(esa)],[56]) ).
thf(209,plain,
! [A: $i] :
( ( ( sk8 @ empty )
!= ( A @ empty ) )
| ~ $true
| ( A = empty_set ) ),
inference(paramod_ordered,[status(thm)],[57,79]) ).
thf(210,plain,
! [A: $i] :
( ( ( sk8 @ empty )
!= ( A @ empty ) )
| ( A = empty_set ) ),
inference(simp,[status(thm)],[209]) ).
thf(211,plain,
sk8 = empty_set,
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( sk8 ))]]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(106,plain,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(89,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(cnf,[status(esa)],[88]) ).
thf(44,plain,
sk2 @ the_carrier @ ( sk5 @ element ),
inference(cnfConj,[status(thm)],[37]) ).
thf(47,plain,
sk5 = sk3,
inference(cnfConj,[status(thm)],[37]) ).
thf(49,plain,
sk5 = sk3,
inference(lifteq,[status(thm)],[47]) ).
thf(160,plain,
sk2 @ the_carrier @ ( sk3 @ element ),
inference(rewrite,[status(thm)],[44,49]) ).
thf(11,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(70,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(31,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(124,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(21,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(96,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)],[21]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(73,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(125,plain,
! [A: $i] :
( ( ( A @ sk15 @ finite )
| ( A @ empty ) )
& ( ~ ( A @ sk15 @ empty )
| ( A @ empty ) )
& ( ( A @ powerset @ ( A @ sk15 @ element ) )
| ( A @ empty ) ) ),
inference(cnf,[status(esa)],[124]) ).
thf(128,plain,
! [A: $i] :
( ( A @ sk15 @ finite )
| ( A @ empty ) ),
inference(cnfConj,[status(thm)],[125]) ).
thf(71,plain,
~ ? [A: $i,B: $i] :
( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(miniscope,[status(thm)],[70]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[71]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ empty )
!= ( B @ empty ) )
| ~ $true
| ~ ( B @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[61,72]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ empty )
!= ( B @ empty ) )
| ~ ( B @ ( A @ in ) ) ),
inference(simp,[status(thm)],[164]) ).
thf(166,plain,
! [A: $i] :
~ ( empty_set @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[165:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).
thf(45,plain,
sk1 @ ( sk2 @ subrelstr ),
inference(cnfConj,[status(thm)],[37]) ).
thf(41,plain,
sk6 @ ( sk5 @ ( sk2 @ related ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(155,plain,
sk4 @ ( sk3 @ ( sk2 @ related ) ),
inference(rewrite,[status(thm)],[41,48,49]) ).
thf(39,plain,
~ ( sk4 @ ( sk3 @ ( sk1 @ related ) ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(156,plain,
( ( ( sk4 @ ( sk3 @ ( sk2 @ related ) ) )
!= ( sk4 @ ( sk3 @ ( sk1 @ related ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[155,39]) ).
thf(157,plain,
( ( sk4 @ ( sk3 @ ( sk2 @ related ) ) )
!= ( sk4 @ ( sk3 @ ( sk1 @ related ) ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(158,plain,
( ( sk4 != sk4 )
| ( sk3 != sk3 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[157]) ).
thf(159,plain,
sk2 != sk1,
inference(simp,[status(thm)],[158]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(113,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(13,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(75,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(76,plain,
sk12 @ one_sorted_str,
inference(cnf,[status(esa)],[75]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(98,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)],[22]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ? [B: $i] : ( A @ ( B @ subrelstr ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_yellow_0) ).
thf(108,plain,
! [A: $i] :
( ( A @ rel_str )
=> ? [B: $i] : ( A @ ( B @ subrelstr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(33,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(131,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(132,plain,
! [A: $i] :
( ( ( A @ sk16 @ finite )
| ( A @ empty ) )
& ( ~ ( A @ sk16 @ empty )
| ( A @ empty ) )
& ( ( A @ powerset @ ( A @ sk16 @ element ) )
| ( A @ empty ) ) ),
inference(cnf,[status(esa)],[131]) ).
thf(135,plain,
! [A: $i] :
( ( A @ sk16 @ finite )
| ( A @ empty ) ),
inference(cnfConj,[status(thm)],[132]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(80,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(8,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(62,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(63,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ ( B @ sk10 ) @ relation_of2_as_subset ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(3,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(50,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(67,plain,
sk11 @ finite,
inference(cnfConj,[status(thm)],[65]) ).
thf(38,plain,
sk2 @ the_carrier @ ( sk6 @ element ),
inference(cnfConj,[status(thm)],[37]) ).
thf(154,plain,
sk2 @ the_carrier @ ( sk4 @ element ),
inference(rewrite,[status(thm)],[38,48]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
<=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(82,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)],[16]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( B @ rel_str )
=> ( ( A @ ( B @ subrelstr ) )
<=> ( ( A @ the_InternalRel @ ( B @ the_InternalRel @ subset ) )
& ( A @ the_carrier @ ( B @ the_carrier @ subset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_yellow_0) ).
thf(119,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( B @ rel_str )
=> ( ( ( ( A @ the_InternalRel @ ( B @ the_InternalRel @ subset ) )
& ( A @ the_carrier @ ( B @ the_carrier @ subset ) ) )
=> ( A @ ( B @ subrelstr ) ) )
& ( ( A @ ( B @ subrelstr ) )
=> ( ( A @ the_InternalRel @ ( B @ the_InternalRel @ subset ) )
& ( A @ the_carrier @ ( B @ the_carrier @ subset ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(51,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ ( B @ sk7 ) @ relation_of2 ) ) ),
inference(cnf,[status(esa)],[50]) ).
thf(34,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/sandbox2/benchmark/theBenchmark.p',d9_orders_2) ).
thf(136,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)],[34]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ the_carrier @ ( A @ the_carrier @ ( A @ the_InternalRel @ relation_of2_as_subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_orders_2) ).
thf(94,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)],[20]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ cartesian_product2 ) @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
thf(68,plain,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ cartesian_product2 ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1142,plain,
$false,
inference(e,[status(thm)],[88,115,92,141,129,118,104,40,90,56,153,42,288,52,110,189,46,152,211,106,61,89,60,117,160,70,124,77,96,73,128,166,45,64,49,159,113,76,39,98,140,66,155,108,135,80,48,63,50,67,154,72,75,82,119,58,36,51,136,79,94,131,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU362+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % 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
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.06/15.47 % CPULimit : 300
% 0.06/15.47 % WCLimit : 300
% 0.06/15.47 % DateTime : Sat Sep 26 09:19:08 UTC 2026
% 0.06/15.47 % CPUTime :
% 0.06/15.47 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.19/15.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/15.88 % [INFO] Parsing done (107ms).
% 0.19/15.89 % [INFO] Running in sequential loop mode.
% 1.11/16.10 % [INFO] eprover registered as external prover.
% 1.11/16.11 % [INFO] Scanning for conjecture ...
% 1.30/16.17 % [INFO] Found a conjecture (or negated_conjecture) and 41 axioms. Running axiom selection ...
% 1.46/16.21 % [INFO] Axiom selection finished. Selected 33 axioms (removed 8 axioms).
% 1.46/16.24 % [INFO] Problem is first-order (TPTP FOF).
% 1.46/16.24 % [INFO] Type checking passed.
% 1.46/16.25 % [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 ...
% 5.94/17.35 % External prover 'e' found a proof!
% 5.94/17.36 % [INFO] Killing All external provers ...
% 5.94/17.36 % Time passed: 1806ms (effective reasoning time: 1467ms)
% 5.94/17.36 % 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)>
% 5.94/17.36 % Axioms used in derivation (33): redefinition_m2_relset_1, cc2_finset_1, rc4_finset_1, d13_yellow_0, dt_m2_relset_1, dt_u1_orders_2, d9_orders_2, t6_boole, t5_subset, existence_m1_relset_1, t4_subset, existence_m2_relset_1, dt_l1_orders_2, reflexivity_r1_tarski, t2_subset, existence_l1_struct_0, antisymmetry_r2_hidden, fc1_xboole_0, t1_subset, t7_boole, existence_l1_orders_2, t3_subset, cc1_relset_1, existence_m1_subset_1, existence_m1_yellow_0, dt_m1_yellow_0, rc3_finset_1, rc1_finset_1, cc1_finset_1, t8_boole, rc1_xboole_0, fc14_finset_1, rc2_xboole_0
% 5.94/17.36 % No. of inferences in proof: 127
% 5.94/17.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1806 ms resp. 1467 ms w/o parsing
% 6.11/17.42 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.11/17.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------