%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU110+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 : n020.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 08:37:36 AM UTC 2026
% Result : Theorem 53.93s 12.04s
% Output : Refutation 46.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 42
% Syntax : Number of formulae : 145 ( 61 unt; 0 typ; 8 def)
% Number of atoms : 393 ( 52 equ; 0 cnn)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 882 ( 119 ~; 36 |; 122 &; 551 @)
% ( 4 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 9 con; 0-2 aty)
% Number of variables : 180 ( 2 ^; 142 !; 28 ?; 180 :)
% ( 0 !>; 0 ?*; 0 @-; 8 @+)
% Comments :
%------------------------------------------------------------------------------
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(finite_subsets_decl,type,
finite_subsets: $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(finite_decl,type,
finite: $i > $o ).
thf(cup_closed_decl,type,
cup_closed: $i > $o ).
thf(diff_closed_decl,type,
diff_closed: $i > $o ).
thf(preboolean_decl,type,
preboolean: $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(cap_closed_decl,type,
cap_closed: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk9_decl,type,
sk9: $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ subset ) )
=> ( B @ finite_subsets @ ( A @ finite_subsets @ subset ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A @ ( sk1 @ subset ) )
=> ( A @ finite_subsets @ ( sk1 @ finite_subsets @ subset ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [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(sk11_def,definition,
( sk11
= ( @+[A: $i] :
( ( A @ preboolean )
& ( A @ diff_closed )
& ( A @ cap_closed )
& ( A @ cup_closed )
& ~ ( A @ empty ) ) ) ) ).
thf(25,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(112,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)],[25]) ).
thf(113,plain,
! [A: $i] :
( ( A @ sk10 @ finite )
& ( A @ sk10 @ natural )
& ( A @ sk10 @ ordinal )
& ( A @ sk10 @ epsilon_connected )
& ( A @ sk10 @ epsilon_transitive )
& ( A @ sk10 @ one_to_one )
& ( A @ sk10 @ function )
& ( A @ sk10 @ relation )
& ( A @ sk10 @ empty )
& ( A @ powerset @ ( A @ sk10 @ element ) ) ),
inference(cnf,[status(esa)],[112]) ).
thf(115,plain,
! [A: $i] : ( A @ sk10 @ finite ),
inference(cnfConj,[status(thm)],[113]) ).
thf(8,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(54,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(55,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[54]) ).
thf(56,plain,
~ ( sk4 @ empty ),
inference(cnf,[status(esa)],[55]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,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(84,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ element ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(26,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(124,plain,
? [A: $i] :
( ( A @ preboolean )
& ( A @ diff_closed )
& ( A @ cap_closed )
& ( A @ cup_closed )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(125,plain,
( ( sk11 @ preboolean )
& ( sk11 @ diff_closed )
& ( sk11 @ cap_closed )
& ( sk11 @ cup_closed )
& ~ ( sk11 @ empty ) ),
inference(cnf,[status(esa)],[124]) ).
thf(129,plain,
sk11 @ diff_closed,
inference(cnfConj,[status(thm)],[125]) ).
thf(130,plain,
sk11 @ cap_closed,
inference(cnfConj,[status(thm)],[125]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(40,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(41,plain,
~ ? [A: $i] :
( ? [B: $i] :
( ( B @ empty )
& ( A != B ) )
& ( A @ empty ) ),
inference(miniscope,[status(thm)],[40]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ( A = B )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[41]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( A @ empty )
| ( A = B ) ),
inference(lifteq,[status(thm)],[42]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( B @ finite_subsets @ ( A @ finite_subsets @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finsub_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( B @ finite_subsets @ ( A @ finite_subsets @ subset ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(36,plain,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( B @ finite_subsets @ ( A @ finite_subsets @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(37,plain,
( ~ ( sk2 @ finite_subsets @ ( sk1 @ finite_subsets @ subset ) )
& ( sk2 @ ( sk1 @ subset ) ) ),
inference(cnf,[status(esa)],[36]) ).
thf(38,plain,
sk2 @ ( sk1 @ subset ),
inference(cnfConj,[status(thm)],[37]) ).
thf(39,plain,
~ ( sk2 @ finite_subsets @ ( sk1 @ finite_subsets @ subset ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(205,plain,
( ( ( sk2 @ finite_subsets @ ( sk1 @ finite_subsets @ subset ) )
!= ( sk2 @ ( sk1 @ subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[38,39]) ).
thf(206,plain,
( ( sk2 @ finite_subsets @ ( sk1 @ finite_subsets @ subset ) )
!= ( sk2 @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[205]) ).
thf(207,plain,
( ( ( sk2 @ finite_subsets )
!= sk2 )
| ( ( sk1 @ finite_subsets )
!= sk1 ) ),
inference(simp,[status(thm)],[206]) ).
thf(352,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ finite_subsets ) )
| ( B != sk2 )
| ( ( sk1 @ finite_subsets )
!= sk1 )
| ~ ( B @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[43,207]) ).
thf(353,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( sk1 @ finite_subsets )
!= sk1 )
| ~ ( A @ empty )
| ~ ( sk2 @ finite_subsets @ empty ) ),
inference(pattern_uni,[status(thm)],[352:[bind(A,$thf( sk2 @ finite_subsets )),bind(B,$thf( B ))]]) ).
thf(364,plain,
( ( ( sk1 @ finite_subsets )
!= sk1 )
| ~ ( sk2 @ empty )
| ~ ( sk2 @ finite_subsets @ empty ) ),
inference(simp,[status(thm)],[353]) ).
thf(4,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(44,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(45,plain,
sk3 @ empty,
inference(cnf,[status(esa)],[44]) ).
thf(187,plain,
( ( ( sk4 @ empty )
!= ( sk3 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[45,56]) ).
thf(188,plain,
( ( sk4 @ empty )
!= ( sk3 @ empty ) ),
inference(simp,[status(thm)],[187]) ).
thf(189,plain,
sk4 != sk3,
inference(simp,[status(thm)],[188]) ).
thf(5,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(46,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(93,plain,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(9,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(57,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(116,plain,
! [A: $i] : ( A @ sk10 @ relation ),
inference(cnfConj,[status(thm)],[113]) ).
thf(20,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(89,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ finite_subsets @ preboolean )
& ( A @ finite_subsets @ diff_closed )
& ( A @ finite_subsets @ cup_closed )
& ~ ( A @ finite_subsets @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_finsub_1) ).
thf(133,plain,
! [A: $i] :
( ( A @ finite_subsets @ preboolean )
& ( A @ finite_subsets @ diff_closed )
& ( A @ finite_subsets @ cup_closed )
& ~ ( A @ finite_subsets @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(356,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk1 @ finite_subsets ) )
| ( ( sk2 @ finite_subsets )
!= sk2 )
| ( A != sk1 )
| ~ ( B @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[43,207]) ).
thf(357,plain,
! [A: $i] :
( ( ( sk2 @ finite_subsets )
!= sk2 )
| ( A != sk1 )
| ~ ( sk1 @ finite_subsets @ empty )
| ~ ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[356:[bind(A,$thf( A )),bind(B,$thf( sk1 @ finite_subsets ))]]) ).
thf(366,plain,
( ( ( sk2 @ finite_subsets )
!= sk2 )
| ~ ( sk1 @ finite_subsets @ empty )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[357]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ powerset @ preboolean )
& ( A @ powerset @ diff_closed )
& ( A @ powerset @ cup_closed )
& ~ ( A @ powerset @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finsub_1) ).
thf(95,plain,
! [A: $i] :
( ( A @ powerset @ preboolean )
& ( A @ powerset @ diff_closed )
& ( A @ powerset @ cup_closed )
& ~ ( A @ powerset @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(96,plain,
( ! [A: $i] : ( A @ powerset @ preboolean )
& ! [A: $i] : ( A @ powerset @ diff_closed )
& ! [A: $i] : ( A @ powerset @ cup_closed )
& ~ ? [A: $i] : ( A @ powerset @ empty ) ),
inference(miniscope,[status(thm)],[95]) ).
thf(97,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ powerset @ preboolean )
& ( C @ powerset @ diff_closed )
& ( B @ powerset @ cup_closed )
& ~ ( A @ powerset @ empty ) ),
inference(cnf,[status(esa)],[96]) ).
thf(99,plain,
! [A: $i] : ( A @ powerset @ cup_closed ),
inference(cnfConj,[status(thm)],[97]) ).
thf(102,plain,
! [A: $i] : ( A @ powerset @ cup_closed ),
inference(simp,[status(thm)],[99]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(60,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(117,plain,
! [A: $i] : ( A @ sk10 @ epsilon_transitive ),
inference(cnfConj,[status(thm)],[113]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(190,plain,
( ( ( sk4 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[57,56]) ).
thf(191,plain,
( ( sk4 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[190]) ).
thf(192,plain,
sk4 != empty_set,
inference(simp,[status(thm)],[191]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( B @ preboolean )
=> ( ( B
= ( A @ finite_subsets ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( ( C @ finite )
& ( A @ ( C @ subset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_finsub_1) ).
thf(165,plain,
! [A: $i,B: $i] :
( ( B @ preboolean )
=> ( ( ! [C: $i] :
( ( ( ( C @ finite )
& ( A @ ( C @ subset ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( ( C @ finite )
& ( A @ ( C @ subset ) ) ) ) )
=> ( B
= ( A @ finite_subsets ) ) )
& ( ( B
= ( A @ finite_subsets ) )
=> ! [C: $i] :
( ( ( ( C @ finite )
& ( A @ ( C @ subset ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( ( C @ finite )
& ( A @ ( C @ subset ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(90,plain,
! [A: $i] :
( ( A @ sk9 @ empty )
& ( A @ powerset @ ( A @ sk9 @ element ) ) ),
inference(cnf,[status(esa)],[89]) ).
thf(92,plain,
! [A: $i] : ( A @ sk9 @ empty ),
inference(cnfConj,[status(thm)],[90]) ).
thf(12,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)],[12]) ).
thf(65,plain,
( ( sk6 @ finite )
& ~ ( sk6 @ empty ) ),
inference(cnf,[status(esa)],[64]) ).
thf(66,plain,
~ ( sk6 @ empty ),
inference(cnfConj,[status(thm)],[65]) ).
thf(193,plain,
( ( ( sk6 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[57,66]) ).
thf(194,plain,
( ( sk6 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[193]) ).
thf(197,plain,
sk6 != empty_set,
inference(simp,[status(thm)],[194]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(77,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(128,plain,
sk11 @ preboolean,
inference(cnfConj,[status(thm)],[125]) ).
thf(23,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(105,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(33,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(161,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( A @ finite_subsets @ ( B @ element ) )
=> ( B @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_finsub_1) ).
thf(149,plain,
! [A: $i,B: $i] :
( ( A @ finite_subsets @ ( B @ element ) )
=> ( B @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(118,plain,
! [A: $i] : ( A @ sk10 @ one_to_one ),
inference(cnfConj,[status(thm)],[113]) ).
thf(127,plain,
~ ( sk11 @ empty ),
inference(cnfConj,[status(thm)],[125]) ).
thf(201,plain,
( ( ( sk11 @ empty )
!= ( sk3 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[45,127]) ).
thf(202,plain,
( ( sk11 @ empty )
!= ( sk3 @ empty ) ),
inference(simp,[status(thm)],[201]) ).
thf(204,plain,
sk11 != sk3,
inference(simp,[status(thm)],[202]) ).
thf(6,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(49,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(32,axiom,
! [A: $i] : ( A @ finite_subsets @ preboolean ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
thf(159,plain,
! [A: $i] : ( A @ finite_subsets @ preboolean ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(98,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(cnfConj,[status(thm)],[97]) ).
thf(100,plain,
! [A: $i] : ( A @ powerset @ diff_closed ),
inference(cnfConj,[status(thm)],[97]) ).
thf(103,plain,
! [A: $i] : ( A @ powerset @ diff_closed ),
inference(simp,[status(thm)],[100]) ).
thf(195,plain,
( ( ( sk6 @ empty )
!= ( sk3 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[45,66]) ).
thf(196,plain,
( ( sk6 @ empty )
!= ( sk3 @ empty ) ),
inference(simp,[status(thm)],[195]) ).
thf(198,plain,
sk6 != sk3,
inference(simp,[status(thm)],[196]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ preboolean )
=> ( ( A @ diff_closed )
& ( A @ cup_closed ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finsub_1) ).
thf(108,plain,
! [A: $i] :
( ( A @ preboolean )
=> ( ( A @ diff_closed )
& ( A @ cup_closed ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(47,plain,
~ ? [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ empty )
& ( C @ powerset @ ( B @ element ) ) )
& ( B @ ( A @ in ) ) ),
inference(miniscope,[status(thm)],[46]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ empty )
| ~ ( C @ powerset @ ( B @ element ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(67,plain,
sk6 @ finite,
inference(cnfConj,[status(thm)],[65]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(72,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(143,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)],[29]) ).
thf(199,plain,
( ( ( sk11 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[57,127]) ).
thf(200,plain,
( ( sk11 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[199]) ).
thf(203,plain,
sk11 != empty_set,
inference(simp,[status(thm)],[200]) ).
thf(101,plain,
! [A: $i] : ( A @ powerset @ preboolean ),
inference(cnfConj,[status(thm)],[97]) ).
thf(104,plain,
! [A: $i] : ( A @ powerset @ preboolean ),
inference(simp,[status(thm)],[101]) ).
thf(114,plain,
! [A: $i] : ( A @ sk10 @ empty ),
inference(cnfConj,[status(thm)],[113]) ).
thf(16,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(75,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)],[16]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(151,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(50,plain,
~ ? [A: $i,B: $i] :
( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(miniscope,[status(thm)],[49]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[50]) ).
thf(126,plain,
sk11 @ cup_closed,
inference(cnfConj,[status(thm)],[125]) ).
thf(18,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(79,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(27,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(131,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(163,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(13,axiom,
! [A: $i] :
( ( ( A @ diff_closed )
& ( A @ cup_closed ) )
=> ( A @ preboolean ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finsub_1) ).
thf(68,plain,
! [A: $i] :
( ( ( A @ diff_closed )
& ( A @ cup_closed ) )
=> ( A @ preboolean ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(12130,plain,
$false,
inference(e,[status(thm)],[115,56,52,84,53,129,130,112,364,189,46,93,57,116,89,133,366,102,60,117,38,70,192,165,92,197,124,77,128,105,45,161,64,149,44,118,204,54,49,159,39,98,103,66,198,108,48,95,67,127,72,143,43,203,104,40,114,75,58,207,151,36,51,126,79,131,163,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU110+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.11 % 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
% 0.22/0.49 % Computer : n020.cluster.edu
% 0.22/0.49 % Model : x86_64 x86_64
% 0.22/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.49 % Memory : 8046.5625MB
% 0.22/0.49 % OS : Linux 6.8.0-71-generic
% 0.22/0.49 % CPULimit : 300
% 0.22/0.49 % WCLimit : 300
% 0.22/0.49 % DateTime : Sat Sep 26 08:37:33 UTC 2026
% 0.22/0.50 % CPUTime :
% 0.22/0.50 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
% 1.41/1.35 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.95/1.67 % [INFO] Parsing done (313ms).
% 1.95/1.69 % [INFO] Running in sequential loop mode.
% 3.30/2.33 % [INFO] eprover registered as external prover.
% 3.30/2.34 % [INFO] Scanning for conjecture ...
% 3.71/2.50 % [INFO] Found a conjecture (or negated_conjecture) and 33 axioms. Running axiom selection ...
% 3.90/2.62 % [INFO] Axiom selection finished. Selected 33 axioms (removed 0 axioms).
% 4.14/2.70 % [INFO] Problem is first-order (TPTP FOF).
% 4.14/2.71 % [INFO] Type checking passed.
% 4.14/2.72 % [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 ...
% 53.93/12.03 % External prover 'e' found a proof!
% 53.93/12.03 % [INFO] Killing All external provers ...
% 53.93/12.03 % Time passed: 11323ms (effective reasoning time: 10327ms)
% 53.93/12.03 % 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)>
% 53.93/12.03 % Axioms used in derivation (33): cc2_finset_1, cc2_finsub_1, t4_subset, rc1_subset_1, cc3_finsub_1, t2_subset, antisymmetry_r2_hidden, fc1_finsub_1, rc4_finset_1, rc1_finsub_1, fc1_xboole_0, t1_subset, t6_boole, rc2_subset_1, t1_xboole_1, t5_subset, t7_boole, fc1_subset_1, t3_subset, existence_m1_subset_1, cc1_finsub_1, d3_tarski, rc2_finset_1, reflexivity_r1_tarski, rc3_finset_1, fc2_finsub_1, rc1_finset_1, cc1_finset_1, t8_boole, rc1_xboole_0, dt_k5_finsub_1, d5_finsub_1, rc2_xboole_0
% 53.93/12.03 % No. of inferences in proof: 137
% 53.93/12.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 11323 ms resp. 10327 ms w/o parsing
% 46.32/12.13 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 46.32/12.13 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------