TSTP Solution File: SEU109+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU109+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:57:02 EDT 2023
% Result : Theorem 9.04s 2.84s
% Output : Refutation 9.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 73
% Syntax : Number of formulae : 173 ( 80 unt; 28 typ; 0 def)
% Number of atoms : 331 ( 51 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 752 ( 88 ~; 3 |; 94 &; 504 @)
% ( 4 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 8 con; 0-2 aty)
% Number of variables : 180 ( 0 ^; 159 !; 21 ?; 180 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_type,type,
empty: $i > $o ).
thf(preboolean_type,type,
preboolean: $i > $o ).
thf(set_intersection2_type,type,
set_intersection2: $i > $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(set_difference_type,type,
set_difference: $i > $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(set_union2_type,type,
set_union2: $i > $i > $i ).
thf(finite_type,type,
finite: $i > $o ).
thf(cup_closed_type,type,
cup_closed: $i > $o ).
thf(diff_closed_type,type,
diff_closed: $i > $o ).
thf(relation_type,type,
relation: $i > $o ).
thf(function_type,type,
function: $i > $o ).
thf(one_to_one_type,type,
one_to_one: $i > $o ).
thf(epsilon_transitive_type,type,
epsilon_transitive: $i > $o ).
thf(epsilon_connected_type,type,
epsilon_connected: $i > $o ).
thf(ordinal_type,type,
ordinal: $i > $o ).
thf(natural_type,type,
natural: $i > $o ).
thf(cap_closed_type,type,
cap_closed: $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk7_type,type,
sk7: $i ).
thf(sk10_type,type,
sk10: $i > $i ).
thf(sk17_type,type,
sk17: $i ).
thf(42,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B )
& ( relation @ B )
& ( function @ B )
& ( one_to_one @ B )
& ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B )
& ( natural @ B )
& ( finite @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_finset_1) ).
thf(173,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B )
& ( relation @ B )
& ( function @ B )
& ( one_to_one @ B )
& ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B )
& ( natural @ B )
& ( finite @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(27,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(117,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(118,plain,
finite @ sk7,
inference(cnf,[status(esa)],[117]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( empty @ A )
& ( preboolean @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( preboolean @ B ) )
=> ( ~ ( empty @ ( set_intersection2 @ A @ B ) )
& ( preboolean @ ( set_intersection2 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_finsub_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( empty @ A )
& ( preboolean @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( preboolean @ B ) )
=> ( ~ ( empty @ ( set_intersection2 @ A @ B ) )
& ( preboolean @ ( set_intersection2 @ A @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(47,plain,
~ ! [A: $i] :
( ( ~ ( empty @ A )
& ( preboolean @ A ) )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( preboolean @ B ) )
=> ( ~ ( empty @ ( set_intersection2 @ A @ B ) )
& ( preboolean @ ( set_intersection2 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(50,plain,
( ( empty @ ( set_intersection2 @ sk1 @ sk2 ) )
| ~ ( preboolean @ ( set_intersection2 @ sk1 @ sk2 ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(99,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(34,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(138,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(16,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(88,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(41,axiom,
! [A: $i] :
( ( preboolean @ A )
=> ( ( cup_closed @ A )
& ( diff_closed @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finsub_1) ).
thf(170,plain,
! [A: $i] :
( ( preboolean @ A )
=> ( ( cup_closed @ A )
& ( diff_closed @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(120,plain,
! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(52,plain,
~ ( empty @ sk1 ),
inference(cnf,[status(esa)],[47]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(184,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( set_intersection2 @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
& ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
& ( in @ D @ B ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
& ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
& ( in @ D @ B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( set_intersection2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(23,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(108,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(109,plain,
~ ! [A: $i] : ( empty @ A ),
inference(miniscope,[status(thm)],[108]) ).
thf(110,plain,
~ ( empty @ sk5 ),
inference(cnf,[status(esa)],[109]) ).
thf(36,axiom,
! [A: $i] :
( ~ ( empty @ ( powerset @ A ) )
& ( cup_closed @ ( powerset @ A ) )
& ( diff_closed @ ( powerset @ A ) )
& ( preboolean @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finsub_1) ).
thf(151,plain,
! [A: $i] :
( ~ ( empty @ ( powerset @ A ) )
& ( cup_closed @ ( powerset @ A ) )
& ( diff_closed @ ( powerset @ A ) )
& ( preboolean @ ( powerset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(152,plain,
( ~ ? [A: $i] : ( empty @ ( powerset @ A ) )
& ! [A: $i] : ( cup_closed @ ( powerset @ A ) )
& ! [A: $i] : ( diff_closed @ ( powerset @ A ) )
& ! [A: $i] : ( preboolean @ ( powerset @ A ) ) ),
inference(miniscope,[status(thm)],[151]) ).
thf(153,plain,
! [A: $i] : ( preboolean @ ( powerset @ A ) ),
inference(cnf,[status(esa)],[152]) ).
thf(157,plain,
! [A: $i] : ( preboolean @ ( powerset @ A ) ),
inference(simp,[status(thm)],[153]) ).
thf(19,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(97,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(98,plain,
empty @ sk4,
inference(cnf,[status(esa)],[97]) ).
thf(224,plain,
( ( empty @ sk4 )
!= ( empty @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[98,52]) ).
thf(228,plain,
sk4 != sk1,
inference(simp,[status(thm)],[224]) ).
thf(4,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(55,plain,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(56,plain,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
inference(cnf,[status(esa)],[55]) ).
thf(57,plain,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
inference(lifteq,[status(thm)],[56]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(216,plain,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(24,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(111,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(49,plain,
~ ( empty @ sk2 ),
inference(cnf,[status(esa)],[47]) ).
thf(234,plain,
( ( empty @ sk2 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[111,49]) ).
thf(238,plain,
sk2 != empty_set,
inference(simp,[status(thm)],[234]) ).
thf(44,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( cup_closed @ A )
& ( cap_closed @ A )
& ( diff_closed @ A )
& ( preboolean @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finsub_1) ).
thf(210,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( cup_closed @ A )
& ( cap_closed @ A )
& ( diff_closed @ A )
& ( preboolean @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(211,plain,
cup_closed @ sk17,
inference(cnf,[status(esa)],[210]) ).
thf(139,plain,
! [A: $i] : ( empty @ ( sk10 @ A ) ),
inference(cnf,[status(esa)],[138]) ).
thf(249,plain,
! [A: $i] :
( ( empty @ ( sk10 @ A ) )
!= ( empty @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[139,52]) ).
thf(253,plain,
! [A: $i] :
( ( sk10 @ A )
!= sk1 ),
inference(simp,[status(thm)],[249]) ).
thf(15,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(85,plain,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(21,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(102,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(60,plain,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(37,axiom,
! [A: $i] :
( ( ( cup_closed @ A )
& ( diff_closed @ A ) )
=> ( preboolean @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finsub_1) ).
thf(160,plain,
! [A: $i] :
( ( ( cup_closed @ A )
& ( diff_closed @ A ) )
=> ( preboolean @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(9,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(70,plain,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(39,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( preboolean @ A ) )
=> ( in @ empty_set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_finsub_1) ).
thf(165,plain,
! [A: $i] :
( ( ~ ( empty @ A )
& ( preboolean @ A ) )
=> ( in @ empty_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(225,plain,
( ( empty @ sk5 )
!= ( empty @ sk4 ) ),
inference(paramod_ordered,[status(thm)],[98,110]) ).
thf(229,plain,
sk5 != sk4,
inference(simp,[status(thm)],[225]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(65,plain,
! [A: $i,B: $i] :
( ( ( element @ A @ ( powerset @ B ) )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( element @ A @ ( powerset @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(156,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(cnf,[status(esa)],[152]) ).
thf(3,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(53,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(35,axiom,
! [A: $i] :
( ( preboolean @ A )
<=> ! [B: $i,C: $i] :
( ( ( in @ B @ A )
& ( in @ C @ A ) )
=> ( ( in @ ( set_union2 @ B @ C ) @ A )
& ( in @ ( set_difference @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_finsub_1) ).
thf(141,plain,
! [A: $i] :
( ( ( preboolean @ A )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ A )
& ( in @ C @ A ) )
=> ( ( in @ ( set_union2 @ B @ C ) @ A )
& ( in @ ( set_difference @ B @ C ) @ A ) ) ) )
& ( ! [B: $i,C: $i] :
( ( ( in @ B @ A )
& ( in @ C @ A ) )
=> ( ( in @ ( set_union2 @ B @ C ) @ A )
& ( in @ ( set_difference @ B @ C ) @ A ) ) )
=> ( preboolean @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(251,plain,
! [A: $i] :
( ( empty @ ( sk10 @ A ) )
!= ( empty @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[139,49]) ).
thf(256,plain,
! [A: $i] :
( ( sk10 @ A )
!= sk2 ),
inference(simp,[status(thm)],[251]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(77,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(212,plain,
~ ( empty @ sk17 ),
inference(cnf,[status(esa)],[210]) ).
thf(33,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(134,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(10,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(73,plain,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( finite @ B )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(128,plain,
! [A: $i,B: $i] :
( ( finite @ B )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(105,plain,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(242,plain,
( ( empty @ sk17 )
!= ( empty @ sk4 ) ),
inference(paramod_ordered,[status(thm)],[98,212]) ).
thf(244,plain,
sk17 != sk4,
inference(simp,[status(thm)],[242]) ).
thf(54,plain,
! [A: $i] : ( subset @ A @ A ),
inference(cnf,[status(esa)],[53]) ).
thf(155,plain,
! [A: $i] : ( cup_closed @ ( powerset @ A ) ),
inference(cnf,[status(esa)],[152]) ).
thf(159,plain,
! [A: $i] : ( cup_closed @ ( powerset @ A ) ),
inference(simp,[status(thm)],[155]) ).
thf(46,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(219,plain,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(243,plain,
( ( empty @ sk17 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[111,212]) ).
thf(245,plain,
sk17 != empty_set,
inference(simp,[status(thm)],[243]) ).
thf(213,plain,
cap_closed @ sk17,
inference(cnf,[status(esa)],[210]) ).
thf(236,plain,
( ( empty @ sk1 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[111,52]) ).
thf(240,plain,
sk1 != empty_set,
inference(simp,[status(thm)],[236]) ).
thf(32,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(130,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(222,plain,
( ( empty @ sk4 )
!= ( empty @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[98,49]) ).
thf(226,plain,
sk4 != sk2,
inference(simp,[status(thm)],[222]) ).
thf(237,plain,
( ( empty @ sk5 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[111,110]) ).
thf(241,plain,
sk5 != empty_set,
inference(simp,[status(thm)],[237]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(167,plain,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(38,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(162,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(112,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(29,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(123,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(48,plain,
preboolean @ sk1,
inference(cnf,[status(esa)],[47]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(63,plain,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(154,plain,
! [A: $i] : ( diff_closed @ ( powerset @ A ) ),
inference(cnf,[status(esa)],[152]) ).
thf(158,plain,
! [A: $i] : ( diff_closed @ ( powerset @ A ) ),
inference(simp,[status(thm)],[154]) ).
thf(26,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(114,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(75,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(82,plain,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(214,plain,
diff_closed @ sk17,
inference(cnf,[status(esa)],[210]) ).
thf(119,plain,
~ ( empty @ sk7 ),
inference(cnf,[status(esa)],[117]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(58,plain,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(51,plain,
preboolean @ sk2,
inference(cnf,[status(esa)],[47]) ).
thf(235,plain,
( ( empty @ sk7 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[111,119]) ).
thf(239,plain,
sk7 != empty_set,
inference(simp,[status(thm)],[235]) ).
thf(30,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(126,plain,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(79,plain,
! [A: $i] :
( ( set_union2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(94,plain,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(215,plain,
preboolean @ sk17,
inference(cnf,[status(esa)],[210]) ).
thf(17,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(90,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(248,plain,
! [A: $i] :
( ( empty @ ( sk10 @ A ) )
!= ( empty @ sk17 ) ),
inference(paramod_ordered,[status(thm)],[139,212]) ).
thf(254,plain,
! [A: $i] :
( ( sk10 @ A )
!= sk17 ),
inference(simp,[status(thm)],[248]) ).
thf(223,plain,
( ( empty @ sk7 )
!= ( empty @ sk4 ) ),
inference(paramod_ordered,[status(thm)],[98,119]) ).
thf(227,plain,
sk7 != sk4,
inference(simp,[status(thm)],[223]) ).
thf(467,plain,
$false,
inference(cvc4,[status(thm)],[173,118,50,99,47,138,88,170,120,52,184,110,157,228,57,216,238,211,253,85,102,60,117,160,70,165,229,65,97,156,53,141,256,77,212,134,73,128,105,244,54,49,159,219,245,98,213,240,108,130,226,241,167,162,112,123,48,63,158,139,55,114,75,82,214,119,58,151,51,210,239,126,79,94,215,90,111,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU109+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n014.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Thu May 18 12:25:28 EDT 2023
% 0.17/0.38 % CPUTime :
% 0.98/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.08/1.02 % [INFO] Parsing done (143ms).
% 1.40/1.03 % [INFO] Running in sequential loop mode.
% 1.76/1.30 % [INFO] eprover registered as external prover.
% 1.76/1.30 % [INFO] cvc4 registered as external prover.
% 1.91/1.30 % [INFO] Scanning for conjecture ...
% 2.05/1.36 % [INFO] Found a conjecture and 44 axioms. Running axiom selection ...
% 2.05/1.42 % [INFO] Axiom selection finished. Selected 44 axioms (removed 0 axioms).
% 2.36/1.46 % [INFO] Problem is first-order (TPTP FOF).
% 2.36/1.47 % [INFO] Type checking passed.
% 2.36/1.47 % [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 ...
% 9.04/2.84 % External prover 'cvc4' found a proof!
% 9.04/2.84 % [INFO] Killing All external provers ...
% 9.04/2.84 % Time passed: 2300ms (effective reasoning time: 1810ms)
% 9.04/2.84 % 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)>
% 9.04/2.84 % Axioms used in derivation (44): t2_boole, commutativity_k3_xboole_0, rc1_subset_1, rc3_finset_1, t2_subset, idempotence_k2_xboole_0, rc2_xboole_0, cc2_finset_1, t18_finsub_1, fc1_finsub_1, idempotence_k3_xboole_0, rc4_finset_1, t1_boole, rc1_finsub_1, fc1_xboole_0, t1_subset, fc11_finset_1, cc2_finsub_1, fc2_xboole_0, fc10_finset_1, t6_boole, rc2_subset_1, fc9_finset_1, commutativity_k2_xboole_0, t5_subset, t4_boole, t4_subset, fc3_xboole_0, t7_boole, fc1_subset_1, t3_subset, existence_m1_subset_1, cc1_finsub_1, rc2_finset_1, reflexivity_r1_tarski, rc1_finset_1, cc1_finset_1, fc12_finset_1, t8_boole, rc1_xboole_0, t3_boole, t10_finsub_1, d3_xboole_0, antisymmetry_r2_hidden
% 9.04/2.84 % No. of inferences in proof: 145
% 9.04/2.84 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2300 ms resp. 1810 ms w/o parsing
% 9.04/2.88 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.04/2.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------