TSTP Solution File: SEU103+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU103+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.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 11:57:01 EDT 2023
% Result : Theorem 20.32s 4.21s
% Output : Refutation 20.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 78
% Syntax : Number of formulae : 177 ( 77 unt; 32 typ; 0 def)
% Number of atoms : 335 ( 58 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 809 ( 93 ~; 6 |; 103 &; 550 @)
% ( 1 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 32 usr; 9 con; 0-3 aty)
% Number of variables : 191 ( 0 ^; 170 !; 21 ?; 191 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_type,type,
empty: $i > $o ).
thf(preboolean_type,type,
preboolean: $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(symmetric_difference_type,type,
symmetric_difference: $i > $i > $i ).
thf(set_union2_type,type,
set_union2: $i > $i > $i ).
thf(finite_type,type,
finite: $i > $o ).
thf(empty_set_type,type,
empty_set: $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(set_difference_type,type,
set_difference: $i > $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(prebool_difference_type,type,
prebool_difference: $i > $i > $i > $i ).
thf(prebool_union2_type,type,
prebool_union2: $i > $i > $i > $i ).
thf(cup_closed_type,type,
cup_closed: $i > $o ).
thf(cap_closed_type,type,
cap_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(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $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(sk11_type,type,
sk11: $i ).
thf(sk13_type,type,
sk13: $i > $i ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
inference(cnf,[status(esa)],[54]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
inference(lifteq,[status(thm)],[55]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ A )
& ( preboolean @ A )
& ( element @ B @ A )
& ( element @ C @ A ) )
=> ( element @ ( prebool_difference @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_finsub_1) ).
thf(102,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ A )
& ( preboolean @ A )
& ( element @ B @ A )
& ( element @ C @ A ) )
=> ( element @ ( prebool_difference @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(13,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(82,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(83,plain,
empty @ sk4,
inference(cnf,[status(esa)],[82]) ).
thf(36,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( cup_closed @ A )
& ( cap_closed @ A )
& ( diff_closed @ A )
& ( preboolean @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finsub_1) ).
thf(143,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( cup_closed @ A )
& ( cap_closed @ A )
& ( diff_closed @ A )
& ( preboolean @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(147,plain,
~ ( empty @ sk11 ),
inference(cnf,[status(esa)],[143]) ).
thf(196,plain,
( ( empty @ sk11 )
!= ( empty @ sk4 ) ),
inference(paramod_ordered,[status(thm)],[83,147]) ).
thf(197,plain,
sk11 != sk4,
inference(simp,[status(thm)],[196]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ C )
& ( preboolean @ C ) )
=> ( ( ( element @ A @ C )
& ( element @ B @ C ) )
=> ( element @ ( symmetric_difference @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_finsub_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ C )
& ( preboolean @ C ) )
=> ( ( ( element @ A @ C )
& ( element @ B @ C ) )
=> ( element @ ( symmetric_difference @ A @ B ) @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(48,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ C )
& ( preboolean @ C ) )
=> ( ( ( element @ A @ C )
& ( element @ B @ C ) )
=> ( element @ ( symmetric_difference @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(53,plain,
element @ sk1 @ sk3,
inference(cnf,[status(esa)],[48]) ).
thf(17,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(91,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ A )
& ( preboolean @ A )
& ( element @ B @ A )
& ( element @ C @ A ) )
=> ( ( prebool_union2 @ A @ B @ C )
= ( prebool_union2 @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k1_finsub_1) ).
thf(167,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ A )
& ( preboolean @ A )
& ( element @ B @ A )
& ( element @ C @ A ) )
=> ( ( prebool_union2 @ A @ B @ C )
= ( prebool_union2 @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(20,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(99,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(100,plain,
~ ! [A: $i] : ( empty @ A ),
inference(miniscope,[status(thm)],[99]) ).
thf(101,plain,
~ ( empty @ sk5 ),
inference(cnf,[status(esa)],[100]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(88,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(44,axiom,
! [A: $i] :
( ( preboolean @ A )
=> ( ( cup_closed @ A )
& ( diff_closed @ A ) ) ),
file('/export/starexec/sandbox/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)],[44]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ A )
& ( preboolean @ A )
& ( element @ B @ A )
& ( element @ C @ A ) )
=> ( ( prebool_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_finsub_1) ).
thf(115,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ A )
& ( preboolean @ A )
& ( element @ B @ A )
& ( element @ C @ A ) )
=> ( ( prebool_difference @ A @ B @ C )
= ( set_difference @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(22,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(104,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(198,plain,
( ( empty @ sk5 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[104,101]) ).
thf(202,plain,
sk5 != empty_set,
inference(simp,[status(thm)],[198]) ).
thf(52,plain,
~ ( element @ ( symmetric_difference @ sk1 @ sk2 ) @ sk3 ),
inference(cnf,[status(esa)],[48]) ).
thf(31,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(125,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(78,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(34,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(136,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(137,plain,
! [A: $i] : ( empty @ ( sk10 @ A ) ),
inference(cnf,[status(esa)],[136]) ).
thf(212,plain,
! [A: $i] :
( ( empty @ ( sk10 @ A ) )
!= ( empty @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[137,101]) ).
thf(216,plain,
! [A: $i] :
( ( sk10 @ A )
!= sk5 ),
inference(simp,[status(thm)],[212]) ).
thf(42,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(164,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',rc2_finset_1) ).
thf(176,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)],[46]) ).
thf(179,plain,
! [A: $i] : ( epsilon_connected @ ( sk13 @ A ) ),
inference(cnf,[status(esa)],[176]) ).
thf(51,plain,
element @ sk2 @ sk3,
inference(cnf,[status(esa)],[48]) ).
thf(207,plain,
( ( element @ ( symmetric_difference @ sk1 @ sk2 ) @ sk3 )
!= ( element @ sk2 @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[51,52]) ).
thf(209,plain,
( ( ( symmetric_difference @ sk1 @ sk2 )
!= sk2 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[207]) ).
thf(211,plain,
( ( symmetric_difference @ sk1 @ sk2 )
!= sk2 ),
inference(simp,[status(thm)],[209]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(121,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)],[29]) ).
thf(14,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(84,plain,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(33,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(132,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(9,axiom,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(25,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(109,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(192,plain,
( ( empty @ sk5 )
!= ( empty @ sk4 ) ),
inference(paramod_ordered,[status(thm)],[83,101]) ).
thf(193,plain,
sk5 != sk4,
inference(simp,[status(thm)],[192]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(96,plain,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(45,axiom,
! [A: $i] :
( ( symmetric_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_boole) ).
thf(173,plain,
! [A: $i] :
( ( symmetric_difference @ A @ empty_set )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ A )
& ( preboolean @ A )
& ( element @ B @ A )
& ( element @ C @ A ) )
=> ( ( prebool_union2 @ A @ B @ C )
= ( set_union2 @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_finsub_1) ).
thf(129,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ A )
& ( preboolean @ A )
& ( element @ B @ A )
& ( element @ C @ A ) )
=> ( ( prebool_union2 @ A @ B @ C )
= ( set_union2 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(10,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(73,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ A )
& ( preboolean @ A )
& ( element @ B @ A )
& ( element @ C @ A ) )
=> ( element @ ( prebool_union2 @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_finsub_1) ).
thf(105,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ A )
& ( preboolean @ A )
& ( element @ B @ A )
& ( element @ C @ A ) )
=> ( element @ ( prebool_union2 @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(26,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(112,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(114,plain,
~ ( empty @ sk7 ),
inference(cnf,[status(esa)],[112]) ).
thf(201,plain,
( ( empty @ sk7 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[104,114]) ).
thf(205,plain,
sk7 != empty_set,
inference(simp,[status(thm)],[201]) ).
thf(165,plain,
~ ? [A: $i] : ( empty @ ( powerset @ A ) ),
inference(miniscope,[status(thm)],[164]) ).
thf(166,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(cnf,[status(esa)],[165]) ).
thf(148,plain,
diff_closed @ sk11,
inference(cnf,[status(esa)],[143]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( set_union2 @ ( set_difference @ A @ B ) @ ( set_difference @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_xboole_0) ).
thf(161,plain,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( set_union2 @ ( set_difference @ A @ B ) @ ( set_difference @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(64,plain,
! [A: $i] :
( ( set_union2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(180,plain,
! [A: $i] : ( ordinal @ ( sk13 @ A ) ),
inference(cnf,[status(esa)],[176]) ).
thf(37,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(149,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(49,plain,
~ ( empty @ sk3 ),
inference(cnf,[status(esa)],[48]) ).
thf(190,plain,
( ( empty @ sk4 )
!= ( empty @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[83,49]) ).
thf(191,plain,
sk4 != sk3,
inference(simp,[status(thm)],[190]) ).
thf(200,plain,
( ( empty @ sk3 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[104,49]) ).
thf(204,plain,
sk3 != empty_set,
inference(simp,[status(thm)],[200]) ).
thf(5,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
thf(59,plain,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(28,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(118,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(144,plain,
cap_closed @ sk11,
inference(cnf,[status(esa)],[143]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( symmetric_difference @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc17_finset_1) ).
thf(86,plain,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( symmetric_difference @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(40,axiom,
! [A: $i] :
( ( ( cup_closed @ A )
& ( diff_closed @ A ) )
=> ( preboolean @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finsub_1) ).
thf(159,plain,
! [A: $i] :
( ( ( cup_closed @ A )
& ( diff_closed @ A ) )
=> ( preboolean @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(187,plain,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(113,plain,
finite @ sk7,
inference(cnf,[status(esa)],[112]) ).
thf(215,plain,
! [A: $i] :
( ( empty @ ( sk10 @ A ) )
!= ( empty @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[137,49]) ).
thf(219,plain,
! [A: $i] :
( ( sk10 @ A )
!= sk3 ),
inference(simp,[status(thm)],[215]) ).
thf(30,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(123,plain,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(145,plain,
preboolean @ sk11,
inference(cnf,[status(esa)],[143]) ).
thf(50,plain,
preboolean @ sk3,
inference(cnf,[status(esa)],[48]) ).
thf(8,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(67,plain,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(177,plain,
! [A: $i] : ( empty @ ( sk13 @ A ) ),
inference(cnf,[status(esa)],[176]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(154,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)],[39]) ).
thf(199,plain,
( ( empty @ sk11 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[104,147]) ).
thf(203,plain,
sk11 != empty_set,
inference(simp,[status(thm)],[199]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ A )
& ( preboolean @ A )
& ( element @ B @ A )
& ( element @ C @ A ) )
=> ( ( prebool_union2 @ A @ B @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k1_finsub_1) ).
thf(139,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( empty @ A )
& ( preboolean @ A )
& ( element @ B @ A )
& ( element @ C @ A ) )
=> ( ( prebool_union2 @ A @ B @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(11,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(75,plain,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ~ ( finite @ A )
| ~ ( finite @ B )
| ( finite @ ( set_union2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[57]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( symmetric_difference @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).
thf(151,plain,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( symmetric_difference @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(146,plain,
cup_closed @ sk11,
inference(cnf,[status(esa)],[143]) ).
thf(206,plain,
( ( element @ ( symmetric_difference @ sk1 @ sk2 ) @ sk3 )
!= ( element @ sk1 @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[53,52]) ).
thf(208,plain,
( ( ( symmetric_difference @ sk1 @ sk2 )
!= sk1 )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[206]) ).
thf(210,plain,
( ( symmetric_difference @ sk1 @ sk2 )
!= sk1 ),
inference(simp,[status(thm)],[208]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(107,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(194,plain,
( ( empty @ sk7 )
!= ( empty @ sk4 ) ),
inference(paramod_ordered,[status(thm)],[83,114]) ).
thf(195,plain,
sk7 != sk4,
inference(simp,[status(thm)],[194]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(94,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(62,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(178,plain,
! [A: $i] : ( function @ ( sk13 @ A ) ),
inference(cnf,[status(esa)],[176]) ).
thf(3671,plain,
$false,
inference(e,[status(thm)],[56,102,197,53,91,167,48,83,101,88,170,115,202,52,125,57,78,216,164,179,211,121,84,147,132,70,137,109,193,96,173,129,73,105,205,166,148,161,64,180,149,176,191,204,59,118,54,144,49,86,159,187,113,219,112,123,145,50,67,177,154,143,99,203,104,114,139,75,58,82,151,146,51,210,107,136,195,94,62,178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU103+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu May 18 12:56:46 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.83/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.99 % [INFO] Parsing done (132ms).
% 1.18/1.00 % [INFO] Running in sequential loop mode.
% 1.74/1.20 % [INFO] eprover registered as external prover.
% 1.74/1.21 % [INFO] cvc4 registered as external prover.
% 1.74/1.21 % [INFO] Scanning for conjecture ...
% 1.74/1.28 % [INFO] Found a conjecture and 45 axioms. Running axiom selection ...
% 2.16/1.33 % [INFO] Axiom selection finished. Selected 45 axioms (removed 0 axioms).
% 2.30/1.38 % [INFO] Problem is first-order (TPTP FOF).
% 2.30/1.39 % [INFO] Type checking passed.
% 2.30/1.39 % [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 ...
% 20.32/4.20 % External prover 'e' found a proof!
% 20.32/4.21 % [INFO] Killing All external provers ...
% 20.32/4.21 % Time passed: 3684ms (effective reasoning time: 3205ms)
% 20.32/4.21 % 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)>
% 20.32/4.21 % Axioms used in derivation (45): cc2_finset_1, dt_k2_finsub_1, commutativity_k5_xboole_0, rc1_subset_1, d6_xboole_0, rc3_finset_1, t2_subset, idempotence_k2_xboole_0, t3_boole, rc2_xboole_0, antisymmetry_r2_hidden, idempotence_k1_finsub_1, t5_boole, commutativity_k1_finsub_1, rc4_finset_1, t1_boole, rc1_finsub_1, fc1_xboole_0, t1_subset, redefinition_k2_finsub_1, cc2_finsub_1, fc2_xboole_0, t6_boole, rc2_subset_1, fc9_finset_1, fc17_finset_1, commutativity_k2_xboole_0, t5_subset, t4_boole, t4_subset, fc3_xboole_0, dt_k1_finsub_1, t7_boole, fc1_subset_1, t3_subset, existence_m1_subset_1, cc1_finsub_1, rc2_finset_1, reflexivity_r1_tarski, redefinition_k1_finsub_1, rc1_finset_1, cc1_finset_1, fc12_finset_1, t8_boole, rc1_xboole_0
% 20.32/4.21 % No. of inferences in proof: 145
% 20.32/4.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3684 ms resp. 3205 ms w/o parsing
% 20.32/4.25 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.32/4.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------