TSTP Solution File: SEU138+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU138+1 : TPTP v8.1.2. Released v3.3.0.
% 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 11:57:09 EDT 2023
% Result : Theorem 50.86s 10.08s
% Output : Refutation 50.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 31
% Syntax : Number of formulae : 131 ( 42 unt; 13 typ; 0 def)
% Number of atoms : 309 ( 121 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 836 ( 141 ~; 102 |; 40 &; 512 @)
% ( 6 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 176 ( 0 ^; 170 !; 6 ?; 176 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_difference_type,type,
set_difference: $i > $i > $i ).
thf(set_intersection2_type,type,
set_intersection2: $i > $i > $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(empty_set_type,type,
empty_set: $i ).
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 > $i > $i ).
thf(sk6_type,type,
sk6: $i > $i > $i > $o ).
thf(sk8_type,type,
sk8: $i > $i > $i > $i ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(67,plain,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(cnf,[status(esa)],[67]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(lifteq,[status(thm)],[68]) ).
thf(4,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(27,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,plain,
empty @ sk3,
inference(cnf,[status(esa)],[27]) ).
thf(9,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(52,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(53,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( empty @ A ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(1289,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ sk3 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28,54]) ).
thf(1290,plain,
sk3 = empty_set,
inference(pattern_uni,[status(thm)],[1289:[bind(A,$thf( sk3 ))]]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(61,plain,
! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(14,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(64,plain,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(65,plain,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
inference(cnf,[status(esa)],[64]) ).
thf(66,plain,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
inference(lifteq,[status(thm)],[65]) ).
thf(19,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
thf(125,plain,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(126,plain,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
inference(cnf,[status(esa)],[125]) ).
thf(127,plain,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
inference(lifteq,[status(thm)],[126]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(20,plain,
~ ! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(21,plain,
( ( set_difference @ sk1 @ ( set_difference @ sk1 @ sk2 ) )
!= ( set_intersection2 @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[20]) ).
thf(22,plain,
( ( set_intersection2 @ sk1 @ sk2 )
!= ( set_difference @ sk1 @ ( set_difference @ sk1 @ sk2 ) ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(198,plain,
! [A: $i] :
( ( ( set_difference @ sk1 @ ( set_difference @ sk1 @ sk2 ) )
!= empty_set )
| ( ( set_intersection2 @ A @ empty_set )
!= ( set_intersection2 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[127,22]) ).
thf(207,plain,
! [A: $i] :
( ( ( set_difference @ sk1 @ ( set_difference @ sk1 @ sk2 ) )
!= empty_set )
| ( A != sk1 )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[198]) ).
thf(212,plain,
( ( ( set_difference @ sk1 @ ( set_difference @ sk1 @ sk2 ) )
!= empty_set )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[207]) ).
thf(281,plain,
! [A: $i] :
( ( ( set_difference @ sk1 @ A )
!= empty_set )
| ( sk2 != empty_set )
| ( ( set_difference @ A @ empty_set )
!= ( set_difference @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[66,212]) ).
thf(309,plain,
! [A: $i] :
( ( ( set_difference @ sk1 @ A )
!= empty_set )
| ( sk2 != empty_set )
| ( A != sk1 )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[281]) ).
thf(317,plain,
( ( ( set_difference @ sk1 @ sk1 )
!= empty_set )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[309]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(23,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(24,plain,
~ ? [A: $i] :
( ( empty @ A )
& ? [B: $i] :
( ( A != B )
& ( empty @ B ) ) ),
inference(miniscope,[status(thm)],[23]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( A = B )
| ~ ( empty @ B ) ),
inference(cnf,[status(esa)],[24]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(17,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(96,plain,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(97,plain,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
inference(cnf,[status(esa)],[96]) ).
thf(98,plain,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
inference(lifteq,[status(thm)],[97]) ).
thf(278,plain,
! [A: $i] :
( ( sk2 != empty_set )
| ( ( set_difference @ empty_set @ A )
!= ( set_difference @ sk1 @ ( set_difference @ sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[98,212]) ).
thf(310,plain,
! [A: $i] :
( ( sk2 != empty_set )
| ( sk1 != empty_set )
| ( A
!= ( set_difference @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(318,plain,
( ( sk2 != empty_set )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[310]) ).
thf(322,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( B != empty_set )
| ( sk1 != empty_set )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[26,318]) ).
thf(323,plain,
! [A: $i] :
( ~ ( empty @ sk2 )
| ~ ( empty @ A )
| ( A != empty_set )
| ( sk1 != empty_set ) ),
inference(pattern_uni,[status(thm)],[322:[bind(A,$thf( sk2 ))]]) ).
thf(330,plain,
( ~ ( empty @ sk2 )
| ~ ( empty @ empty_set )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[323]) ).
thf(11,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(58,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(599,plain,
( ~ ( empty @ sk2 )
| ~ $true
| ( sk1 != empty_set ) ),
inference(rewrite,[status(thm)],[330,58]) ).
thf(600,plain,
( ~ ( empty @ sk2 )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[599]) ).
thf(613,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ~ ( empty @ sk2 )
| ( B != empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[26,600]) ).
thf(614,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ~ ( empty @ A )
| ~ ( empty @ sk2 )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[613:[bind(A,$thf( sk1 ))]]) ).
thf(623,plain,
( ~ ( empty @ sk1 )
| ~ ( empty @ empty_set )
| ~ ( empty @ sk2 ) ),
inference(simp,[status(thm)],[614]) ).
thf(1173,plain,
( ~ ( empty @ sk1 )
| ~ $true
| ~ ( empty @ sk2 ) ),
inference(rewrite,[status(thm)],[623,58]) ).
thf(1174,plain,
( ~ ( empty @ sk1 )
| ~ ( empty @ sk2 ) ),
inference(simp,[status(thm)],[1173]) ).
thf(1197,plain,
( ~ ( empty @ sk1 )
| ( ( empty @ sk2 )
!= ( empty @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[1174]) ).
thf(1202,plain,
( ~ ( empty @ sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[1197]) ).
thf(62,plain,
! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ),
inference(cnf,[status(esa)],[61]) ).
thf(63,plain,
! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ),
inference(lifteq,[status(thm)],[62]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(45,plain,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) )
& ( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(46,plain,
( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) )
& ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) ) ),
inference(miniscope,[status(thm)],[45]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk5 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[46]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk5 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[48]) ).
thf(324,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( sk2 != empty_set )
| ( B != empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[26,318]) ).
thf(325,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ~ ( empty @ A )
| ( sk2 != empty_set )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[324:[bind(A,$thf( sk1 ))]]) ).
thf(331,plain,
( ~ ( empty @ sk1 )
| ~ ( empty @ empty_set )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[325]) ).
thf(828,plain,
( ~ ( empty @ sk1 )
| ~ $true
| ( sk2 != empty_set ) ),
inference(rewrite,[status(thm)],[331,58]) ).
thf(829,plain,
( ~ ( empty @ sk1 )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[828]) ).
thf(256,plain,
! [C: $i,B: $i,A: $i] :
( ( ( set_intersection2 @ B @ A )
= empty_set )
| ( ( set_intersection2 @ A @ B )
!= ( set_intersection2 @ C @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[69,127]) ).
thf(257,plain,
! [A: $i] :
( ( set_intersection2 @ empty_set @ A )
= empty_set ),
inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( A )),bind(B,$thf( empty_set )),bind(C,$thf( A ))]]) ).
thf(5,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(29,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(70,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)],[16]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(32,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) )
& ( ( ( subset @ A @ B )
& ( subset @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(33,plain,
( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) )
& ! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ A ) )
=> ( A = B ) ) ),
inference(miniscope,[status(thm)],[32]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ),
inference(cnf,[status(esa)],[33]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ~ ( subset @ B @ A ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( subset @ A @ B )
| ~ ( subset @ B @ A ) ),
inference(simp,[status(thm)],[37]) ).
thf(71,plain,
( ! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
=> ( ! [D: $i] :
( ( in @ D @ C )
=> ( ( in @ D @ A )
& ( in @ D @ B ) ) )
& ! [D: $i] :
( ( ( in @ D @ A )
& ( in @ D @ B ) )
=> ( in @ D @ C ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( in @ D @ C )
=> ( ( in @ D @ A )
& ( in @ D @ B ) ) )
& ! [D: $i] :
( ( ( in @ D @ A )
& ( in @ D @ B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( set_intersection2 @ A @ B ) ) ) ),
inference(miniscope,[status(thm)],[70]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ( sk6 @ A @ B @ C )
| ( in @ ( sk8 @ C @ B @ A ) @ A )
| ( C
= ( set_intersection2 @ A @ B ) ) ),
inference(cnf,[status(esa)],[71]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
| ( sk6 @ A @ B @ C )
| ( in @ ( sk8 @ C @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(87,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
| ( sk6 @ A @ B @ C )
| ( in @ ( sk8 @ C @ B @ A ) @ A ) ),
inference(simp,[status(thm)],[86]) ).
thf(746,plain,
! [C: $i,B: $i,A: $i] :
( ( sk6 @ A @ B @ C )
| ( in @ ( sk8 @ C @ B @ A ) @ A )
| ( C
!= ( set_difference @ sk1 @ ( set_difference @ sk1 @ sk2 ) ) )
| ( ( set_intersection2 @ A @ B )
!= ( set_intersection2 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[87,22]) ).
thf(747,plain,
! [A: $i] :
( ( sk6 @ sk1 @ sk2 @ A )
| ( in @ ( sk8 @ A @ sk2 @ sk1 ) @ sk1 )
| ( A
!= ( set_difference @ sk1 @ ( set_difference @ sk1 @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[746:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(819,plain,
( ( sk6 @ sk1 @ sk2 @ ( set_difference @ sk1 @ ( set_difference @ sk1 @ sk2 ) ) )
| ( in @ ( sk8 @ ( set_difference @ sk1 @ ( set_difference @ sk1 @ sk2 ) ) @ sk2 @ sk1 ) @ sk1 ) ),
inference(simp,[status(thm)],[747]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(59,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( in @ C @ A )
| ( in @ C @ B ) ),
inference(cnf,[status(esa)],[46]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( in @ ( sk5 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[46]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( in @ ( sk5 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[47]) ).
thf(30,plain,
~ ! [A: $i] : ( empty @ A ),
inference(miniscope,[status(thm)],[29]) ).
thf(31,plain,
~ ( empty @ sk4 ),
inference(cnf,[status(esa)],[30]) ).
thf(130,plain,
( ( empty @ sk4 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[58,31]) ).
thf(131,plain,
sk4 != empty_set,
inference(simp,[status(thm)],[130]) ).
thf(398,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( B != empty_set )
| ( A != sk4 ) ),
inference(paramod_ordered,[status(thm)],[38,131]) ).
thf(399,plain,
! [A: $i] :
( ~ ( subset @ sk4 @ A )
| ~ ( subset @ A @ sk4 )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[398:[bind(A,$thf( sk4 ))]]) ).
thf(446,plain,
( ~ ( subset @ sk4 @ empty_set )
| ~ ( subset @ empty_set @ sk4 ) ),
inference(simp,[status(thm)],[399]) ).
thf(7,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(43,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(99,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( set_difference @ 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_difference @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(725,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk6 @ A @ B @ C )
| ( in @ ( sk8 @ C @ B @ A ) @ A )
| ( C = empty_set )
| ( ( set_intersection2 @ A @ B )
!= ( set_intersection2 @ empty_set @ D ) ) ),
inference(paramod_ordered,[status(thm)],[87,257]) ).
thf(726,plain,
! [B: $i,A: $i] :
( ( sk6 @ empty_set @ A @ B )
| ( in @ ( sk8 @ B @ A @ empty_set ) @ empty_set )
| ( B = empty_set ) ),
inference(pattern_uni,[status(thm)],[725:[bind(A,$thf( empty_set )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).
thf(813,plain,
! [B: $i,A: $i] :
( ( sk6 @ empty_set @ A @ B )
| ( in @ ( sk8 @ B @ A @ empty_set ) @ empty_set )
| ( B = empty_set ) ),
inference(simp,[status(thm)],[726]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[33]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( subset @ A @ B ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(40,plain,
! [A: $i] : ( subset @ A @ A ),
inference(simp,[status(thm)],[39]) ).
thf(10,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(55,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1410,plain,
( ( sk2 != sk1 )
| ( ( empty @ sk1 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[58,1202]) ).
thf(1431,plain,
( ( sk2 != sk1 )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[1410]) ).
thf(40735,plain,
$false,
inference(e,[status(thm)],[69,1290,61,317,1202,66,63,58,51,829,257,52,125,20,29,70,1174,38,212,96,32,45,64,819,22,59,27,54,49,318,98,50,67,127,31,600,446,43,99,87,813,40,26,55,23,131,1431]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU138+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n003.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu May 18 12:55:46 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.99/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.15/0.99 % [INFO] Parsing done (120ms).
% 1.15/0.99 % [INFO] Running in sequential loop mode.
% 1.70/1.19 % [INFO] eprover registered as external prover.
% 1.70/1.19 % [INFO] cvc4 registered as external prover.
% 1.70/1.19 % [INFO] Scanning for conjecture ...
% 1.87/1.25 % [INFO] Found a conjecture and 20 axioms. Running axiom selection ...
% 1.87/1.29 % [INFO] Axiom selection finished. Selected 17 axioms (removed 3 axioms).
% 1.87/1.31 % [INFO] Problem is first-order (TPTP FOF).
% 1.87/1.31 % [INFO] Type checking passed.
% 1.87/1.31 % [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 ...
% 50.86/10.07 % External prover 'e' found a proof!
% 50.86/10.07 % [INFO] Killing All external provers ...
% 50.86/10.07 % Time passed: 9541ms (effective reasoning time: 9076ms)
% 50.86/10.07 % 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)>
% 50.86/10.07 % Axioms used in derivation (17): idempotence_k3_xboole_0, fc1_xboole_0, t2_boole, commutativity_k3_xboole_0, t6_boole, t4_boole, t7_boole, d4_xboole_0, d10_xboole_0, t3_boole, rc2_xboole_0, d3_tarski, reflexivity_r1_tarski, t8_boole, rc1_xboole_0, d3_xboole_0, antisymmetry_r2_hidden
% 50.86/10.08 % No. of inferences in proof: 118
% 50.86/10.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9541 ms resp. 9076 ms w/o parsing
% 50.86/10.14 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 50.86/10.14 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------