TSTP Solution File: SEU197+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU197+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 11:57:30 EDT 2023
% Result : Theorem 64.79s 11.03s
% Output : Refutation 64.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 44
% Syntax : Number of formulae : 128 ( 55 unt; 19 typ; 0 def)
% Number of atoms : 250 ( 55 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 622 ( 89 ~; 38 |; 34 &; 416 @)
% ( 6 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 11 con; 0-2 aty)
% Number of variables : 126 ( 0 ^; 106 !; 20 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
thf(relation_type,type,
relation: $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(relation_rng_type,type,
relation_rng: $i > $i ).
thf(relation_rng_restriction_type,type,
relation_rng_restriction: $i > $i > $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(element_type,type,
element: $i > $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: $o ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i > $i ).
thf(sk8_type,type,
sk8: $i ).
thf(sk9_type,type,
sk9: $i ).
thf(11,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(56,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(10,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(53,plain,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(19,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(77,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(41,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(42,plain,
empty @ sk5,
inference(cnf,[status(esa)],[41]) ).
thf(7,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(46,plain,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(47,plain,
~ ? [A: $i] : ( empty @ ( singleton @ A ) ),
inference(miniscope,[status(thm)],[46]) ).
thf(48,plain,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
inference(cnf,[status(esa)],[47]) ).
thf(169,plain,
! [A: $i] :
( ( empty @ ( singleton @ A ) )
!= ( empty @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[42,48]) ).
thf(172,plain,
! [A: $i] :
( ( singleton @ A )
!= sk5 ),
inference(simp,[status(thm)],[169]) ).
thf(15,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(66,plain,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(87,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(18,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(74,plain,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(75,plain,
relation @ empty_set,
inference(cnf,[status(esa)],[74]) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(37,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(38,plain,
~ ? [A: $i] :
( ( empty @ A )
& ? [B: $i] :
( ( A != B )
& ( empty @ B ) ) ),
inference(miniscope,[status(thm)],[37]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( A = B )
| ~ ( empty @ B ) ),
inference(cnf,[status(esa)],[38]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_rng @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_relat_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
<=> ( ( in @ A @ B )
& ( in @ A @ ( relation_rng @ C ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(27,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( relation @ C )
=> ( ( ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) )
=> ( ( in @ A @ B )
& ( in @ A @ ( relation_rng @ C ) ) ) )
& ( ( ( in @ A @ B )
& ( in @ A @ ( relation_rng @ C ) ) )
=> ( in @ A @ ( relation_rng @ ( relation_rng_restriction @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(31,plain,
( sk4
| ( in @ sk1 @ ( relation_rng @ sk3 ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(28,plain,
( sk4
| ~ ( in @ sk1 @ ( relation_rng @ ( relation_rng_restriction @ sk2 @ sk3 ) ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(141,plain,
( sk4
| ( ( in @ sk1 @ ( relation_rng @ ( relation_rng_restriction @ sk2 @ sk3 ) ) )
!= ( in @ sk1 @ ( relation_rng @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,28]) ).
thf(143,plain,
( sk4
| ( sk1 != sk1 )
| ( ( relation_rng @ ( relation_rng_restriction @ sk2 @ sk3 ) )
!= ( relation_rng @ sk3 ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(145,plain,
( sk4
| ( ( relation_rng @ ( relation_rng_restriction @ sk2 @ sk3 ) )
!= ( relation_rng @ sk3 ) ) ),
inference(simp,[status(thm)],[143]) ).
thf(181,plain,
( sk4
| ( ( relation_rng_restriction @ sk2 @ sk3 )
!= sk3 ) ),
inference(simp,[status(thm)],[145]) ).
thf(334,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| sk4
| ( B != sk3 )
| ( A
!= ( relation_rng_restriction @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[40,181]) ).
thf(335,plain,
! [A: $i] :
( ~ ( empty @ ( relation_rng_restriction @ sk2 @ sk3 ) )
| ~ ( empty @ A )
| sk4
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[334:[bind(A,$thf( relation_rng_restriction @ sk2 @ sk3 )),bind(B,$thf( B ))]]) ).
thf(437,plain,
( ~ ( empty @ ( relation_rng_restriction @ sk2 @ sk3 ) )
| ~ ( empty @ sk3 )
| sk4 ),
inference(simp,[status(thm)],[335]) ).
thf(68,plain,
empty @ sk8,
inference(cnf,[status(esa)],[66]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(83,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(16,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(69,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(71,plain,
~ ( empty @ sk9 ),
inference(cnf,[status(esa)],[69]) ).
thf(136,plain,
( ( empty @ sk9 )
!= ( empty @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[42,71]) ).
thf(138,plain,
sk9 != sk5,
inference(simp,[status(thm)],[136]) ).
thf(8,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(49,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(171,plain,
! [A: $i] :
( ( empty @ ( singleton @ A ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[49,48]) ).
thf(174,plain,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
inference(simp,[status(thm)],[171]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(50,plain,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
inference(cnf,[status(esa)],[50]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
inference(lifteq,[status(thm)],[51]) ).
thf(25,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(110,plain,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(29,plain,
( ~ ( in @ sk1 @ sk2 )
| ~ ( in @ sk1 @ ( relation_rng @ sk3 ) )
| ~ sk4 ),
inference(cnf,[status(esa)],[27]) ).
thf(13,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(61,plain,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_rng_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_relat_1) ).
thf(89,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( ( C
= ( relation_rng_restriction @ A @ B ) )
=> ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) )
& ( ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) )
& ( ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) )
=> ( C
= ( relation_rng_restriction @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(6,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(43,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(44,plain,
~ ! [A: $i] : ( empty @ A ),
inference(miniscope,[status(thm)],[43]) ).
thf(45,plain,
~ ( empty @ sk6 ),
inference(cnf,[status(esa)],[44]) ).
thf(132,plain,
( ( empty @ sk6 )
!= ( empty @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[42,45]) ).
thf(133,plain,
sk6 != sk5,
inference(simp,[status(thm)],[132]) ).
thf(12,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(59,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(60,plain,
! [A: $i] : ( element @ ( sk7 @ A ) @ A ),
inference(cnf,[status(esa)],[59]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(85,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(70,plain,
relation @ sk9,
inference(cnf,[status(esa)],[69]) ).
thf(33,plain,
( sk4
| ( in @ sk1 @ sk2 ) ),
inference(cnf,[status(esa)],[27]) ).
thf(170,plain,
! [A: $i] :
( ( empty @ ( singleton @ A ) )
!= ( empty @ sk8 ) ),
inference(paramod_ordered,[status(thm)],[68,48]) ).
thf(173,plain,
! [A: $i] :
( ( singleton @ A )
!= sk8 ),
inference(simp,[status(thm)],[170]) ).
thf(146,plain,
( ( empty @ sk8 )
!= ( empty @ sk6 ) ),
inference(paramod_ordered,[status(thm)],[68,45]) ).
thf(148,plain,
sk8 != sk6,
inference(simp,[status(thm)],[146]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(64,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(147,plain,
( ( empty @ sk9 )
!= ( empty @ sk8 ) ),
inference(paramod_ordered,[status(thm)],[68,71]) ).
thf(149,plain,
sk9 != sk8,
inference(simp,[status(thm)],[147]) ).
thf(32,plain,
relation @ sk3,
inference(cnf,[status(esa)],[27]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(34,plain,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(140,plain,
( sk4
| ( ( in @ sk1 @ ( relation_rng @ ( relation_rng_restriction @ sk2 @ sk3 ) ) )
!= ( in @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[33,28]) ).
thf(142,plain,
( sk4
| ( sk1 != sk1 )
| ( ( relation_rng @ ( relation_rng_restriction @ sk2 @ sk3 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[140]) ).
thf(144,plain,
( sk4
| ( ( relation_rng @ ( relation_rng_restriction @ sk2 @ sk3 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[142]) ).
thf(134,plain,
( ( empty @ sk6 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[49,45]) ).
thf(135,plain,
sk6 != empty_set,
inference(simp,[status(thm)],[134]) ).
thf(20,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(80,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(161,plain,
( ~ ( in @ sk1 @ sk2 )
| ~ sk4
| ( ( in @ sk1 @ ( relation_rng @ sk3 ) )
!= ( in @ sk1 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[29]) ).
thf(164,plain,
( ~ ( in @ sk1 @ sk2 )
| ~ sk4
| ( sk1 != sk1 )
| ( ( relation_rng @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[161]) ).
thf(167,plain,
( ~ ( in @ sk1 @ sk2 )
| ~ sk4
| ( ( relation_rng @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[164]) ).
thf(26,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
thf(112,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( ( B
= ( relation_rng @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) )
& ( ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A ) )
& ( ? [D: $i] : ( in @ ( ordered_pair @ D @ C ) @ A )
=> ( in @ C @ B ) ) )
=> ( B
= ( relation_rng @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(67,plain,
relation @ sk8,
inference(cnf,[status(esa)],[66]) ).
thf(17,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(72,plain,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(54,plain,
~ ? [A: $i,B: $i] : ( empty @ ( unordered_pair @ A @ B ) ),
inference(miniscope,[status(thm)],[53]) ).
thf(55,plain,
! [B: $i,A: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
inference(cnf,[status(esa)],[54]) ).
thf(137,plain,
( ( empty @ sk9 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[49,71]) ).
thf(139,plain,
sk9 != empty_set,
inference(simp,[status(thm)],[137]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(cnf,[status(esa)],[34]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(30,plain,
( ( in @ sk1 @ ( relation_rng @ ( relation_rng_restriction @ sk2 @ sk3 ) ) )
| ~ sk4 ),
inference(cnf,[status(esa)],[27]) ).
thf(14523,plain,
$false,
inference(e,[status(thm)],[56,53,77,172,66,48,87,75,437,68,83,69,138,174,42,37,52,110,46,29,61,74,89,133,60,85,28,70,33,173,41,148,45,64,149,32,34,59,27,71,144,49,181,135,80,167,112,145,50,67,31,72,43,40,55,139,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU197+1 : TPTP v8.1.2. Released v3.3.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 12:48:13 EDT 2023
% 0.20/0.36 % CPUTime :
% 0.95/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.95 % [INFO] Parsing done (118ms).
% 1.32/0.96 % [INFO] Running in sequential loop mode.
% 1.69/1.16 % [INFO] eprover registered as external prover.
% 1.69/1.17 % [INFO] cvc4 registered as external prover.
% 1.69/1.17 % [INFO] Scanning for conjecture ...
% 1.78/1.23 % [INFO] Found a conjecture and 30 axioms. Running axiom selection ...
% 1.92/1.27 % [INFO] Axiom selection finished. Selected 24 axioms (removed 6 axioms).
% 1.92/1.30 % [INFO] Problem is first-order (TPTP FOF).
% 1.92/1.30 % [INFO] Type checking passed.
% 1.92/1.31 % [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 ...
% 64.79/11.03 % External prover 'e' found a proof!
% 64.79/11.03 % [INFO] Killing All external provers ...
% 64.79/11.03 % Time passed: 10512ms (effective reasoning time: 10063ms)
% 64.79/11.03 % 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)>
% 64.79/11.03 % Axioms used in derivation (24): fc1_zfmisc_1, d5_relat_1, cc1_relat_1, t6_boole, fc3_subset_1, fc2_subset_1, t7_boole, rc1_relat_1, fc6_relat_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, d5_tarski, fc4_relat_1, d12_relat_1, t1_subset, existence_m1_subset_1, commutativity_k2_tarski, dt_k8_relat_1, rc2_relat_1, t8_boole, rc1_xboole_0, t2_subset, fc8_relat_1
% 64.79/11.03 % No. of inferences in proof: 109
% 64.79/11.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 10512 ms resp. 10063 ms w/o parsing
% 64.79/11.09 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 64.79/11.09 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------