TSTP Solution File: SEU051+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU051+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n001.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 11:56:55 EDT 2023
% Result : Theorem 193.57s 37.23s
% Output : Refutation 194.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 64
% Syntax : Number of formulae : 168 ( 56 unt; 28 typ; 0 def)
% Number of atoms : 345 ( 51 equ; 0 cnn)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 820 ( 77 ~; 30 |; 94 &; 556 @)
% ( 6 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 13 con; 0-2 aty)
% Number of variables : 183 ( 0 ^; 148 !; 35 ?; 183 :)
% Comments :
%------------------------------------------------------------------------------
thf(relation_type,type,
relation: $i > $o ).
thf(function_type,type,
function: $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(relation_image_type,type,
relation_image: $i > $i > $i ).
thf(relation_rng_restriction_type,type,
relation_rng_restriction: $i > $i > $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(one_to_one_type,type,
one_to_one: $i > $o ).
thf(relation_dom_type,type,
relation_dom: $i > $i ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(relation_empty_yielding_type,type,
relation_empty_yielding: $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(sk6_type,type,
sk6: $i > $i ).
thf(sk7_type,type,
sk7: $i > $i ).
thf(sk8_type,type,
sk8: $i > $i ).
thf(sk9_type,type,
sk9: $i ).
thf(sk15_type,type,
sk15: $i ).
thf(sk16_type,type,
sk16: $i ).
thf(sk22_type,type,
sk22: $i ).
thf(sk23_type,type,
sk23: $i ).
thf(sk25_type,type,
sk25: $i ).
thf(23,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(125,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(126,plain,
! [A: $i] : ( subset @ A @ A ),
inference(cnf,[status(esa)],[125]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( subset @ ( relation_image @ ( relation_rng_restriction @ A @ C ) @ B ) @ ( relation_image @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_funct_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( subset @ ( relation_image @ ( relation_rng_restriction @ A @ C ) @ B ) @ ( relation_image @ C @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(38,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( subset @ ( relation_image @ ( relation_rng_restriction @ A @ C ) @ B ) @ ( relation_image @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(39,plain,
~ ( subset @ ( relation_image @ ( relation_rng_restriction @ sk1 @ sk3 ) @ sk2 ) @ ( relation_image @ sk3 @ sk2 ) ),
inference(cnf,[status(esa)],[38]) ).
thf(595,plain,
! [A: $i] :
( ( subset @ A @ A )
!= ( subset @ ( relation_image @ ( relation_rng_restriction @ sk1 @ sk3 ) @ sk2 ) @ ( relation_image @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[126,39]) ).
thf(596,plain,
! [A: $i] :
( ( A
!= ( relation_image @ ( relation_rng_restriction @ sk1 @ sk3 ) @ sk2 ) )
| ( A
!= ( relation_image @ sk3 @ sk2 ) ) ),
inference(simp,[status(thm)],[595]) ).
thf(597,plain,
( ( relation_image @ ( relation_rng_restriction @ sk1 @ sk3 ) @ sk2 )
!= ( relation_image @ sk3 @ sk2 ) ),
inference(simp,[status(thm)],[596]) ).
thf(8,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(56,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(84,plain,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(6,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(51,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(52,plain,
~ ? [A: $i,B: $i] :
( ( in @ A @ B )
& ( empty @ B ) ),
inference(miniscope,[status(thm)],[51]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( empty @ B ) ),
inference(cnf,[status(esa)],[52]) ).
thf(36,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(192,plain,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(193,plain,
relation_empty_yielding @ empty_set,
inference(cnf,[status(esa)],[192]) ).
thf(9,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(59,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(57,plain,
~ ! [A: $i] : ( empty @ A ),
inference(miniscope,[status(thm)],[56]) ).
thf(58,plain,
~ ( empty @ sk5 ),
inference(cnf,[status(esa)],[57]) ).
thf(203,plain,
( ( empty @ sk5 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[59,58]) ).
thf(205,plain,
sk5 != empty_set,
inference(simp,[status(thm)],[203]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(89,plain,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(91,plain,
empty @ sk9,
inference(cnf,[status(esa)],[89]) ).
thf(12,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(65,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(66,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ),
inference(cnf,[status(esa)],[65]) ).
thf(67,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( empty @ A ) ),
inference(lifteq,[status(thm)],[66]) ).
thf(939,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ sk9 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[91,67]) ).
thf(940,plain,
sk9 = empty_set,
inference(pattern_uni,[status(thm)],[939:[bind(A,$thf( sk9 ))]]) ).
thf(13,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(68,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)],[13]) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( element @ B @ ( powerset @ C ) )
| ( element @ A @ C ) ),
inference(cnf,[status(esa)],[68]) ).
thf(27,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(137,plain,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(138,plain,
relation_empty_yielding @ sk16,
inference(cnf,[status(esa)],[137]) ).
thf(30,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(171,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(174,plain,
relation @ sk23,
inference(cnf,[status(esa)],[171]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(42,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(72,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(73,plain,
~ ? [A: $i] : ( empty @ ( powerset @ A ) ),
inference(miniscope,[status(thm)],[72]) ).
thf(74,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(cnf,[status(esa)],[73]) ).
thf(500,plain,
! [A: $i] :
( ( empty @ ( powerset @ A ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[59,74]) ).
thf(504,plain,
! [A: $i] :
( ( powerset @ A )
!= empty_set ),
inference(simp,[status(thm)],[500]) ).
thf(29,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(168,plain,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(170,plain,
empty @ sk22,
inference(cnf,[status(esa)],[168]) ).
thf(837,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ sk22 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[170,67]) ).
thf(838,plain,
sk22 = empty_set,
inference(pattern_uni,[status(thm)],[837:[bind(A,$thf( sk22 ))]]) ).
thf(37,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(196,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_rng_restriction @ A @ B ) )
& ( function @ ( relation_rng_restriction @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).
thf(189,plain,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_rng_restriction @ A @ B ) )
& ( function @ ( relation_rng_restriction @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(4,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(46,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ? [E: $i] :
( ( in @ E @ ( relation_dom @ A ) )
& ( in @ E @ B )
& ( D
= ( apply @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
thf(93,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( C
= ( relation_image @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ? [E: $i] :
( ( in @ E @ ( relation_dom @ A ) )
& ( in @ E @ B )
& ( D
= ( apply @ A @ E ) ) ) )
& ( ? [E: $i] :
( ( in @ E @ ( relation_dom @ A ) )
& ( in @ E @ B )
& ( D
= ( apply @ A @ E ) ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ? [E: $i] :
( ( in @ E @ ( relation_dom @ A ) )
& ( in @ E @ B )
& ( D
= ( apply @ A @ E ) ) ) )
& ( ? [E: $i] :
( ( in @ E @ ( relation_dom @ A ) )
& ( in @ E @ B )
& ( D
= ( apply @ A @ E ) ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( relation_image @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(17,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(78,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(60,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ),
inference(cnf,[status(esa)],[60]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(132,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)],[26]) ).
thf(25,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(129,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(131,plain,
~ ( empty @ sk15 ),
inference(cnf,[status(esa)],[129]) ).
thf(204,plain,
( ( empty @ sk15 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[59,131]) ).
thf(206,plain,
sk15 != empty_set,
inference(simp,[status(thm)],[204]) ).
thf(438,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( ( empty @ empty_set )
!= ( empty @ B ) ) ),
inference(paramod_ordered,[status(thm)],[59,53]) ).
thf(439,plain,
! [A: $i] :
~ ( in @ A @ empty_set ),
inference(pattern_uni,[status(thm)],[438:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).
thf(85,plain,
relation @ empty_set,
inference(cnf,[status(esa)],[84]) ).
thf(90,plain,
function @ sk9,
inference(cnf,[status(esa)],[89]) ).
thf(1021,plain,
function @ empty_set,
inference(rewrite,[status(thm)],[90,940]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(197,plain,
function @ sk25,
inference(cnf,[status(esa)],[196]) ).
thf(41,plain,
relation @ sk3,
inference(cnf,[status(esa)],[38]) ).
thf(16,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(75,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(76,plain,
! [A: $i] : ( empty @ ( sk7 @ A ) ),
inference(cnf,[status(esa)],[75]) ).
thf(915,plain,
! [B: $i,A: $i] :
( ( B = empty_set )
| ( ( empty @ ( sk7 @ A ) )
!= ( empty @ B ) ) ),
inference(paramod_ordered,[status(thm)],[76,67]) ).
thf(916,plain,
! [A: $i] :
( ( sk7 @ A )
= empty_set ),
inference(pattern_uni,[status(thm)],[915:[bind(A,$thf( C )),bind(B,$thf( sk7 @ C ))]]) ).
thf(984,plain,
! [A: $i] :
( ( sk7 @ A )
= empty_set ),
inference(simp,[status(thm)],[916]) ).
thf(173,plain,
function @ sk23,
inference(cnf,[status(esa)],[171]) ).
thf(43,plain,
~ ? [A: $i] :
( ( empty @ A )
& ? [B: $i] :
( ( A != B )
& ( empty @ B ) ) ),
inference(miniscope,[status(thm)],[42]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( A = B )
| ~ ( empty @ B ) ),
inference(cnf,[status(esa)],[43]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ),
inference(lifteq,[status(thm)],[44]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(62,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(64,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( sk6 @ A ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(33,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(180,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)],[33]) ).
thf(34,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(187,plain,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(172,plain,
one_to_one @ sk23,
inference(cnf,[status(esa)],[171]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( B
= ( relation_rng_restriction @ A @ C ) )
<=> ( ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
<=> ( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ D ) @ A ) ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_1) ).
thf(140,plain,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( ( B
= ( relation_rng_restriction @ A @ C ) )
=> ( ! [D: $i] :
( ( ( in @ D @ ( relation_dom @ B ) )
=> ( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ D ) @ A ) ) )
& ( ( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ D ) @ A ) )
=> ( in @ D @ ( relation_dom @ B ) ) ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) ) )
& ( ( ! [D: $i] :
( ( ( in @ D @ ( relation_dom @ B ) )
=> ( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ D ) @ A ) ) )
& ( ( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ D ) @ A ) )
=> ( in @ D @ ( relation_dom @ B ) ) ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) )
=> ( B
= ( relation_rng_restriction @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(198,plain,
relation @ sk25,
inference(cnf,[status(esa)],[196]) ).
thf(130,plain,
relation @ sk15,
inference(cnf,[status(esa)],[129]) ).
thf(18,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(80,plain,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(5,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(48,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(63,plain,
! [A: $i] :
( ( empty @ A )
| ( element @ ( sk6 @ A ) @ ( powerset @ A ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(49,plain,
~ ? [A: $i,B: $i] :
( ( in @ A @ B )
& ? [C: $i] :
( ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) ),
inference(miniscope,[status(thm)],[48]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( element @ B @ ( powerset @ C ) )
| ~ ( empty @ C ) ),
inference(cnf,[status(esa)],[49]) ).
thf(32,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(177,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(24,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(127,plain,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(31,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(175,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(47,plain,
empty @ sk4,
inference(cnf,[status(esa)],[46]) ).
thf(977,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ sk4 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47,67]) ).
thf(978,plain,
sk4 = empty_set,
inference(pattern_uni,[status(thm)],[977:[bind(A,$thf( sk4 ))]]) ).
thf(20,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(87,plain,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(733,plain,
( ( ( relation_rng_restriction @ sk1 @ sk3 )
!= sk3 )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[597]) ).
thf(759,plain,
( ( relation_rng_restriction @ sk1 @ sk3 )
!= sk3 ),
inference(simp,[status(thm)],[733]) ).
thf(40,plain,
function @ sk3,
inference(cnf,[status(esa)],[38]) ).
thf(77,plain,
! [A: $i] : ( element @ ( sk7 @ A ) @ ( powerset @ A ) ),
inference(cnf,[status(esa)],[75]) ).
thf(1062,plain,
! [A: $i] : ( element @ empty_set @ ( powerset @ A ) ),
inference(rewrite,[status(thm)],[77,984]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ),
inference(cnf,[status(esa)],[54]) ).
thf(139,plain,
relation @ sk16,
inference(cnf,[status(esa)],[137]) ).
thf(213,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( relation @ A )
| ( B != sk3 ) ),
inference(paramod_ordered,[status(thm)],[45,41]) ).
thf(214,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk3 )
| ( relation @ A ) ),
inference(pattern_uni,[status(thm)],[213:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(79,plain,
! [A: $i] : ( element @ ( sk8 @ A ) @ A ),
inference(cnf,[status(esa)],[78]) ).
thf(46169,plain,
$false,
inference(cvc4,[status(thm)],[597,56,84,53,193,205,59,54,940,69,138,174,42,504,838,125,196,189,46,93,78,61,132,89,74,206,60,439,85,1021,38,70,192,137,197,65,129,41,984,173,45,64,180,187,172,39,140,198,130,80,48,63,50,67,177,127,72,175,978,87,759,40,1062,55,171,139,75,58,214,168,51,126,79,131,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SEU051+1 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.13 % Command : run_Leo-III %s %d
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu May 18 12:56:50 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.80/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.97 % [INFO] Parsing done (139ms).
% 1.21/0.98 % [INFO] Running in sequential loop mode.
% 1.71/1.21 % [INFO] eprover registered as external prover.
% 1.71/1.22 % [INFO] cvc4 registered as external prover.
% 1.71/1.22 % [INFO] Scanning for conjecture ...
% 1.85/1.29 % [INFO] Found a conjecture and 35 axioms. Running axiom selection ...
% 1.99/1.34 % [INFO] Axiom selection finished. Selected 35 axioms (removed 0 axioms).
% 2.20/1.38 % [INFO] Problem is first-order (TPTP FOF).
% 2.20/1.38 % [INFO] Type checking passed.
% 2.20/1.39 % [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 ...
% 193.57/37.22 % External prover 'cvc4' found a proof!
% 193.57/37.22 % [INFO] Killing All external provers ...
% 193.57/37.22 % Time passed: 36735ms (effective reasoning time: 36237ms)
% 193.57/37.22 % 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)>
% 193.57/37.23 % Axioms used in derivation (35): t85_funct_1, rc3_funct_1, cc1_relat_1, rc1_funct_1, t5_subset, t4_subset, fc5_relat_1, d12_funct_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, fc4_relat_1, t1_subset, rc3_relat_1, t6_boole, rc2_subset_1, t7_boole, cc1_funct_1, fc1_subset_1, fc5_funct_1, rc2_funct_1, rc1_subset_1, cc2_funct_1, t3_subset, existence_m1_subset_1, dt_k8_relat_1, rc2_relat_1, d3_tarski, rc1_relat_1, reflexivity_r1_tarski, t8_boole, rc1_xboole_0, t2_subset, fc7_relat_1, fc12_relat_1
% 193.57/37.23 % No. of inferences in proof: 140
% 193.57/37.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 36735 ms resp. 36237 ms w/o parsing
% 194.09/37.28 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 194.09/37.28 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------