TSTP Solution File: SEU012+1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : SEU012+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 : Tue May 7 08:08:39 EDT 2024
% Result : Theorem 7.88s 2.67s
% Output : Refutation 7.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 62
% Syntax : Number of formulae : 153 ( 62 unt; 23 typ; 0 def)
% Number of atoms : 309 ( 55 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 685 ( 55 ~; 3 |; 90 &; 467 @)
% ( 4 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 10 con; 0-2 aty)
% Number of variables : 150 ( 0 ^ 126 !; 24 ?; 150 :)
% Comments :
%------------------------------------------------------------------------------
thf(relation_type,type,
relation: $i > $o ).
thf(function_type,type,
function: $i > $o ).
thf(relation_rng_type,type,
relation_rng: $i > $i ).
thf(relation_dom_type,type,
relation_dom: $i > $i ).
thf(relation_composition_type,type,
relation_composition: $i > $i > $i ).
thf(identity_relation_type,type,
identity_relation: $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(empty_set_type,type,
empty_set: $i ).
thf(relation_empty_yielding_type,type,
relation_empty_yielding: $i > $o ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk4_type,type,
sk4: $i > $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i ).
thf(sk8_type,type,
sk8: $i ).
thf(sk9_type,type,
sk9: $i ).
thf(sk10_type,type,
sk10: $i ).
thf(sk11_type,type,
sk11: $i ).
thf(16,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(88,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)],[16]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( ( relation_rng @ A )
= ( relation_dom @ B ) )
& ( ( relation_composition @ A @ B )
= A ) )
=> ( B
= ( identity_relation @ ( relation_dom @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_funct_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( ( relation_rng @ A )
= ( relation_dom @ B ) )
& ( ( relation_composition @ A @ B )
= A ) )
=> ( B
= ( identity_relation @ ( relation_dom @ B ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(41,plain,
~ ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( ( relation_rng @ A )
= ( relation_dom @ B ) )
& ( ( relation_composition @ A @ B )
= A ) )
=> ( B
= ( identity_relation @ ( relation_dom @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(42,plain,
relation @ sk1,
inference(cnf,[status(esa)],[41]) ).
thf(15,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(85,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(20,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(97,plain,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(99,plain,
relation @ sk8,
inference(cnf,[status(esa)],[97]) ).
thf(28,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(118,plain,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(119,plain,
relation_empty_yielding @ empty_set,
inference(cnf,[status(esa)],[118]) ).
thf(47,plain,
( ( relation_rng @ sk1 )
= ( relation_dom @ sk2 ) ),
inference(cnf,[status(esa)],[41]) ).
thf(51,plain,
( ( relation_dom @ sk2 )
= ( relation_rng @ sk1 ) ),
inference(lifteq,[status(thm)],[47]) ).
thf(6,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(62,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(26,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(113,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(115,plain,
~ ( empty @ sk9 ),
inference(cnf,[status(esa)],[113]) ).
thf(120,plain,
relation @ empty_set,
inference(cnf,[status(esa)],[118]) ).
thf(3,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(52,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ A @ B ) )
& ( relation @ ( relation_composition @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(110,plain,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ A @ B ) )
& ( relation @ ( relation_composition @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(37,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(157,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(36,axiom,
! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(152,plain,
! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(54,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)],[4]) ).
thf(55,plain,
( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
=> ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( element @ A @ ( powerset @ B ) ) ) ),
inference(miniscope,[status(thm)],[54]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[55]) ).
thf(23,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(106,plain,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(14,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(84,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(33,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(133,plain,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(27,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(116,plain,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(38,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
thf(160,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( ( B
= ( relation_rng @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) )
& ( ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) )
& ( ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) )
=> ( in @ C @ B ) ) )
=> ( B
= ( relation_rng @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(9,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(71,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(72,plain,
empty @ sk6,
inference(cnf,[status(esa)],[71]) ).
thf(190,plain,
( ( empty @ sk9 )
!= ( empty @ sk6 ) ),
inference(paramod_ordered,[status(thm)],[72,115]) ).
thf(192,plain,
sk9 != sk6,
inference(simp,[status(thm)],[190]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(92,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(195,plain,
( ( empty @ sk9 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[84,115]) ).
thf(197,plain,
sk9 != empty_set,
inference(simp,[status(thm)],[195]) ).
thf(7,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(65,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(153,plain,
( ! [A: $i] : ( relation @ ( identity_relation @ A ) )
& ! [A: $i] : ( function @ ( identity_relation @ A ) ) ),
inference(miniscope,[status(thm)],[152]) ).
thf(154,plain,
! [A: $i] : ( function @ ( identity_relation @ A ) ),
inference(cnf,[status(esa)],[153]) ).
thf(156,plain,
! [A: $i] : ( function @ ( identity_relation @ A ) ),
inference(simp,[status(thm)],[154]) ).
thf(40,axiom,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(188,plain,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(53,plain,
! [A: $i] : ( subset @ A @ A ),
inference(cnf,[status(esa)],[52]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ B ) )
=> ( ( apply @ ( relation_composition @ B @ C ) @ A )
= ( apply @ C @ ( apply @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
thf(124,plain,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ B ) )
=> ( ( apply @ ( relation_composition @ B @ C ) @ A )
= ( apply @ C @ ( apply @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(13,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(81,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(82,plain,
~ ! [A: $i] : ( empty @ A ),
inference(miniscope,[status(thm)],[81]) ).
thf(83,plain,
~ ( empty @ sk7 ),
inference(cnf,[status(esa)],[82]) ).
thf(191,plain,
( ( empty @ sk7 )
!= ( empty @ sk6 ) ),
inference(paramod_ordered,[status(thm)],[72,83]) ).
thf(193,plain,
sk7 != sk6,
inference(simp,[status(thm)],[191]) ).
thf(19,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(94,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(95,plain,
~ ? [A: $i] : ( empty @ ( powerset @ A ) ),
inference(miniscope,[status(thm)],[94]) ).
thf(96,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(cnf,[status(esa)],[95]) ).
thf(31,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(127,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(129,plain,
relation @ sk10,
inference(cnf,[status(esa)],[127]) ).
thf(134,plain,
relation @ sk11,
inference(cnf,[status(esa)],[133]) ).
thf(10,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(73,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(128,plain,
function @ sk10,
inference(cnf,[status(esa)],[127]) ).
thf(135,plain,
empty @ sk11,
inference(cnf,[status(esa)],[133]) ).
thf(203,plain,
( ( empty @ sk11 )
!= ( empty @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[135,115]) ).
thf(205,plain,
sk11 != sk9,
inference(simp,[status(thm)],[203]) ).
thf(44,plain,
relation @ sk2,
inference(cnf,[status(esa)],[41]) ).
thf(202,plain,
( ( empty @ sk11 )
!= ( empty @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[135,83]) ).
thf(204,plain,
sk11 != sk7,
inference(simp,[status(thm)],[202]) ).
thf(5,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(59,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(46,plain,
( ( relation_composition @ sk1 @ sk2 )
= sk1 ),
inference(cnf,[status(esa)],[41]) ).
thf(49,plain,
( ( relation_composition @ sk1 @ sk2 )
= sk1 ),
inference(lifteq,[status(thm)],[46]) ).
thf(11,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(76,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(98,plain,
relation_empty_yielding @ sk8,
inference(cnf,[status(esa)],[97]) ).
thf(63,plain,
! [A: $i] : ( empty @ ( sk4 @ A ) ),
inference(cnf,[status(esa)],[62]) ).
thf(206,plain,
! [A: $i] :
( ( empty @ ( sk4 @ A ) )
!= ( empty @ sk7 ) ),
inference(paramod_ordered,[status(thm)],[63,83]) ).
thf(208,plain,
! [A: $i] :
( ( sk4 @ A )
!= sk7 ),
inference(simp,[status(thm)],[206]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_composition @ A @ B ) )
& ( function @ ( relation_composition @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(103,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_composition @ A @ B ) )
& ( function @ ( relation_composition @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(155,plain,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
inference(cnf,[status(esa)],[153]) ).
thf(196,plain,
( ( empty @ sk7 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[84,83]) ).
thf(198,plain,
sk7 != empty_set,
inference(simp,[status(thm)],[196]) ).
thf(24,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(108,plain,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(32,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(130,plain,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(207,plain,
! [A: $i] :
( ( empty @ ( sk4 @ A ) )
!= ( empty @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[63,115]) ).
thf(209,plain,
! [A: $i] :
( ( sk4 @ A )
!= sk9 ),
inference(simp,[status(thm)],[207]) ).
thf(45,plain,
( sk2
!= ( identity_relation @ ( relation_dom @ sk2 ) ) ),
inference(cnf,[status(esa)],[41]) ).
thf(50,plain,
( ( identity_relation @ ( relation_dom @ sk2 ) )
!= sk2 ),
inference(lifteq,[status(thm)],[45]) ).
thf(194,plain,
( ( identity_relation @ ( relation_rng @ sk1 ) )
!= sk2 ),
inference(rewrite,[status(thm)],[50,51]) ).
thf(48,plain,
function @ sk1,
inference(cnf,[status(esa)],[41]) ).
thf(8,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(67,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(43,plain,
function @ sk2,
inference(cnf,[status(esa)],[41]) ).
thf(39,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(186,plain,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(114,plain,
relation @ sk9,
inference(cnf,[status(esa)],[113]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( B
= ( identity_relation @ A ) )
<=> ( ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
thf(139,plain,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( ( B
= ( identity_relation @ A ) )
=> ( ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= C ) ) ) )
& ( ( ( ( relation_dom @ B )
= A )
& ! [C: $i] :
( ( in @ C @ A )
=> ( ( apply @ B @ C )
= C ) ) )
=> ( B
= ( identity_relation @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ B @ A ) )
& ( relation @ ( relation_composition @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(136,plain,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ B @ A ) )
& ( relation @ ( relation_composition @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(79,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(90,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(122,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(21,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(100,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(446,plain,
$false,
inference(e,[status(thm)],[88,42,85,99,119,51,62,115,120,52,110,157,152,57,106,84,133,116,160,192,92,197,65,97,156,188,53,124,193,96,129,41,134,73,128,205,44,204,59,118,71,54,49,113,81,76,98,208,103,155,198,108,130,135,209,194,48,63,67,127,72,43,186,114,139,136,79,94,90,122,83,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU012+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n023.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 6 10:35:24 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.96/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.33/1.06 % [INFO] Parsing done (176ms).
% 1.52/1.07 % [INFO] Running in sequential loop mode.
% 1.88/1.28 % [INFO] eprover registered as external prover.
% 1.88/1.28 % [INFO] cvc4 registered as external prover.
% 1.88/1.28 % [INFO] Scanning for conjecture ...
% 2.11/1.34 % [INFO] Found a conjecture and 38 axioms. Running axiom selection ...
% 2.25/1.40 % [INFO] Axiom selection finished. Selected 38 axioms (removed 0 axioms).
% 2.25/1.44 % [INFO] Problem is first-order (TPTP FOF).
% 2.25/1.44 % [INFO] Type checking passed.
% 2.46/1.44 % [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 ...
% 7.88/2.67 % External prover 'e' found a proof!
% 7.88/2.67 % [INFO] Killing All external provers ...
% 7.88/2.67 % Time passed: 2122ms (effective reasoning time: 1593ms)
% 7.88/2.67 % 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)>
% 7.88/2.67 % Axioms used in derivation (38): fc9_relat_1, fc1_funct_1, cc1_relat_1, rc1_funct_1, t23_funct_1, t5_subset, fc2_funct_1, t4_subset, fc5_relat_1, rc2_relat_1, d5_funct_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, fc4_relat_1, t1_subset, t34_funct_1, rc3_relat_1, t6_boole, rc2_subset_1, t7_boole, cc1_funct_1, fc1_subset_1, fc10_relat_1, rc1_subset_1, t3_subset, existence_m1_subset_1, rc1_relat_1, dt_k5_relat_1, reflexivity_r1_tarski, dt_k6_relat_1, fc6_relat_1, t8_boole, rc1_xboole_0, t2_subset, fc7_relat_1, fc12_relat_1, fc8_relat_1
% 7.88/2.67 % No. of inferences in proof: 130
% 7.88/2.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2122 ms resp. 1593 ms w/o parsing
% 7.88/2.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.88/2.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------