TSTP Solution File: SEU213+1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : SEU213+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n018.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 08:09:13 EDT 2024
% Result : Theorem 30.71s 5.63s
% Output : Refutation 30.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 57
% Syntax : Number of formulae : 138 ( 53 unt; 24 typ; 0 def)
% Number of atoms : 288 ( 47 equ; 0 cnn)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 735 ( 58 ~; 18 |; 70 &; 519 @)
% ( 8 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 12 con; 0-2 aty)
% Number of variables : 132 ( 0 ^ 107 !; 25 ?; 132 :)
% Comments :
%------------------------------------------------------------------------------
thf(relation_type,type,
relation: $i > $o ).
thf(function_type,type,
function: $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(relation_dom_type,type,
relation_dom: $i > $i ).
thf(relation_composition_type,type,
relation_composition: $i > $i > $i ).
thf(apply_type,type,
apply: $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(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: $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(sk10_type,type,
sk10: $i ).
thf(sk22_type,type,
sk22: $i ).
thf(19,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(88,plain,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(6,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(54,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(55,plain,
~ ! [A: $i] : ( empty @ A ),
inference(miniscope,[status(thm)],[54]) ).
thf(56,plain,
~ ( empty @ sk6 ),
inference(cnf,[status(esa)],[55]) ).
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(61,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(1,conjecture,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(35,plain,
~ ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) ) ) )
& ( ( ( in @ A @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ A ) @ ( relation_dom @ B ) ) )
=> ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(41,plain,
( sk4
| ( in @ ( apply @ sk3 @ sk1 ) @ ( relation_dom @ sk2 ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(37,plain,
( sk4
| ~ ( in @ sk1 @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(196,plain,
( sk4
| ( ( in @ ( apply @ sk3 @ sk1 ) @ ( relation_dom @ sk2 ) )
!= ( in @ sk1 @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[41,37]) ).
thf(197,plain,
( sk4
| ( ( apply @ sk3 @ sk1 )
!= sk1 )
| ( ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) )
!= ( relation_dom @ sk2 ) ) ),
inference(simp,[status(thm)],[196]) ).
thf(5,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(52,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(53,plain,
empty @ sk5,
inference(cnf,[status(esa)],[52]) ).
thf(21,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(104,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(105,plain,
relation @ sk9,
inference(cnf,[status(esa)],[104]) ).
thf(43,plain,
( sk4
| ( in @ sk1 @ ( relation_dom @ sk3 ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(183,plain,
( sk4
| ( ( in @ sk1 @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ) )
!= ( in @ sk1 @ ( relation_dom @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[43,37]) ).
thf(184,plain,
( sk4
| ( sk1 != sk1 )
| ( ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) )
!= ( relation_dom @ sk3 ) ) ),
inference(simp,[status(thm)],[183]) ).
thf(185,plain,
( sk4
| ( ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) )
!= ( relation_dom @ sk3 ) ) ),
inference(simp,[status(thm)],[184]) ).
thf(198,plain,
( sk4
| ( ( relation_composition @ sk3 @ sk2 )
!= sk3 ) ),
inference(simp,[status(thm)],[185]) ).
thf(15,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(77,plain,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(79,plain,
empty @ sk8,
inference(cnf,[status(esa)],[77]) ).
thf(192,plain,
( ( empty @ sk8 )
!= ( empty @ sk6 ) ),
inference(paramod_ordered,[status(thm)],[79,56]) ).
thf(194,plain,
sk8 != sk6,
inference(simp,[status(thm)],[192]) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(48,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(40,plain,
( ( in @ sk1 @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ) )
| ~ sk4 ),
inference(cnf,[status(esa)],[35]) ).
thf(25,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(115,plain,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(26,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(118,plain,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(120,plain,
relation @ sk10,
inference(cnf,[status(esa)],[118]) ).
thf(42,plain,
( ~ ( in @ sk1 @ ( relation_dom @ sk3 ) )
| ~ ( in @ ( apply @ sk3 @ sk1 ) @ ( relation_dom @ sk2 ) )
| ~ sk4 ),
inference(cnf,[status(esa)],[35]) ).
thf(23,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(109,plain,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(110,plain,
relation_empty_yielding @ empty_set,
inference(cnf,[status(esa)],[109]) ).
thf(32,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(152,plain,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(7,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(57,plain,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(78,plain,
relation @ sk8,
inference(cnf,[status(esa)],[77]) ).
thf(216,plain,
( sk4
| ( ( apply @ sk3 @ sk1 )
!= sk1 )
| ( ( relation_composition @ sk3 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[197]) ).
thf(106,plain,
~ ( empty @ sk9 ),
inference(cnf,[status(esa)],[104]) ).
thf(27,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(121,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(8,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(60,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(18,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(85,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)],[18]) ).
thf(38,plain,
function @ sk3,
inference(cnf,[status(esa)],[35]) ).
thf(12,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(70,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(124,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(30,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
thf(129,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( ( B
= ( relation_dom @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) )
& ( ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) )
& ( ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ C @ B ) ) )
=> ( B
= ( relation_dom @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
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(45,plain,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(64,plain,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,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(149,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)],[31]) ).
thf(34,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(176,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(189,plain,
( ( empty @ sk9 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[60,106]) ).
thf(191,plain,
sk9 != empty_set,
inference(simp,[status(thm)],[189]) ).
thf(44,plain,
function @ sk2,
inference(cnf,[status(esa)],[35]) ).
thf(58,plain,
~ ? [A: $i] : ( empty @ ( singleton @ A ) ),
inference(miniscope,[status(thm)],[57]) ).
thf(59,plain,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
inference(cnf,[status(esa)],[58]) ).
thf(71,plain,
! [A: $i] : ( element @ ( sk7 @ A ) @ A ),
inference(cnf,[status(esa)],[70]) ).
thf(179,plain,
( ( empty @ sk6 )
!= ( empty @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[53,56]) ).
thf(181,plain,
sk6 != sk5,
inference(simp,[status(thm)],[179]) ).
thf(24,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(113,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(39,plain,
relation @ sk3,
inference(cnf,[status(esa)],[35]) ).
thf(16,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(80,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)],[16]) ).
thf(11,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(67,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(177,plain,
function @ sk22,
inference(cnf,[status(esa)],[176]) ).
thf(180,plain,
( ( empty @ sk9 )
!= ( empty @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[53,106]) ).
thf(182,plain,
sk9 != sk5,
inference(simp,[status(thm)],[180]) ).
thf(33,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_composition @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
thf(154,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( ( C
= ( relation_composition @ A @ B ) )
=> ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) )
& ( ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) )
& ( ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) )
=> ( C
= ( relation_composition @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(13,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(72,plain,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(75,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(119,plain,
relation_empty_yielding @ sk10,
inference(cnf,[status(esa)],[118]) ).
thf(36,plain,
relation @ sk2,
inference(cnf,[status(esa)],[35]) ).
thf(188,plain,
( ( empty @ sk6 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[60,56]) ).
thf(190,plain,
sk6 != empty_set,
inference(simp,[status(thm)],[188]) ).
thf(22,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(107,plain,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(29,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(126,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(193,plain,
( ( empty @ sk9 )
!= ( empty @ sk8 ) ),
inference(paramod_ordered,[status(thm)],[79,106]) ).
thf(195,plain,
sk9 != sk8,
inference(simp,[status(thm)],[193]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(cnf,[status(esa)],[45]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(lifteq,[status(thm)],[46]) ).
thf(178,plain,
relation @ sk22,
inference(cnf,[status(esa)],[176]) ).
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(83,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(20,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ( ~ ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( C = empty_set ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
thf(90,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
=> ( ( ( C
= ( apply @ A @ B ) )
=> ( in @ ( ordered_pair @ B @ C ) @ A ) )
& ( ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( C
= ( apply @ A @ B ) ) ) ) )
& ( ~ ( in @ B @ ( relation_dom @ A ) )
=> ( ( ( C
= ( apply @ A @ B ) )
=> ( C = empty_set ) )
& ( ( C = empty_set )
=> ( C
= ( apply @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(111,plain,
relation @ empty_set,
inference(cnf,[status(esa)],[109]) ).
thf(5985,plain,
$false,
inference(e,[status(thm)],[88,56,61,197,53,105,198,194,48,104,40,115,120,185,42,37,52,110,152,57,78,216,106,121,60,85,38,70,109,124,77,129,41,45,64,149,176,191,44,59,118,71,54,181,113,39,80,35,67,177,182,154,72,43,75,119,36,190,107,126,79,195,47,178,83,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU213+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n018.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 : Mon May 6 11:18:39 EDT 2024
% 0.15/0.37 % CPUTime :
% 1.03/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.31/1.04 % [INFO] Parsing done (142ms).
% 1.31/1.05 % [INFO] Running in sequential loop mode.
% 1.81/1.27 % [INFO] eprover registered as external prover.
% 1.81/1.27 % [INFO] cvc4 registered as external prover.
% 1.81/1.28 % [INFO] Scanning for conjecture ...
% 2.08/1.34 % [INFO] Found a conjecture and 39 axioms. Running axiom selection ...
% 2.25/1.39 % [INFO] Axiom selection finished. Selected 32 axioms (removed 7 axioms).
% 2.25/1.43 % [INFO] Problem is first-order (TPTP FOF).
% 2.25/1.44 % [INFO] Type checking passed.
% 2.25/1.44 % [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 ...
% 30.71/5.62 % External prover 'e' found a proof!
% 30.71/5.62 % [INFO] Killing All external provers ...
% 30.71/5.63 % Time passed: 5085ms (effective reasoning time: 4569ms)
% 30.71/5.63 % 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)>
% 30.71/5.63 % Axioms used in derivation (32): fc9_relat_1, fc1_funct_1, cc1_relat_1, rc1_funct_1, fc3_subset_1, fc10_relat_1, fc5_relat_1, d8_relat_1, rc2_relat_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_zfmisc_1, d4_funct_1, fc1_xboole_0, d5_tarski, fc4_relat_1, t1_subset, rc3_relat_1, t6_boole, d4_relat_1, fc2_subset_1, t7_boole, cc1_funct_1, existence_m1_subset_1, commutativity_k2_tarski, rc1_relat_1, dt_k5_relat_1, t8_boole, rc1_xboole_0, t2_subset, fc7_relat_1, fc12_relat_1
% 30.71/5.63 % No. of inferences in proof: 114
% 30.71/5.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5085 ms resp. 4569 ms w/o parsing
% 30.71/5.68 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 30.71/5.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------