TSTP Solution File: SEU235+1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : SEU235+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.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 08:09:20 EDT 2024
% Result : Theorem 9.10s 2.99s
% Output : Refutation 9.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 68
% Syntax : Number of formulae : 158 ( 46 unt; 27 typ; 0 def)
% Number of atoms : 350 ( 27 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 716 ( 81 ~; 23 |; 120 &; 432 @)
% ( 3 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 27 usr; 14 con; 0-2 aty)
% Number of variables : 139 ( 0 ^ 111 !; 28 ?; 139 :)
% Comments :
%------------------------------------------------------------------------------
thf(ordinal_type,type,
ordinal: $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(empty_set_type,type,
empty_set: $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(ordinal_subset_type,type,
ordinal_subset: $i > $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(relation_type,type,
relation: $i > $o ).
thf(function_type,type,
function: $i > $o ).
thf(one_to_one_type,type,
one_to_one: $i > $o ).
thf(relation_empty_yielding_type,type,
relation_empty_yielding: $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(epsilon_transitive_type,type,
epsilon_transitive: $i > $o ).
thf(epsilon_connected_type,type,
epsilon_connected: $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i > $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $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(sk13_type,type,
sk13: $i ).
thf(sk16_type,type,
sk16: $i ).
thf(41,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(174,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(121,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(5,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(57,plain,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(59,plain,
empty @ sk5,
inference(cnf,[status(esa)],[57]) ).
thf(6,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(60,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(61,plain,
~ ! [A: $i] : ( empty @ A ),
inference(miniscope,[status(thm)],[60]) ).
thf(62,plain,
~ ( empty @ sk6 ),
inference(cnf,[status(esa)],[61]) ).
thf(190,plain,
( ( empty @ sk6 )
!= ( empty @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[59,62]) ).
thf(192,plain,
sk6 != sk5,
inference(simp,[status(thm)],[190]) ).
thf(4,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(55,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(56,plain,
empty @ sk4,
inference(cnf,[status(esa)],[55]) ).
thf(7,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(63,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(65,plain,
~ ( empty @ sk7 ),
inference(cnf,[status(esa)],[63]) ).
thf(187,plain,
( ( empty @ sk7 )
!= ( empty @ sk4 ) ),
inference(paramod_ordered,[status(thm)],[56,65]) ).
thf(188,plain,
sk7 != sk4,
inference(simp,[status(thm)],[187]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(51,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(83,plain,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(101,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(14,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(85,plain,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(88,plain,
relation @ sk11,
inference(cnf,[status(esa)],[85]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(142,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)],[33]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(110,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ~ ( ( subset @ A @ B )
& ( A != empty_set )
& ! [C: $i] :
( ( ordinal @ C )
=> ~ ( ( in @ C @ A )
& ! [D: $i] :
( ( ordinal @ D )
=> ( ( in @ D @ A )
=> ( ordinal_subset @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_ordinal1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ordinal @ B )
=> ~ ( ( subset @ A @ B )
& ( A != empty_set )
& ! [C: $i] :
( ( ordinal @ C )
=> ~ ( ( in @ C @ A )
& ! [D: $i] :
( ( ordinal @ D )
=> ( ( in @ D @ A )
=> ( ordinal_subset @ C @ D ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(43,plain,
~ ! [A: $i,B: $i] :
( ( ordinal @ B )
=> ~ ( ( subset @ A @ B )
& ( A != empty_set )
& ! [C: $i] :
( ( ordinal @ C )
=> ~ ( ( in @ C @ A )
& ! [D: $i] :
( ( ordinal @ D )
=> ( ( in @ D @ A )
=> ( ordinal_subset @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(45,plain,
ordinal @ sk2,
inference(cnf,[status(esa)],[43]) ).
thf(44,plain,
! [A: $i] :
( ~ ( ordinal @ A )
| ~ ( in @ A @ sk1 )
| ~ ( ordinal_subset @ A @ ( sk3 @ A ) ) ),
inference(cnf,[status(esa)],[43]) ).
thf(195,plain,
! [A: $i] :
( ~ ( in @ A @ sk1 )
| ~ ( ordinal_subset @ A @ ( sk3 @ A ) )
| ( ( ordinal @ sk2 )
!= ( ordinal @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45,44]) ).
thf(196,plain,
( ~ ( in @ sk2 @ sk1 )
| ~ ( ordinal_subset @ sk2 @ ( sk3 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( sk2 ))]]) ).
thf(37,axiom,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
thf(157,plain,
? [A: $i] :
( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(46,plain,
subset @ sk1 @ sk2,
inference(cnf,[status(esa)],[43]) ).
thf(16,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(91,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(93,plain,
relation @ sk13,
inference(cnf,[status(esa)],[91]) ).
thf(11,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(75,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(78,plain,
relation @ sk9,
inference(cnf,[status(esa)],[75]) ).
thf(34,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
thf(147,plain,
! [A: $i] :
( ( ordinal @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ordinal_subset @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
thf(132,plain,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ordinal_subset @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(15,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(89,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(72,plain,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(74,plain,
relation @ sk8,
inference(cnf,[status(esa)],[72]) ).
thf(49,plain,
! [A: $i] :
( ~ ( ordinal @ A )
| ~ ( in @ A @ sk1 )
| ( in @ ( sk3 @ A ) @ sk1 ) ),
inference(cnf,[status(esa)],[43]) ).
thf(205,plain,
! [A: $i] :
( ~ ( in @ A @ sk1 )
| ( in @ ( sk3 @ A ) @ sk1 )
| ( ( ordinal @ sk2 )
!= ( ordinal @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45,49]) ).
thf(206,plain,
( ~ ( in @ sk2 @ sk1 )
| ( in @ ( sk3 @ sk2 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[205:[bind(A,$thf( sk2 ))]]) ).
thf(92,plain,
function @ sk13,
inference(cnf,[status(esa)],[91]) ).
thf(18,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).
thf(97,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(22,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(109,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(77,plain,
function @ sk9,
inference(cnf,[status(esa)],[75]) ).
thf(73,plain,
relation_empty_yielding @ sk8,
inference(cnf,[status(esa)],[72]) ).
thf(29,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ( in @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_tarski) ).
thf(128,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i] :
~ ( ( in @ D @ B )
& ( in @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(40,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A )
& ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).
thf(166,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A )
& ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
=> ( ordinal @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).
thf(161,plain,
! [A: $i,B: $i] :
( ( ordinal @ B )
=> ( ( in @ A @ B )
=> ( ordinal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(64,plain,
relation @ sk7,
inference(cnf,[status(esa)],[63]) ).
thf(42,axiom,
( ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set )
& ( function @ empty_set )
& ( one_to_one @ empty_set )
& ( empty @ empty_set )
& ( epsilon_transitive @ empty_set )
& ( epsilon_connected @ empty_set )
& ( ordinal @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_ordinal1) ).
thf(176,plain,
( ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set )
& ( function @ empty_set )
& ( one_to_one @ empty_set )
& ( empty @ empty_set )
& ( epsilon_transitive @ empty_set )
& ( epsilon_connected @ empty_set )
& ( ordinal @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(189,plain,
( ( empty @ sk7 )
!= ( empty @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[59,65]) ).
thf(191,plain,
sk7 != sk5,
inference(simp,[status(thm)],[189]) ).
thf(52,plain,
~ ? [A: $i] :
( ( empty @ A )
& ? [B: $i] :
( ( A != B )
& ( empty @ B ) ) ),
inference(miniscope,[status(thm)],[51]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( A = B )
| ~ ( empty @ B ) ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(86,plain,
function @ sk11,
inference(cnf,[status(esa)],[85]) ).
thf(12,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(79,plain,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(81,plain,
relation_empty_yielding @ sk10,
inference(cnf,[status(esa)],[79]) ).
thf(76,plain,
one_to_one @ sk9,
inference(cnf,[status(esa)],[75]) ).
thf(8,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(66,plain,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(36,axiom,
! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
thf(155,plain,
! [A: $i] :
( ( ( epsilon_transitive @ A )
& ( epsilon_connected @ A ) )
=> ( ordinal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(31,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(135,plain,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(80,plain,
function @ sk10,
inference(cnf,[status(esa)],[79]) ).
thf(24,axiom,
! [A: $i] :
( ( epsilon_transitive @ A )
<=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
thf(112,plain,
! [A: $i] :
( ( ( epsilon_transitive @ A )
=> ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) )
& ( ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) )
=> ( epsilon_transitive @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(27,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(123,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(47,plain,
! [A: $i] :
( ~ ( ordinal @ A )
| ~ ( in @ A @ sk1 )
| ( ordinal @ ( sk3 @ A ) ) ),
inference(cnf,[status(esa)],[43]) ).
thf(193,plain,
! [A: $i] :
( ~ ( in @ A @ sk1 )
| ( ordinal @ ( sk3 @ A ) )
| ( ( ordinal @ sk2 )
!= ( ordinal @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45,47]) ).
thf(194,plain,
( ~ ( in @ sk2 @ sk1 )
| ( ordinal @ ( sk3 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[193:[bind(A,$thf( sk2 ))]]) ).
thf(35,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
thf(150,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( epsilon_transitive @ A )
& ( epsilon_connected @ A )
& ( ordinal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(48,plain,
sk1 != empty_set,
inference(cnf,[status(esa)],[43]) ).
thf(50,plain,
sk1 != empty_set,
inference(lifteq,[status(thm)],[48]) ).
thf(154,plain,
~ ( empty @ sk16 ),
inference(cnf,[status(esa)],[150]) ).
thf(197,plain,
( ( empty @ sk16 )
!= ( empty @ sk4 ) ),
inference(paramod_ordered,[status(thm)],[56,154]) ).
thf(199,plain,
sk16 != sk4,
inference(simp,[status(thm)],[197]) ).
thf(87,plain,
empty @ sk11,
inference(cnf,[status(esa)],[85]) ).
thf(20,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(104,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(185,plain,
( ( empty @ sk6 )
!= ( empty @ sk4 ) ),
inference(paramod_ordered,[status(thm)],[56,62]) ).
thf(186,plain,
sk6 != sk4,
inference(simp,[status(thm)],[185]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
<=> ( subset @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
thf(139,plain,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ( ordinal_subset @ A @ B )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( ordinal_subset @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(82,plain,
relation @ sk10,
inference(cnf,[status(esa)],[79]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
| ( ordinal_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
thf(119,plain,
! [A: $i,B: $i] :
( ( ( ordinal @ A )
& ( ordinal @ B ) )
=> ( ( ordinal_subset @ A @ B )
| ( ordinal_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(58,plain,
relation @ sk5,
inference(cnf,[status(esa)],[57]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(107,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(126,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)],[28]) ).
thf(17,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(94,plain,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(39,axiom,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ~ ( ~ ( in @ A @ B )
& ( A != B )
& ~ ( in @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
thf(163,plain,
! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ~ ( ~ ( in @ A @ B )
& ( A != B )
& ~ ( in @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(9,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(68,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)],[9]) ).
thf(816,plain,
$false,
inference(e,[status(thm)],[174,121,192,188,51,83,101,88,56,142,110,196,157,46,93,57,78,147,132,89,74,206,60,85,92,65,97,109,77,73,128,166,45,161,64,176,191,44,59,54,49,86,81,76,91,66,155,135,80,112,123,194,63,150,50,199,154,72,43,87,104,186,55,139,75,82,119,58,107,126,79,94,47,163,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU235+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n029.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 10:27:24 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.01/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.30/1.03 % [INFO] Parsing done (141ms).
% 1.30/1.04 % [INFO] Running in sequential loop mode.
% 1.94/1.37 % [INFO] eprover registered as external prover.
% 1.94/1.37 % [INFO] cvc4 registered as external prover.
% 1.94/1.37 % [INFO] Scanning for conjecture ...
% 2.11/1.45 % [INFO] Found a conjecture and 43 axioms. Running axiom selection ...
% 2.31/1.50 % [INFO] Axiom selection finished. Selected 40 axioms (removed 3 axioms).
% 2.56/1.54 % [INFO] Problem is first-order (TPTP FOF).
% 2.56/1.54 % [INFO] Type checking passed.
% 2.56/1.54 % [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 ...
% 9.10/2.98 % External prover 'e' found a proof!
% 9.10/2.98 % [INFO] Killing All external provers ...
% 9.10/2.99 % Time passed: 2444ms (effective reasoning time: 1940ms)
% 9.10/2.99 % 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)>
% 9.10/2.99 % Axioms used in derivation (40): redefinition_r1_ordinal1, rc3_funct_1, cc1_relat_1, rc1_funct_1, rc4_funct_1, t4_subset, cc1_ordinal1, rc3_ordinal1, rc2_relat_1, reflexivity_r1_ordinal1, rc2_ordinal1, fc2_ordinal1, t7_tarski, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, fc4_relat_1, t1_subset, rc3_relat_1, t6_boole, cc2_ordinal1, t5_subset, t7_boole, cc1_funct_1, t23_ordinal1, rc2_funct_1, cc3_ordinal1, connectedness_r1_ordinal1, cc2_funct_1, t3_subset, t24_ordinal1, existence_m1_subset_1, rc1_ordinal1, rc1_relat_1, reflexivity_r1_tarski, t8_boole, rc1_xboole_0, t2_subset, d2_ordinal1, fc12_relat_1
% 9.10/2.99 % No. of inferences in proof: 131
% 9.10/2.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2444 ms resp. 1940 ms w/o parsing
% 9.37/3.07 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.37/3.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------