TSTP Solution File: SEU147+2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU147+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:57:12 EDT 2023
% Result : Theorem 5.72s 2.41s
% Output : Refutation 5.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 75
% Syntax : Number of formulae : 140 ( 50 unt; 12 typ; 0 def)
% Number of atoms : 340 ( 105 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 948 ( 55 ~; 15 |; 77 &; 681 @)
% ( 23 <=>; 97 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 2 con; 0-2 aty)
% Number of variables : 272 ( 0 ^; 264 !; 8 ?; 272 :)
% Comments :
%------------------------------------------------------------------------------
thf(powerset_type,type,
powerset: $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(proper_subset_type,type,
proper_subset: $i > $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(set_union2_type,type,
set_union2: $i > $i > $i ).
thf(disjoint_type,type,
disjoint: $i > $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(set_intersection2_type,type,
set_intersection2: $i > $i > $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(set_difference_type,type,
set_difference: $i > $i > $i ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(257,plain,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( B
= ( set_union2 @ A @ ( set_difference @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(53,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(344,plain,
! [A: $i] : ( subset @ empty_set @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(253,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(29,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(233,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(86,plain,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( in @ C @ ( set_intersection2 @ A @ B ) ) )
& ~ ( ? [C: $i] : ( in @ C @ ( set_intersection2 @ A @ B ) )
& ( disjoint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(35,axiom,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(255,plain,
! [A: $i,B: $i] : ( subset @ ( set_difference @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(57,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(363,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(183,plain,
! [A: $i,B: $i] :
( ~ ( ~ ( disjoint @ A @ B )
& ! [C: $i] :
~ ( ( in @ C @ A )
& ( in @ C @ B ) ) )
& ~ ( ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
& ( disjoint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(170,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)],[20]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(308,plain,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(384,plain,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
| ( subset @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(52,axiom,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(340,plain,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(189,plain,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(7,axiom,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(78,plain,
! [A: $i,B: $i] :
~ ( ( subset @ A @ B )
& ( proper_subset @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(243,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( in @ C @ A )
=> ( in @ C @ B ) )
& ( ( in @ C @ B )
=> ( in @ C @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(265,plain,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ C @ B ) )
=> ( subset @ ( set_union2 @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(160,plain,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
=> ~ ( proper_subset @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
=> ~ ( proper_subset @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(192,plain,
! [A: $i,B: $i] :
( ( set_difference @ ( set_union2 @ A @ B ) @ B )
= ( set_difference @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(165,plain,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ A @ C ) )
=> ( subset @ A @ ( set_intersection2 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(260,plain,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(349,plain,
! [A: $i,B: $i] :
( ( ( ( set_difference @ A @ B )
= empty_set )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( ( set_difference @ A @ B )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(1,conjecture,
( ( powerset @ empty_set )
= ( singleton @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(2,negated_conjecture,
( ( powerset @ empty_set )
!= ( singleton @ empty_set ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(65,plain,
( ( powerset @ empty_set )
!= ( singleton @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(49,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(324,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( ( set_difference @ A @ B )
= empty_set )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(317,plain,
! [A: $i,B: $i] :
( ( ( ( set_difference @ A @ B )
= empty_set )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( ( set_difference @ A @ B )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(403,plain,
! [A: $i,B: $i] :
( ( ( B
= ( powerset @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ( subset @ C @ A ) )
& ( ( subset @ C @ A )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ( subset @ C @ A ) )
& ( ( subset @ C @ A )
=> ( in @ C @ B ) ) )
=> ( B
= ( powerset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(56,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_intersection2 @ A @ B )
= empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(356,plain,
! [A: $i,B: $i] :
( ( ( disjoint @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= empty_set ) )
& ( ( ( set_intersection2 @ A @ B )
= empty_set )
=> ( disjoint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(134,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( set_union2 @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
| ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
| ( in @ D @ B ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
| ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
| ( in @ D @ B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( set_union2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(237,plain,
! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( subset @ ( set_intersection2 @ A @ C ) @ ( set_intersection2 @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(105,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( unordered_pair @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( D = A )
| ( D = B ) ) )
& ( ( ( D = A )
| ( D = B ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( D = A )
| ( D = B ) ) )
& ( ( ( D = A )
| ( D = B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( unordered_pair @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(46,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(311,plain,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(279,plain,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(180,plain,
! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(64,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(423,plain,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(204,plain,
! [A: $i,B: $i] :
( ( set_union2 @ A @ ( set_difference @ B @ A ) )
= ( set_union2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(274,plain,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_union2 @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(8,axiom,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(81,plain,
! [A: $i,B: $i] : ( subset @ A @ ( set_union2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(76,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(60,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(387,plain,
! [A: $i] :
( ( ( A = empty_set )
=> ! [B: $i] :
~ ( in @ B @ A ) )
& ( ! [B: $i] :
~ ( in @ B @ A )
=> ( A = empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(11,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(91,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(32,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(240,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(330,plain,
! [A: $i,B: $i] :
( ( ( subset @ A @ ( singleton @ B ) )
=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) )
& ( ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
=> ( subset @ A @ ( singleton @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
<=> ( ( set_difference @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(267,plain,
! [A: $i,B: $i] :
( ( ( disjoint @ A @ B )
=> ( ( set_difference @ A @ B )
= A ) )
& ( ( ( set_difference @ A @ B )
= A )
=> ( disjoint @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(167,plain,
! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( set_intersection2 @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(282,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( set_difference @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
& ~ ( in @ D @ B ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
& ~ ( in @ D @ B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( set_difference @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(50,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(327,plain,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(263,plain,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( subset @ B @ C ) )
=> ( subset @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( proper_subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
thf(67,plain,
! [A: $i] :
~ ( proper_subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(177,plain,
! [A: $i,B: $i] :
( ( set_difference @ A @ ( set_difference @ A @ B ) )
= ( set_intersection2 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(5,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(72,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(47,axiom,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(314,plain,
! [A: $i] :
( ( subset @ A @ empty_set )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(235,plain,
! [A: $i,B: $i,C: $i] :
( ( ( subset @ A @ B )
& ( disjoint @ B @ C ) )
=> ( disjoint @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_intersection2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(207,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( set_intersection2 @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
& ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
& ( in @ D @ B ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
& ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
& ( in @ D @ B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( set_intersection2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(54,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(346,plain,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( proper_subset @ A @ B )
<=> ( ( subset @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(195,plain,
! [A: $i,B: $i] :
( ( ( proper_subset @ A @ B )
=> ( ( subset @ A @ B )
& ( A != B ) ) )
& ( ( ( subset @ A @ B )
& ( A != B ) )
=> ( proper_subset @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(62,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
thf(400,plain,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(94,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) )
& ( ( ( subset @ A @ B )
& ( subset @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(395,plain,
! [A: $i,B: $i] :
( ( ( subset @ ( singleton @ A ) @ B )
=> ( in @ A @ B ) )
& ( ( in @ A @ B )
=> ( subset @ ( singleton @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(131,plain,
! [A: $i] :
( ( set_union2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(163,plain,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(42,axiom,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(277,plain,
! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(83,plain,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(364,plain,
! [A: $i,B: $i] :
( ( ( B
= ( singleton @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( in @ C @ B ) ) )
=> ( B
= ( singleton @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(438,plain,
$false,
inference(cvc4,[status(thm)],[257,344,253,233,86,255,363,183,170,308,384,340,189,78,243,265,160,70,192,165,260,349,65,324,317,403,356,134,237,105,311,279,180,423,204,274,81,76,387,91,240,330,267,167,282,327,263,67,177,72,314,235,207,346,195,400,94,395,131,163,277,83,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU147+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n008.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 13:32:25 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.83/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.42/1.00 % [INFO] Parsing done (149ms).
% 1.42/1.01 % [INFO] Running in sequential loop mode.
% 1.82/1.23 % [INFO] eprover registered as external prover.
% 1.89/1.23 % [INFO] cvc4 registered as external prover.
% 1.89/1.23 % [INFO] Scanning for conjecture ...
% 1.89/1.29 % [INFO] Found a conjecture and 69 axioms. Running axiom selection ...
% 2.15/1.35 % [INFO] Axiom selection finished. Selected 62 axioms (removed 7 axioms).
% 2.39/1.42 % [INFO] Problem is first-order (TPTP FOF).
% 2.39/1.43 % [INFO] Type checking passed.
% 2.39/1.44 % [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 ...
% 5.72/2.40 % External prover 'cvc4' found a proof!
% 5.72/2.41 % [INFO] Killing All external provers ...
% 5.72/2.41 % Time passed: 1882ms (effective reasoning time: 1392ms)
% 5.72/2.41 % 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)>
% 5.72/2.41 % Axioms used in derivation (62): fc1_xboole_0, t2_boole, d1_xboole_0, t6_boole, l2_zfmisc_1, t2_xboole_1, t19_xboole_1, t17_xboole_1, d1_tarski, idempotence_k3_xboole_0, t1_boole, t3_xboole_1, t37_xboole_1, commutativity_k3_xboole_0, d2_tarski, fc2_xboole_0, t1_xboole_1, commutativity_k2_xboole_0, t4_xboole_0, d8_xboole_0, t2_tarski, t33_xboole_1, l32_xboole_1, t4_boole, fc3_xboole_0, d2_xboole_0, t7_boole, t48_xboole_1, d7_xboole_0, t83_xboole_1, l4_zfmisc_1, antisymmetry_r2_xboole_0, l3_zfmisc_1, commutativity_k2_tarski, d1_zfmisc_1, t69_enumset1, t26_xboole_1, t63_xboole_1, t8_xboole_1, t28_xboole_1, d3_tarski, reflexivity_r1_tarski, d4_xboole_0, t36_xboole_1, t8_boole, rc1_xboole_0, t12_xboole_1, symmetry_r1_xboole_0, idempotence_k2_xboole_0, d10_xboole_0, t7_xboole_1, t60_xboole_1, t3_xboole_0, t3_boole, rc2_xboole_0, t45_xboole_1, t40_xboole_1, l1_zfmisc_1, irreflexivity_r2_xboole_0, d3_xboole_0, t39_xboole_1, antisymmetry_r2_hidden
% 5.72/2.41 % No. of inferences in proof: 128
% 5.72/2.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1882 ms resp. 1392 ms w/o parsing
% 5.75/2.48 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.75/2.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------