TSTP Solution File: SEU106+1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU106+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 11:57:01 EDT 2023
% Result : Theorem 3.91s 2.02s
% Output : Refutation 4.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 70
% Syntax : Number of formulae : 120 ( 39 unt; 22 typ; 0 def)
% Number of atoms : 232 ( 30 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 617 ( 43 ~; 2 |; 71 &; 440 @)
% ( 2 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 2 con; 0-2 aty)
% Number of variables : 170 ( 0 ^; 150 !; 20 ?; 170 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_type,type,
empty: $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(symmetric_difference_type,type,
symmetric_difference: $i > $i > $i ).
thf(set_union2_type,type,
set_union2: $i > $i > $i ).
thf(preboolean_type,type,
preboolean: $i > $o ).
thf(set_intersection2_type,type,
set_intersection2: $i > $i > $i ).
thf(set_difference_type,type,
set_difference: $i > $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(finite_type,type,
finite: $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(cup_closed_type,type,
cup_closed: $i > $o ).
thf(diff_closed_type,type,
diff_closed: $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(epsilon_transitive_type,type,
epsilon_transitive: $i > $o ).
thf(epsilon_connected_type,type,
epsilon_connected: $i > $o ).
thf(ordinal_type,type,
ordinal: $i > $o ).
thf(natural_type,type,
natural: $i > $o ).
thf(cap_closed_type,type,
cap_closed: $i > $o ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(69,plain,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_difference @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(24,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(120,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(33,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(142,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)],[33]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(165,plain,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( set_union2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(16,axiom,
! [A: $i] :
( ( preboolean @ A )
<=> ! [B: $i,C: $i] :
( ( ( in @ B @ A )
& ( in @ C @ A ) )
=> ( ( in @ ( set_union2 @ B @ C ) @ A )
& ( in @ ( set_difference @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_finsub_1) ).
thf(92,plain,
! [A: $i] :
( ( ( preboolean @ A )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ A )
& ( in @ C @ A ) )
=> ( ( in @ ( set_union2 @ B @ C ) @ A )
& ( in @ ( set_difference @ B @ C ) @ A ) ) ) )
& ( ! [B: $i,C: $i] :
( ( ( in @ B @ A )
& ( in @ C @ A ) )
=> ( ( in @ ( set_union2 @ B @ C ) @ A )
& ( in @ ( set_difference @ B @ C ) @ A ) ) )
=> ( preboolean @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(28,axiom,
! [A: $i] :
( ( ( cup_closed @ A )
& ( diff_closed @ A ) )
=> ( preboolean @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finsub_1) ).
thf(129,plain,
! [A: $i] :
( ( ( cup_closed @ A )
& ( diff_closed @ A ) )
=> ( preboolean @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(6,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(64,plain,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( set_intersection2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( set_union2 @ ( set_difference @ A @ B ) @ ( set_difference @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).
thf(172,plain,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( set_union2 @ ( set_difference @ A @ B ) @ ( set_difference @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(36,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(150,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(4,axiom,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(58,plain,
! [A: $i] :
( ( set_difference @ A @ empty_set )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(35,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(146,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(47,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B )
& ( relation @ B )
& ( function @ B )
& ( one_to_one @ B )
& ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B )
& ( natural @ B )
& ( finite @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_finset_1) ).
thf(184,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B )
& ( relation @ B )
& ( function @ B )
& ( one_to_one @ B )
& ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B )
& ( natural @ B )
& ( finite @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(38,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(157,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
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(106,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(25,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(121,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( set_difference @ A @ B )
= ( symmetric_difference @ A @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_xboole_1) ).
thf(84,plain,
! [A: $i,B: $i] :
( ( set_difference @ A @ B )
= ( symmetric_difference @ A @ ( set_intersection2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(61,plain,
! [A: $i,B: $i] :
( ( finite @ A )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(74,plain,
! [A: $i] :
( ( set_difference @ empty_set @ A )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(15,axiom,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(89,plain,
! [A: $i] :
( ( set_union2 @ A @ empty_set )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(30,axiom,
! [A: $i] :
( ( preboolean @ A )
=> ( ( cup_closed @ A )
& ( diff_closed @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finsub_1) ).
thf(133,plain,
! [A: $i] :
( ( preboolean @ A )
=> ( ( cup_closed @ A )
& ( diff_closed @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(23,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(117,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(201,plain,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(17,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(102,plain,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(20,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(109,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(11,axiom,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(77,plain,
! [A: $i] :
( ( set_intersection2 @ A @ empty_set )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(34,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(144,plain,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(46,axiom,
! [A: $i] :
( ( symmetric_difference @ A @ empty_set )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_boole) ).
thf(181,plain,
! [A: $i] :
( ( symmetric_difference @ A @ empty_set )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( symmetric_difference @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).
thf(159,plain,
! [A: $i,B: $i] :
( ( symmetric_difference @ A @ B )
= ( symmetric_difference @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(12,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(80,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(167,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)],[42]) ).
thf(40,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(162,plain,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(112,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(26,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(123,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1,conjecture,
! [A: $i] :
( ~ ( empty @ A )
=> ( ! [B: $i] :
( ( element @ B @ A )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ( in @ ( symmetric_difference @ B @ C ) @ A )
& ( in @ ( set_union2 @ B @ C ) @ A ) ) ) )
=> ( preboolean @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_finsub_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ~ ( empty @ A )
=> ( ! [B: $i] :
( ( element @ B @ A )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ( in @ ( symmetric_difference @ B @ C ) @ A )
& ( in @ ( set_union2 @ B @ C ) @ A ) ) ) )
=> ( preboolean @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(50,plain,
~ ! [A: $i] :
( ~ ( empty @ A )
=> ( ! [B: $i] :
( ( element @ B @ A )
=> ! [C: $i] :
( ( element @ C @ A )
=> ( ( in @ ( symmetric_difference @ B @ C ) @ A )
& ( in @ ( set_union2 @ B @ C ) @ A ) ) ) )
=> ( preboolean @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( finite @ B )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(67,plain,
! [A: $i,B: $i] :
( ( finite @ B )
=> ( finite @ ( set_intersection2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(37,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(154,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(9,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(72,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(44,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(175,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(14,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(87,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( symmetric_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc17_finset_1) ).
thf(104,plain,
! [A: $i,B: $i] :
( ( ( finite @ A )
& ( finite @ B ) )
=> ( finite @ ( symmetric_difference @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(32,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(139,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(55,plain,
! [A: $i] :
( ( set_intersection2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(114,plain,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(48,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( cup_closed @ A )
& ( cap_closed @ A )
& ( diff_closed @ A )
& ( preboolean @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finsub_1) ).
thf(195,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( cup_closed @ A )
& ( cap_closed @ A )
& ( diff_closed @ A )
& ( preboolean @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(27,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(126,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( symmetric_difference @ ( symmetric_difference @ A @ B ) @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_xboole_1) ).
thf(136,plain,
! [A: $i,B: $i] :
( ( set_intersection2 @ A @ B )
= ( symmetric_difference @ ( symmetric_difference @ A @ B ) @ ( set_union2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(131,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(178,plain,
! [A: $i] :
( ( set_union2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(204,plain,
$false,
inference(e,[status(thm)],[69,120,142,165,92,129,64,172,150,58,146,184,157,106,121,84,61,74,89,133,117,201,102,109,77,144,181,159,80,167,162,112,123,50,67,154,72,175,87,104,139,55,114,195,126,136,131,178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU106+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.14 % Command : run_Leo-III %s %d
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu May 18 13:40:52 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.78/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.13/0.92 % [INFO] Parsing done (135ms).
% 1.13/0.93 % [INFO] Running in sequential loop mode.
% 1.52/1.15 % [INFO] eprover registered as external prover.
% 1.52/1.16 % [INFO] cvc4 registered as external prover.
% 1.52/1.16 % [INFO] Scanning for conjecture ...
% 1.80/1.23 % [INFO] Found a conjecture and 47 axioms. Running axiom selection ...
% 1.85/1.28 % [INFO] Axiom selection finished. Selected 47 axioms (removed 0 axioms).
% 2.16/1.33 % [INFO] Problem is first-order (TPTP FOF).
% 2.16/1.34 % [INFO] Type checking passed.
% 2.16/1.34 % [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 ...
% 3.91/2.01 % External prover 'e' found a proof!
% 3.91/2.01 % [INFO] Killing All external provers ...
% 3.91/2.02 % Time passed: 1535ms (effective reasoning time: 1080ms)
% 3.91/2.02 % 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)>
% 3.91/2.02 % Axioms used in derivation (47): t5_boole, cc2_finset_1, t2_boole, commutativity_k5_xboole_0, rc1_subset_1, d6_xboole_0, rc3_finset_1, t2_subset, idempotence_k2_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, idempotence_k3_xboole_0, rc4_finset_1, t1_boole, rc1_finsub_1, fc1_xboole_0, t1_subset, t95_xboole_1, commutativity_k3_xboole_0, fc11_finset_1, cc2_finsub_1, fc2_xboole_0, fc10_finset_1, t6_boole, rc2_subset_1, fc9_finset_1, fc17_finset_1, commutativity_k2_xboole_0, t5_subset, t4_boole, t4_subset, fc3_xboole_0, t7_boole, fc1_subset_1, t3_subset, existence_m1_subset_1, t100_xboole_1, cc1_finsub_1, rc2_finset_1, reflexivity_r1_tarski, rc1_finset_1, cc1_finset_1, fc12_finset_1, t8_boole, rc1_xboole_0, t3_boole, t10_finsub_1
% 3.91/2.02 % No. of inferences in proof: 98
% 3.91/2.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1535 ms resp. 1080 ms w/o parsing
% 4.25/2.10 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.25/2.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------