TSTP Solution File: SEU311+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU311+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 11:58:12 EDT 2023
% Result : Theorem 67.89s 12.63s
% Output : Refutation 67.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 62
% Syntax : Number of formulae : 104 ( 11 unt; 22 typ; 0 def)
% Number of atoms : 301 ( 4 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 767 ( 22 ~; 0 |; 116 &; 526 @)
% ( 5 <=>; 98 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 2 con; 0-2 aty)
% Number of variables : 144 ( 0 ^; 125 !; 19 ?; 144 :)
% Comments :
%------------------------------------------------------------------------------
thf(topological_space_type,type,
topological_space: $i > $o ).
thf(top_str_type,type,
top_str: $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(the_carrier_type,type,
the_carrier: $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(set_difference_type,type,
set_difference: $i > $i > $i ).
thf(cast_as_carrier_subset_type,type,
cast_as_carrier_subset: $i > $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(v1_membered_type,type,
v1_membered: $i > $o ).
thf(v2_membered_type,type,
v2_membered: $i > $o ).
thf(v3_membered_type,type,
v3_membered: $i > $o ).
thf(v4_membered_type,type,
v4_membered: $i > $o ).
thf(v5_membered_type,type,
v5_membered: $i > $o ).
thf(empty_set_type,type,
empty_set: $i ).
thf(one_sorted_str_type,type,
one_sorted_str: $i > $o ).
thf(closed_subset_type,type,
closed_subset: $i > $i > $o ).
thf(v1_xcmplx_0_type,type,
v1_xcmplx_0: $i > $o ).
thf(v1_xreal_0_type,type,
v1_xreal_0: $i > $o ).
thf(v1_int_1_type,type,
v1_int_1: $i > $o ).
thf(v1_rat_1_type,type,
v1_rat_1: $i > $o ).
thf(natural_type,type,
natural: $i > $o ).
thf(22,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_membered) ).
thf(115,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(31,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(153,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(40,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_rat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_membered) ).
thf(197,plain,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_rat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( powerset @ ( the_carrier @ A ) ) )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e2_37_1_1__pre_topc__1) ).
thf(109,plain,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ? [C: $i] :
! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ ( powerset @ ( the_carrier @ A ) ) )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B ) ) )
& ( ( ( in @ D @ ( powerset @ ( the_carrier @ A ) ) )
& ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B ) )
=> ( in @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( v5_membered @ A )
=> ( ( v1_membered @ ( set_difference @ A @ B ) )
& ( v2_membered @ ( set_difference @ A @ B ) )
& ( v3_membered @ ( set_difference @ A @ B ) )
& ( v4_membered @ ( set_difference @ A @ B ) )
& ( v5_membered @ ( set_difference @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc41_membered) ).
thf(118,plain,
! [A: $i,B: $i] :
( ( v5_membered @ A )
=> ( ( v1_membered @ ( set_difference @ A @ B ) )
& ( v2_membered @ ( set_difference @ A @ B ) )
& ( v3_membered @ ( set_difference @ A @ B ) )
& ( v4_membered @ ( set_difference @ A @ B ) )
& ( v5_membered @ ( set_difference @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(10,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(71,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ( v2_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_membered) ).
thf(81,plain,
! [A: $i] :
( ( v3_membered @ A )
=> ( v2_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(27,axiom,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_membered) ).
thf(135,plain,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( set_difference @ A @ B ) )
& ( v2_membered @ ( set_difference @ A @ B ) )
& ( v3_membered @ ( set_difference @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc39_membered) ).
thf(143,plain,
! [A: $i,B: $i] :
( ( v3_membered @ A )
=> ( ( v1_membered @ ( set_difference @ A @ B ) )
& ( v2_membered @ ( set_difference @ A @ B ) )
& ( v3_membered @ ( set_difference @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(15,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(87,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
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(38,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(185,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ? [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ! [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( in @ D @ C )
<=> ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_subset_1__e2_37_1_1__pre_topc) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ? [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ! [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( in @ D @ C )
<=> ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(42,plain,
~ ! [A: $i,B: $i] :
( ( ( topological_space @ A )
& ( top_str @ A )
& ( element @ B @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) ) )
=> ? [C: $i] :
( ( element @ C @ ( powerset @ ( powerset @ ( the_carrier @ A ) ) ) )
& ! [D: $i] :
( ( element @ D @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( in @ D @ C )
=> ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B ) )
& ( ( in @ ( set_difference @ ( cast_as_carrier_subset @ A ) @ D ) @ B )
=> ( in @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( v4_membered @ A )
=> ( ( v1_membered @ ( set_difference @ A @ B ) )
& ( v2_membered @ ( set_difference @ A @ B ) )
& ( v3_membered @ ( set_difference @ A @ B ) )
& ( v4_membered @ ( set_difference @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc40_membered) ).
thf(164,plain,
! [A: $i,B: $i] :
( ( v4_membered @ A )
=> ( ( v1_membered @ ( set_difference @ A @ B ) )
& ( v2_membered @ ( set_difference @ A @ B ) )
& ( v3_membered @ ( set_difference @ A @ B ) )
& ( v4_membered @ ( set_difference @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(37,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( natural @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc14_membered) ).
thf(179,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( ( v1_xcmplx_0 @ B )
& ( natural @ B )
& ( v1_xreal_0 @ B )
& ( v1_int_1 @ B )
& ( v1_rat_1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( set_difference @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc37_membered) ).
thf(106,plain,
! [A: $i,B: $i] :
( ( v1_membered @ A )
=> ( v1_membered @ ( set_difference @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(5,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(61,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(26,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc16_membered) ).
thf(133,plain,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( v1_membered @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(11,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_membered) ).
thf(74,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc18_membered) ).
thf(102,plain,
! [A: $i] :
( ( v3_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(14,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(85,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( element @ ( cast_as_carrier_subset @ A ) @ ( powerset @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(41,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(201,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(156,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( element @ B @ A )
<=> ( in @ B @ A ) ) )
& ( ( empty @ A )
=> ( ( element @ B @ A )
<=> ( empty @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(188,plain,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
=> ( ( ( element @ B @ A )
=> ( in @ B @ A ) )
& ( ( in @ B @ A )
=> ( element @ B @ A ) ) ) )
& ( ( empty @ A )
=> ( ( ( element @ B @ A )
=> ( empty @ B ) )
& ( ( empty @ B )
=> ( element @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(36,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc20_membered) ).
thf(173,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B )
& ( v5_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(24,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(129,plain,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(34,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(161,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(7,axiom,
! [A: $i] :
( ( v4_membered @ A )
=> ( v3_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_membered) ).
thf(64,plain,
! [A: $i] :
( ( v4_membered @ A )
=> ( v3_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
thf(140,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( element @ A @ ( powerset @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(8,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ( v1_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_membered) ).
thf(66,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ( v1_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(63,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(30,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( closed_subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_pre_topc) ).
thf(150,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ( closed_subset @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( set_difference @ A @ B ) )
& ( v2_membered @ ( set_difference @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc38_membered) ).
thf(95,plain,
! [A: $i,B: $i] :
( ( v2_membered @ A )
=> ( ( v1_membered @ ( set_difference @ A @ B ) )
& ( v2_membered @ ( set_difference @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(33,axiom,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc17_membered) ).
thf(158,plain,
! [A: $i] :
( ( v2_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(4,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc15_membered) ).
thf(55,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( v1_membered @ A )
& ( v2_membered @ A )
& ( v3_membered @ A )
& ( v4_membered @ A )
& ( v5_membered @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(25,axiom,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( v1_xcmplx_0 @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_membered) ).
thf(131,plain,
! [A: $i] :
( ( v1_membered @ A )
=> ! [B: $i] :
( ( element @ B @ A )
=> ( v1_xcmplx_0 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(9,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(68,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(16,axiom,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc19_membered) ).
thf(90,plain,
! [A: $i] :
( ( v4_membered @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( v1_membered @ B )
& ( v2_membered @ B )
& ( v3_membered @ B )
& ( v4_membered @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
! [A: $i] :
( ( v5_membered @ A )
=> ( v4_membered @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_membered) ).
thf(83,plain,
! [A: $i] :
( ( v5_membered @ A )
=> ( v4_membered @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(18,axiom,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_pre_topc) ).
thf(100,plain,
! [A: $i] :
( ( ( topological_space @ A )
& ( top_str @ A ) )
=> ( closed_subset @ ( cast_as_carrier_subset @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(9600,plain,
$false,
inference(e,[status(thm)],[115,153,197,109,118,71,81,135,143,87,51,185,42,164,179,106,61,133,74,102,85,201,156,188,173,129,161,64,140,66,63,150,95,158,55,131,68,90,83,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU311+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 13:42:43 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.82/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.99 % [INFO] Parsing done (134ms).
% 1.21/1.00 % [INFO] Running in sequential loop mode.
% 1.76/1.20 % [INFO] eprover registered as external prover.
% 1.76/1.20 % [INFO] cvc4 registered as external prover.
% 1.76/1.20 % [INFO] Scanning for conjecture ...
% 1.92/1.27 % [INFO] Found a conjecture and 45 axioms. Running axiom selection ...
% 2.17/1.33 % [INFO] Axiom selection finished. Selected 39 axioms (removed 6 axioms).
% 2.17/1.37 % [INFO] Problem is first-order (TPTP FOF).
% 2.17/1.37 % [INFO] Type checking passed.
% 2.17/1.38 % [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 ...
% 67.89/12.62 % External prover 'e' found a proof!
% 67.89/12.62 % [INFO] Killing All external provers ...
% 67.89/12.62 % Time passed: 12102ms (effective reasoning time: 11623ms)
% 67.89/12.62 % 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)>
% 67.89/12.63 % Axioms used in derivation (39): cc12_membered, fc37_membered, rc1_membered, s1_xboole_0__e2_37_1_1__pre_topc__1, cc19_membered, cc11_membered, cc18_membered, cc17_membered, fc1_xboole_0, cc10_membered, fc5_pre_topc, rc6_pre_topc, dt_l1_pre_topc, t6_boole, rc2_subset_1, cc20_membered, t7_boole, d2_subset_1, fc1_subset_1, fc38_membered, rc1_subset_1, cc4_membered, cc13_membered, existence_m1_subset_1, fc39_membered, cc15_membered, l71_subset_1, t8_boole, rc1_xboole_0, cc1_membered, fc40_membered, fc41_membered, cc2_membered, cc3_membered, cc14_membered, cc16_membered, rc2_xboole_0, antisymmetry_r2_hidden, dt_k2_pre_topc
% 67.89/12.63 % No. of inferences in proof: 82
% 67.89/12.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 12102 ms resp. 11623 ms w/o parsing
% 67.89/12.67 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 67.89/12.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------