%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU311+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:38:25 AM UTC 2026
% Result : Theorem 13.32s 5.78s
% Output : Refutation 14.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 40
% Syntax : Number of formulae : 82 ( 11 unt; 0 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 : 0 ( 0 >; 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_decl,type,
topological_space: $i > $o ).
thf(top_str_decl,type,
top_str: $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(the_carrier_decl,type,
the_carrier: $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(cast_as_carrier_subset_decl,type,
cast_as_carrier_subset: $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(v1_membered_decl,type,
v1_membered: $i > $o ).
thf(v2_membered_decl,type,
v2_membered: $i > $o ).
thf(v3_membered_decl,type,
v3_membered: $i > $o ).
thf(v4_membered_decl,type,
v4_membered: $i > $o ).
thf(v5_membered_decl,type,
v5_membered: $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(closed_subset_decl,type,
closed_subset: $i > $i > $o ).
thf(v1_xcmplx_0_decl,type,
v1_xcmplx_0: $i > $o ).
thf(v1_xreal_0_decl,type,
v1_xreal_0: $i > $o ).
thf(v1_int_1_decl,type,
v1_int_1: $i > $o ).
thf(v1_rat_1_decl,type,
v1_rat_1: $i > $o ).
thf(natural_decl,type,
natural: $i > $o ).
thf(14,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( A @ the_carrier @ powerset @ ( A @ cast_as_carrier_subset @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
thf(88,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( A @ the_carrier @ powerset @ ( A @ cast_as_carrier_subset @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc15_membered) ).
thf(56,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ powerset @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
<=> ( B @ ( D @ ( A @ cast_as_carrier_subset @ set_difference ) @ in ) ) ) )
& ( A @ the_carrier @ powerset @ powerset @ ( C @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s3_subset_1__e2_37_1_1__pre_topc) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ powerset @ ( D @ element ) )
=> ( ( C @ ( D @ in ) )
<=> ( B @ ( D @ ( A @ cast_as_carrier_subset @ set_difference ) @ in ) ) ) )
& ( A @ the_carrier @ powerset @ powerset @ ( C @ element ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(42,plain,
~ ! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ? [C: $i] :
( ! [D: $i] :
( ( A @ the_carrier @ powerset @ ( D @ element ) )
=> ( ( ( B @ ( D @ ( A @ cast_as_carrier_subset @ set_difference ) @ in ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( B @ ( D @ ( A @ cast_as_carrier_subset @ set_difference ) @ in ) ) ) ) )
& ( A @ the_carrier @ powerset @ powerset @ ( C @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ v5_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc20_membered) ).
thf(189,plain,
! [A: $i] :
( ( A @ v5_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ v5_membered )
& ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ? [C: $i] :
! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( B @ ( D @ ( A @ cast_as_carrier_subset @ set_difference ) @ in ) )
& ( A @ the_carrier @ powerset @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e2_37_1_1__pre_topc__1) ).
thf(116,plain,
! [A: $i,B: $i] :
( ( ( A @ the_carrier @ powerset @ powerset @ ( B @ element ) )
& ( A @ top_str )
& ( A @ topological_space ) )
=> ? [C: $i] :
! [D: $i] :
( ( ( ( B @ ( D @ ( A @ cast_as_carrier_subset @ set_difference ) @ in ) )
& ( A @ the_carrier @ powerset @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ ( A @ cast_as_carrier_subset @ set_difference ) @ in ) )
& ( A @ the_carrier @ powerset @ ( D @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(9,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(70,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(65,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ ( B @ element ) )
=> ( B @ v1_xcmplx_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc10_membered) ).
thf(141,plain,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ ( B @ element ) )
=> ( B @ v1_xcmplx_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(73,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(34,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(176,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ v5_membered )
=> ( A @ v4_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_membered) ).
thf(86,plain,
! [A: $i] :
( ( A @ v5_membered )
=> ( A @ v4_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(31,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(167,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(5,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(63,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( A @ v5_membered )
=> ( ( B @ ( A @ set_difference ) @ v5_membered )
& ( B @ ( A @ set_difference ) @ v4_membered )
& ( B @ ( A @ set_difference ) @ v3_membered )
& ( B @ ( A @ set_difference ) @ v2_membered )
& ( B @ ( A @ set_difference ) @ v1_membered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc41_membered) ).
thf(127,plain,
! [A: $i,B: $i] :
( ( A @ v5_membered )
=> ( ( B @ ( A @ set_difference ) @ v5_membered )
& ( B @ ( A @ set_difference ) @ v4_membered )
& ( B @ ( A @ set_difference ) @ v3_membered )
& ( B @ ( A @ set_difference ) @ v2_membered )
& ( B @ ( A @ set_difference ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ v1_membered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc16_membered) ).
thf(143,plain,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(38,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(203,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ top_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(139,plain,
! [A: $i] :
( ( A @ top_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ( A @ empty )
=> ( ( A @ ( B @ element ) )
<=> ( B @ empty ) ) )
& ( ~ ( A @ empty )
=> ( ( A @ ( B @ element ) )
<=> ( A @ ( B @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
thf(207,plain,
! [A: $i,B: $i] :
( ( ( A @ empty )
=> ( ( ( B @ empty )
=> ( A @ ( B @ element ) ) )
& ( ( A @ ( B @ element ) )
=> ( B @ empty ) ) ) )
& ( ~ ( A @ empty )
=> ( ( ( A @ ( B @ in ) )
=> ( A @ ( B @ element ) ) )
& ( ( A @ ( B @ element ) )
=> ( A @ ( B @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ powerset @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
thf(151,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ powerset @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ v4_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc19_membered) ).
thf(94,plain,
! [A: $i] :
( ( A @ v4_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ v4_membered )
& ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(170,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ ( B @ element ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc12_membered) ).
thf(217,plain,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ ( B @ element ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(52,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ v5_membered )
=> ! [B: $i] :
( ( A @ ( B @ element ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_int_1 )
& ( B @ v1_xreal_0 )
& ( B @ natural )
& ( B @ v1_xcmplx_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc14_membered) ).
thf(196,plain,
! [A: $i] :
( ( A @ v5_membered )
=> ! [B: $i] :
( ( A @ ( B @ element ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_int_1 )
& ( B @ v1_xreal_0 )
& ( B @ natural )
& ( B @ v1_xcmplx_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( A @ v4_membered )
=> ( ( B @ ( A @ set_difference ) @ v4_membered )
& ( B @ ( A @ set_difference ) @ v3_membered )
& ( B @ ( A @ set_difference ) @ v2_membered )
& ( B @ ( A @ set_difference ) @ v1_membered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc40_membered) ).
thf(179,plain,
! [A: $i,B: $i] :
( ( A @ v4_membered )
=> ( ( B @ ( A @ set_difference ) @ v4_membered )
& ( B @ ( A @ set_difference ) @ v3_membered )
& ( B @ ( A @ set_difference ) @ v2_membered )
& ( B @ ( A @ set_difference ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(18,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( A @ cast_as_carrier_subset @ closed_subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_pre_topc) ).
thf(106,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ( A @ ( A @ cast_as_carrier_subset @ closed_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ v3_membered )
=> ( A @ v2_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_membered) ).
thf(84,plain,
! [A: $i] :
( ( A @ v3_membered )
=> ( A @ v2_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc17_membered) ).
thf(172,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( B @ ( A @ set_difference ) @ v1_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc37_membered) ).
thf(113,plain,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( B @ ( A @ set_difference ) @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(11,axiom,
? [A: $i] :
( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_membered) ).
thf(76,plain,
? [A: $i] :
( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ v4_membered )
=> ( A @ v3_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_membered) ).
thf(66,plain,
! [A: $i] :
( ( A @ v4_membered )
=> ( A @ v3_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( A @ v3_membered )
=> ( ( B @ ( A @ set_difference ) @ v3_membered )
& ( B @ ( A @ set_difference ) @ v2_membered )
& ( B @ ( A @ set_difference ) @ v1_membered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc39_membered) ).
thf(155,plain,
! [A: $i,B: $i] :
( ( A @ v3_membered )
=> ( ( B @ ( A @ set_difference ) @ v3_membered )
& ( B @ ( A @ set_difference ) @ v2_membered )
& ( B @ ( A @ set_difference ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc18_membered) ).
thf(108,plain,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ ( B @ element ) )
=> ( ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc11_membered) ).
thf(123,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ ( B @ element ) )
=> ( ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ v4_membered )
=> ! [B: $i] :
( ( A @ ( B @ element ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_int_1 )
& ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc13_membered) ).
thf(145,plain,
! [A: $i] :
( ( A @ v4_membered )
=> ! [B: $i] :
( ( A @ ( B @ element ) )
=> ( ( B @ v1_rat_1 )
& ( B @ v1_int_1 )
& ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(30,axiom,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_pre_topc) ).
thf(163,plain,
! [A: $i] :
( ( ( A @ top_str )
& ( A @ topological_space ) )
=> ? [B: $i] :
( ( A @ ( B @ closed_subset ) )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_membered) ).
thf(68,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(15,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(90,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(41,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(222,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( A @ v2_membered )
=> ( ( B @ ( A @ set_difference ) @ v2_membered )
& ( B @ ( A @ set_difference ) @ v1_membered ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc38_membered) ).
thf(100,plain,
! [A: $i,B: $i] :
( ( A @ v2_membered )
=> ( ( B @ ( A @ set_difference ) @ v2_membered )
& ( B @ ( A @ set_difference ) @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(820,plain,
$false,
inference(e,[status(thm)],[88,56,42,189,116,70,65,141,73,176,86,167,63,127,143,203,139,207,151,94,170,217,52,196,179,106,84,172,113,76,66,155,108,123,145,163,68,90,222,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU311+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.24/0.72 % Computer : n015.cluster.edu
% 0.24/0.72 % Model : x86_64 x86_64
% 0.24/0.72 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.72 % Memory : 8046.5625MB
% 0.24/0.72 % OS : Linux 6.8.0-71-generic
% 0.24/0.72 % CPULimit : 300
% 0.24/0.72 % WCLimit : 300
% 0.24/0.72 % DateTime : Sat Sep 26 09:13:14 UTC 2026
% 0.24/0.72 % CPUTime :
% 0.24/0.72 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.40/1.56 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.93/1.88 % [INFO] Parsing done (312ms).
% 2.26/1.90 % [INFO] Running in sequential loop mode.
% 3.26/2.52 % [INFO] eprover registered as external prover.
% 3.26/2.53 % [INFO] Scanning for conjecture ...
% 3.63/2.71 % [INFO] Found a conjecture (or negated_conjecture) and 45 axioms. Running axiom selection ...
% 3.86/2.85 % [INFO] Axiom selection finished. Selected 39 axioms (removed 6 axioms).
% 4.09/2.95 % [INFO] Problem is first-order (TPTP FOF).
% 4.09/2.97 % [INFO] Type checking passed.
% 4.09/2.98 % [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 ...
% 13.32/5.77 % External prover 'e' found a proof!
% 13.32/5.77 % [INFO] Killing All external provers ...
% 13.32/5.77 % Time passed: 4841ms (effective reasoning time: 3858ms)
% 13.32/5.77 % 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)>
% 13.32/5.78 % 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
% 13.32/5.78 % No. of inferences in proof: 82
% 13.32/5.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4841 ms resp. 3858 ms w/o parsing
% 13.76/5.90 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.24/5.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------