%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU327+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n001.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 08:38:28 AM UTC 2026
% Result : Theorem 6.34s 3.09s
% Output : Refutation 7.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 53
% Syntax : Number of formulae : 108 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 326 ( 32 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 906 ( 25 ~; 2 |; 109 &; 663 @)
% ( 1 <=>; 106 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 2 con; 0-3 aty)
% Number of variables : 193 ( 0 ^; 185 !; 8 ?; 193 :)
% Comments :
%------------------------------------------------------------------------------
thf(element_decl,type,
element: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(meet_of_subsets_decl,type,
meet_of_subsets: $i > $i > $i ).
thf(complements_of_subsets_decl,type,
complements_of_subsets: $i > $i > $i ).
thf(subset_complement_decl,type,
subset_complement: $i > $i > $i ).
thf(union_of_subsets_decl,type,
union_of_subsets: $i > $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(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(cast_to_subset_decl,type,
cast_to_subset: $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(subset_difference_decl,type,
subset_difference: $i > $i > $i > $i ).
thf(v1_xcmplx_0_decl,type,
v1_xcmplx_0: $i > $o ).
thf(v1_xreal_0_decl,type,
v1_xreal_0: $i > $o ).
thf(v1_rat_1_decl,type,
v1_rat_1: $i > $o ).
thf(v1_int_1_decl,type,
v1_int_1: $i > $o ).
thf(set_meet_decl,type,
set_meet: $i > $i ).
thf(union_decl,type,
union: $i > $i ).
thf(natural_decl,type,
natural: $i > $o ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(138,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
thf(189,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ v5_membered )
=> ( A @ v4_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_membered) ).
thf(84,plain,
! [A: $i] :
( ( A @ v5_membered )
=> ( A @ v4_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(221,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ union_of_subsets ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
thf(141,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ union_of_subsets ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(30,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/sandbox/benchmark/theBenchmark.p',cc20_membered) ).
thf(173,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)],[30]) ).
thf(17,axiom,
? [A: $i] :
( ( A @ v5_membered )
& ( A @ v4_membered )
& ( A @ v3_membered )
& ( A @ v2_membered )
& ( A @ v1_membered )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_membered) ).
thf(118,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)],[17]) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',fc39_membered) ).
thf(86,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)],[11]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ subset_complement ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(230,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ subset_complement ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ powerset @ ( B @ ( A @ complements_of_subsets ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
thf(199,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ powerset @ ( B @ ( A @ complements_of_subsets ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(62,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc16_membered) ).
thf(201,plain,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( A @ v2_membered )
=> ( ( B @ ( A @ set_difference ) @ v2_membered )
& ( B @ ( A @ set_difference ) @ v1_membered ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc38_membered) ).
thf(102,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)],[15]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ v3_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ v3_membered )
& ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc18_membered) ).
thf(160,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)],[26]) ).
thf(35,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/sandbox/benchmark/theBenchmark.p',cc12_membered) ).
thf(192,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)],[35]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(165,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ ( B @ element ) )
=> ( B @ v1_xcmplx_0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc10_membered) ).
thf(197,plain,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ ( B @ element ) )
=> ( B @ v1_xcmplx_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(13,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(97,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( B @ ( A @ set_difference ) @ v1_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc37_membered) ).
thf(77,plain,
! [A: $i,B: $i] :
( ( A @ v1_membered )
=> ( B @ ( A @ set_difference ) @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(212,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( B @ powerset @ ( A @ element ) ) )
& ( ( B @ powerset @ ( A @ element ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_membered) ).
thf(73,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(49,axiom,
! [A: $i] : ( A @ powerset @ ( A @ cast_to_subset @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
thf(237,plain,
! [A: $i] : ( A @ powerset @ ( A @ cast_to_subset @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ complements_of_subsets ) @ ( A @ complements_of_subsets ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
thf(180,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ complements_of_subsets ) @ ( A @ complements_of_subsets ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ subset_difference ) ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(149,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ subset_difference ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
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/sandbox/benchmark/theBenchmark.p',cc15_membered) ).
thf(66,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(16,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/sandbox/benchmark/theBenchmark.p',fc40_membered) ).
thf(108,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)],[16]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ union_of_subsets ) )
= ( B @ union ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
thf(223,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ union_of_subsets ) )
= ( B @ union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ v2_membered )
& ( B @ v1_membered ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc17_membered) ).
thf(226,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)],[45]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ v3_membered )
=> ( A @ v2_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_membered) ).
thf(80,plain,
! [A: $i] :
( ( A @ v3_membered )
=> ( A @ v2_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ meet_of_subsets ) )
= ( B @ set_meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
thf(209,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ meet_of_subsets ) )
= ( B @ set_meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(22,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(145,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(25,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/sandbox/benchmark/theBenchmark.p',cc19_membered) ).
thf(154,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)],[25]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(143,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(52,axiom,
( ( empty_set @ v5_membered )
& ( empty_set @ v4_membered )
& ( empty_set @ v3_membered )
& ( empty_set @ v2_membered )
& ( empty_set @ v1_membered )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_membered) ).
thf(250,plain,
( ( empty_set @ v5_membered )
& ( empty_set @ v4_membered )
& ( empty_set @ v3_membered )
& ( empty_set @ v2_membered )
& ( empty_set @ v1_membered )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',cc13_membered) ).
thf(203,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)],[39]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B != empty_set )
=> ( ( B @ ( A @ union_of_subsets ) @ ( A @ cast_to_subset @ ( A @ subset_difference ) ) )
= ( B @ ( A @ complements_of_subsets ) @ ( A @ meet_of_subsets ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_setfam_1) ).
thf(218,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B != empty_set )
=> ( ( B @ ( A @ union_of_subsets ) @ ( A @ cast_to_subset @ ( A @ subset_difference ) ) )
= ( B @ ( A @ complements_of_subsets ) @ ( A @ meet_of_subsets ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ! [B: $i] :
( ( A @ ( B @ element ) )
=> ( ( B @ v1_xreal_0 )
& ( B @ v1_xcmplx_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc11_membered) ).
thf(258,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)],[53]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ subset_complement ) )
= ( B @ ( A @ set_difference ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
thf(186,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ subset_complement ) )
= ( B @ ( A @ set_difference ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B != empty_set )
=> ( ( B @ ( A @ complements_of_subsets ) @ ( A @ meet_of_subsets ) )
= ( B @ ( A @ union_of_subsets ) @ ( A @ subset_complement ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11_tops_2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B != empty_set )
=> ( ( B @ ( A @ complements_of_subsets ) @ ( A @ meet_of_subsets ) )
= ( B @ ( A @ union_of_subsets ) @ ( A @ subset_complement ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(55,plain,
~ ! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( ( B != empty_set )
=> ( ( B @ ( A @ complements_of_subsets ) @ ( A @ meet_of_subsets ) )
= ( B @ ( A @ union_of_subsets ) @ ( A @ subset_complement ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(171,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ v4_membered )
=> ( A @ v3_membered ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_membered) ).
thf(75,plain,
! [A: $i] :
( ( A @ v4_membered )
=> ( A @ v3_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(82,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ meet_of_subsets ) @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
thf(235,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ meet_of_subsets ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(51,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(246,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_difference ) ) )
= ( C @ ( B @ set_difference ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(151,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_difference ) ) )
= ( C @ ( B @ set_difference ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ subset_complement ) @ ( A @ subset_complement ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(183,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ subset_complement ) @ ( A @ subset_complement ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(28,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
thf(168,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(54,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(262,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',cc14_membered) ).
thf(239,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)],[50]) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',fc41_membered) ).
thf(126,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)],[18]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ cast_to_subset )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
thf(94,plain,
! [A: $i] :
( ( A @ cast_to_subset )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(47,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(232,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(100,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(435,plain,
$false,
inference(e,[status(thm)],[138,189,84,221,141,173,118,86,230,199,62,201,102,160,192,165,197,97,77,212,73,237,180,149,66,108,223,226,80,209,145,154,143,250,203,218,258,186,55,171,75,82,235,246,151,183,168,262,239,126,94,232,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU327+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.41 % Computer : n001.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sat Sep 26 09:18:43 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.47/1.22 % [INFO] Parsing done (225ms).
% 1.47/1.23 % [INFO] Running in sequential loop mode.
% 2.20/1.63 % [INFO] eprover registered as external prover.
% 2.20/1.64 % [INFO] Scanning for conjecture ...
% 2.44/1.76 % [INFO] Found a conjecture (or negated_conjecture) and 58 axioms. Running axiom selection ...
% 2.62/1.85 % [INFO] Axiom selection finished. Selected 52 axioms (removed 6 axioms).
% 2.88/1.93 % [INFO] Problem is first-order (TPTP FOF).
% 2.88/1.94 % [INFO] Type checking passed.
% 2.88/1.95 % [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 ...
% 6.34/3.09 % External prover 'e' found a proof!
% 6.34/3.09 % [INFO] Killing All external provers ...
% 6.34/3.09 % Time passed: 2529ms (effective reasoning time: 1848ms)
% 6.34/3.09 % 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)>
% 6.34/3.09 % Axioms used in derivation (52): cc12_membered, fc37_membered, rc1_membered, t47_setfam_1, redefinition_k6_setfam_1, t5_subset, cc19_membered, fc6_membered, redefinition_k5_setfam_1, cc18_membered, involutiveness_k7_setfam_1, reflexivity_r1_tarski, cc17_membered, dt_k5_setfam_1, cc16_membered, cc10_membered, dt_k2_subset_1, t1_subset, d4_subset_1, involutiveness_k3_subset_1, t6_boole, rc2_subset_1, dt_k6_subset_1, t4_boole, cc11_membered, t4_subset, cc20_membered, t7_boole, fc1_subset_1, fc38_membered, rc1_subset_1, cc4_membered, t3_subset, cc13_membered, dt_k6_setfam_1, existence_m1_subset_1, fc39_membered, cc15_membered, d5_subset_1, dt_k7_setfam_1, t8_boole, t2_subset, cc1_membered, fc40_membered, fc41_membered, cc2_membered, cc3_membered, cc14_membered, t3_boole, redefinition_k6_subset_1, dt_k3_subset_1, antisymmetry_r2_hidden
% 6.34/3.09 % No. of inferences in proof: 108
% 6.34/3.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2529 ms resp. 1848 ms w/o parsing
% 7.07/3.14 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.07/3.14 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------