%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU321+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 : n012.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 08:38:27 AM UTC 2026
% Result : Theorem 3.96s 2.29s
% Output : Refutation 4.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 37
% Syntax : Number of formulae : 76 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 267 ( 8 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 650 ( 37 ~; 2 |; 95 &; 422 @)
% ( 3 <=>; 91 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 2 con; 0-2 aty)
% Number of variables : 136 ( 0 ^; 126 !; 10 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_carrier_decl,type,
empty_carrier: $i > $o ).
thf(one_sorted_str_decl,type,
one_sorted_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(subset_complement_decl,type,
subset_complement: $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(subset_decl,type,
subset: $i > $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(v1_xcmplx_0_decl,type,
v1_xcmplx_0: $i > $o ).
thf(natural_decl,type,
natural: $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(27,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(138,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(37,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(170,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)],[37]) ).
thf(20,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(110,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
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(152,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(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ powerset @ ( C @ element ) )
=> ~ ( ( C @ ( B @ in ) )
& ( C @ ( A @ subset_complement ) @ ( B @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
thf(97,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ powerset @ ( C @ element ) )
=> ~ ( ( C @ ( B @ in ) )
& ( C @ ( A @ subset_complement ) @ ( B @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(24,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(124,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)],[24]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(129,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)],[25]) ).
thf(18,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(105,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(23,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(118,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)],[23]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( B @ ( A @ the_carrier @ subset_complement ) @ ( C @ in ) )
<=> ~ ( B @ ( C @ in ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l40_tops_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( B @ ( A @ the_carrier @ subset_complement ) @ ( C @ in ) )
<=> ~ ( B @ ( C @ in ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(39,plain,
~ ! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ~ ( B @ ( C @ in ) )
=> ( B @ ( A @ the_carrier @ subset_complement ) @ ( C @ in ) ) )
& ( ( B @ ( A @ the_carrier @ subset_complement ) @ ( C @ in ) )
=> ~ ( B @ ( C @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(38,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(175,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)],[38]) ).
thf(21,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(114,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(30,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(146,plain,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ v1_membered ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',fc6_membered) ).
thf(79,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)],[11]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(89,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)],[13]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ subset_complement ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(116,plain,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( A @ powerset @ ( B @ ( A @ subset_complement ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_membered) ).
thf(60,plain,
! [A: $i] :
( ( A @ v2_membered )
=> ( A @ v1_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(102,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( ( B @ ( A @ subset_complement ) @ ( A @ subset_complement ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(156,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)],[34]) ).
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(53,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(36,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(166,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)],[36]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(148,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(7,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(64,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10,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(71,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)],[10]) ).
thf(29,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(144,plain,
! [A: $i] :
( ( A @ v1_membered )
=> ! [B: $i] :
( ( A @ ( B @ element ) )
=> ( B @ v1_xcmplx_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(49,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(35,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(159,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)],[35]) ).
thf(28,axiom,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(140,plain,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ v5_membered )
=> ( A @ v4_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_membered) ).
thf(66,plain,
! [A: $i] :
( ( A @ v5_membered )
=> ( A @ v4_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(108,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(150,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(14,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(95,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ ( C @ element ) )
=> ( ~ ( B @ ( C @ in ) )
=> ( B @ ( A @ subset_complement ) @ ( C @ in ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
thf(99,plain,
! [A: $i] :
( ( A != empty_set )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ ( C @ element ) )
=> ( ~ ( B @ ( C @ in ) )
=> ( B @ ( A @ subset_complement ) @ ( C @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ v3_membered )
=> ( A @ v2_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_membered) ).
thf(87,plain,
! [A: $i] :
( ( A @ v3_membered )
=> ( A @ v2_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(26,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(131,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)],[26]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(68,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ v4_membered )
=> ( A @ v3_membered ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_membered) ).
thf(62,plain,
! [A: $i] :
( ( A @ v4_membered )
=> ( A @ v3_membered ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(181,plain,
$false,
inference(e,[status(thm)],[138,170,110,152,97,124,129,105,118,39,175,114,146,79,89,116,60,102,156,53,166,148,64,71,144,49,159,140,66,108,150,95,99,87,131,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU321+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % 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
% 0.12/0.37 % Computer : n012.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 09:11:50 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 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
% 0.74/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.92/1.01 % [INFO] Parsing done (170ms).
% 0.92/1.02 % [INFO] Running in sequential loop mode.
% 1.68/1.34 % [INFO] eprover registered as external prover.
% 1.68/1.34 % [INFO] Scanning for conjecture ...
% 1.90/1.43 % [INFO] Found a conjecture (or negated_conjecture) and 41 axioms. Running axiom selection ...
% 2.10/1.50 % [INFO] Axiom selection finished. Selected 36 axioms (removed 5 axioms).
% 2.10/1.55 % [INFO] Problem is first-order (TPTP FOF).
% 2.10/1.56 % [INFO] Type checking passed.
% 2.10/1.56 % [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 ...
% 3.96/2.29 % External prover 'e' found a proof!
% 3.96/2.29 % [INFO] Killing All external provers ...
% 3.96/2.29 % Time passed: 1787ms (effective reasoning time: 1261ms)
% 3.96/2.29 % 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)>
% 3.96/2.29 % Axioms used in derivation (36): cc12_membered, rc1_membered, involutiveness_k3_subset_1, t6_boole, t5_subset, cc19_membered, fc6_membered, cc4_membered, cc18_membered, cc15_membered, cc17_membered, existence_l1_struct_0, cc16_membered, cc10_membered, t1_subset, cc11_membered, t4_subset, cc20_membered, t7_boole, rc3_struct_0, t3_subset, cc13_membered, existence_m1_subset_1, fc1_struct_0, reflexivity_r1_tarski, t54_subset_1, t8_boole, rc5_struct_0, t2_subset, cc1_membered, cc2_membered, cc14_membered, cc3_membered, t50_subset_1, dt_k3_subset_1, antisymmetry_r2_hidden
% 3.96/2.29 % No. of inferences in proof: 76
% 3.96/2.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1787 ms resp. 1261 ms w/o parsing
% 4.30/2.37 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.30/2.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------