%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU103+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n006.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 08:37:35 AM UTC 2026
% Result : Theorem 5.71s 3.30s
% Output : Refutation 6.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 46
% Syntax : Number of formulae : 94 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 256 ( 28 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 676 ( 55 ~; 2 |; 103 &; 459 @)
% ( 1 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 2 con; 0-3 aty)
% Number of variables : 173 ( 0 ^; 153 !; 20 ?; 173 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_decl,type,
empty: $i > $o ).
thf(preboolean_decl,type,
preboolean: $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(symmetric_difference_decl,type,
symmetric_difference: $i > $i > $i ).
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(finite_decl,type,
finite: $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(prebool_difference_decl,type,
prebool_difference: $i > $i > $i > $i ).
thf(prebool_union2_decl,type,
prebool_union2: $i > $i > $i > $i ).
thf(cup_closed_decl,type,
cup_closed: $i > $o ).
thf(cap_closed_decl,type,
cap_closed: $i > $o ).
thf(diff_closed_decl,type,
diff_closed: $i > $o ).
thf(relation_decl,type,
relation: $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
thf(epsilon_transitive_decl,type,
epsilon_transitive: $i > $o ).
thf(epsilon_connected_decl,type,
epsilon_connected: $i > $o ).
thf(ordinal_decl,type,
ordinal: $i > $o ).
thf(natural_decl,type,
natural: $i > $o ).
thf(46,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ finite )
& ( B @ natural )
& ( B @ ordinal )
& ( B @ epsilon_connected )
& ( B @ epsilon_transitive )
& ( B @ one_to_one )
& ( B @ function )
& ( B @ relation )
& ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_finset_1) ).
thf(185,plain,
! [A: $i] :
? [B: $i] :
( ( B @ finite )
& ( B @ natural )
& ( B @ ordinal )
& ( B @ epsilon_connected )
& ( B @ epsilon_transitive )
& ( B @ one_to_one )
& ( B @ function )
& ( B @ relation )
& ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(25,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(110,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(29,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(124,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(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ element ) )
& ( A @ ( B @ element ) )
& ( A @ preboolean )
& ~ ( A @ empty ) )
=> ( ( C @ ( B @ ( A @ prebool_difference ) ) )
= ( C @ ( B @ set_difference ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k2_finsub_1) ).
thf(118,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ element ) )
& ( A @ ( B @ element ) )
& ( A @ preboolean )
& ~ ( A @ empty ) )
=> ( ( C @ ( B @ ( A @ prebool_difference ) ) )
= ( C @ ( B @ set_difference ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A @ finite )
=> ( B @ ( A @ set_difference ) @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( A @ finite )
=> ( B @ ( A @ set_difference ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(40,axiom,
! [A: $i] :
( ( ( A @ diff_closed )
& ( A @ cup_closed ) )
=> ( A @ preboolean ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finsub_1) ).
thf(167,plain,
! [A: $i] :
( ( ( A @ diff_closed )
& ( A @ cup_closed ) )
=> ( A @ preboolean ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ element ) )
& ( A @ ( B @ element ) )
& ( A @ preboolean )
& ~ ( A @ empty ) )
=> ( ( B @ ( B @ ( A @ prebool_union2 ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k1_finsub_1) ).
thf(145,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ element ) )
& ( A @ ( B @ element ) )
& ( A @ preboolean )
& ~ ( A @ empty ) )
=> ( ( B @ ( B @ ( A @ prebool_union2 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(45,axiom,
! [A: $i] :
( ( empty_set @ ( A @ symmetric_difference ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_boole) ).
thf(182,plain,
! [A: $i] :
( ( empty_set @ ( A @ symmetric_difference ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ element ) )
& ( A @ ( B @ element ) )
& ( A @ preboolean )
& ~ ( A @ empty ) )
=> ( ( C @ ( B @ ( A @ prebool_union2 ) ) )
= ( B @ ( C @ ( A @ prebool_union2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k1_finsub_1) ).
thf(175,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ element ) )
& ( A @ ( B @ element ) )
& ( A @ preboolean )
& ~ ( A @ empty ) )
=> ( ( C @ ( B @ ( A @ prebool_union2 ) ) )
= ( B @ ( C @ ( A @ prebool_union2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ symmetric_difference ) @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc17_finset_1) ).
thf(87,plain,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ symmetric_difference ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ set_union2 ) @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ set_union2 ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ element ) )
& ( A @ ( B @ element ) )
& ( A @ preboolean )
& ~ ( A @ empty ) )
=> ( A @ ( C @ ( B @ ( A @ prebool_union2 ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_finsub_1) ).
thf(106,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ element ) )
& ( A @ ( B @ element ) )
& ( A @ preboolean )
& ~ ( A @ empty ) )
=> ( A @ ( C @ ( B @ ( A @ prebool_union2 ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(121,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(10,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(74,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,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(89,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ element ) )
& ( A @ ( B @ element ) )
& ( A @ preboolean )
& ~ ( A @ empty ) )
=> ( ( C @ ( B @ ( A @ prebool_union2 ) ) )
= ( C @ ( B @ set_union2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_finsub_1) ).
thf(133,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ element ) )
& ( A @ ( B @ element ) )
& ( A @ preboolean )
& ~ ( A @ empty ) )
=> ( ( C @ ( B @ ( A @ prebool_union2 ) ) )
= ( C @ ( B @ set_union2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(5,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(60,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(85,plain,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(17,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(92,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(197,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(65,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(97,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(37,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(156,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ symmetric_difference ) )
= ( A @ ( B @ set_difference ) @ ( B @ ( A @ set_difference ) @ set_union2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).
thf(169,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ symmetric_difference ) )
= ( A @ ( B @ set_difference ) @ ( B @ ( A @ set_difference ) @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(34,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(141,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(31,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(128,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(22,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(105,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(161,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)],[39]) ).
thf(36,axiom,
? [A: $i] :
( ( A @ preboolean )
& ( A @ diff_closed )
& ( A @ cap_closed )
& ( A @ cup_closed )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finsub_1) ).
thf(149,plain,
? [A: $i] :
( ( A @ preboolean )
& ( A @ diff_closed )
& ( A @ cap_closed )
& ( A @ cup_closed )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(42,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(172,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(76,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ element ) )
& ( A @ ( B @ element ) )
& ( A @ preboolean )
& ~ ( A @ empty ) )
=> ( A @ ( C @ ( B @ ( A @ prebool_difference ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_finsub_1) ).
thf(103,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ element ) )
& ( A @ ( B @ element ) )
& ( A @ preboolean )
& ~ ( A @ empty ) )
=> ( A @ ( C @ ( B @ ( A @ prebool_difference ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(108,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( C @ preboolean )
& ~ ( C @ empty ) )
=> ( ( ( C @ ( B @ element ) )
& ( C @ ( A @ element ) ) )
=> ( C @ ( B @ ( A @ symmetric_difference ) @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_finsub_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ preboolean )
& ~ ( C @ empty ) )
=> ( ( ( C @ ( B @ element ) )
& ( C @ ( A @ element ) ) )
=> ( C @ ( B @ ( A @ symmetric_difference ) @ element ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(48,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ preboolean )
& ~ ( C @ empty ) )
=> ( ( ( C @ ( B @ element ) )
& ( C @ ( A @ element ) ) )
=> ( C @ ( B @ ( A @ symmetric_difference ) @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(63,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(95,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ symmetric_difference ) )
= ( A @ ( B @ symmetric_difference ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).
thf(158,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ symmetric_difference ) )
= ( A @ ( B @ symmetric_difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(55,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(26,axiom,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(114,plain,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(12,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(79,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(126,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(33,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(136,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(8,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(68,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ preboolean )
=> ( ( A @ diff_closed )
& ( A @ cup_closed ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finsub_1) ).
thf(178,plain,
! [A: $i] :
( ( A @ preboolean )
=> ( ( A @ diff_closed )
& ( A @ cup_closed ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(13,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(83,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(100,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(203,plain,
$false,
inference(e,[status(thm)],[185,110,124,118,71,167,145,182,175,87,58,106,121,74,89,133,60,85,92,197,65,97,156,169,141,128,105,161,149,172,76,103,108,48,63,95,158,55,114,79,126,136,68,178,83,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU103+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % 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
% 0.15/0.40 % Computer : n006.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 08:35:55 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 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
% 1.31/1.23 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.83/1.54 % [INFO] Parsing done (313ms).
% 1.83/1.57 % [INFO] Running in sequential loop mode.
% 2.69/2.12 % [INFO] eprover registered as external prover.
% 2.69/2.12 % [INFO] Scanning for conjecture ...
% 3.00/2.23 % [INFO] Found a conjecture (or negated_conjecture) and 45 axioms. Running axiom selection ...
% 3.18/2.31 % [INFO] Axiom selection finished. Selected 45 axioms (removed 0 axioms).
% 3.18/2.38 % [INFO] Problem is first-order (TPTP FOF).
% 3.18/2.39 % [INFO] Type checking passed.
% 3.18/2.39 % [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 ...
% 5.39/3.29 % External prover 'e' found a proof!
% 5.39/3.29 % [INFO] Killing All external provers ...
% 5.39/3.30 % Time passed: 2683ms (effective reasoning time: 1716ms)
% 5.39/3.30 % 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)>
% 5.71/3.30 % Axioms used in derivation (45): cc2_finset_1, dt_k2_finsub_1, commutativity_k5_xboole_0, rc1_subset_1, d6_xboole_0, rc3_finset_1, t2_subset, idempotence_k2_xboole_0, t3_boole, rc2_xboole_0, antisymmetry_r2_hidden, idempotence_k1_finsub_1, t5_boole, commutativity_k1_finsub_1, rc4_finset_1, t1_boole, rc1_finsub_1, fc1_xboole_0, t1_subset, redefinition_k2_finsub_1, cc2_finsub_1, fc2_xboole_0, t6_boole, rc2_subset_1, fc9_finset_1, fc17_finset_1, commutativity_k2_xboole_0, t5_subset, t4_boole, t4_subset, fc3_xboole_0, dt_k1_finsub_1, t7_boole, fc1_subset_1, t3_subset, existence_m1_subset_1, cc1_finsub_1, rc2_finset_1, reflexivity_r1_tarski, redefinition_k1_finsub_1, rc1_finset_1, cc1_finset_1, fc12_finset_1, t8_boole, rc1_xboole_0
% 5.71/3.30 % No. of inferences in proof: 94
% 5.71/3.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2683 ms resp. 1716 ms w/o parsing
% 6.01/3.40 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.01/3.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------