%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU291+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 : n016.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 08:38:20 AM UTC 2026
% Result : Theorem 46.11s 15.87s
% Output : Refutation 39.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 58
% Syntax : Number of formulae : 173 ( 66 unt; 0 typ; 12 def)
% Number of atoms : 473 ( 90 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 1036 ( 116 ~; 45 |; 139 &; 664 @)
% ( 4 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 28 usr; 15 con; 0-3 aty)
% Number of variables : 198 ( 0 ^; 150 !; 36 ?; 198 :)
% ( 0 !>; 0 ?*; 0 @-; 12 @+)
% Comments :
%------------------------------------------------------------------------------
thf(function_decl,type,
function: $i > $o ).
thf(quasi_total_decl,type,
quasi_total: $i > $i > $i > $o ).
thf(relation_of2_as_subset_decl,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(relation_decl,type,
relation: $i > $o ).
thf(relation_empty_yielding_decl,type,
relation_empty_yielding: $i > $o ).
thf(relation_of2_decl,type,
relation_of2: $i > $i > $i > $o ).
thf(relation_dom_as_subset_decl,type,
relation_dom_as_subset: $i > $i > $i > $i ).
thf(relation_dom_decl,type,
relation_dom: $i > $i ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk15_decl,type,
sk15: $i ).
thf(sk16_decl,type,
sk16: $i ).
thf(sk17_decl,type,
sk17: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( B @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
=> ( ( C @ ( B @ subset ) )
=> ( ( ( C @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( C @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
| ( ( A != empty_set )
& ( B = empty_set ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( A @ ( sk1 @ ( C @ relation_of2_as_subset ) ) )
& ( A @ ( sk1 @ ( C @ quasi_total ) ) )
& ( C @ function ) )
=> ( ( B @ ( A @ subset ) )
=> ( ( ( B @ ( sk1 @ ( C @ relation_of2_as_subset ) ) )
& ( B @ ( sk1 @ ( C @ quasi_total ) ) )
& ( C @ function ) )
| ( ( sk1 != empty_set )
& ( A = empty_set ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk2 @ ( sk1 @ ( B @ relation_of2_as_subset ) ) )
& ( sk2 @ ( sk1 @ ( B @ quasi_total ) ) )
& ( B @ function ) )
=> ( ( A @ ( sk2 @ subset ) )
=> ( ( ( A @ ( sk1 @ ( B @ relation_of2_as_subset ) ) )
& ( A @ ( sk1 @ ( B @ quasi_total ) ) )
& ( B @ function ) )
| ( ( sk1 != empty_set )
& ( sk2 = empty_set ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ( sk2 @ ( sk1 @ ( A @ relation_of2_as_subset ) ) )
& ( sk2 @ ( sk1 @ ( A @ quasi_total ) ) )
& ( A @ function ) )
=> ( ( sk3 @ ( sk2 @ subset ) )
=> ( ( ( sk3 @ ( sk1 @ ( A @ relation_of2_as_subset ) ) )
& ( sk3 @ ( sk1 @ ( A @ quasi_total ) ) )
& ( A @ function ) )
| ( ( sk1 != empty_set )
& ( sk2 = empty_set ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
( ( A @ relation )
& ( A @ empty ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( @+[A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( @+[A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( B @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
=> ( ( C @ ( B @ subset ) )
=> ( ( ( C @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( C @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
| ( ( A != empty_set )
& ( B = empty_set ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( B @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
=> ( ( C @ ( B @ subset ) )
=> ( ( ( C @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( C @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
| ( ( A != empty_set )
& ( B = empty_set ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(48,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( B @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
=> ( ( C @ ( B @ subset ) )
=> ( ( ( C @ ( A @ ( D @ relation_of2_as_subset ) ) )
& ( C @ ( A @ ( D @ quasi_total ) ) )
& ( D @ function ) )
| ( ( A != empty_set )
& ( B = empty_set ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(49,plain,
( ( ~ ( sk3 @ ( sk1 @ ( sk4 @ relation_of2_as_subset ) ) )
| ~ ( sk3 @ ( sk1 @ ( sk4 @ quasi_total ) ) )
| ~ ( sk4 @ function ) )
& ( ( sk1 = empty_set )
| ( sk2 != empty_set ) )
& ( sk3 @ ( sk2 @ subset ) )
& ( sk2 @ ( sk1 @ ( sk4 @ relation_of2_as_subset ) ) )
& ( sk2 @ ( sk1 @ ( sk4 @ quasi_total ) ) )
& ( sk4 @ function ) ),
inference(cnf,[status(esa)],[48]) ).
thf(55,plain,
( ( sk1 = empty_set )
| ( sk2 != empty_set ) ),
inference(cnfConj,[status(thm)],[49]) ).
thf(56,plain,
( ( sk1 = empty_set )
| ( sk2 != empty_set ) ),
inference(lifteq,[status(thm)],[55]) ).
thf(28,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(129,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(16,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(95,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(96,plain,
( ( sk11 @ relation )
& ~ ( sk11 @ empty ) ),
inference(cnf,[status(esa)],[95]) ).
thf(98,plain,
sk11 @ relation,
inference(cnfConj,[status(thm)],[96]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( C @ ( B @ ( A @ relation_dom_as_subset ) ) )
= ( C @ relation_dom ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
thf(69,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( C @ ( B @ ( A @ relation_dom_as_subset ) ) )
= ( C @ relation_dom ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(30,axiom,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(135,plain,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(136,plain,
( ( sk15 @ one_to_one )
& ( sk15 @ function )
& ( sk15 @ relation ) ),
inference(cnf,[status(esa)],[135]) ).
thf(138,plain,
sk15 @ function,
inference(cnfConj,[status(thm)],[136]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(101,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(50,plain,
( ~ ( sk3 @ ( sk1 @ ( sk4 @ relation_of2_as_subset ) ) )
| ~ ( sk3 @ ( sk1 @ ( sk4 @ quasi_total ) ) )
| ~ ( sk4 @ function ) ),
inference(cnfConj,[status(thm)],[49]) ).
thf(52,plain,
sk4 @ function,
inference(cnfConj,[status(thm)],[49]) ).
thf(233,plain,
( ~ ( sk3 @ ( sk1 @ ( sk4 @ relation_of2_as_subset ) ) )
| ~ ( sk3 @ ( sk1 @ ( sk4 @ quasi_total ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[50,52]) ).
thf(234,plain,
( ~ ( sk3 @ ( sk1 @ ( sk4 @ relation_of2_as_subset ) ) )
| ~ ( sk3 @ ( sk1 @ ( sk4 @ quasi_total ) ) ) ),
inference(simp,[status(thm)],[233]) ).
thf(34,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(166,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(167,plain,
( ( sk17 @ function )
& ( sk17 @ empty )
& ( sk17 @ relation ) ),
inference(cnf,[status(esa)],[166]) ).
thf(170,plain,
sk17 @ function,
inference(cnfConj,[status(thm)],[167]) ).
thf(47,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(217,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(25,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(120,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(38,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( C @ relation )
& ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(184,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( C @ relation )
& ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(15,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(93,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(78,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(33,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(161,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(162,plain,
( ( sk16 @ function )
& ( sk16 @ relation_empty_yielding )
& ( sk16 @ relation ) ),
inference(cnf,[status(esa)],[161]) ).
thf(164,plain,
sk16 @ relation_empty_yielding,
inference(cnfConj,[status(thm)],[162]) ).
thf(12,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(84,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(130,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(cnf,[status(esa)],[129]) ).
thf(132,plain,
empty_set @ relation,
inference(cnfConj,[status(thm)],[130]) ).
thf(14,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(89,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(29,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(133,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(24,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(116,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(131,plain,
empty_set @ empty,
inference(cnfConj,[status(thm)],[130]) ).
thf(97,plain,
~ ( sk11 @ empty ),
inference(cnfConj,[status(thm)],[96]) ).
thf(239,plain,
( ( ( sk11 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[131,97]) ).
thf(240,plain,
( ( sk11 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[239]) ).
thf(243,plain,
sk11 != empty_set,
inference(simp,[status(thm)],[240]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(192,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(137,plain,
sk15 @ relation,
inference(cnfConj,[status(thm)],[136]) ).
thf(165,plain,
sk16 @ function,
inference(cnfConj,[status(thm)],[162]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(197,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(6,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(65,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(53,plain,
sk2 @ ( sk1 @ ( sk4 @ relation_of2_as_subset ) ),
inference(cnfConj,[status(thm)],[49]) ).
thf(169,plain,
sk17 @ empty,
inference(cnfConj,[status(thm)],[167]) ).
thf(27,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(124,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(46,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(212,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(20,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(105,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(85,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[84]) ).
thf(86,plain,
~ ( sk8 @ empty ),
inference(cnf,[status(esa)],[85]) ).
thf(241,plain,
( ( ( sk8 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[131,86]) ).
thf(242,plain,
( ( sk8 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[241]) ).
thf(244,plain,
sk8 != empty_set,
inference(simp,[status(thm)],[242]) ).
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(64,plain,
sk5 @ empty,
inference(cnf,[status(esa)],[63]) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(59,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(44,axiom,
? [A: $i] :
( ( A @ empty )
& ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(204,plain,
? [A: $i] :
( ( A @ empty )
& ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(54,plain,
sk2 @ ( sk1 @ ( sk4 @ quasi_total ) ),
inference(cnfConj,[status(thm)],[49]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ relation_dom_as_subset ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
thf(103,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ relation_dom_as_subset ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(31,axiom,
! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(140,plain,
! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(108,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(221,plain,
( ( ( sk8 @ empty )
!= ( sk5 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[64,86]) ).
thf(222,plain,
( ( sk8 @ empty )
!= ( sk5 @ empty ) ),
inference(simp,[status(thm)],[221]) ).
thf(223,plain,
sk8 != sk5,
inference(simp,[status(thm)],[222]) ).
thf(224,plain,
( ( ( sk11 @ empty )
!= ( sk5 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[64,97]) ).
thf(225,plain,
( ( sk11 @ empty )
!= ( sk5 @ empty ) ),
inference(simp,[status(thm)],[224]) ).
thf(226,plain,
sk11 != sk5,
inference(simp,[status(thm)],[225]) ).
thf(11,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(80,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(235,plain,
( ( ( sk3 @ ( sk1 @ ( sk4 @ relation_of2_as_subset ) ) )
!= ( sk2 @ ( sk1 @ ( sk4 @ relation_of2_as_subset ) ) ) )
| ~ $true
| ~ ( sk3 @ ( sk1 @ ( sk4 @ quasi_total ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,234]) ).
thf(236,plain,
( ( ( sk3 @ ( sk1 @ ( sk4 @ relation_of2_as_subset ) ) )
!= ( sk2 @ ( sk1 @ ( sk4 @ relation_of2_as_subset ) ) ) )
| ~ ( sk3 @ ( sk1 @ ( sk4 @ quasi_total ) ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(237,plain,
( ( sk3 != sk2 )
| ( sk1 != sk1 )
| ( sk4 != sk4 )
| ~ ( sk3 @ ( sk1 @ ( sk4 @ quasi_total ) ) ) ),
inference(simp,[status(thm)],[236]) ).
thf(238,plain,
( ( sk3 != sk2 )
| ~ ( sk3 @ ( sk1 @ ( sk4 @ quasi_total ) ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(252,plain,
( ( ( sk3 @ ( sk1 @ ( sk4 @ quasi_total ) ) )
!= ( sk2 @ ( sk1 @ ( sk4 @ quasi_total ) ) ) )
| ( sk3 != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54,238]) ).
thf(253,plain,
( ( ( sk3 @ ( sk1 @ ( sk4 @ quasi_total ) ) )
!= ( sk2 @ ( sk1 @ ( sk4 @ quasi_total ) ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[252]) ).
thf(254,plain,
( ( sk3 != sk2 )
| ( sk1 != sk1 )
| ( sk4 != sk4 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[253]) ).
thf(255,plain,
sk3 != sk2,
inference(simp,[status(thm)],[254]) ).
thf(22,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(112,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)],[22]) ).
thf(66,plain,
( ( sk6 @ relation_empty_yielding )
& ( sk6 @ relation ) ),
inference(cnf,[status(esa)],[65]) ).
thf(67,plain,
sk6 @ relation,
inference(cnfConj,[status(thm)],[66]) ).
thf(43,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ function )
& ( C @ relation )
& ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(199,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ function )
& ( C @ relation )
& ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(177,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)],[36]) ).
thf(8,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(72,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( ( ( B = empty_set )
=> ( ( ( B @ ( A @ ( C @ quasi_total ) ) )
<=> ( C = empty_set ) )
| ( A = empty_set ) ) )
& ( ( ( B = empty_set )
=> ( A = empty_set ) )
=> ( ( B @ ( A @ ( C @ quasi_total ) ) )
<=> ( A
= ( C @ ( B @ ( A @ relation_dom_as_subset ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
thf(143,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( ( ( B = empty_set )
=> ( ( ( ( C = empty_set )
=> ( B @ ( A @ ( C @ quasi_total ) ) ) )
& ( ( B @ ( A @ ( C @ quasi_total ) ) )
=> ( C = empty_set ) ) )
| ( A = empty_set ) ) )
& ( ( ( B = empty_set )
=> ( A = empty_set ) )
=> ( ( ( A
= ( C @ ( B @ ( A @ relation_dom_as_subset ) ) ) )
=> ( B @ ( A @ ( C @ quasi_total ) ) ) )
& ( ( B @ ( A @ ( C @ quasi_total ) ) )
=> ( A
= ( C @ ( B @ ( A @ relation_dom_as_subset ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(81,plain,
( ( sk7 @ relation )
& ( sk7 @ empty ) ),
inference(cnf,[status(esa)],[80]) ).
thf(82,plain,
sk7 @ empty,
inference(cnfConj,[status(thm)],[81]) ).
thf(227,plain,
( ( ( sk11 @ empty )
!= ( sk7 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,97]) ).
thf(228,plain,
( ( sk11 @ empty )
!= ( sk7 @ empty ) ),
inference(simp,[status(thm)],[227]) ).
thf(231,plain,
sk11 != sk7,
inference(simp,[status(thm)],[228]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(99,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(87,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(114,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
<=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(171,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ) )
& ( ( B @ ( A @ ( C @ relation_of2_as_subset ) ) )
=> ( B @ ( A @ ( C @ relation_of2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(139,plain,
sk15 @ one_to_one,
inference(cnfConj,[status(thm)],[136]) ).
thf(9,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(75,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[57]) ).
thf(168,plain,
sk17 @ relation,
inference(cnfConj,[status(thm)],[167]) ).
thf(51,plain,
sk3 @ ( sk2 @ subset ),
inference(cnfConj,[status(thm)],[49]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ relation_of2_as_subset ) ) )
=> ( ( B @ ( A @ subset ) )
=> ( B @ ( C @ ( D @ relation_of2_as_subset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
thf(190,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( C @ ( D @ relation_of2_as_subset ) ) )
=> ( ( B @ ( A @ subset ) )
=> ( B @ ( C @ ( D @ relation_of2_as_subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(37,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(183,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(45,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(210,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(195,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(163,plain,
sk16 @ relation,
inference(cnfConj,[status(thm)],[162]) ).
thf(68,plain,
sk6 @ relation_empty_yielding,
inference(cnfConj,[status(thm)],[66]) ).
thf(60,plain,
~ ? [A: $i] :
( ? [B: $i] :
( ( B @ empty )
& ( A != B ) )
& ( A @ empty ) ),
inference(miniscope,[status(thm)],[59]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ( A = B )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[60]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( A @ empty )
| ( A = B ) ),
inference(lifteq,[status(thm)],[61]) ).
thf(26,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(122,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(83,plain,
sk7 @ relation,
inference(cnfConj,[status(thm)],[81]) ).
thf(229,plain,
( ( ( sk8 @ empty )
!= ( sk7 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,86]) ).
thf(230,plain,
( ( sk8 @ empty )
!= ( sk7 @ empty ) ),
inference(simp,[status(thm)],[229]) ).
thf(232,plain,
sk8 != sk7,
inference(simp,[status(thm)],[230]) ).
thf(8274,plain,
$false,
inference(e,[status(thm)],[56,129,98,69,138,101,234,170,217,120,52,184,93,57,78,164,84,132,89,133,116,243,192,137,165,197,65,97,53,169,124,212,105,244,166,161,64,59,204,54,86,103,140,108,223,135,226,80,255,112,48,63,95,67,199,177,72,143,231,99,87,114,171,139,75,58,82,168,51,190,183,210,195,131,163,68,62,122,83,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU291+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.17/5.62 % Computer : n016.cluster.edu
% 0.17/5.62 % Model : x86_64 x86_64
% 0.17/5.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.62 % Memory : 8046.5625MB
% 0.17/5.62 % OS : Linux 6.8.0-71-generic
% 0.17/5.62 % CPULimit : 300
% 0.17/5.62 % WCLimit : 300
% 0.17/5.62 % DateTime : Sat Sep 26 09:11:20 UTC 2026
% 0.17/5.62 % CPUTime :
% 0.17/5.62 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
% 1.13/6.34 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.68/6.63 % [INFO] Parsing done (283ms).
% 1.68/6.65 % [INFO] Running in sequential loop mode.
% 2.67/7.22 % [INFO] eprover registered as external prover.
% 2.67/7.23 % [INFO] Scanning for conjecture ...
% 2.86/7.39 % [INFO] Found a conjecture (or negated_conjecture) and 51 axioms. Running axiom selection ...
% 3.04/7.49 % [INFO] Axiom selection finished. Selected 45 axioms (removed 6 axioms).
% 3.23/7.58 % [INFO] Problem is first-order (TPTP FOF).
% 3.23/7.59 % [INFO] Type checking passed.
% 3.47/7.60 % [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 ...
% 46.11/15.87 % External prover 'e' found a proof!
% 46.11/15.87 % [INFO] Killing All external provers ...
% 46.11/15.87 % Time passed: 10050ms (effective reasoning time: 9209ms)
% 46.11/15.87 % 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)>
% 46.11/15.87 % Axioms used in derivation (45): redefinition_m2_relset_1, fc4_subset_1, rc1_funct_1, t5_subset, existence_m1_relset_1, rc4_funct_1, t4_subset, fc5_relat_1, d1_funct_2, rc2_xboole_0, antisymmetry_r2_hidden, t3_xboole_1, dt_k4_relset_1, fc1_xboole_0, fc4_relat_1, t1_subset, rc2_partfun1, rc3_funct_1, dt_m2_relset_1, cc1_relat_1, t16_relset_1, rc3_relat_1, t6_boole, rc2_subset_1, t7_boole, cc1_funct_1, fc1_subset_1, rc2_funct_1, rc1_subset_1, rc1_funct_2, cc2_funct_1, t3_subset, cc1_relset_1, existence_m1_subset_1, rc2_relat_1, existence_m2_relset_1, rc1_relat_1, reflexivity_r1_tarski, t8_boole, rc1_xboole_0, t2_subset, fc7_relat_1, fc12_relat_1, rc1_partfun1, redefinition_k4_relset_1
% 46.11/15.87 % No. of inferences in proof: 161
% 46.11/15.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10050 ms resp. 9209 ms w/o parsing
% 39.61/16.00 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 39.61/16.00 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------