%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU191+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 : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:37:58 AM UTC 2026
% Result : Theorem 56.04s 11.15s
% Output : Refutation 48.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 35
% Syntax : Number of formulae : 137 ( 69 unt; 0 typ; 9 def)
% Number of atoms : 381 ( 78 equ; 0 cnn)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 991 ( 123 ~; 57 |; 67 &; 685 @)
% ( 6 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 12 con; 0-2 aty)
% Number of variables : 164 ( 1 ^; 132 !; 22 ?; 164 :)
% ( 0 !>; 0 ?*; 0 @-; 9 @+)
% Comments :
%------------------------------------------------------------------------------
thf(relation_decl,type,
relation: $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(relation_composition_decl,type,
relation_composition: $i > $i > $i ).
thf(identity_relation_decl,type,
identity_relation: $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(element_decl,type,
element: $i > $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: $o ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i > $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( D @ relation )
=> ( ( ( ( D @ ( B @ ( A @ ordered_pair ) @ in ) )
& ( C @ ( A @ in ) ) )
=> ( D @ ( C @ identity_relation @ relation_composition ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
& ( ( D @ ( C @ identity_relation @ relation_composition ) @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( D @ ( B @ ( A @ ordered_pair ) @ in ) )
& ( C @ ( A @ in ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( C @ relation )
=> ( ( ( ( C @ ( A @ ( sk1 @ ordered_pair ) @ in ) )
& ( B @ ( sk1 @ in ) ) )
=> ( C @ ( B @ identity_relation @ relation_composition ) @ ( A @ ( sk1 @ ordered_pair ) @ in ) ) )
& ( ( C @ ( B @ identity_relation @ relation_composition ) @ ( A @ ( sk1 @ ordered_pair ) @ in ) )
=> ( ( C @ ( A @ ( sk1 @ ordered_pair ) @ in ) )
& ( B @ ( sk1 @ in ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ relation )
=> ( ( ( ( B @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) )
& ( A @ ( sk1 @ in ) ) )
=> ( B @ ( A @ identity_relation @ relation_composition ) @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) ) )
& ( ( B @ ( A @ identity_relation @ relation_composition ) @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) )
=> ( ( B @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) )
& ( A @ ( sk1 @ in ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( A @ relation )
=> ( ( ( ( A @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) )
& ( sk3 @ ( sk1 @ in ) ) )
=> ( A @ ( sk3 @ identity_relation @ relation_composition ) @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) ) )
& ( ( A @ ( sk3 @ identity_relation @ relation_composition ) @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) )
=> ( ( A @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) )
& ( sk3 @ ( sk1 @ in ) ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ element ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
( ( A @ relation )
& ( A @ empty ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ) ) ) ).
thf(5,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(42,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(62,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(63,plain,
( ( sk9 @ relation )
& ( sk9 @ empty ) ),
inference(cnf,[status(esa)],[62]) ).
thf(65,plain,
sk9 @ relation,
inference(cnfConj,[status(thm)],[63]) ).
thf(4,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(40,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(41,plain,
sk6 @ empty,
inference(cnf,[status(esa)],[40]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ relation )
=> ( ( D @ ( C @ identity_relation @ relation_composition ) @ ( B @ ( A @ ordered_pair ) @ in ) )
<=> ( ( D @ ( B @ ( A @ ordered_pair ) @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_relat_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ relation )
=> ( ( D @ ( C @ identity_relation @ relation_composition ) @ ( B @ ( A @ ordered_pair ) @ in ) )
<=> ( ( D @ ( B @ ( A @ ordered_pair ) @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(28,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ relation )
=> ( ( ( ( D @ ( B @ ( A @ ordered_pair ) @ in ) )
& ( C @ ( A @ in ) ) )
=> ( D @ ( C @ identity_relation @ relation_composition ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
& ( ( D @ ( C @ identity_relation @ relation_composition ) @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( D @ ( B @ ( A @ ordered_pair ) @ in ) )
& ( C @ ( A @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(29,plain,
( ( ~ ( sk4 @ ( sk3 @ identity_relation @ relation_composition ) @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) )
| sk5 )
& ( ( sk4 @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) )
| sk5 )
& ( ( sk3 @ ( sk1 @ in ) )
| sk5 )
& ( ~ sk5
| ~ ( sk4 @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) )
| ~ ( sk3 @ ( sk1 @ in ) ) )
& ( ~ sk5
| ( sk4 @ ( sk3 @ identity_relation @ relation_composition ) @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) ) )
& ( sk4 @ relation ) ),
inference(cnf,[status(esa)],[28]) ).
thf(35,plain,
( ( sk3 @ ( sk1 @ in ) )
| sk5 ),
inference(cnfConj,[status(thm)],[29]) ).
thf(7,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(48,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(31,plain,
( ~ sk5
| ( sk4 @ ( sk3 @ identity_relation @ relation_composition ) @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) ) ),
inference(cnfConj,[status(thm)],[29]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(107,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( A @ singleton @ ( B @ ( A @ unordered_pair ) @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(19,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(100,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(34,plain,
( ( sk4 @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) )
| sk5 ),
inference(cnfConj,[status(thm)],[29]) ).
thf(30,plain,
( ~ ( sk4 @ ( sk3 @ identity_relation @ relation_composition ) @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) )
| sk5 ),
inference(cnfConj,[status(thm)],[29]) ).
thf(166,plain,
( ( ( sk4 @ ( sk3 @ identity_relation @ relation_composition ) @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) )
!= ( sk4 @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) ) )
| ~ $true
| sk5
| sk5 ),
inference(paramod_ordered,[status(thm)],[34,30]) ).
thf(167,plain,
( ( ( sk4 @ ( sk3 @ identity_relation @ relation_composition ) @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) )
!= ( sk4 @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) ) )
| sk5 ),
inference(simp,[status(thm)],[166]) ).
thf(169,plain,
( ( ( sk4 @ ( sk3 @ identity_relation @ relation_composition ) )
!= sk4 )
| ( ( sk2 @ ( sk1 @ ordered_pair ) )
!= ( sk2 @ ( sk1 @ ordered_pair ) ) )
| sk5 ),
inference(simp,[status(thm)],[167]) ).
thf(170,plain,
( ( ( sk4 @ ( sk3 @ identity_relation @ relation_composition ) )
!= sk4 )
| sk5 ),
inference(simp,[status(thm)],[169]) ).
thf(6,axiom,
! [A: $i] :
~ ( A @ singleton @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(45,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(46,plain,
~ ? [A: $i] : ( A @ singleton @ empty ),
inference(miniscope,[status(thm)],[45]) ).
thf(47,plain,
! [A: $i] :
~ ( A @ singleton @ empty ),
inference(cnf,[status(esa)],[46]) ).
thf(197,plain,
! [A: $i] :
( ( ( A @ singleton @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,47]) ).
thf(198,plain,
! [A: $i] :
( ( A @ singleton @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[197]) ).
thf(202,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(simp,[status(thm)],[198]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(110,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(64,plain,
sk9 @ empty,
inference(cnfConj,[status(thm)],[63]) ).
thf(10,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(55,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(56,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ unordered_pair ) @ empty ),
inference(miniscope,[status(thm)],[55]) ).
thf(57,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ unordered_pair ) @ empty ),
inference(cnf,[status(esa)],[56]) ).
thf(585,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ empty )
!= ( sk9 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[64,57]) ).
thf(586,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ empty )
!= ( sk9 @ empty ) ),
inference(simp,[status(thm)],[585]) ).
thf(587,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
!= sk9 ),
inference(simp,[status(thm)],[586]) ).
thf(16,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(72,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(73,plain,
( ( sk10 @ relation )
& ~ ( sk10 @ empty ) ),
inference(cnf,[status(esa)],[72]) ).
thf(74,plain,
~ ( sk10 @ empty ),
inference(cnfConj,[status(thm)],[73]) ).
thf(154,plain,
( ( ( sk10 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,74]) ).
thf(155,plain,
( ( sk10 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[154]) ).
thf(157,plain,
sk10 != empty_set,
inference(simp,[status(thm)],[155]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( B
= ( A @ identity_relation ) )
<=> ! [C: $i,D: $i] :
( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
<=> ( ( C = D )
& ( A @ ( C @ in ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).
thf(78,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( ( ! [C: $i,D: $i] :
( ( ( ( C = D )
& ( A @ ( C @ in ) ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) )
& ( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( ( C = D )
& ( A @ ( C @ in ) ) ) ) )
=> ( B
= ( A @ identity_relation ) ) )
& ( ( B
= ( A @ identity_relation ) )
=> ! [C: $i,D: $i] :
( ( ( ( C = D )
& ( A @ ( C @ in ) ) )
=> ( B @ ( D @ ( C @ ordered_pair ) @ in ) ) )
& ( ( B @ ( D @ ( C @ ordered_pair ) @ in ) )
=> ( ( C = D )
& ( A @ ( C @ in ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( C @ relation )
=> ( ( C
= ( B @ ( A @ relation_composition ) ) )
<=> ! [D: $i,E: $i] :
( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
<=> ? [F: $i] :
( ( B @ ( E @ ( F @ ordered_pair ) @ in ) )
& ( A @ ( F @ ( D @ ordered_pair ) @ in ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
thf(116,plain,
! [A: $i] :
( ( A @ relation )
=> ! [B: $i] :
( ( B @ relation )
=> ! [C: $i] :
( ( C @ relation )
=> ( ( ! [D: $i,E: $i] :
( ( ? [F: $i] :
( ( B @ ( E @ ( F @ ordered_pair ) @ in ) )
& ( A @ ( F @ ( D @ ordered_pair ) @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ? [F: $i] :
( ( B @ ( E @ ( F @ ordered_pair ) @ in ) )
& ( A @ ( F @ ( D @ ordered_pair ) @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ relation_composition ) ) ) )
& ( ( C
= ( B @ ( A @ relation_composition ) ) )
=> ! [D: $i,E: $i] :
( ( ? [F: $i] :
( ( B @ ( E @ ( F @ ordered_pair ) @ in ) )
& ( A @ ( F @ ( D @ ordered_pair ) @ in ) ) )
=> ( C @ ( E @ ( D @ ordered_pair ) @ in ) ) )
& ( ( C @ ( E @ ( D @ ordered_pair ) @ in ) )
=> ? [F: $i] :
( ( B @ ( E @ ( F @ ordered_pair ) @ in ) )
& ( A @ ( F @ ( D @ ordered_pair ) @ in ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(60,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(195,plain,
! [A: $i] :
( ( ( A @ singleton @ empty )
!= ( sk6 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41,47]) ).
thf(196,plain,
! [A: $i] :
( ( A @ singleton @ empty )
!= ( sk6 @ empty ) ),
inference(simp,[status(thm)],[195]) ).
thf(201,plain,
! [A: $i] :
( ( A @ singleton )
!= sk6 ),
inference(simp,[status(thm)],[196]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(33,plain,
( ~ sk5
| ~ ( sk4 @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) )
| ~ ( sk3 @ ( sk1 @ in ) ) ),
inference(cnfConj,[status(thm)],[29]) ).
thf(152,plain,
( ( ( sk10 @ empty )
!= ( sk6 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41,74]) ).
thf(153,plain,
( ( sk10 @ empty )
!= ( sk6 @ empty ) ),
inference(simp,[status(thm)],[152]) ).
thf(156,plain,
sk10 != sk6,
inference(simp,[status(thm)],[153]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ relation_composition ) @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(141,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ relation_composition ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(43,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[42]) ).
thf(44,plain,
~ ( sk7 @ empty ),
inference(cnf,[status(esa)],[43]) ).
thf(146,plain,
( ( ( sk7 @ empty )
!= ( sk6 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41,44]) ).
thf(147,plain,
( ( sk7 @ empty )
!= ( sk6 @ empty ) ),
inference(simp,[status(thm)],[146]) ).
thf(148,plain,
sk7 != sk6,
inference(simp,[status(thm)],[147]) ).
thf(32,plain,
sk4 @ relation,
inference(cnfConj,[status(thm)],[29]) ).
thf(11,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(58,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(59,plain,
! [A: $i] : ( A @ ( A @ sk8 @ element ) ),
inference(cnf,[status(esa)],[58]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(49,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(76,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(36,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(37,plain,
~ ? [A: $i] :
( ? [B: $i] :
( ( B @ empty )
& ( A != B ) )
& ( A @ empty ) ),
inference(miniscope,[status(thm)],[36]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ( A = B )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[37]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( A @ empty )
| ( A = B ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(101,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(cnf,[status(esa)],[100]) ).
thf(103,plain,
empty_set @ relation,
inference(cnfConj,[status(thm)],[101]) ).
thf(25,axiom,
! [A: $i] : ( A @ identity_relation @ relation ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(139,plain,
! [A: $i] : ( A @ identity_relation @ relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(140,plain,
! [A: $i] : ( A @ identity_relation @ relation ),
inference(cnf,[status(esa)],[139]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ empty ) )
=> ( ( A @ ( B @ relation_composition ) @ relation )
& ( A @ ( B @ relation_composition ) @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(66,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ empty ) )
=> ( ( A @ ( B @ relation_composition ) @ relation )
& ( A @ ( B @ relation_composition ) @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(158,plain,
( ( ( sk10 @ empty )
!= ( sk9 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[64,74]) ).
thf(159,plain,
( ( sk10 @ empty )
!= ( sk9 @ empty ) ),
inference(simp,[status(thm)],[158]) ).
thf(162,plain,
sk10 != sk9,
inference(simp,[status(thm)],[159]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ empty ) )
=> ( ( B @ ( A @ relation_composition ) @ relation )
& ( B @ ( A @ relation_composition ) @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(112,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ empty ) )
=> ( ( B @ ( A @ relation_composition ) @ relation )
& ( B @ ( A @ relation_composition ) @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(354,plain,
! [B: $i,A: $i] :
( ( B != sk4 )
| ( A @ relation )
| ~ ( B @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[39,32]) ).
thf(355,plain,
! [A: $i] :
( ( A @ relation )
| ~ ( sk4 @ empty )
| ~ ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[354:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(182,plain,
( ( ( sk4 @ ( sk3 @ identity_relation @ relation_composition ) @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) )
!= ( sk4 @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) ) )
| ~ sk5
| ~ $true
| ~ ( sk3 @ ( sk1 @ in ) )
| ~ sk5 ),
inference(paramod_ordered,[status(thm)],[31,33]) ).
thf(183,plain,
( ( ( sk4 @ ( sk3 @ identity_relation @ relation_composition ) @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) )
!= ( sk4 @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) ) )
| ~ ( sk3 @ ( sk1 @ in ) )
| ~ sk5 ),
inference(simp,[status(thm)],[182]) ).
thf(193,plain,
( ( ( sk4 @ ( sk3 @ identity_relation @ relation_composition ) )
!= sk4 )
| ( ( sk2 @ ( sk1 @ ordered_pair ) )
!= ( sk2 @ ( sk1 @ ordered_pair ) ) )
| ~ ( sk3 @ ( sk1 @ in ) )
| ~ sk5 ),
inference(simp,[status(thm)],[183]) ).
thf(194,plain,
( ( ( sk4 @ ( sk3 @ identity_relation @ relation_composition ) )
!= sk4 )
| ~ ( sk3 @ ( sk1 @ in ) )
| ~ sk5 ),
inference(simp,[status(thm)],[193]) ).
thf(27,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(143,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(144,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ ordered_pair ) @ empty ),
inference(miniscope,[status(thm)],[143]) ).
thf(145,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ordered_pair ) @ empty ),
inference(cnf,[status(esa)],[144]) ).
thf(199,plain,
! [A: $i] :
( ( ( A @ singleton @ empty )
!= ( sk9 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[64,47]) ).
thf(200,plain,
! [A: $i] :
( ( A @ singleton @ empty )
!= ( sk9 @ empty ) ),
inference(simp,[status(thm)],[199]) ).
thf(203,plain,
! [A: $i] :
( ( A @ singleton )
!= sk9 ),
inference(simp,[status(thm)],[200]) ).
thf(20,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(104,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(75,plain,
sk10 @ relation,
inference(cnfConj,[status(thm)],[73]) ).
thf(149,plain,
( ( ( sk7 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,44]) ).
thf(150,plain,
( ( sk7 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[149]) ).
thf(151,plain,
sk7 != empty_set,
inference(simp,[status(thm)],[150]) ).
thf(164,plain,
( ( ( sk4 @ ( sk3 @ identity_relation @ relation_composition ) @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) )
!= ( sk3 @ ( sk1 @ in ) ) )
| ~ $true
| sk5
| sk5 ),
inference(paramod_ordered,[status(thm)],[35,30]) ).
thf(165,plain,
( ( ( sk4 @ ( sk3 @ identity_relation @ relation_composition ) @ ( sk2 @ ( sk1 @ ordered_pair ) @ in ) )
!= ( sk3 @ ( sk1 @ in ) ) )
| sk5 ),
inference(simp,[status(thm)],[164]) ).
thf(168,plain,
( ( ( sk4 @ ( sk3 @ identity_relation @ relation_composition ) )
!= sk3 )
| ( ( sk2 @ ( sk1 @ ordered_pair ) )
!= sk1 )
| sk5 ),
inference(simp,[status(thm)],[165]) ).
thf(160,plain,
( ( ( sk9 @ empty )
!= ( sk7 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[64,44]) ).
thf(161,plain,
( ( sk9 @ empty )
!= ( sk7 @ empty ) ),
inference(simp,[status(thm)],[160]) ).
thf(163,plain,
sk9 != sk7,
inference(simp,[status(thm)],[161]) ).
thf(14665,plain,
$false,
inference(e,[status(thm)],[42,65,41,35,48,31,107,100,170,202,52,110,587,157,57,78,116,74,60,201,28,70,33,156,141,148,45,64,32,34,44,59,54,49,76,39,103,140,66,162,112,355,194,145,72,143,203,104,40,55,139,75,58,151,36,168,30,47,163,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU191+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.09 % 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
% 0.16/0.42 % Computer : n015.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 08:50:28 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 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
% 1.26/1.23 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.58/1.48 % [INFO] Parsing done (244ms).
% 1.58/1.49 % [INFO] Running in sequential loop mode.
% 2.52/1.81 % [INFO] eprover registered as external prover.
% 2.52/1.82 % [INFO] Scanning for conjecture ...
% 2.76/1.90 % [INFO] Found a conjecture (or negated_conjecture) and 30 axioms. Running axiom selection ...
% 2.76/1.96 % [INFO] Axiom selection finished. Selected 25 axioms (removed 5 axioms).
% 2.76/1.99 % [INFO] Problem is first-order (TPTP FOF).
% 2.76/2.00 % [INFO] Type checking passed.
% 2.76/2.00 % [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 ...
% 56.04/11.15 % External prover 'e' found a proof!
% 56.04/11.15 % [INFO] Killing All external provers ...
% 56.04/11.15 % Time passed: 10544ms (effective reasoning time: 9655ms)
% 56.04/11.15 % 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)>
% 56.04/11.15 % Axioms used in derivation (25): fc1_zfmisc_1, fc9_relat_1, cc1_relat_1, t6_boole, fc3_subset_1, fc2_subset_1, fc10_relat_1, d8_relat_1, rc2_relat_1, dt_k6_relat_1, t2_subset, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, d5_tarski, fc4_relat_1, t1_subset, t7_boole, d10_relat_1, existence_m1_subset_1, commutativity_k2_tarski, rc1_relat_1, dt_k5_relat_1, t8_boole, rc1_xboole_0
% 56.04/11.15 % No. of inferences in proof: 128
% 56.04/11.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 10544 ms resp. 9655 ms w/o parsing
% 48.47/11.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 48.47/11.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------