%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU044+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 : n007.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 08:37:30 AM UTC 2026
% Result : Theorem 13.87s 4.74s
% Output : Refutation 12.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 44
% Syntax : Number of formulae : 142 ( 56 unt; 0 typ; 10 def)
% Number of atoms : 402 ( 54 equ; 0 cnn)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 928 ( 93 ~; 41 |; 111 &; 623 @)
% ( 5 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 14 con; 0-2 aty)
% Number of variables : 125 ( 0 ^; 93 !; 22 ?; 125 :)
% ( 0 !>; 0 ?*; 0 @-; 10 @+)
% Comments :
%------------------------------------------------------------------------------
thf(relation_decl,type,
relation: $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(relation_dom_decl,type,
relation_dom: $i > $i ).
thf(relation_rng_restriction_decl,type,
relation_rng_restriction: $i > $i > $i ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
thf(relation_empty_yielding_decl,type,
relation_empty_yielding: $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: $o ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk12_decl,type,
sk12: $i ).
thf(sk13_decl,type,
sk13: $i ).
thf(sk14_decl,type,
sk14: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( ( ( A @ ( B @ ( C @ apply ) @ in ) )
& ( C @ relation_dom @ ( B @ in ) ) )
=> ( C @ ( A @ relation_rng_restriction ) @ relation_dom @ ( B @ in ) ) )
& ( ( C @ ( A @ relation_rng_restriction ) @ relation_dom @ ( B @ in ) )
=> ( ( A @ ( B @ ( C @ apply ) @ in ) )
& ( C @ relation_dom @ ( B @ in ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( ( ( sk1 @ ( A @ ( B @ apply ) @ in ) )
& ( B @ relation_dom @ ( A @ in ) ) )
=> ( B @ ( sk1 @ relation_rng_restriction ) @ relation_dom @ ( A @ in ) ) )
& ( ( B @ ( sk1 @ relation_rng_restriction ) @ relation_dom @ ( A @ in ) )
=> ( ( sk1 @ ( A @ ( B @ apply ) @ in ) )
& ( B @ relation_dom @ ( A @ in ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( A @ function )
& ( A @ relation ) )
=> ( ( ( ( sk1 @ ( sk2 @ ( A @ apply ) @ in ) )
& ( A @ relation_dom @ ( sk2 @ in ) ) )
=> ( A @ ( sk1 @ relation_rng_restriction ) @ relation_dom @ ( sk2 @ in ) ) )
& ( ( A @ ( sk1 @ relation_rng_restriction ) @ relation_dom @ ( sk2 @ in ) )
=> ( ( sk1 @ ( sk2 @ ( A @ apply ) @ in ) )
& ( A @ relation_dom @ ( sk2 @ in ) ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
( ( A @ relation )
& ( A @ empty ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ) ) ) ).
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(88,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(15,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(84,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(24,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(114,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(115,plain,
( ( sk13 @ relation )
& ~ ( sk13 @ empty ) ),
inference(cnf,[status(esa)],[114]) ).
thf(116,plain,
~ ( sk13 @ empty ),
inference(cnfConj,[status(thm)],[115]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( C @ ( A @ relation_rng_restriction ) @ relation_dom @ ( B @ in ) )
<=> ( ( A @ ( B @ ( C @ apply ) @ in ) )
& ( C @ relation_dom @ ( B @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_funct_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( C @ ( A @ relation_rng_restriction ) @ relation_dom @ ( B @ in ) )
<=> ( ( A @ ( B @ ( C @ apply ) @ in ) )
& ( C @ relation_dom @ ( B @ in ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(36,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( ( ( A @ ( B @ ( C @ apply ) @ in ) )
& ( C @ relation_dom @ ( B @ in ) ) )
=> ( C @ ( A @ relation_rng_restriction ) @ relation_dom @ ( B @ in ) ) )
& ( ( C @ ( A @ relation_rng_restriction ) @ relation_dom @ ( B @ in ) )
=> ( ( A @ ( B @ ( C @ apply ) @ in ) )
& ( C @ relation_dom @ ( B @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(37,plain,
( ( ~ ( sk3 @ ( sk1 @ relation_rng_restriction ) @ relation_dom @ ( sk2 @ in ) )
| sk4 )
& ( ( sk1 @ ( sk2 @ ( sk3 @ apply ) @ in ) )
| sk4 )
& ( ( sk3 @ relation_dom @ ( sk2 @ in ) )
| sk4 )
& ( ~ sk4
| ~ ( sk1 @ ( sk2 @ ( sk3 @ apply ) @ in ) )
| ~ ( sk3 @ relation_dom @ ( sk2 @ in ) ) )
& ( ~ sk4
| ( sk3 @ ( sk1 @ relation_rng_restriction ) @ relation_dom @ ( sk2 @ in ) ) )
& ( sk3 @ function )
& ( sk3 @ relation ) ),
inference(cnf,[status(esa)],[36]) ).
thf(41,plain,
sk3 @ relation,
inference(cnfConj,[status(thm)],[37]) ).
thf(42,plain,
( ~ sk4
| ~ ( sk1 @ ( sk2 @ ( sk3 @ apply ) @ in ) )
| ~ ( sk3 @ relation_dom @ ( sk2 @ in ) ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(222,plain,
( ~ $true
| ( ( sk1 @ ( sk2 @ ( sk3 @ apply ) @ in ) )
!= ( sk3 @ relation_dom @ ( sk2 @ in ) ) )
| ~ sk4
| ~ ( sk3 @ relation_dom @ ( sk2 @ in ) ) ),
inference(eqfactor_ordered,[status(thm)],[42]) ).
thf(226,plain,
( ( ( sk3 @ relation_dom )
!= sk1 )
| ( ( sk2 @ ( sk3 @ apply ) )
!= sk2 )
| ~ sk4
| ~ ( sk3 @ relation_dom @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[222]) ).
thf(9,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(63,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(67,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(43,plain,
( ( sk3 @ relation_dom @ ( sk2 @ in ) )
| sk4 ),
inference(cnfConj,[status(thm)],[37]) ).
thf(39,plain,
( ~ ( sk3 @ ( sk1 @ relation_rng_restriction ) @ relation_dom @ ( sk2 @ in ) )
| sk4 ),
inference(cnfConj,[status(thm)],[37]) ).
thf(192,plain,
( ( ( sk3 @ ( sk1 @ relation_rng_restriction ) @ relation_dom @ ( sk2 @ in ) )
!= ( sk3 @ relation_dom @ ( sk2 @ in ) ) )
| ~ $true
| sk4
| sk4 ),
inference(paramod_ordered,[status(thm)],[43,39]) ).
thf(193,plain,
( ( ( sk3 @ ( sk1 @ relation_rng_restriction ) @ relation_dom @ ( sk2 @ in ) )
!= ( sk3 @ relation_dom @ ( sk2 @ in ) ) )
| sk4 ),
inference(simp,[status(thm)],[192]) ).
thf(195,plain,
( ( ( sk3 @ ( sk1 @ relation_rng_restriction ) @ relation_dom )
!= ( sk3 @ relation_dom ) )
| ( sk2 != sk2 )
| sk4 ),
inference(simp,[status(thm)],[193]) ).
thf(196,plain,
( ( ( sk3 @ ( sk1 @ relation_rng_restriction ) @ relation_dom )
!= ( sk3 @ relation_dom ) )
| sk4 ),
inference(simp,[status(thm)],[195]) ).
thf(207,plain,
( ( ( sk3 @ ( sk1 @ relation_rng_restriction ) )
!= sk3 )
| sk4 ),
inference(simp,[status(thm)],[196]) ).
thf(26,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(120,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(19,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(96,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(97,plain,
( ( sk10 @ relation )
& ( sk10 @ empty ) ),
inference(cnf,[status(esa)],[96]) ).
thf(98,plain,
sk10 @ empty,
inference(cnfConj,[status(thm)],[97]) ).
thf(198,plain,
( ( ( sk13 @ empty )
!= ( sk10 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[98,116]) ).
thf(199,plain,
( ( sk13 @ empty )
!= ( sk10 @ empty ) ),
inference(simp,[status(thm)],[198]) ).
thf(202,plain,
sk13 != sk10,
inference(simp,[status(thm)],[199]) ).
thf(7,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(56,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(153,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(35,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(174,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(5,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(51,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(52,plain,
sk5 @ empty,
inference(cnf,[status(esa)],[51]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(157,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(6,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(53,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(54,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[53]) ).
thf(55,plain,
~ ( sk6 @ empty ),
inference(cnf,[status(esa)],[54]) ).
thf(186,plain,
( ( ( sk6 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[56,55]) ).
thf(187,plain,
( ( sk6 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[186]) ).
thf(189,plain,
sk6 != empty_set,
inference(simp,[status(thm)],[187]) ).
thf(3,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(45,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(46,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(cnf,[status(esa)],[45]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(57,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)],[8]) ).
thf(117,plain,
sk13 @ relation,
inference(cnfConj,[status(thm)],[115]) ).
thf(20,axiom,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(100,plain,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(101,plain,
( ( sk11 @ one_to_one )
& ( sk11 @ function )
& ( sk11 @ relation ) ),
inference(cnf,[status(esa)],[100]) ).
thf(102,plain,
sk11 @ relation,
inference(cnfConj,[status(thm)],[101]) ).
thf(38,plain,
sk3 @ function,
inference(cnfConj,[status(thm)],[37]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(70,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( B @ ( A @ relation_rng_restriction ) @ function )
& ( B @ ( A @ relation_rng_restriction ) @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
thf(165,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( B @ ( A @ relation_rng_restriction ) @ function )
& ( B @ ( A @ relation_rng_restriction ) @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(184,plain,
( ( ( sk13 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[56,116]) ).
thf(185,plain,
( ( sk13 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[184]) ).
thf(188,plain,
sk13 != empty_set,
inference(simp,[status(thm)],[185]) ).
thf(34,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(169,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(23,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(109,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( B
= ( C @ ( A @ relation_rng_restriction ) ) )
<=> ( ! [D: $i] :
( ( B @ relation_dom @ ( D @ in ) )
=> ( ( D @ ( B @ apply ) )
= ( D @ ( C @ apply ) ) ) )
& ! [D: $i] :
( ( B @ relation_dom @ ( D @ in ) )
<=> ( ( A @ ( D @ ( C @ apply ) @ in ) )
& ( C @ relation_dom @ ( D @ in ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_1) ).
thf(124,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ! [C: $i] :
( ( ( C @ function )
& ( C @ relation ) )
=> ( ( ( ! [D: $i] :
( ( B @ relation_dom @ ( D @ in ) )
=> ( ( D @ ( B @ apply ) )
= ( D @ ( C @ apply ) ) ) )
& ! [D: $i] :
( ( ( ( A @ ( D @ ( C @ apply ) @ in ) )
& ( C @ relation_dom @ ( D @ in ) ) )
=> ( B @ relation_dom @ ( D @ in ) ) )
& ( ( B @ relation_dom @ ( D @ in ) )
=> ( ( A @ ( D @ ( C @ apply ) @ in ) )
& ( C @ relation_dom @ ( D @ in ) ) ) ) ) )
=> ( B
= ( C @ ( A @ relation_rng_restriction ) ) ) )
& ( ( B
= ( C @ ( A @ relation_rng_restriction ) ) )
=> ( ! [D: $i] :
( ( B @ relation_dom @ ( D @ in ) )
=> ( ( D @ ( B @ apply ) )
= ( D @ ( C @ apply ) ) ) )
& ! [D: $i] :
( ( ( ( A @ ( D @ ( C @ apply ) @ in ) )
& ( C @ relation_dom @ ( D @ in ) ) )
=> ( B @ relation_dom @ ( D @ in ) ) )
& ( ( B @ relation_dom @ ( D @ in ) )
=> ( ( A @ ( D @ ( C @ apply ) @ in ) )
& ( C @ relation_dom @ ( D @ in ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(13,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(77,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(12,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(73,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(105,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(31,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(161,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)],[31]) ).
thf(178,plain,
( ( ( sk6 @ empty )
!= ( sk5 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[52,55]) ).
thf(179,plain,
( ( sk6 @ empty )
!= ( sk5 @ empty ) ),
inference(simp,[status(thm)],[178]) ).
thf(180,plain,
sk6 != sk5,
inference(simp,[status(thm)],[179]) ).
thf(44,plain,
( ( sk1 @ ( sk2 @ ( sk3 @ apply ) @ in ) )
| sk4 ),
inference(cnfConj,[status(thm)],[37]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(118,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(110,plain,
( ( sk12 @ function )
& ( sk12 @ empty )
& ( sk12 @ relation ) ),
inference(cnf,[status(esa)],[109]) ).
thf(113,plain,
sk12 @ function,
inference(cnfConj,[status(thm)],[110]) ).
thf(103,plain,
sk11 @ function,
inference(cnfConj,[status(thm)],[101]) ).
thf(17,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(91,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ ( A @ relation_rng_restriction ) @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(155,plain,
! [A: $i,B: $i] :
( ( B @ relation )
=> ( B @ ( A @ relation_rng_restriction ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(112,plain,
sk12 @ empty,
inference(cnfConj,[status(thm)],[110]) ).
thf(121,plain,
( ( sk14 @ relation_empty_yielding )
& ( sk14 @ relation ) ),
inference(cnf,[status(esa)],[120]) ).
thf(123,plain,
sk14 @ relation_empty_yielding,
inference(cnfConj,[status(thm)],[121]) ).
thf(190,plain,
( ( ( sk1 @ ( sk2 @ ( sk3 @ apply ) @ in ) )
!= ( sk3 @ ( sk1 @ relation_rng_restriction ) @ relation_dom @ ( sk2 @ in ) ) )
| ~ $true
| sk4
| sk4 ),
inference(paramod_ordered,[status(thm)],[44,39]) ).
thf(191,plain,
( ( ( sk1 @ ( sk2 @ ( sk3 @ apply ) @ in ) )
!= ( sk3 @ ( sk1 @ relation_rng_restriction ) @ relation_dom @ ( sk2 @ in ) ) )
| sk4 ),
inference(simp,[status(thm)],[190]) ).
thf(194,plain,
( ( ( sk3 @ ( sk1 @ relation_rng_restriction ) @ relation_dom )
!= sk1 )
| ( ( sk2 @ ( sk3 @ apply ) )
!= sk2 )
| sk4 ),
inference(simp,[status(thm)],[191]) ).
thf(99,plain,
sk10 @ relation,
inference(cnfConj,[status(thm)],[97]) ).
thf(85,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(cnf,[status(esa)],[84]) ).
thf(87,plain,
empty_set @ relation,
inference(cnfConj,[status(thm)],[85]) ).
thf(200,plain,
( ( ( sk10 @ empty )
!= ( sk6 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[98,55]) ).
thf(201,plain,
( ( sk10 @ empty )
!= ( sk6 @ empty ) ),
inference(simp,[status(thm)],[200]) ).
thf(203,plain,
sk10 != sk6,
inference(simp,[status(thm)],[201]) ).
thf(104,plain,
sk11 @ one_to_one,
inference(cnfConj,[status(thm)],[101]) ).
thf(40,plain,
( ~ sk4
| ( sk3 @ ( sk1 @ relation_rng_restriction ) @ relation_dom @ ( sk2 @ in ) ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(181,plain,
( ( ( sk13 @ empty )
!= ( sk5 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[52,116]) ).
thf(182,plain,
( ( sk13 @ empty )
!= ( sk5 @ empty ) ),
inference(simp,[status(thm)],[181]) ).
thf(183,plain,
sk13 != sk5,
inference(simp,[status(thm)],[182]) ).
thf(22,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(107,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(14,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(79,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)],[14]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(94,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(47,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(163,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(111,plain,
sk12 @ relation,
inference(cnfConj,[status(thm)],[110]) ).
thf(122,plain,
sk14 @ relation,
inference(cnfConj,[status(thm)],[121]) ).
thf(228,plain,
( ( ( sk13 @ empty )
!= ( sk12 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[112,116]) ).
thf(229,plain,
( ( sk13 @ empty )
!= ( sk12 @ empty ) ),
inference(simp,[status(thm)],[228]) ).
thf(232,plain,
sk13 != sk12,
inference(simp,[status(thm)],[229]) ).
thf(696,plain,
$false,
inference(e,[status(thm)],[88,84,116,41,226,63,67,43,207,120,202,56,153,174,42,52,196,157,189,46,57,117,102,38,70,165,188,53,169,109,124,77,96,73,105,45,161,180,44,118,113,39,98,103,91,155,112,123,194,99,87,203,104,40,55,114,36,51,183,107,79,94,47,163,111,122,232,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU044+1 : TPTP v9.3.1. Released v3.2.0.
% 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
% 0.11/0.39 % Computer : n007.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sat Sep 26 08:30:24 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 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
% 1.15/1.07 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.59/1.38 % [INFO] Parsing done (306ms).
% 1.91/1.40 % [INFO] Running in sequential loop mode.
% 2.73/1.99 % [INFO] eprover registered as external prover.
% 2.73/2.00 % [INFO] Scanning for conjecture ...
% 3.08/2.10 % [INFO] Found a conjecture (or negated_conjecture) and 33 axioms. Running axiom selection ...
% 3.41/2.22 % [INFO] Axiom selection finished. Selected 33 axioms (removed 0 axioms).
% 3.64/2.30 % [INFO] Problem is first-order (TPTP FOF).
% 3.64/2.31 % [INFO] Type checking passed.
% 3.64/2.32 % [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 ...
% 13.87/4.73 % External prover 'e' found a proof!
% 13.87/4.73 % [INFO] Killing All external provers ...
% 13.87/4.73 % Time passed: 4137ms (effective reasoning time: 3320ms)
% 13.87/4.74 % 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)>
% 13.87/4.74 % Axioms used in derivation (33): t85_funct_1, rc3_funct_1, cc1_relat_1, rc1_funct_1, t5_subset, t4_subset, fc5_relat_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, fc4_relat_1, t1_subset, rc3_relat_1, t6_boole, rc2_subset_1, t7_boole, cc1_funct_1, fc1_subset_1, fc5_funct_1, rc2_funct_1, rc1_subset_1, cc2_funct_1, t3_subset, existence_m1_subset_1, dt_k8_relat_1, rc2_relat_1, rc1_relat_1, reflexivity_r1_tarski, t8_boole, rc1_xboole_0, t2_subset, fc7_relat_1, fc12_relat_1
% 13.87/4.74 % No. of inferences in proof: 132
% 13.87/4.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4137 ms resp. 3320 ms w/o parsing
% 12.84/4.88 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.84/4.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------