%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU221+3 : TPTP v9.3.1. Released v3.2.0.
% 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 : n026.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 08:38:05 AM UTC 2026
% Result : Theorem 20.44s 10.91s
% Output : Refutation 20.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 50
% Syntax : Number of formulae : 158 ( 64 unt; 0 typ; 9 def)
% Number of atoms : 438 ( 68 equ; 0 cnn)
% Maximal formula atoms : 25 ( 2 avg)
% Number of connectives : 909 ( 80 ~; 16 |; 143 &; 594 @)
% ( 3 <=>; 73 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 12 con; 0-2 aty)
% Number of variables : 153 ( 0 ^; 122 !; 22 ?; 153 :)
% ( 0 !>; 0 ?*; 0 @-; 9 @+)
% Comments :
%------------------------------------------------------------------------------
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(function_inverse_decl,type,
function_inverse: $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(relation_empty_yielding_decl,type,
relation_empty_yielding: $i > $o ).
thf(relation_rng_decl,type,
relation_rng: $i > $i ).
thf(relation_composition_decl,type,
relation_composition: $i > $i > $i ).
thf(relation_dom_decl,type,
relation_dom: $i > $i ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $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(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk14_decl,type,
sk14: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ( A @ function_inverse @ one_to_one ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
( ( A @ function )
& ( A @ relation ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i] :
( ( A @ relation )
& ( A @ empty ) ) ) ) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) )
=> ( C @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(88,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)],[16]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(51,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)],[4]) ).
thf(52,plain,
( ! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( B @ powerset @ ( A @ element ) ) )
& ! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(miniscope,[status(thm)],[51]) ).
thf(53,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ powerset @ ( C @ element ) )
| ~ ( D @ ( C @ subset ) ) )
& ( ( B @ ( A @ subset ) )
| ~ ( B @ powerset @ ( A @ element ) ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( B @ powerset @ ( A @ element ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[53]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( B @ powerset @ ( A @ element ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(38,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(165,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(22,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(106,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(107,plain,
( ( sk7 @ relation_empty_yielding )
& ( sk7 @ relation ) ),
inference(cnf,[status(esa)],[106]) ).
thf(109,plain,
sk7 @ relation_empty_yielding,
inference(cnfConj,[status(thm)],[107]) ).
thf(28,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ function_inverse @ function )
& ( A @ function_inverse @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
thf(129,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ function_inverse @ function )
& ( A @ function_inverse @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(24,axiom,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(114,plain,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(115,plain,
( ( sk8 @ one_to_one )
& ( sk8 @ function )
& ( sk8 @ relation ) ),
inference(cnf,[status(esa)],[114]) ).
thf(118,plain,
sk8 @ one_to_one,
inference(cnfConj,[status(thm)],[115]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ( A @ function_inverse @ one_to_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ( A @ function_inverse @ one_to_one ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(43,plain,
~ ! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ( A @ function_inverse @ one_to_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(44,plain,
( ~ ( sk1 @ function_inverse @ one_to_one )
& ( sk1 @ one_to_one )
& ( sk1 @ function )
& ( sk1 @ relation ) ),
inference(cnf,[status(esa)],[43]) ).
thf(47,plain,
sk1 @ one_to_one,
inference(cnfConj,[status(thm)],[44]) ).
thf(48,plain,
~ ( sk1 @ function_inverse @ one_to_one ),
inference(cnfConj,[status(thm)],[44]) ).
thf(229,plain,
( ( ( sk1 @ function_inverse @ one_to_one )
!= ( sk1 @ one_to_one ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,48]) ).
thf(230,plain,
( ( sk1 @ function_inverse @ one_to_one )
!= ( sk1 @ one_to_one ) ),
inference(simp,[status(thm)],[229]) ).
thf(231,plain,
( ( sk1 @ function_inverse )
!= sk1 ),
inference(simp,[status(thm)],[230]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_rng @ relation )
& ( A @ relation_rng @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(110,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_rng @ relation )
& ( A @ relation_rng @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(36,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(157,plain,
! [A: $i,B: $i] :
( ( ( B @ relation )
& ( A @ relation ) )
=> ( B @ ( A @ relation_composition ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(46,plain,
sk1 @ function,
inference(cnfConj,[status(thm)],[44]) ).
thf(35,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(152,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(14,axiom,
empty_set @ empty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(84,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(33,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(146,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(147,plain,
( ( sk10 @ relation )
& ~ ( sk10 @ empty ) ),
inference(cnf,[status(esa)],[146]) ).
thf(148,plain,
~ ( sk10 @ empty ),
inference(cnfConj,[status(thm)],[147]) ).
thf(225,plain,
( ( ( sk10 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[84,148]) ).
thf(226,plain,
( ( sk10 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[225]) ).
thf(228,plain,
sk10 != empty_set,
inference(simp,[status(thm)],[226]) ).
thf(5,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(57,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(40,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(179,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(6,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(61,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(29,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_rng @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(133,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_rng @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(116,plain,
sk8 @ relation,
inference(cnfConj,[status(thm)],[115]) ).
thf(117,plain,
sk8 @ function,
inference(cnfConj,[status(thm)],[115]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(85,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(21,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(102,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(92,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(7,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(65,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(20,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ empty )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(97,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)],[20]) ).
thf(153,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(cnf,[status(esa)],[152]) ).
thf(156,plain,
empty_set @ relation_empty_yielding,
inference(cnfConj,[status(thm)],[153]) ).
thf(39,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
<=> ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ apply ) )
= ( C @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( C @ in ) )
& ( A @ relation_dom @ ( B @ in ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
thf(169,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ apply ) )
= ( C @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( C @ in ) )
& ( A @ relation_dom @ ( B @ in ) ) )
=> ( B = C ) )
=> ( A @ one_to_one ) )
& ( ( A @ one_to_one )
=> ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ apply ) )
= ( C @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( C @ in ) )
& ( A @ relation_dom @ ( B @ in ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(32,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(141,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(73,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(103,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(cnf,[status(esa)],[102]) ).
thf(105,plain,
empty_set @ relation,
inference(cnfConj,[status(thm)],[103]) ).
thf(45,plain,
sk1 @ relation,
inference(cnfConj,[status(thm)],[44]) ).
thf(149,plain,
sk10 @ relation,
inference(cnfConj,[status(thm)],[147]) ).
thf(9,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(71,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ powerset @ ( A @ element ) ) ),
inference(cnfConj,[status(thm)],[53]) ).
thf(142,plain,
( ( sk9 @ function )
& ( sk9 @ empty )
& ( sk9 @ relation ) ),
inference(cnf,[status(esa)],[141]) ).
thf(144,plain,
sk9 @ empty,
inference(cnfConj,[status(thm)],[142]) ).
thf(3,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(49,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(180,plain,
( ( sk14 @ relation )
& ( sk14 @ empty ) ),
inference(cnf,[status(esa)],[179]) ).
thf(181,plain,
sk14 @ empty,
inference(cnfConj,[status(thm)],[180]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( ( B @ relation_rng @ ( A @ in ) )
& ( B @ one_to_one ) )
=> ( ( A
= ( A @ ( B @ ( B @ function_inverse @ relation_composition ) @ apply ) ) )
& ( A
= ( A @ ( B @ function_inverse @ apply ) @ ( B @ apply ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
thf(159,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( ( B @ relation_rng @ ( A @ in ) )
& ( B @ one_to_one ) )
=> ( ( A
= ( A @ ( B @ ( B @ function_inverse @ relation_composition ) @ apply ) ) )
& ( A
= ( A @ ( B @ function_inverse @ apply ) @ ( B @ apply ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(42,axiom,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ! [B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( B
= ( A @ function_inverse ) )
<=> ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( ( D
= ( C @ ( B @ apply ) ) )
& ( A @ relation_rng @ ( C @ in ) ) ) )
& ( ( ( D
= ( C @ ( B @ apply ) ) )
& ( A @ relation_rng @ ( C @ in ) ) )
=> ( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) )
& ( ( B @ relation_dom )
= ( A @ relation_rng ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
thf(187,plain,
! [A: $i] :
( ( ( A @ function )
& ( A @ relation ) )
=> ( ( A @ one_to_one )
=> ! [B: $i] :
( ( ( B @ function )
& ( B @ relation ) )
=> ( ( ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( ( D
= ( C @ ( B @ apply ) ) )
& ( A @ relation_rng @ ( C @ in ) ) ) )
& ( ( ( D
= ( C @ ( B @ apply ) ) )
& ( A @ relation_rng @ ( C @ in ) ) )
=> ( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) )
& ( ( B @ relation_dom )
= ( A @ relation_rng ) ) )
=> ( B
= ( A @ function_inverse ) ) )
& ( ( B
= ( A @ function_inverse ) )
=> ( ! [C: $i,D: $i] :
( ( ( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) )
=> ( ( D
= ( C @ ( B @ apply ) ) )
& ( A @ relation_rng @ ( C @ in ) ) ) )
& ( ( ( D
= ( C @ ( B @ apply ) ) )
& ( A @ relation_rng @ ( C @ in ) ) )
=> ( ( C
= ( D @ ( A @ apply ) ) )
& ( A @ relation_dom @ ( D @ in ) ) ) ) )
& ( ( B @ relation_dom )
= ( A @ relation_rng ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(72,plain,
sk5 @ empty,
inference(cnf,[status(esa)],[71]) ).
thf(13,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(81,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(82,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[81]) ).
thf(83,plain,
~ ( sk6 @ empty ),
inference(cnf,[status(esa)],[82]) ).
thf(217,plain,
( ( ( sk6 @ empty )
!= ( sk5 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72,83]) ).
thf(218,plain,
( ( sk6 @ empty )
!= ( sk5 @ empty ) ),
inference(simp,[status(thm)],[217]) ).
thf(219,plain,
sk6 != sk5,
inference(simp,[status(thm)],[218]) ).
thf(11,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(76,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(236,plain,
( ( ( sk10 @ empty )
!= ( sk9 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[144,148]) ).
thf(237,plain,
( ( sk10 @ empty )
!= ( sk9 @ empty ) ),
inference(simp,[status(thm)],[236]) ).
thf(240,plain,
sk10 != sk9,
inference(simp,[status(thm)],[237]) ).
thf(108,plain,
sk7 @ relation,
inference(cnfConj,[status(thm)],[107]) ).
thf(30,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(135,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)],[30]) ).
thf(238,plain,
( ( ( sk9 @ empty )
!= ( sk6 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[144,83]) ).
thf(239,plain,
( ( sk9 @ empty )
!= ( sk6 @ empty ) ),
inference(simp,[status(thm)],[238]) ).
thf(241,plain,
sk9 != sk6,
inference(simp,[status(thm)],[239]) ).
thf(166,plain,
( ( sk11 @ function )
& ( sk11 @ relation ) ),
inference(cnf,[status(esa)],[165]) ).
thf(167,plain,
sk11 @ relation,
inference(cnfConj,[status(thm)],[166]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation )
& ( A @ function )
& ( A @ relation ) )
=> ( ( B @ ( A @ relation_composition ) @ function )
& ( B @ ( A @ relation_composition ) @ relation ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(123,plain,
! [A: $i,B: $i] :
( ( ( B @ function )
& ( B @ relation )
& ( A @ function )
& ( A @ relation ) )
=> ( ( B @ ( A @ relation_composition ) @ function )
& ( B @ ( A @ relation_composition ) @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(145,plain,
sk9 @ function,
inference(cnfConj,[status(thm)],[142]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(150,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(50,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(cnf,[status(esa)],[49]) ).
thf(8,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(67,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(182,plain,
sk14 @ relation,
inference(cnfConj,[status(thm)],[180]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(127,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(143,plain,
sk9 @ relation,
inference(cnfConj,[status(thm)],[142]) ).
thf(31,axiom,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(139,plain,
! [A: $i] :
( ( ( A @ relation )
& ~ ( A @ empty ) )
=> ~ ( A @ relation_dom @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(25,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(119,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)],[25]) ).
thf(233,plain,
( ( ( sk1 @ function_inverse @ one_to_one )
!= ( sk8 @ one_to_one ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[118,48]) ).
thf(234,plain,
( ( sk1 @ function_inverse @ one_to_one )
!= ( sk8 @ one_to_one ) ),
inference(simp,[status(thm)],[233]) ).
thf(235,plain,
( ( sk1 @ function_inverse )
!= sk8 ),
inference(simp,[status(thm)],[234]) ).
thf(168,plain,
sk11 @ function,
inference(cnfConj,[status(thm)],[166]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(183,plain,
! [A: $i] :
( ( A @ empty )
=> ( ( A @ relation_dom @ relation )
& ( A @ relation_dom @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(79,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(94,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(90,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(220,plain,
( ( ( sk10 @ empty )
!= ( sk5 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72,148]) ).
thf(221,plain,
( ( sk10 @ empty )
!= ( sk5 @ empty ) ),
inference(simp,[status(thm)],[220]) ).
thf(222,plain,
sk10 != sk5,
inference(simp,[status(thm)],[221]) ).
thf(250,plain,
( ( ( sk14 @ empty )
!= ( sk10 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[181,148]) ).
thf(251,plain,
( ( sk14 @ empty )
!= ( sk10 @ empty ) ),
inference(simp,[status(thm)],[250]) ).
thf(254,plain,
sk14 != sk10,
inference(simp,[status(thm)],[251]) ).
thf(223,plain,
( ( ( sk6 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[84,83]) ).
thf(224,plain,
( ( sk6 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[223]) ).
thf(227,plain,
sk6 != empty_set,
inference(simp,[status(thm)],[224]) ).
thf(5411,plain,
$false,
inference(e,[status(thm)],[88,56,165,109,129,118,231,47,110,157,46,152,228,57,179,106,84,61,133,116,117,85,102,92,65,97,156,169,141,73,105,148,45,149,71,54,144,49,181,159,187,219,81,76,240,108,135,241,167,123,145,48,150,50,67,182,127,72,143,43,114,139,119,235,168,146,51,183,79,94,90,83,222,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU221+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.11 % 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
% 0.11/5.50 % Computer : n026.cluster.edu
% 0.11/5.50 % Model : x86_64 x86_64
% 0.11/5.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.50 % Memory : 8046.5625MB
% 0.11/5.50 % OS : Linux 6.8.0-71-generic
% 0.11/5.50 % CPULimit : 300
% 0.11/5.50 % WCLimit : 300
% 0.11/5.50 % DateTime : Sat Sep 26 08:56:16 UTC 2026
% 0.11/5.50 % CPUTime :
% 0.11/5.50 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
% 1.43/6.32 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.97/6.63 % [INFO] Parsing done (308ms).
% 1.97/6.65 % [INFO] Running in sequential loop mode.
% 2.98/7.21 % [INFO] eprover registered as external prover.
% 2.98/7.22 % [INFO] Scanning for conjecture ...
% 3.16/7.36 % [INFO] Found a conjecture (or negated_conjecture) and 40 axioms. Running axiom selection ...
% 3.32/7.44 % [INFO] Axiom selection finished. Selected 40 axioms (removed 0 axioms).
% 3.55/7.51 % [INFO] Problem is first-order (TPTP FOF).
% 3.55/7.52 % [INFO] Type checking passed.
% 3.55/7.53 % [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 ...
% 20.44/10.91 % External prover 'e' found a proof!
% 20.44/10.91 % [INFO] Killing All external provers ...
% 20.44/10.91 % Time passed: 5206ms (effective reasoning time: 4248ms)
% 20.44/10.91 % 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)>
% 20.44/10.91 % Axioms used in derivation (40): d8_funct_1, fc9_relat_1, cc1_relat_1, rc1_funct_1, t5_subset, fc5_relat_1, rc2_relat_1, fc6_relat_1, t57_funct_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, fc4_relat_1, t1_subset, rc3_funct_1, fc1_funct_1, rc3_relat_1, t6_boole, rc2_subset_1, t4_subset, dt_k2_funct_1, t7_boole, cc1_funct_1, fc1_subset_1, rc2_funct_1, fc10_relat_1, rc1_subset_1, cc2_funct_1, t3_subset, existence_m1_subset_1, rc1_relat_1, t54_funct_1, dt_k5_relat_1, reflexivity_r1_tarski, t8_boole, rc1_xboole_0, t2_subset, fc7_relat_1, fc12_relat_1, fc8_relat_1
% 20.44/10.91 % No. of inferences in proof: 149
% 20.44/10.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5206 ms resp. 4248 ms w/o parsing
% 20.44/11.00 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.44/11.00 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------