%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU353+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 : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:38:32 AM UTC 2026
% Result : Theorem 5.27s 8.43s
% Output : Refutation 5.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 49
% Syntax : Number of formulae : 100 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 339 ( 15 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 995 ( 51 ~; 2 |; 163 &; 705 @)
% ( 2 <=>; 72 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 28 usr; 2 con; 0-4 aty)
% Number of variables : 199 ( 0 ^; 169 !; 30 ?; 199 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_carrier_decl,type,
empty_carrier: $i > $o ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(the_carrier_decl,type,
the_carrier: $i > $i ).
thf(apply_as_element_decl,type,
apply_as_element: $i > $i > $i > $i > $i ).
thf(identity_on_carrier_decl,type,
identity_on_carrier: $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(relation_of2_decl,type,
relation_of2: $i > $i > $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(quasi_total_decl,type,
quasi_total: $i > $i > $i > $o ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
thf(onto_decl,type,
onto: $i > $i > $i > $o ).
thf(bijective_decl,type,
bijective: $i > $i > $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(relation_decl,type,
relation: $i > $o ).
thf(symmetric_decl,type,
symmetric: $i > $o ).
thf(transitive_decl,type,
transitive: $i > $o ).
thf(reflexive_decl,type,
reflexive: $i > $o ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(identity_relation_decl,type,
identity_relation: $i > $i ).
thf(antisymmetric_decl,type,
antisymmetric: $i > $o ).
thf(identity_as_relation_of_decl,type,
identity_as_relation_of: $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(relation_of2_as_subset_decl,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ in ) )
=> ( ( B @ ( A @ identity_relation @ apply ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
thf(142,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ in ) )
=> ( ( B @ ( A @ identity_relation @ apply ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(31,axiom,
! [A: $i] : ( A @ identity_relation @ relation ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(185,plain,
! [A: $i] : ( A @ identity_relation @ relation ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(13,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(93,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(201,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(27,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(165,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(26,axiom,
! [A: $i] :
? [B: $i] :
( ( A @ ( A @ ( B @ bijective ) ) )
& ( A @ ( A @ ( B @ onto ) ) )
& ( A @ ( A @ ( B @ quasi_total ) ) )
& ( B @ one_to_one )
& ( B @ function )
& ( B @ relation )
& ( A @ ( A @ ( B @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_2) ).
thf(156,plain,
! [A: $i] :
? [B: $i] :
( ( A @ ( A @ ( B @ bijective ) ) )
& ( A @ ( A @ ( B @ onto ) ) )
& ( A @ ( A @ ( B @ quasi_total ) ) )
& ( B @ one_to_one )
& ( B @ function )
& ( B @ relation )
& ( A @ ( A @ ( B @ relation_of2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(29,axiom,
? [A: $i] :
( ( A @ empty )
& ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(173,plain,
? [A: $i] :
( ( A @ empty )
& ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(24,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(148,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(39,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(213,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ identity_on_carrier )
= ( A @ the_carrier @ identity_as_relation_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_grcat_1) ).
thf(226,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ identity_on_carrier )
= ( A @ the_carrier @ identity_as_relation_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(7,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(72,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(36,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(203,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ the_carrier @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ~ ( B @ empty )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function ) )
=> ( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ function ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(62,plain,
! [A: $i,B: $i] :
( ~ ( B @ empty )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function ) )
=> ( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ function ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(69,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(46,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(234,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)],[46]) ).
thf(30,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(179,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)],[30]) ).
thf(48,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(238,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(84,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(42,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(221,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(19,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(132,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ identity_on_carrier @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ identity_on_carrier @ quasi_total ) ) )
& ( A @ identity_on_carrier @ function ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_grcat_1) ).
thf(229,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ( ( A @ the_carrier @ ( A @ the_carrier @ ( A @ identity_on_carrier @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( A @ the_carrier @ ( A @ identity_on_carrier @ quasi_total ) ) )
& ( A @ identity_on_carrier @ function ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(43,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(224,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ identity_as_relation_of )
= ( A @ identity_relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
thf(109,plain,
! [A: $i] :
( ( A @ identity_as_relation_of )
= ( A @ identity_relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(193,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)],[33]) ).
thf(20,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(134,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function ) )
=> ( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ~ ( C @ empty )
& ( C @ function ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(73,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function ) )
=> ( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ~ ( C @ empty )
& ( C @ function ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(47,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(236,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)],[47]) ).
thf(11,axiom,
! [A: $i] :
( ( ( A @ transitive )
& ( A @ symmetric )
& ( A @ relation ) )
=> ( ( A @ reflexive )
& ( A @ relation ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_partfun1) ).
thf(86,plain,
! [A: $i] :
( ( ( A @ transitive )
& ( A @ symmetric )
& ( A @ relation ) )
=> ( ( A @ reflexive )
& ( A @ relation ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ identity_as_relation_of @ relation_of2_as_subset ) ) )
& ( A @ ( A @ ( A @ identity_as_relation_of @ v1_partfun1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_partfun1) ).
thf(187,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ identity_as_relation_of @ relation_of2_as_subset ) ) )
& ( A @ ( A @ ( A @ identity_as_relation_of @ v1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(41,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(219,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ element ) )
& ( B @ ( A @ ( C @ relation_of2 ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function )
& ~ ( A @ empty ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ apply_as_element ) ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_funct_2) ).
thf(245,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ element ) )
& ( B @ ( A @ ( C @ relation_of2 ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function )
& ~ ( A @ empty ) )
=> ( B @ ( D @ ( C @ ( B @ ( A @ apply_as_element ) ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(38,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(209,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ relation_of2 ) ) )
=> ( ( ( A @ ( A @ ( B @ quasi_total ) ) )
& ( B @ reflexive )
& ( A @ ( A @ ( B @ v1_partfun1 ) ) )
& ( B @ function ) )
=> ( ( A @ ( A @ ( B @ bijective ) ) )
& ( A @ ( A @ ( B @ onto ) ) )
& ( A @ ( A @ ( B @ quasi_total ) ) )
& ( B @ one_to_one )
& ( B @ function ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_funct_2) ).
thf(112,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ relation_of2 ) ) )
=> ( ( ( A @ ( A @ ( B @ quasi_total ) ) )
& ( B @ reflexive )
& ( A @ ( A @ ( B @ v1_partfun1 ) ) )
& ( B @ function ) )
=> ( ( A @ ( A @ ( B @ bijective ) ) )
& ( A @ ( A @ ( B @ onto ) ) )
& ( A @ ( A @ ( B @ quasi_total ) ) )
& ( B @ one_to_one )
& ( B @ function ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(18,axiom,
! [A: $i] :
? [B: $i] :
( ( A @ ( A @ ( B @ v1_partfun1 ) ) )
& ( B @ transitive )
& ( B @ antisymmetric )
& ( B @ symmetric )
& ( B @ reflexive )
& ( B @ relation )
& ( A @ ( A @ ( B @ relation_of2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_partfun1) ).
thf(123,plain,
! [A: $i] :
? [B: $i] :
( ( A @ ( A @ ( B @ v1_partfun1 ) ) )
& ( B @ transitive )
& ( B @ antisymmetric )
& ( B @ symmetric )
& ( B @ reflexive )
& ( B @ relation )
& ( A @ ( A @ ( B @ relation_of2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(23,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(145,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(25,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(150,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)],[25]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ identity_relation @ transitive )
& ( A @ identity_relation @ antisymmetric )
& ( A @ identity_relation @ symmetric )
& ( A @ identity_relation @ reflexive )
& ( A @ identity_relation @ function )
& ( A @ identity_relation @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_partfun1) ).
thf(95,plain,
! [A: $i] :
( ( A @ identity_relation @ transitive )
& ( A @ identity_relation @ antisymmetric )
& ( A @ identity_relation @ symmetric )
& ( A @ identity_relation @ reflexive )
& ( A @ identity_relation @ function )
& ( A @ identity_relation @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(5,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(67,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(34,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(199,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(207,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ function ) )
=> ( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(119,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ function ) )
=> ( ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function ) ) ) ),
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/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(58,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(28,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(168,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ function )
& ( C @ relation )
& ( B @ ( A @ ( C @ relation_of2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( A @ identity_on_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_as_element ) ) ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t91_tmap_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( A @ identity_on_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_as_element ) ) ) )
= B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(51,plain,
~ ! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ( ( B @ ( A @ identity_on_carrier @ ( A @ the_carrier @ ( A @ the_carrier @ apply_as_element ) ) ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ element ) )
& ( B @ ( A @ ( C @ relation_of2 ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function )
& ~ ( A @ empty ) )
=> ( ( D @ ( C @ ( B @ ( A @ apply_as_element ) ) ) )
= ( D @ ( C @ apply ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
thf(242,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( D @ element ) )
& ( B @ ( A @ ( C @ relation_of2 ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function )
& ~ ( A @ empty ) )
=> ( ( D @ ( C @ ( B @ ( A @ apply_as_element ) ) ) )
= ( D @ ( C @ apply ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( ( B @ ( A @ ( C @ bijective ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function ) )
=> ( ( B @ ( A @ ( C @ onto ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ one_to_one )
& ( C @ function ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_2) ).
thf(136,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( ( B @ ( A @ ( C @ bijective ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function ) )
=> ( ( B @ ( A @ ( C @ onto ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ one_to_one )
& ( C @ function ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( ( B @ ( A @ ( C @ onto ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ one_to_one )
& ( C @ function ) )
=> ( ( B @ ( A @ ( C @ bijective ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_funct_2) ).
thf(79,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ relation_of2 ) ) )
=> ( ( ( B @ ( A @ ( C @ onto ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ one_to_one )
& ( C @ function ) )
=> ( ( B @ ( A @ ( C @ bijective ) ) )
& ( B @ ( A @ ( C @ quasi_total ) ) )
& ( C @ function ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(90,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(40,axiom,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(215,plain,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(250,plain,
$false,
inference(e,[status(thm)],[142,185,93,201,165,156,173,148,213,226,72,203,62,69,234,179,238,84,221,132,229,224,109,193,134,73,236,86,187,219,245,209,112,123,145,150,95,67,199,207,119,58,168,51,242,136,79,90,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU353+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.13 % 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
% 0.25/5.73 % Computer : n006.cluster.edu
% 0.25/5.73 % Model : x86_64 x86_64
% 0.25/5.73 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/5.73 % Memory : 8046.5625MB
% 0.25/5.73 % OS : Linux 6.8.0-71-generic
% 0.25/5.73 % CPULimit : 300
% 0.25/5.73 % WCLimit : 300
% 0.25/5.73 % DateTime : Sat Sep 26 09:17:48 UTC 2026
% 0.25/5.74 % CPUTime :
% 0.25/5.74 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
% 1.28/6.45 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.53/6.68 % [INFO] Parsing done (222ms).
% 1.53/6.69 % [INFO] Running in sequential loop mode.
% 2.29/7.08 % [INFO] eprover registered as external prover.
% 2.29/7.09 % [INFO] Scanning for conjecture ...
% 2.60/7.21 % [INFO] Found a conjecture (or negated_conjecture) and 56 axioms. Running axiom selection ...
% 2.81/7.30 % [INFO] Axiom selection finished. Selected 48 axioms (removed 8 axioms).
% 2.81/7.39 % [INFO] Problem is first-order (TPTP FOF).
% 3.02/7.41 % [INFO] Type checking passed.
% 3.02/7.41 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 5.27/8.42 % External prover 'e' found a proof!
% 5.27/8.42 % [INFO] Killing All external provers ...
% 5.27/8.42 % Time passed: 2474ms (effective reasoning time: 1724ms)
% 5.27/8.42 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 5.27/8.43 % Axioms used in derivation (48): fc2_partfun1, cc4_funct_2, fc4_subset_1, dt_m2_relset_1, cc3_funct_2, existence_m2_relset_1, t35_funct_1, rc2_xboole_0, redefinition_m2_relset_1, dt_k7_grcat_1, fc1_xboole_0, t1_subset, rc2_partfun1, dt_k6_partfun1, cc2_funct_2, t6_boole, rc2_subset_1, rc3_partfun1, t5_subset, existence_m1_relset_1, dt_k8_funct_2, t4_subset, cc1_funct_2, cc1_partfun1, t7_boole, rc3_struct_0, fc1_subset_1, redefinition_k6_partfun1, rc1_subset_1, rc1_funct_2, t3_subset, cc1_relset_1, existence_m1_subset_1, fc1_struct_0, cc6_funct_2, reflexivity_r1_tarski, dt_k6_relat_1, d11_grcat_1, redefinition_k8_funct_2, t8_boole, rc1_xboole_0, rc5_struct_0, t2_subset, existence_l1_struct_0, rc1_partfun1, cc5_funct_2, antisymmetry_r2_hidden, rc2_funct_2
% 5.27/8.43 % No. of inferences in proof: 100
% 5.27/8.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2474 ms resp. 1724 ms w/o parsing
% 5.56/8.53 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.56/8.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------