%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU376+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 : n010.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 08:38:37 AM UTC 2026
% Result : Theorem 6.90s 8.23s
% Output : Refutation 7.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 53
% Syntax : Number of formulae : 108 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 383 ( 8 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1115 ( 78 ~; 2 |; 164 &; 762 @)
% ( 5 <=>; 104 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 2 con; 0-4 aty)
% Number of variables : 217 ( 0 ^; 172 !; 45 ?; 217 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_carrier_decl,type,
empty_carrier: $i > $o ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(transitive_relstr_decl,type,
transitive_relstr: $i > $o ).
thf(directed_relstr_decl,type,
directed_relstr: $i > $o ).
thf(net_str_decl,type,
net_str: $i > $i > $o ).
thf(is_eventually_in_decl,type,
is_eventually_in: $i > $i > $i > $o ).
thf(is_often_in_decl,type,
is_often_in: $i > $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(relation_decl,type,
relation: $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(one_to_one_decl,type,
one_to_one: $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(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(relation_of2_as_subset_decl,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(relation_of2_decl,type,
relation_of2: $i > $i > $i > $o ).
thf(relation_empty_yielding_decl,type,
relation_empty_yielding: $i > $o ).
thf(rel_str_decl,type,
rel_str: $i > $o ).
thf(quasi_total_decl,type,
quasi_total: $i > $i > $i > $o ).
thf(the_carrier_decl,type,
the_carrier: $i > $i ).
thf(apply_on_structs_decl,type,
apply_on_structs: $i > $i > $i > $i > $i ).
thf(apply_netmap_decl,type,
apply_netmap: $i > $i > $i > $i ).
thf(the_mapping_decl,type,
the_mapping: $i > $i > $i ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(related_decl,type,
related: $i > $i > $i > $o ).
thf(v1_yellow_3_decl,type,
v1_yellow_3: $i > $o ).
thf(47,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ apply_netmap ) ) )
= ( C @ ( B @ ( A @ the_mapping ) @ ( A @ ( B @ apply_on_structs ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_waybel_0) ).
thf(217,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( B @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ apply_netmap ) ) )
= ( C @ ( B @ ( A @ the_mapping ) @ ( A @ ( B @ apply_on_structs ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ the_carrier @ ( C @ element ) )
& ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ apply_netmap ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_waybel_0) ).
thf(185,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ the_carrier @ ( C @ element ) )
& ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( A @ the_carrier @ ( C @ ( B @ ( A @ apply_netmap ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(125,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(48,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(220,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(34,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(169,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)],[34]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(193,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(23,axiom,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(129,plain,
( ( empty_set @ relation_empty_yielding )
& ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(24,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(134,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(27,axiom,
? [A: $i] : ( A @ rel_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(148,plain,
? [A: $i] : ( A @ rel_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(44,axiom,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(209,plain,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(150,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
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(119,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( D @ element ) )
& ( B @ the_carrier @ ( A @ the_carrier @ ( C @ relation_of2 ) ) )
& ( B @ the_carrier @ ( A @ the_carrier @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( B @ one_sorted_str )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( D @ ( C @ ( B @ ( A @ apply_on_structs ) ) ) )
= ( D @ ( C @ apply ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_waybel_0) ).
thf(195,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( D @ element ) )
& ( B @ the_carrier @ ( A @ the_carrier @ ( C @ relation_of2 ) ) )
& ( B @ the_carrier @ ( A @ the_carrier @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( B @ one_sorted_str )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( D @ ( C @ ( B @ ( A @ apply_on_structs ) ) ) )
= ( D @ ( C @ apply ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(138,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)],[25]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] : ( A @ ( B @ net_str ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_waybel_0) ).
thf(234,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ? [B: $i] : ( A @ ( B @ net_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(29,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(152,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(7,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(78,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( D @ element ) )
& ( B @ the_carrier @ ( A @ the_carrier @ ( C @ relation_of2 ) ) )
& ( B @ the_carrier @ ( A @ the_carrier @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( B @ one_sorted_str )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( B @ the_carrier @ ( D @ ( C @ ( B @ ( A @ apply_on_structs ) ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_waybel_0) ).
thf(179,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ the_carrier @ ( D @ element ) )
& ( B @ the_carrier @ ( A @ the_carrier @ ( C @ relation_of2 ) ) )
& ( B @ the_carrier @ ( A @ the_carrier @ ( C @ quasi_total ) ) )
& ( C @ function )
& ( B @ one_sorted_str )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( B @ the_carrier @ ( D @ ( C @ ( B @ ( A @ apply_on_structs ) ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(16,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(106,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(20,axiom,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(121,plain,
? [A: $i] :
( ( A @ relation )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(84,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(31,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
thf(160,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(32,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(165,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(12,axiom,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(92,plain,
? [A: $i] :
( ( A @ one_to_one )
& ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(65,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(97,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(26,axiom,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(144,plain,
? [A: $i] :
( ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ quasi_total ) ) )
& ( B @ ( A @ the_mapping ) @ function ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_waybel_0) ).
thf(236,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( A @ one_sorted_str ) )
=> ( ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ relation_of2_as_subset ) ) )
& ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ quasi_total ) ) )
& ( B @ ( A @ the_mapping ) @ function ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(38,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(181,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)],[38]) ).
thf(10,axiom,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(86,plain,
? [A: $i] :
( ( A @ relation )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ quasi_total ) ) )
& ( B @ ( A @ the_mapping ) @ function )
& ( B @ ( A @ the_mapping ) @ relation )
& ~ ( B @ ( A @ the_mapping ) @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc15_yellow_6) ).
thf(187,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier )
& ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ the_carrier @ ( B @ the_carrier @ ( B @ ( A @ the_mapping ) @ quasi_total ) ) )
& ( B @ ( A @ the_mapping ) @ function )
& ( B @ ( A @ the_mapping ) @ relation )
& ~ ( B @ ( A @ the_mapping ) @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(18,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(113,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)],[18]) ).
thf(8,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(81,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,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(76,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(103,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(45,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(213,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(30,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_pboole) ).
thf(155,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation_empty_yielding )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(43,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ is_eventually_in ) ) )
<=> ? [D: $i] :
( ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ( ( E @ ( D @ ( B @ related ) ) )
=> ( C @ ( E @ ( B @ ( A @ apply_netmap ) ) @ in ) ) ) )
& ( B @ the_carrier @ ( D @ element ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_waybel_0) ).
thf(198,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ( ( E @ ( D @ ( B @ related ) ) )
=> ( C @ ( E @ ( B @ ( A @ apply_netmap ) ) @ in ) ) ) )
& ( B @ the_carrier @ ( D @ element ) ) )
=> ( C @ ( B @ ( A @ is_eventually_in ) ) ) )
& ( ( C @ ( B @ ( A @ is_eventually_in ) ) )
=> ? [D: $i] :
( ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ( ( E @ ( D @ ( B @ related ) ) )
=> ( C @ ( E @ ( B @ ( A @ apply_netmap ) ) @ in ) ) ) )
& ( B @ the_carrier @ ( D @ element ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(17,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(108,plain,
? [A: $i] :
( ( A @ function )
& ( A @ empty )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(53,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ directed_relstr )
<=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ? [D: $i] :
( ( D @ ( C @ ( A @ related ) ) )
& ( D @ ( B @ ( A @ related ) ) )
& ( A @ the_carrier @ ( D @ element ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_yellow_6) ).
thf(241,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ~ ( A @ empty_carrier ) )
=> ( ( ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ? [D: $i] :
( ( D @ ( C @ ( A @ related ) ) )
& ( D @ ( B @ ( A @ related ) ) )
& ( A @ the_carrier @ ( D @ element ) ) ) ) )
=> ( A @ directed_relstr ) )
& ( ( A @ directed_relstr )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ? [D: $i] :
( ( D @ ( C @ ( A @ related ) ) )
& ( D @ ( B @ ( A @ related ) ) )
& ( A @ the_carrier @ ( D @ element ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(167,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(4,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(67,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)],[4]) ).
thf(22,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(127,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(5,axiom,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(72,plain,
( ( empty_set @ relation )
& ( empty_set @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(36,axiom,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(175,plain,
? [A: $i] :
( ( A @ function )
& ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ( B @ rel_str ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
thf(250,plain,
! [A: $i] :
( ( A @ one_sorted_str )
=> ! [B: $i] :
( ( A @ ( B @ net_str ) )
=> ( B @ rel_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(14,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(99,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ is_eventually_in ) ) )
=> ( C @ ( B @ ( A @ is_often_in ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_yellow_6) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ is_eventually_in ) ) )
=> ( C @ ( B @ ( A @ is_often_in ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(55,plain,
~ ! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ( B @ directed_relstr )
& ( B @ transitive_relstr )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ is_eventually_in ) ) )
=> ( C @ ( B @ ( A @ is_often_in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(35,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(171,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(11,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(90,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ empty_carrier )
=> ( A @ v1_yellow_3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_yellow_3) ).
thf(215,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ empty_carrier )
=> ( A @ v1_yellow_3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(49,axiom,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ is_often_in ) ) )
<=> ! [D: $i] :
( ( B @ the_carrier @ ( D @ element ) )
=> ? [E: $i] :
( ( C @ ( E @ ( B @ ( A @ apply_netmap ) ) @ in ) )
& ( E @ ( D @ ( B @ related ) ) )
& ( B @ the_carrier @ ( E @ element ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_waybel_0) ).
thf(222,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ! [B: $i] :
( ( ( A @ ( B @ net_str ) )
& ~ ( B @ empty_carrier ) )
=> ! [C: $i] :
( ( ! [D: $i] :
( ( B @ the_carrier @ ( D @ element ) )
=> ? [E: $i] :
( ( C @ ( E @ ( B @ ( A @ apply_netmap ) ) @ in ) )
& ( E @ ( D @ ( B @ related ) ) )
& ( B @ the_carrier @ ( E @ element ) ) ) )
=> ( C @ ( B @ ( A @ is_often_in ) ) ) )
& ( ( C @ ( B @ ( A @ is_often_in ) ) )
=> ! [D: $i] :
( ( B @ the_carrier @ ( D @ element ) )
=> ? [E: $i] :
( ( C @ ( E @ ( B @ ( A @ apply_netmap ) ) @ in ) )
& ( E @ ( D @ ( B @ related ) ) )
& ( B @ the_carrier @ ( E @ element ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ~ ( A @ v1_yellow_3 )
=> ~ ( A @ empty_carrier ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_yellow_3) ).
thf(232,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ~ ( A @ v1_yellow_3 )
=> ~ ( A @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(258,plain,
$false,
inference(e,[status(thm)],[217,185,125,220,169,193,129,134,148,209,150,119,195,138,234,152,78,179,106,121,84,160,165,92,65,97,144,236,181,86,187,113,81,76,103,213,155,198,108,241,167,67,127,72,175,250,99,55,171,90,215,222,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU376+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.14/5.42 % Computer : n010.cluster.edu
% 0.14/5.42 % Model : x86_64 x86_64
% 0.14/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.42 % Memory : 8046.5625MB
% 0.14/5.42 % OS : Linux 6.8.0-71-generic
% 0.14/5.43 % CPULimit : 300
% 0.14/5.43 % WCLimit : 300
% 0.14/5.43 % DateTime : Sat Sep 26 09:22:23 UTC 2026
% 0.14/5.43 % CPUTime :
% 0.14/5.43 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
% 0.19/6.02 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.37/6.26 % [INFO] Parsing done (229ms).
% 1.37/6.27 % [INFO] Running in sequential loop mode.
% 2.17/6.67 % [INFO] eprover registered as external prover.
% 2.17/6.67 % [INFO] Scanning for conjecture ...
% 2.41/6.79 % [INFO] Found a conjecture (or negated_conjecture) and 60 axioms. Running axiom selection ...
% 2.59/6.89 % [INFO] Axiom selection finished. Selected 52 axioms (removed 8 axioms).
% 2.83/6.99 % [INFO] Problem is first-order (TPTP FOF).
% 2.83/7.00 % [INFO] Type checking passed.
% 2.83/7.01 % [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 ...
% 6.90/8.22 % External prover 'e' found a proof!
% 6.90/8.22 % [INFO] Killing All external provers ...
% 6.90/8.22 % Time passed: 2654ms (effective reasoning time: 1948ms)
% 6.90/8.22 % 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)>
% 6.90/8.23 % Axioms used in derivation (52): redefinition_m2_relset_1, fc4_subset_1, dt_k1_waybel_0, rc3_funct_1, t5_subset, existence_m1_relset_1, t4_subset, t8_boole, cc2_yellow_3, antisymmetry_r2_hidden, fc4_relat_1, t1_subset, dt_m2_relset_1, cc1_relat_1, d11_waybel_0, d12_waybel_0, rc1_funct_1, dt_u1_waybel_0, rc3_relat_1, t6_boole, rc2_subset_1, rc4_funct_1, dt_l1_waybel_0, existence_l1_waybel_0, d8_waybel_0, t7_boole, existence_l1_orders_2, cc1_funct_1, rc3_struct_0, fc1_subset_1, rc2_funct_1, rc1_subset_1, fc15_yellow_6, redefinition_k1_waybel_0, cc2_funct_1, t3_subset, cc1_relset_1, existence_m1_subset_1, rc2_relat_1, existence_m2_relset_1, dt_l1_orders_2, d5_yellow_6, fc1_struct_0, rc1_relat_1, reflexivity_r1_tarski, cc1_yellow_3, rc1_pboole, rc5_struct_0, t2_subset, fc12_relat_1, existence_l1_struct_0, dt_k3_waybel_0
% 6.90/8.23 % No. of inferences in proof: 108
% 6.90/8.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2654 ms resp. 1948 ms w/o parsing
% 7.30/8.33 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.30/8.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------