TSTP Solution File: SEU353+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU353+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:58:27 EDT 2023
% Result : Theorem 4.60s 2.18s
% Output : Refutation 4.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 77
% Syntax : Number of formulae : 128 ( 23 unt; 28 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 : 47 ( 47 >; 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_type,type,
empty_carrier: $i > $o ).
thf(one_sorted_str_type,type,
one_sorted_str: $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(the_carrier_type,type,
the_carrier: $i > $i ).
thf(apply_as_element_type,type,
apply_as_element: $i > $i > $i > $i > $i ).
thf(identity_on_carrier_type,type,
identity_on_carrier: $i > $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(relation_of2_type,type,
relation_of2: $i > $i > $i > $o ).
thf(function_type,type,
function: $i > $o ).
thf(quasi_total_type,type,
quasi_total: $i > $i > $i > $o ).
thf(v1_partfun1_type,type,
v1_partfun1: $i > $i > $i > $o ).
thf(empty_set_type,type,
empty_set: $i ).
thf(one_to_one_type,type,
one_to_one: $i > $o ).
thf(onto_type,type,
onto: $i > $i > $i > $o ).
thf(bijective_type,type,
bijective: $i > $i > $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(relation_type,type,
relation: $i > $o ).
thf(symmetric_type,type,
symmetric: $i > $o ).
thf(transitive_type,type,
transitive: $i > $o ).
thf(reflexive_type,type,
reflexive: $i > $o ).
thf(cartesian_product2_type,type,
cartesian_product2: $i > $i > $i ).
thf(identity_relation_type,type,
identity_relation: $i > $i ).
thf(antisymmetric_type,type,
antisymmetric: $i > $o ).
thf(identity_as_relation_of_type,type,
identity_as_relation_of: $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(relation_of2_as_subset_type,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(27,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(153,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ( ( ( function @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( reflexive @ B )
& ( quasi_total @ B @ A @ A ) )
=> ( ( function @ B )
& ( one_to_one @ B )
& ( quasi_total @ B @ A @ A )
& ( onto @ B @ A @ A )
& ( bijective @ B @ A @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc4_funct_2) ).
thf(106,plain,
! [A: $i,B: $i] :
( ( relation_of2 @ B @ A @ A )
=> ( ( ( function @ B )
& ( v1_partfun1 @ B @ A @ A )
& ( reflexive @ B )
& ( quasi_total @ B @ A @ A ) )
=> ( ( function @ B )
& ( one_to_one @ B )
& ( quasi_total @ B @ A @ A )
& ( onto @ B @ A @ A )
& ( bijective @ B @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(5,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(65,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(28,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(156,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ! [C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( quasi_total @ C @ A @ B ) )
=> ( ( function @ C )
& ~ ( empty @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( quasi_total @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ! [C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( quasi_total @ C @ A @ B ) )
=> ( ( function @ C )
& ~ ( empty @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( quasi_total @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(36,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(186,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(11,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( symmetric @ A )
& ( transitive @ A ) )
=> ( ( relation @ A )
& ( reflexive @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_partfun1) ).
thf(82,plain,
! [A: $i] :
( ( ( relation @ A )
& ( symmetric @ A )
& ( transitive @ A ) )
=> ( ( relation @ A )
& ( reflexive @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,conjecture,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( apply_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( identity_on_carrier @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t91_tmap_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( apply_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( identity_on_carrier @ A ) @ B )
= B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(51,plain,
~ ! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ! [B: $i] :
( ( element @ B @ ( the_carrier @ A ) )
=> ( ( apply_as_element @ ( the_carrier @ A ) @ ( the_carrier @ A ) @ ( identity_on_carrier @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(138,plain,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2_as_subset @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(88,plain,
! [A: $i,B: $i] :
( ( ~ ( empty @ A )
& ~ ( empty @ B ) )
=> ~ ( empty @ ( cartesian_product2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(31,axiom,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(170,plain,
! [A: $i] : ( relation @ ( identity_relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(18,axiom,
! [A: $i] :
? [B: $i] :
( ( relation_of2 @ B @ A @ A )
& ( relation @ B )
& ( reflexive @ B )
& ( symmetric @ B )
& ( antisymmetric @ B )
& ( transitive @ B )
& ( v1_partfun1 @ B @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_partfun1) ).
thf(115,plain,
! [A: $i] :
? [B: $i] :
( ( relation_of2 @ B @ A @ A )
& ( relation @ B )
& ( reflexive @ B )
& ( symmetric @ B )
& ( antisymmetric @ B )
& ( transitive @ B )
& ( v1_partfun1 @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(48,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(217,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(184,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(20,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(125,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(40,axiom,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(196,plain,
? [A: $i] :
( ( one_sorted_str @ A )
& ~ ( empty_carrier @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(189,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(57,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ B )
=> ! [C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( quasi_total @ C @ A @ B ) )
=> ( ( function @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( quasi_total @ C @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(61,plain,
! [A: $i,B: $i] :
( ~ ( empty @ B )
=> ! [C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( quasi_total @ C @ A @ B ) )
=> ( ( function @ C )
& ( v1_partfun1 @ C @ A @ B )
& ( quasi_total @ C @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t35_funct_1) ).
thf(132,plain,
! [A: $i,B: $i] :
( ( in @ B @ A )
=> ( ( apply @ ( identity_relation @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(44,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( identity_on_carrier @ A )
= ( identity_as_relation_of @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_grcat_1) ).
thf(206,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( identity_on_carrier @ A )
= ( identity_as_relation_of @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ( function @ C )
& ( quasi_total @ C @ A @ B )
& ( relation_of2 @ C @ A @ B )
& ( element @ D @ A ) )
=> ( ( apply_as_element @ A @ B @ C @ D )
= ( apply @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_funct_2) ).
thf(220,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ( function @ C )
& ( quasi_total @ C @ A @ B )
& ( relation_of2 @ C @ A @ B )
& ( element @ D @ A ) )
=> ( ( apply_as_element @ A @ B @ C @ D )
= ( apply @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(12,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(85,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(201,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(29,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A )
& ( empty @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(160,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A )
& ( empty @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(7,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(70,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
<=> ( relation_of2 @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(165,plain,
! [A: $i,B: $i,C: $i] :
( ( ( relation_of2_as_subset @ C @ A @ B )
=> ( relation_of2 @ C @ A @ B ) )
& ( ( relation_of2 @ C @ A @ B )
=> ( relation_of2_as_subset @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(38,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(191,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(43,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(204,plain,
? [A: $i] : ( one_sorted_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(32,axiom,
! [A: $i] :
( ( v1_partfun1 @ ( identity_as_relation_of @ A ) @ A @ A )
& ( relation_of2_as_subset @ ( identity_as_relation_of @ A ) @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_partfun1) ).
thf(172,plain,
! [A: $i] :
( ( v1_partfun1 @ ( identity_as_relation_of @ A ) @ A @ A )
& ( relation_of2_as_subset @ ( identity_as_relation_of @ A ) @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( one_to_one @ C )
& ( quasi_total @ C @ A @ B )
& ( onto @ C @ A @ B ) )
=> ( ( function @ C )
& ( quasi_total @ C @ A @ B )
& ( bijective @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_funct_2) ).
thf(76,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( one_to_one @ C )
& ( quasi_total @ C @ A @ B )
& ( onto @ C @ A @ B ) )
=> ( ( function @ C )
& ( quasi_total @ C @ A @ B )
& ( bijective @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [A: $i] :
( ( identity_as_relation_of @ A )
= ( identity_relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
thf(103,plain,
! [A: $i] :
( ( identity_as_relation_of @ A )
= ( identity_relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(25,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C )
& ( quasi_total @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(140,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( relation_of2 @ C @ A @ B )
& ( relation @ C )
& ( function @ C )
& ( quasi_total @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(213,plain,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ( function @ C )
& ( quasi_total @ C @ A @ B )
& ( relation_of2 @ C @ A @ B )
& ( element @ D @ A ) )
=> ( element @ ( apply_as_element @ A @ B @ C @ D ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_funct_2) ).
thf(223,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( empty @ A )
& ( function @ C )
& ( quasi_total @ C @ A @ B )
& ( relation_of2 @ C @ A @ B )
& ( element @ D @ A ) )
=> ( element @ ( apply_as_element @ A @ B @ C @ D ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(23,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(135,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(80,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(45,axiom,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( function @ ( identity_on_carrier @ A ) )
& ( quasi_total @ ( identity_on_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( identity_on_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_grcat_1) ).
thf(209,plain,
! [A: $i] :
( ( one_sorted_str @ A )
=> ( ( function @ ( identity_on_carrier @ A ) )
& ( quasi_total @ ( identity_on_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) )
& ( relation_of2_as_subset @ ( identity_on_carrier @ A ) @ ( the_carrier @ A ) @ ( the_carrier @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( v1_partfun1 @ C @ A @ B ) )
=> ( ( function @ C )
& ( quasi_total @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(112,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( v1_partfun1 @ C @ A @ B ) )
=> ( ( function @ C )
& ( quasi_total @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(19,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(123,plain,
! [A: $i,B: $i] :
? [C: $i] : ( relation_of2 @ C @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(39,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(194,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(26,axiom,
! [A: $i] :
? [B: $i] :
( ( relation_of2 @ B @ A @ A )
& ( relation @ B )
& ( function @ B )
& ( one_to_one @ B )
& ( quasi_total @ B @ A @ A )
& ( onto @ B @ A @ A )
& ( bijective @ B @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_2) ).
thf(145,plain,
! [A: $i] :
? [B: $i] :
( ( relation_of2 @ B @ A @ A )
& ( relation @ B )
& ( function @ B )
& ( one_to_one @ B )
& ( quasi_total @ B @ A @ A )
& ( onto @ B @ A @ A )
& ( bijective @ B @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(6,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(67,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(199,plain,
! [A: $i,B: $i,C: $i] :
( ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) )
=> ( relation @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( quasi_total @ C @ A @ B )
& ( bijective @ C @ A @ B ) )
=> ( ( function @ C )
& ( one_to_one @ C )
& ( quasi_total @ C @ A @ B )
& ( onto @ C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_funct_2) ).
thf(127,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2 @ C @ A @ B )
=> ( ( ( function @ C )
& ( quasi_total @ C @ A @ B )
& ( bijective @ C @ A @ B ) )
=> ( ( function @ C )
& ( one_to_one @ C )
& ( quasi_total @ C @ A @ B )
& ( onto @ C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(177,plain,
! [A: $i,B: $i] :
( ( ( element @ A @ ( powerset @ B ) )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( element @ A @ ( powerset @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(34,axiom,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(182,plain,
! [A: $i] :
( ( ~ ( empty_carrier @ A )
& ( one_sorted_str @ A ) )
=> ~ ( empty @ ( the_carrier @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(14,axiom,
! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) )
& ( reflexive @ ( identity_relation @ A ) )
& ( symmetric @ ( identity_relation @ A ) )
& ( antisymmetric @ ( identity_relation @ A ) )
& ( transitive @ ( identity_relation @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_partfun1) ).
thf(90,plain,
! [A: $i] :
( ( relation @ ( identity_relation @ A ) )
& ( function @ ( identity_relation @ A ) )
& ( reflexive @ ( identity_relation @ A ) )
& ( symmetric @ ( identity_relation @ A ) )
& ( antisymmetric @ ( identity_relation @ A ) )
& ( transitive @ ( identity_relation @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(215,plain,
! [A: $i,B: $i,C: $i] :
( ( relation_of2_as_subset @ C @ A @ B )
=> ( element @ C @ ( powerset @ ( cartesian_product2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(227,plain,
$false,
inference(e,[status(thm)],[153,106,65,156,71,186,82,51,138,88,170,115,217,184,125,196,189,57,61,132,206,220,85,201,160,70,165,191,204,172,76,103,140,213,223,135,80,209,112,123,194,145,67,199,127,177,182,90,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU353+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n029.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 13:55:44 EDT 2023
% 0.16/0.36 % CPUTime :
% 1.01/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/1.07 % [INFO] Parsing done (163ms).
% 1.52/1.08 % [INFO] Running in sequential loop mode.
% 1.82/1.29 % [INFO] eprover registered as external prover.
% 1.82/1.29 % [INFO] cvc4 registered as external prover.
% 1.82/1.30 % [INFO] Scanning for conjecture ...
% 2.04/1.36 % [INFO] Found a conjecture and 56 axioms. Running axiom selection ...
% 2.21/1.42 % [INFO] Axiom selection finished. Selected 48 axioms (removed 8 axioms).
% 2.54/1.48 % [INFO] Problem is first-order (TPTP FOF).
% 2.54/1.48 % [INFO] Type checking passed.
% 2.54/1.49 % [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 ...
% 4.60/2.18 % External prover 'e' found a proof!
% 4.60/2.18 % [INFO] Killing All external provers ...
% 4.60/2.18 % Time passed: 1657ms (effective reasoning time: 1092ms)
% 4.60/2.18 % 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)>
% 4.60/2.18 % 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
% 4.60/2.18 % No. of inferences in proof: 100
% 4.60/2.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1657 ms resp. 1092 ms w/o parsing
% 4.95/2.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.95/2.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------