TSTP Solution File: SET658+3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET658+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 11:54:00 EDT 2023
% Result : Theorem 4.20s 2.02s
% Output : Refutation 4.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 46
% Syntax : Number of formulae : 77 ( 5 unt; 17 typ; 0 def)
% Number of atoms : 245 ( 7 equ; 0 cnn)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 806 ( 11 ~; 0 |; 34 &; 610 @)
% ( 9 <=>; 142 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 3 con; 0-3 aty)
% Number of variables : 135 ( 0 ^; 115 !; 20 ?; 135 :)
% Comments :
%------------------------------------------------------------------------------
thf(ilf_type_type,type,
ilf_type: $i > $i > $o ).
thf(binary_relation_type_type,type,
binary_relation_type: $i ).
thf(relation_type_type,type,
relation_type: $i > $i > $i ).
thf(domain_of_type,type,
domain_of: $i > $i ).
thf(range_of_type,type,
range_of: $i > $i ).
thf(set_type_type,type,
set_type: $i ).
thf(subset_type_type,type,
subset_type: $i > $i ).
thf(cross_product_type,type,
cross_product: $i > $i > $i ).
thf(relation_like_type,type,
relation_like: $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(member_type_type,type,
member_type: $i > $i ).
thf(member_type,type,
member: $i > $i > $o ).
thf(range_type,type,
range: $i > $i > $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(domain_type,type,
domain: $i > $i > $i > $i ).
thf(power_set_type,type,
power_set: $i > $i ).
thf(17,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ilf_type @ ( domain @ A @ B @ C ) @ ( subset_type @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p25) ).
thf(69,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ilf_type @ ( domain @ A @ B @ C ) @ ( subset_type @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(12,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ? [B: $i] : ( ilf_type @ B @ ( subset_type @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
thf(56,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ? [B: $i] : ( ilf_type @ B @ ( subset_type @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( relation_type @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9) ).
thf(42,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ? [C: $i] : ( ilf_type @ C @ ( relation_type @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ilf_type @ ( range @ A @ B @ C ) @ ( subset_type @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
thf(46,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ilf_type @ ( range @ A @ B @ C ) @ ( subset_type @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(30,axiom,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( member @ B @ ( domain_of @ A ) )
<=> ? [C: $i] :
( ( ilf_type @ C @ set_type )
& ( member @ ( ordered_pair @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
thf(116,plain,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( ( member @ B @ ( domain_of @ A ) )
=> ? [C: $i] :
( ( ilf_type @ C @ set_type )
& ( member @ ( ordered_pair @ B @ C ) @ A ) ) )
& ( ? [C: $i] :
( ( ilf_type @ C @ set_type )
& ( member @ ( ordered_pair @ B @ C ) @ A ) )
=> ( member @ B @ ( domain_of @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(21,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( ilf_type @ B @ ( subset_type @ A ) )
<=> ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12) ).
thf(77,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( ( ilf_type @ B @ ( subset_type @ A ) )
=> ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) ) )
& ( ( ilf_type @ B @ ( member_type @ ( power_set @ A ) ) )
=> ( ilf_type @ B @ ( subset_type @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(19,axiom,
! [A: $i] :
( ( ( empty @ A )
& ( ilf_type @ A @ set_type ) )
=> ( relation_like @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23) ).
thf(73,plain,
! [A: $i] :
( ( ( empty @ A )
& ( ilf_type @ A @ set_type ) )
=> ( relation_like @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(7,axiom,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ( ilf_type @ ( range_of @ A ) @ set_type ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
thf(44,plain,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ( ilf_type @ ( range_of @ A ) @ set_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ( range @ A @ B @ C )
= ( range_of @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p26) ).
thf(39,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ( range @ A @ B @ C )
= ( range_of @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(22,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ( domain @ A @ B @ C )
= ( domain_of @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p24) ).
thf(80,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ( domain @ A @ B @ C )
= ( domain_of @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(29,axiom,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( member @ B @ ( range_of @ A ) )
<=> ? [C: $i] :
( ( ilf_type @ C @ set_type )
& ( member @ ( ordered_pair @ C @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
thf(112,plain,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( ( member @ B @ ( range_of @ A ) )
=> ? [C: $i] :
( ( ilf_type @ C @ set_type )
& ( member @ ( ordered_pair @ C @ B ) @ A ) ) )
& ( ? [C: $i] :
( ( ilf_type @ C @ set_type )
& ( member @ ( ordered_pair @ C @ B ) @ A ) )
=> ( member @ B @ ( range_of @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(9,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( ilf_type @ A @ set_type ) )
=> ? [B: $i] : ( ilf_type @ B @ ( member_type @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21) ).
thf(48,plain,
! [A: $i] :
( ( ~ ( empty @ A )
& ( ilf_type @ A @ set_type ) )
=> ? [B: $i] : ( ilf_type @ B @ ( member_type @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(24,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ~ ( empty @ ( power_set @ A ) )
& ( ilf_type @ ( power_set @ A ) @ set_type ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
thf(87,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ~ ( empty @ ( power_set @ A ) )
& ( ilf_type @ ( power_set @ A ) @ set_type ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(4,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( ilf_type @ B @ set_type ) )
=> ( ( ilf_type @ A @ ( member_type @ B ) )
<=> ( member @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).
thf(36,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ~ ( empty @ B )
& ( ilf_type @ B @ set_type ) )
=> ( ( ( ilf_type @ A @ ( member_type @ B ) )
=> ( member @ A @ B ) )
& ( ( member @ A @ B )
=> ( ilf_type @ A @ ( member_type @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,axiom,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ( ilf_type @ ( domain_of @ A ) @ set_type ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
thf(62,plain,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ( ilf_type @ ( domain_of @ A ) @ set_type ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(14,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ilf_type @ ( ordered_pair @ A @ B ) @ set_type ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p11) ).
thf(60,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ilf_type @ ( ordered_pair @ A @ B ) @ set_type ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(28,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ( relation_like @ A )
<=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( member @ B @ A )
=> ? [C: $i] :
( ( ilf_type @ C @ set_type )
& ? [D: $i] :
( ( ilf_type @ D @ set_type )
& ( B
= ( ordered_pair @ C @ D ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16) ).
thf(102,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ( ( relation_like @ A )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( member @ B @ A )
=> ? [C: $i] :
( ( ilf_type @ C @ set_type )
& ? [D: $i] :
( ( ilf_type @ D @ set_type )
& ( B
= ( ordered_pair @ C @ D ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( member @ B @ A )
=> ? [C: $i] :
( ( ilf_type @ C @ set_type )
& ? [D: $i] :
( ( ilf_type @ D @ set_type )
& ( B
= ( ordered_pair @ C @ D ) ) ) ) ) )
=> ( relation_like @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(26,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( member @ A @ ( power_set @ B ) )
<=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ C @ A )
=> ( member @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18) ).
thf(92,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( ( member @ A @ ( power_set @ B ) )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ C @ A )
=> ( member @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ C @ A )
=> ( member @ C @ B ) ) )
=> ( member @ A @ ( power_set @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(27,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ( ilf_type @ A @ binary_relation_type )
<=> ( ( relation_like @ A )
& ( ilf_type @ A @ set_type ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
thf(97,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ( ( ilf_type @ A @ binary_relation_type )
=> ( ( relation_like @ A )
& ( ilf_type @ A @ set_type ) ) )
& ( ( ( relation_like @ A )
& ( ilf_type @ A @ set_type ) )
=> ( ilf_type @ A @ binary_relation_type ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(3,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
=> ( relation_like @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p17) ).
thf(34,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ! [C: $i] :
( ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
=> ( relation_like @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( subset @ A @ B )
<=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ C @ A )
=> ( member @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).
thf(64,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ( ( subset @ A @ B )
=> ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ C @ A )
=> ( member @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ilf_type @ C @ set_type )
=> ( ( member @ C @ A )
=> ( member @ C @ B ) ) )
=> ( subset @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(18,axiom,
? [A: $i] : ( ilf_type @ A @ binary_relation_type ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p7) ).
thf(71,plain,
? [A: $i] : ( ilf_type @ A @ binary_relation_type ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(11,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ilf_type @ ( cross_product @ A @ B ) @ set_type ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
thf(54,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ilf_type @ ( cross_product @ A @ B ) @ set_type ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(10,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ! [C: $i] :
( ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
=> ( ilf_type @ C @ ( relation_type @ A @ B ) ) )
& ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8) ).
thf(50,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ( ! [C: $i] :
( ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) )
=> ( ilf_type @ C @ ( relation_type @ A @ B ) ) )
& ! [C: $i] :
( ( ilf_type @ C @ ( relation_type @ A @ B ) )
=> ( ilf_type @ C @ ( subset_type @ ( cross_product @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,conjecture,
! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ( ilf_type @ A @ ( relation_type @ ( domain_of @ A ) @ ( range_of @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_20) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ( ilf_type @ A @ ( relation_type @ ( domain_of @ A ) @ ( range_of @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(31,plain,
~ ! [A: $i] :
( ( ilf_type @ A @ binary_relation_type )
=> ( ilf_type @ A @ ( relation_type @ ( domain_of @ A ) @ ( range_of @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,axiom,
! [A: $i] : ( ilf_type @ A @ set_type ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p28) ).
thf(75,plain,
! [A: $i] : ( ilf_type @ A @ set_type ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(13,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ( ( subset @ ( domain_of @ B ) @ A )
=> ( ilf_type @ B @ ( relation_type @ A @ ( range_of @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
thf(58,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ! [B: $i] :
( ( ilf_type @ B @ binary_relation_type )
=> ( ( subset @ ( domain_of @ B ) @ A )
=> ( ilf_type @ B @ ( relation_type @ A @ ( range_of @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(25,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( subset @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
thf(90,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( subset @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(23,axiom,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ( empty @ A )
<=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ~ ( member @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
thf(83,plain,
! [A: $i] :
( ( ilf_type @ A @ set_type )
=> ( ( ( empty @ A )
=> ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ~ ( member @ B @ A ) ) )
& ( ! [B: $i] :
( ( ilf_type @ B @ set_type )
=> ~ ( member @ B @ A ) )
=> ( empty @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(120,plain,
$false,
inference(e,[status(thm)],[69,56,42,46,116,77,73,44,39,80,112,48,87,36,62,60,102,92,97,34,64,71,54,50,31,75,58,90,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET658+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n024.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 18:50:52 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.94/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.39/1.05 % [INFO] Parsing done (149ms).
% 1.39/1.06 % [INFO] Running in sequential loop mode.
% 1.85/1.26 % [INFO] eprover registered as external prover.
% 1.85/1.27 % [INFO] cvc4 registered as external prover.
% 1.85/1.27 % [INFO] Scanning for conjecture ...
% 2.04/1.33 % [INFO] Found a conjecture and 28 axioms. Running axiom selection ...
% 2.17/1.37 % [INFO] Axiom selection finished. Selected 28 axioms (removed 0 axioms).
% 2.17/1.42 % [INFO] Problem is first-order (TPTP FOF).
% 2.17/1.43 % [INFO] Type checking passed.
% 2.17/1.43 % [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 ...
% 4.20/2.02 % External prover 'e' found a proof!
% 4.20/2.02 % [INFO] Killing All external provers ...
% 4.20/2.02 % Time passed: 1491ms (effective reasoning time: 956ms)
% 4.20/2.02 % 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)>
% 4.20/2.02 % Axioms used in derivation (28): p27, p12, p18, p15, p26, p3, p22, p11, p2, p17, p9, p1, p24, p13, p16, p20, p10, p19, p4, p7, p5, p23, p21, p25, p14, p28, p6, p8
% 4.20/2.02 % No. of inferences in proof: 60
% 4.20/2.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1491 ms resp. 956 ms w/o parsing
% 4.38/2.08 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.38/2.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------