TSTP Solution File: SEU078+1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU078+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 11:56:58 EDT 2023
% Result : Theorem 181.48s 37.40s
% Output : Refutation 182.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 85
% Syntax : Number of formulae : 632 ( 177 unt; 42 typ; 0 def)
% Number of atoms : 1682 ( 593 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 4890 ( 727 ~; 666 |; 120 &;3269 @)
% ( 12 <=>; 96 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 42 usr; 13 con; 0-3 aty)
% Number of variables : 787 ( 0 ^; 739 !; 48 ?; 787 :)
% Comments :
%------------------------------------------------------------------------------
thf(relation_type,type,
relation: $i > $o ).
thf(function_type,type,
function: $i > $o ).
thf(one_to_one_type,type,
one_to_one: $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(relation_inverse_image_type,type,
relation_inverse_image: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(disjoint_type,type,
disjoint: $i > $i > $o ).
thf(relation_empty_yielding_type,type,
relation_empty_yielding: $i > $o ).
thf(relation_rng_type,type,
relation_rng: $i > $i ).
thf(relation_dom_type,type,
relation_dom: $i > $i ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i > $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i > $i ).
thf(sk7_type,type,
sk7: $i > $i ).
thf(sk8_type,type,
sk8: $i > $i ).
thf(sk9_type,type,
sk9: $i ).
thf(sk10_type,type,
sk10: $i ).
thf(sk11_type,type,
sk11: $i > $i ).
thf(sk12_type,type,
sk12: $i > $i > $i ).
thf(sk13_type,type,
sk13: $i ).
thf(sk14_type,type,
sk14: $i ).
thf(sk15_type,type,
sk15: $i ).
thf(sk16_type,type,
sk16: $i > $i > $i ).
thf(sk17_type,type,
sk17: $i > $i > $i ).
thf(sk18_type,type,
sk18: $i > $i > $i > $i ).
thf(sk19_type,type,
sk19: $i > $i > $o ).
thf(sk20_type,type,
sk20: $i > $i > $i ).
thf(sk21_type,type,
sk21: $i > $i > $i ).
thf(sk22_type,type,
sk22: $i > $i > $i ).
thf(sk23_type,type,
sk23: $i > $i > $i > $o ).
thf(sk24_type,type,
sk24: $i > $i > $i > $i ).
thf(sk25_type,type,
sk25: $i > $i > $i > $i ).
thf(sk26_type,type,
sk26: $i ).
thf(8,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(67,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(68,plain,
~ ! [A: $i] : ( empty @ A ),
inference(miniscope,[status(thm)],[67]) ).
thf(69,plain,
~ ( empty @ sk5 ),
inference(cnf,[status(esa)],[68]) ).
thf(12,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(76,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(77,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ),
inference(cnf,[status(esa)],[76]) ).
thf(78,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( empty @ A ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(155,plain,
! [A: $i,B: $i] :
( ( ( B
= ( singleton @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( in @ C @ B ) ) )
=> ( B
= ( singleton @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(156,plain,
( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( C = A ) )
& ! [C: $i] :
( ( C = A )
=> ( in @ C @ B ) ) ) )
& ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( in @ C @ B )
=> ( C = A ) )
& ! [C: $i] :
( ( C = A )
=> ( in @ C @ B ) ) )
=> ( B
= ( singleton @ A ) ) ) ),
inference(miniscope,[status(thm)],[155]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ( in @ ( sk16 @ B @ A ) @ B )
| ( ( sk17 @ B @ A )
= A )
| ( B
= ( singleton @ A ) ) ),
inference(cnf,[status(esa)],[156]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ( ( sk17 @ B @ A )
= A )
| ( B
= ( singleton @ A ) )
| ( in @ ( sk16 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[158]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ( ( sk17 @ B @ A )
= A )
| ( B
= ( singleton @ A ) )
| ( in @ ( sk16 @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[173]) ).
thf(2535,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( empty @ A )
| ( empty_set = B )
| ( C
= ( singleton @ B ) )
| ( in @ ( sk16 @ C @ B ) @ C )
| ( A
!= ( sk17 @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[78,174]) ).
thf(2536,plain,
! [B: $i,A: $i] :
( ~ ( empty @ ( sk17 @ A @ B ) )
| ( empty_set = B )
| ( A
= ( singleton @ B ) )
| ( in @ ( sk16 @ A @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[2535:[bind(A,$thf( sk17 @ D @ E )),bind(B,$thf( E )),bind(C,$thf( D ))]]) ).
thf(2540,plain,
! [B: $i,A: $i] :
( ~ ( empty @ ( sk17 @ A @ B ) )
| ( empty_set = B )
| ( A
= ( singleton @ B ) )
| ( in @ ( sk16 @ A @ B ) @ A ) ),
inference(simp,[status(thm)],[2536]) ).
thf(2584,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( empty @ ( sk17 @ A @ B ) )
| ( empty_set = B )
| ( in @ ( sk16 @ A @ B ) @ A )
| ( ( singleton @ B )
= C )
| ( D
= ( singleton @ C ) )
| ( in @ ( sk16 @ D @ C ) @ D )
| ( A
!= ( sk17 @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[2540,174]) ).
thf(2585,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( empty @ ( sk17 @ ( sk17 @ B @ C ) @ A ) )
| ( empty_set = A )
| ( in @ ( sk16 @ ( sk17 @ B @ C ) @ A ) @ ( sk17 @ B @ C ) )
| ( ( singleton @ A )
= C )
| ( B
= ( singleton @ C ) )
| ( in @ ( sk16 @ B @ C ) @ B ) ),
inference(pattern_uni,[status(thm)],[2584:[bind(A,$thf( sk17 @ E @ F )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( E ))]]) ).
thf(2894,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( empty @ ( sk17 @ ( sk17 @ B @ C ) @ A ) )
| ( empty_set = A )
| ( in @ ( sk16 @ ( sk17 @ B @ C ) @ A ) @ ( sk17 @ B @ C ) )
| ( ( singleton @ A )
= C )
| ( B
= ( singleton @ C ) )
| ( in @ ( sk16 @ B @ C ) @ B ) ),
inference(simp,[status(thm)],[2585]) ).
thf(3211,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( empty @ ( sk17 @ ( sk17 @ B @ C ) @ A ) )
| ( empty_set = A )
| ( in @ ( sk16 @ ( sk17 @ B @ C ) @ A ) @ ( sk17 @ B @ C ) )
| ( B
= ( singleton @ C ) )
| ( in @ ( sk16 @ B @ C ) @ B )
| ( ( singleton @ A )
= D )
| ( E
= ( singleton @ D ) )
| ( in @ ( sk16 @ E @ D ) @ E )
| ( C
!= ( sk17 @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[2894,174]) ).
thf(3212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( empty @ ( sk17 @ ( sk17 @ B @ ( sk17 @ C @ D ) ) @ A ) )
| ( empty_set = A )
| ( in @ ( sk16 @ ( sk17 @ B @ ( sk17 @ C @ D ) ) @ A ) @ ( sk17 @ B @ ( sk17 @ C @ D ) ) )
| ( B
= ( singleton @ ( sk17 @ C @ D ) ) )
| ( in @ ( sk16 @ B @ ( sk17 @ C @ D ) ) @ B )
| ( ( singleton @ A )
= D )
| ( C
= ( singleton @ D ) )
| ( in @ ( sk16 @ C @ D ) @ C ) ),
inference(pattern_uni,[status(thm)],[3211:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk17 @ F @ G )),bind(D,$thf( G )),bind(E,$thf( F ))]]) ).
thf(3944,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( empty @ ( sk17 @ ( sk17 @ B @ ( sk17 @ C @ D ) ) @ A ) )
| ( empty_set = A )
| ( in @ ( sk16 @ ( sk17 @ B @ ( sk17 @ C @ D ) ) @ A ) @ ( sk17 @ B @ ( sk17 @ C @ D ) ) )
| ( B
= ( singleton @ ( sk17 @ C @ D ) ) )
| ( in @ ( sk16 @ B @ ( sk17 @ C @ D ) ) @ B )
| ( ( singleton @ A )
= D )
| ( C
= ( singleton @ D ) )
| ( in @ ( sk16 @ C @ D ) @ C ) ),
inference(simp,[status(thm)],[3212]) ).
thf(21,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(100,plain,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(101,plain,
relation_empty_yielding @ sk9,
inference(cnf,[status(esa)],[100]) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( singleton @ A ) )
| ( C != A )
| ( in @ C @ B ) ),
inference(cnf,[status(esa)],[156]) ).
thf(163,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( singleton @ A ) )
| ( C != A )
| ( in @ C @ B ) ),
inference(lifteq,[status(thm)],[157]) ).
thf(164,plain,
! [A: $i] : ( in @ A @ ( singleton @ A ) ),
inference(simp,[status(thm)],[163]) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( singleton @ A ) )
| ~ ( in @ C @ B )
| ( C = A ) ),
inference(cnf,[status(esa)],[156]) ).
thf(167,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( singleton @ A ) )
| ( C = A )
| ~ ( in @ C @ B ) ),
inference(lifteq,[status(thm)],[161]) ).
thf(168,plain,
! [B: $i,A: $i] :
( ( B = A )
| ~ ( in @ B @ ( singleton @ A ) ) ),
inference(simp,[status(thm)],[167]) ).
thf(9,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(70,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(35,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(143,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(145,plain,
~ ( empty @ sk14 ),
inference(cnf,[status(esa)],[143]) ).
thf(252,plain,
( ( empty @ sk14 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[70,145]) ).
thf(254,plain,
sk14 != empty_set,
inference(simp,[status(thm)],[252]) ).
thf(13237,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( singleton @ A ) )
| ( A != empty_set )
| ( B != sk14 ) ),
inference(paramod_ordered,[status(thm)],[168,254]) ).
thf(13238,plain,
! [A: $i] :
( ~ ( in @ sk14 @ ( singleton @ A ) )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[13237:[bind(A,$thf( A )),bind(B,$thf( sk14 ))]]) ).
thf(13674,plain,
~ ( in @ sk14 @ ( singleton @ empty_set ) ),
inference(simp,[status(thm)],[13238]) ).
thf(14056,plain,
! [A: $i] :
( ( in @ A @ ( singleton @ A ) )
!= ( in @ sk14 @ ( singleton @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[164,13674]) ).
thf(14099,plain,
! [A: $i] :
( ( A != sk14 )
| ( ( singleton @ A )
!= ( singleton @ empty_set ) ) ),
inference(simp,[status(thm)],[14056]) ).
thf(14113,plain,
( ( singleton @ sk14 )
!= ( singleton @ empty_set ) ),
inference(simp,[status(thm)],[14099]) ).
thf(14849,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( singleton @ A ) )
| ( B
!= ( singleton @ empty_set ) )
| ( A
!= ( singleton @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[168,14113]) ).
thf(14850,plain,
! [A: $i] :
( ~ ( in @ A @ ( singleton @ ( singleton @ sk14 ) ) )
| ( A
!= ( singleton @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[14849:[bind(A,$thf( singleton @ sk14 )),bind(B,$thf( B ))]]) ).
thf(14919,plain,
~ ( in @ ( singleton @ empty_set ) @ ( singleton @ ( singleton @ sk14 ) ) ),
inference(simp,[status(thm)],[14850]) ).
thf(23686,plain,
! [A: $i] :
( ( in @ A @ ( singleton @ A ) )
!= ( in @ ( singleton @ empty_set ) @ ( singleton @ ( singleton @ sk14 ) ) ) ),
inference(paramod_ordered,[status(thm)],[164,14919]) ).
thf(23798,plain,
! [A: $i] :
( ( A
!= ( singleton @ empty_set ) )
| ( ( singleton @ A )
!= ( singleton @ ( singleton @ sk14 ) ) ) ),
inference(simp,[status(thm)],[23686]) ).
thf(23842,plain,
( ( singleton @ ( singleton @ sk14 ) )
!= ( singleton @ ( singleton @ empty_set ) ) ),
inference(simp,[status(thm)],[23798]) ).
thf(17,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(88,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(159,plain,
! [B: $i,A: $i] :
( ( ( sk16 @ B @ A )
!= A )
| ( ( sk17 @ B @ A )
= A )
| ( B
= ( singleton @ A ) ) ),
inference(cnf,[status(esa)],[156]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( ( sk16 @ B @ A )
!= A )
| ( ( sk17 @ B @ A )
= A )
| ( B
= ( singleton @ A ) ) ),
inference(lifteq,[status(thm)],[159]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( ( sk16 @ B @ A )
!= A )
| ( ( sk17 @ B @ A )
= A )
| ( B
= ( singleton @ A ) ) ),
inference(simp,[status(thm)],[169]) ).
thf(4,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(57,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(58,plain,
empty @ sk4,
inference(cnf,[status(esa)],[57]) ).
thf(1210,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ sk4 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[58,78]) ).
thf(1211,plain,
sk4 = empty_set,
inference(pattern_uni,[status(thm)],[1210:[bind(A,$thf( sk4 ))]]) ).
thf(33,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(139,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(140,plain,
! [A: $i] : ( subset @ A @ A ),
inference(cnf,[status(esa)],[139]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(146,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)],[36]) ).
thf(147,plain,
( ! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
=> ( subset @ A @ B ) )
& ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( element @ A @ ( powerset @ B ) ) ) ),
inference(miniscope,[status(thm)],[146]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ),
inference(cnf,[status(esa)],[147]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ),
inference(simp,[status(thm)],[148]) ).
thf(11055,plain,
! [C: $i,B: $i,A: $i] :
( ( element @ B @ ( powerset @ C ) )
| ( ( subset @ A @ A )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[140,150]) ).
thf(11056,plain,
! [A: $i] : ( element @ A @ ( powerset @ A ) ),
inference(pattern_uni,[status(thm)],[11055:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ),
inference(cnf,[status(esa)],[71]) ).
thf(11116,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ C )
| ( in @ B @ C )
| ( ( element @ A @ ( powerset @ A ) )
!= ( element @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[11056,72]) ).
thf(11117,plain,
! [A: $i] :
( ( empty @ ( powerset @ A ) )
| ( in @ A @ ( powerset @ A ) ) ),
inference(pattern_uni,[status(thm)],[11116:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( powerset @ D ))]]) ).
thf(11123,plain,
! [A: $i] :
( ( empty @ ( powerset @ A ) )
| ( in @ A @ ( powerset @ A ) ) ),
inference(simp,[status(thm)],[11117]) ).
thf(15,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(83,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(84,plain,
~ ? [A: $i] : ( empty @ ( powerset @ A ) ),
inference(miniscope,[status(thm)],[83]) ).
thf(85,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(cnf,[status(esa)],[84]) ).
thf(11867,plain,
! [A: $i] :
( $false
| ( in @ A @ ( powerset @ A ) ) ),
inference(rewrite,[status(thm)],[11123,85]) ).
thf(11868,plain,
! [A: $i] : ( in @ A @ ( powerset @ A ) ),
inference(simp,[status(thm)],[11867]) ).
thf(14086,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ sk14 @ ( singleton @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[11868,13674]) ).
thf(14100,plain,
! [A: $i] :
( ( A != sk14 )
| ( ( powerset @ A )
!= ( singleton @ empty_set ) ) ),
inference(simp,[status(thm)],[14086]) ).
thf(14114,plain,
( ( powerset @ sk14 )
!= ( singleton @ empty_set ) ),
inference(simp,[status(thm)],[14100]) ).
thf(14943,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( singleton @ A ) )
| ( B
!= ( singleton @ empty_set ) )
| ( A
!= ( powerset @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[168,14114]) ).
thf(14944,plain,
! [A: $i] :
( ~ ( in @ A @ ( singleton @ ( powerset @ sk14 ) ) )
| ( A
!= ( singleton @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[14943:[bind(A,$thf( powerset @ sk14 )),bind(B,$thf( B ))]]) ).
thf(14992,plain,
~ ( in @ ( singleton @ empty_set ) @ ( singleton @ ( powerset @ sk14 ) ) ),
inference(simp,[status(thm)],[14944]) ).
thf(24709,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( singleton @ empty_set ) @ ( singleton @ ( powerset @ sk14 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11868,14992]) ).
thf(24743,plain,
! [A: $i] :
( ( A
!= ( singleton @ empty_set ) )
| ( ( powerset @ A )
!= ( singleton @ ( powerset @ sk14 ) ) ) ),
inference(simp,[status(thm)],[24709]) ).
thf(24759,plain,
( ( powerset @ ( singleton @ empty_set ) )
!= ( singleton @ ( powerset @ sk14 ) ) ),
inference(simp,[status(thm)],[24743]) ).
thf(26,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(114,plain,
! [A: $i] : ( subset @ empty_set @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(115,plain,
! [A: $i] : ( subset @ empty_set @ A ),
inference(cnf,[status(esa)],[114]) ).
thf(144,plain,
relation @ sk14,
inference(cnf,[status(esa)],[143]) ).
thf(29,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
thf(126,plain,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_rng @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(127,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_rng @ A ) ) ),
inference(cnf,[status(esa)],[126]) ).
thf(2556,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( relation_rng @ A ) )
| ( ( relation @ sk14 )
!= ( relation @ A ) ) ),
inference(paramod_ordered,[status(thm)],[144,127]) ).
thf(2557,plain,
( ( empty @ sk14 )
| ~ ( empty @ ( relation_rng @ sk14 ) ) ),
inference(pattern_uni,[status(thm)],[2556:[bind(A,$thf( sk14 ))]]) ).
thf(10724,plain,
( $false
| ~ ( empty @ ( relation_rng @ sk14 ) ) ),
inference(rewrite,[status(thm)],[2557,145]) ).
thf(10725,plain,
~ ( empty @ ( relation_rng @ sk14 ) ),
inference(simp,[status(thm)],[10724]) ).
thf(10726,plain,
( ( empty @ ( relation_rng @ sk14 ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[70,10725]) ).
thf(10780,plain,
( ( relation_rng @ sk14 )
!= empty_set ),
inference(simp,[status(thm)],[10726]) ).
thf(251,plain,
( ( empty @ sk5 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[70,69]) ).
thf(253,plain,
sk5 != empty_set,
inference(simp,[status(thm)],[251]) ).
thf(12533,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( singleton @ A ) )
| ( A != empty_set )
| ( B != sk5 ) ),
inference(paramod_ordered,[status(thm)],[168,253]) ).
thf(12534,plain,
! [A: $i] :
( ~ ( in @ sk5 @ ( singleton @ A ) )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[12533:[bind(A,$thf( A )),bind(B,$thf( sk5 ))]]) ).
thf(13377,plain,
~ ( in @ sk5 @ ( singleton @ empty_set ) ),
inference(simp,[status(thm)],[12534]) ).
thf(13820,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ sk5 @ ( singleton @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[11868,13377]) ).
thf(13829,plain,
! [A: $i] :
( ( A != sk5 )
| ( ( powerset @ A )
!= ( singleton @ empty_set ) ) ),
inference(simp,[status(thm)],[13820]) ).
thf(13842,plain,
( ( powerset @ sk5 )
!= ( singleton @ empty_set ) ),
inference(simp,[status(thm)],[13829]) ).
thf(14259,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( singleton @ A ) )
| ( B
!= ( singleton @ empty_set ) )
| ( A
!= ( powerset @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[168,13842]) ).
thf(14260,plain,
! [A: $i] :
( ~ ( in @ A @ ( singleton @ ( powerset @ sk5 ) ) )
| ( A
!= ( singleton @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[14259:[bind(A,$thf( powerset @ sk5 )),bind(B,$thf( B ))]]) ).
thf(14315,plain,
~ ( in @ ( singleton @ empty_set ) @ ( singleton @ ( powerset @ sk5 ) ) ),
inference(simp,[status(thm)],[14260]) ).
thf(18650,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( singleton @ empty_set ) @ ( singleton @ ( powerset @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11868,14315]) ).
thf(18662,plain,
! [A: $i] :
( ( A
!= ( singleton @ empty_set ) )
| ( ( powerset @ A )
!= ( singleton @ ( powerset @ sk5 ) ) ) ),
inference(simp,[status(thm)],[18650]) ).
thf(18706,plain,
( ( powerset @ ( singleton @ empty_set ) )
!= ( singleton @ ( powerset @ sk5 ) ) ),
inference(simp,[status(thm)],[18662]) ).
thf(14845,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( singleton @ A ) )
| ( A
!= ( singleton @ empty_set ) )
| ( B
!= ( singleton @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[168,14113]) ).
thf(14846,plain,
! [A: $i] :
( ~ ( in @ ( singleton @ sk14 ) @ ( singleton @ A ) )
| ( A
!= ( singleton @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[14845:[bind(A,$thf( A )),bind(B,$thf( singleton @ sk14 ))]]) ).
thf(14937,plain,
~ ( in @ ( singleton @ sk14 ) @ ( singleton @ ( singleton @ empty_set ) ) ),
inference(simp,[status(thm)],[14846]) ).
thf(4297,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( empty @ ( sk17 @ ( sk17 @ B @ ( sk17 @ C @ D ) ) @ A ) )
| ( empty_set = A )
| ( in @ ( sk16 @ ( sk17 @ B @ ( sk17 @ C @ D ) ) @ A ) @ ( sk17 @ B @ ( sk17 @ C @ D ) ) )
| ( in @ ( sk16 @ B @ ( sk17 @ C @ D ) ) @ B )
| ( ( singleton @ A )
= D )
| ( C
= ( singleton @ D ) )
| ( in @ ( sk16 @ C @ D ) @ C )
| ( ( singleton @ ( sk17 @ C @ D ) )
= E )
| ( F
= ( singleton @ E ) )
| ( in @ ( sk16 @ F @ E ) @ F )
| ( B
!= ( sk17 @ F @ E ) ) ),
inference(paramod_ordered,[status(thm)],[3944,174]) ).
thf(4298,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( empty @ ( sk17 @ ( sk17 @ ( sk17 @ D @ E ) @ ( sk17 @ B @ C ) ) @ A ) )
| ( empty_set = A )
| ( in @ ( sk16 @ ( sk17 @ ( sk17 @ D @ E ) @ ( sk17 @ B @ C ) ) @ A ) @ ( sk17 @ ( sk17 @ D @ E ) @ ( sk17 @ B @ C ) ) )
| ( in @ ( sk16 @ ( sk17 @ D @ E ) @ ( sk17 @ B @ C ) ) @ ( sk17 @ D @ E ) )
| ( ( singleton @ A )
= C )
| ( B
= ( singleton @ C ) )
| ( in @ ( sk16 @ B @ C ) @ B )
| ( ( singleton @ ( sk17 @ B @ C ) )
= E )
| ( D
= ( singleton @ E ) )
| ( in @ ( sk16 @ D @ E ) @ D ) ),
inference(pattern_uni,[status(thm)],[4297:[bind(A,$thf( A )),bind(B,$thf( sk17 @ G @ H )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( H )),bind(F,$thf( G ))]]) ).
thf(5220,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( empty @ ( sk17 @ ( sk17 @ ( sk17 @ D @ E ) @ ( sk17 @ B @ C ) ) @ A ) )
| ( empty_set = A )
| ( in @ ( sk16 @ ( sk17 @ ( sk17 @ D @ E ) @ ( sk17 @ B @ C ) ) @ A ) @ ( sk17 @ ( sk17 @ D @ E ) @ ( sk17 @ B @ C ) ) )
| ( in @ ( sk16 @ ( sk17 @ D @ E ) @ ( sk17 @ B @ C ) ) @ ( sk17 @ D @ E ) )
| ( ( singleton @ A )
= C )
| ( B
= ( singleton @ C ) )
| ( in @ ( sk16 @ B @ C ) @ B )
| ( ( singleton @ ( sk17 @ B @ C ) )
= E )
| ( D
= ( singleton @ E ) )
| ( in @ ( sk16 @ D @ E ) @ D ) ),
inference(simp,[status(thm)],[4298]) ).
thf(5583,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( empty @ ( sk17 @ ( sk17 @ ( sk17 @ D @ E ) @ ( sk17 @ B @ C ) ) @ A ) )
| ( empty_set = A )
| ( in @ ( sk16 @ ( sk17 @ ( sk17 @ D @ E ) @ ( sk17 @ B @ C ) ) @ A ) @ ( sk17 @ ( sk17 @ D @ E ) @ ( sk17 @ B @ C ) ) )
| ( in @ ( sk16 @ ( sk17 @ D @ E ) @ ( sk17 @ B @ C ) ) @ ( sk17 @ D @ E ) )
| ( B
= ( singleton @ C ) )
| ( in @ ( sk16 @ B @ C ) @ B )
| ( ( singleton @ ( sk17 @ B @ C ) )
= E )
| ( D
= ( singleton @ E ) )
| ( in @ ( sk16 @ D @ E ) @ D )
| ( ( singleton @ A )
= F )
| ( G
= ( singleton @ F ) )
| ( in @ ( sk16 @ G @ F ) @ G )
| ( C
!= ( sk17 @ G @ F ) ) ),
inference(paramod_ordered,[status(thm)],[5220,174]) ).
thf(5584,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( empty @ ( sk17 @ ( sk17 @ ( sk17 @ C @ D ) @ ( sk17 @ B @ ( sk17 @ E @ F ) ) ) @ A ) )
| ( empty_set = A )
| ( in @ ( sk16 @ ( sk17 @ ( sk17 @ C @ D ) @ ( sk17 @ B @ ( sk17 @ E @ F ) ) ) @ A ) @ ( sk17 @ ( sk17 @ C @ D ) @ ( sk17 @ B @ ( sk17 @ E @ F ) ) ) )
| ( in @ ( sk16 @ ( sk17 @ C @ D ) @ ( sk17 @ B @ ( sk17 @ E @ F ) ) ) @ ( sk17 @ C @ D ) )
| ( B
= ( singleton @ ( sk17 @ E @ F ) ) )
| ( in @ ( sk16 @ B @ ( sk17 @ E @ F ) ) @ B )
| ( ( singleton @ ( sk17 @ B @ ( sk17 @ E @ F ) ) )
= D )
| ( C
= ( singleton @ D ) )
| ( in @ ( sk16 @ C @ D ) @ C )
| ( ( singleton @ A )
= F )
| ( E
= ( singleton @ F ) )
| ( in @ ( sk16 @ E @ F ) @ E ) ),
inference(pattern_uni,[status(thm)],[5583:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk17 @ H @ I )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( I )),bind(G,$thf( H ))]]) ).
thf(7208,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( empty @ ( sk17 @ ( sk17 @ ( sk17 @ C @ D ) @ ( sk17 @ B @ ( sk17 @ E @ F ) ) ) @ A ) )
| ( empty_set = A )
| ( in @ ( sk16 @ ( sk17 @ ( sk17 @ C @ D ) @ ( sk17 @ B @ ( sk17 @ E @ F ) ) ) @ A ) @ ( sk17 @ ( sk17 @ C @ D ) @ ( sk17 @ B @ ( sk17 @ E @ F ) ) ) )
| ( in @ ( sk16 @ ( sk17 @ C @ D ) @ ( sk17 @ B @ ( sk17 @ E @ F ) ) ) @ ( sk17 @ C @ D ) )
| ( B
= ( singleton @ ( sk17 @ E @ F ) ) )
| ( in @ ( sk16 @ B @ ( sk17 @ E @ F ) ) @ B )
| ( ( singleton @ ( sk17 @ B @ ( sk17 @ E @ F ) ) )
= D )
| ( C
= ( singleton @ D ) )
| ( in @ ( sk16 @ C @ D ) @ C )
| ( ( singleton @ A )
= F )
| ( E
= ( singleton @ F ) )
| ( in @ ( sk16 @ E @ F ) @ E ) ),
inference(simp,[status(thm)],[5584]) ).
thf(32,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(135,plain,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(136,plain,
function @ sk13,
inference(cnf,[status(esa)],[135]) ).
thf(137,plain,
empty @ sk13,
inference(cnf,[status(esa)],[135]) ).
thf(1120,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ sk13 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[137,78]) ).
thf(1121,plain,
sk13 = empty_set,
inference(pattern_uni,[status(thm)],[1120:[bind(A,$thf( sk13 ))]]) ).
thf(1305,plain,
function @ empty_set,
inference(rewrite,[status(thm)],[136,1121]) ).
thf(14939,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( singleton @ A ) )
| ( A
!= ( singleton @ empty_set ) )
| ( B
!= ( powerset @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[168,14114]) ).
thf(14940,plain,
! [A: $i] :
( ~ ( in @ ( powerset @ sk14 ) @ ( singleton @ A ) )
| ( A
!= ( singleton @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[14939:[bind(A,$thf( A )),bind(B,$thf( powerset @ sk14 ))]]) ).
thf(15003,plain,
~ ( in @ ( powerset @ sk14 ) @ ( singleton @ ( singleton @ empty_set ) ) ),
inference(simp,[status(thm)],[14940]) ).
thf(24985,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk14 ) @ ( singleton @ ( singleton @ empty_set ) ) ) ),
inference(paramod_ordered,[status(thm)],[11868,15003]) ).
thf(25006,plain,
! [A: $i] :
( ( A
!= ( powerset @ sk14 ) )
| ( ( powerset @ A )
!= ( singleton @ ( singleton @ empty_set ) ) ) ),
inference(simp,[status(thm)],[24985]) ).
thf(25039,plain,
( ( powerset @ ( powerset @ sk14 ) )
!= ( singleton @ ( singleton @ empty_set ) ) ),
inference(simp,[status(thm)],[25006]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
<=> ! [B: $i] :
? [C: $i] : ( subset @ ( relation_inverse_image @ A @ ( singleton @ B ) ) @ ( singleton @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_funct_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( one_to_one @ A )
<=> ! [B: $i] :
? [C: $i] : ( subset @ ( relation_inverse_image @ A @ ( singleton @ B ) ) @ ( singleton @ C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(45,plain,
~ ! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( ( one_to_one @ A )
=> ! [B: $i] :
? [C: $i] : ( subset @ ( relation_inverse_image @ A @ ( singleton @ B ) ) @ ( singleton @ C ) ) )
& ( ! [B: $i] :
? [C: $i] : ( subset @ ( relation_inverse_image @ A @ ( singleton @ B ) ) @ ( singleton @ C ) )
=> ( one_to_one @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(50,plain,
relation @ sk1,
inference(cnf,[status(esa)],[45]) ).
thf(31,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(133,plain,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(134,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ),
inference(cnf,[status(esa)],[133]) ).
thf(5549,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( relation_dom @ A ) )
| ( ( relation @ sk1 )
!= ( relation @ A ) ) ),
inference(paramod_ordered,[status(thm)],[50,134]) ).
thf(5550,plain,
( ( empty @ sk1 )
| ~ ( empty @ ( relation_dom @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[5549:[bind(A,$thf( sk1 ))]]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(53,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(54,plain,
~ ? [A: $i] :
( ( empty @ A )
& ? [B: $i] :
( ( A != B )
& ( empty @ B ) ) ),
inference(miniscope,[status(thm)],[53]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( A = B )
| ~ ( empty @ B ) ),
inference(cnf,[status(esa)],[54]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ),
inference(lifteq,[status(thm)],[55]) ).
thf(13239,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( singleton @ A ) )
| ( B != empty_set )
| ( A != sk14 ) ),
inference(paramod_ordered,[status(thm)],[168,254]) ).
thf(13240,plain,
! [A: $i] :
( ~ ( in @ A @ ( singleton @ sk14 ) )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[13239:[bind(A,$thf( sk14 ))]]) ).
thf(13675,plain,
~ ( in @ empty_set @ ( singleton @ sk14 ) ),
inference(simp,[status(thm)],[13240]) ).
thf(12284,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( singleton @ A ) )
| ( A != empty_set )
| ( B
!= ( relation_rng @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[168,10780]) ).
thf(12285,plain,
! [A: $i] :
( ~ ( in @ ( relation_rng @ sk14 ) @ ( singleton @ A ) )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[12284:[bind(A,$thf( A )),bind(B,$thf( relation_rng @ sk14 ))]]) ).
thf(13722,plain,
~ ( in @ ( relation_rng @ sk14 ) @ ( singleton @ empty_set ) ),
inference(simp,[status(thm)],[12285]) ).
thf(34,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(141,plain,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(142,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ),
inference(cnf,[status(esa)],[141]) ).
thf(37,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(151,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(153,plain,
function @ sk15,
inference(cnf,[status(esa)],[151]) ).
thf(22,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
thf(103,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_rng @ A ) )
& ( relation @ ( relation_rng @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(104,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ A ) ) ),
inference(cnf,[status(esa)],[103]) ).
thf(1675,plain,
! [A: $i] :
( ( empty @ ( relation_rng @ A ) )
| ( ( empty @ empty_set )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[70,104]) ).
thf(1676,plain,
empty @ ( relation_rng @ empty_set ),
inference(pattern_uni,[status(thm)],[1675:[bind(A,$thf( empty_set ))]]) ).
thf(1752,plain,
! [A: $i] :
( ( empty @ ( relation_rng @ A ) )
| ( ( empty @ ( relation_rng @ empty_set ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1676,104]) ).
thf(1753,plain,
empty @ ( relation_rng @ ( relation_rng @ empty_set ) ),
inference(pattern_uni,[status(thm)],[1752:[bind(A,$thf( relation_rng @ empty_set ))]]) ).
thf(1737,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ ( relation_rng @ empty_set ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1676,78]) ).
thf(1738,plain,
( ( relation_rng @ empty_set )
= empty_set ),
inference(pattern_uni,[status(thm)],[1737:[bind(A,$thf( relation_rng @ empty_set ))]]) ).
thf(1788,plain,
empty @ ( relation_rng @ empty_set ),
inference(rewrite,[status(thm)],[1753,1738]) ).
thf(90,plain,
! [A: $i] : ( element @ ( sk7 @ A ) @ ( powerset @ A ) ),
inference(cnf,[status(esa)],[88]) ).
thf(89,plain,
! [A: $i] : ( empty @ ( sk7 @ A ) ),
inference(cnf,[status(esa)],[88]) ).
thf(1098,plain,
! [B: $i,A: $i] :
( ( B = empty_set )
| ( ( empty @ ( sk7 @ A ) )
!= ( empty @ B ) ) ),
inference(paramod_ordered,[status(thm)],[89,78]) ).
thf(1099,plain,
! [A: $i] :
( ( sk7 @ A )
= empty_set ),
inference(pattern_uni,[status(thm)],[1098:[bind(A,$thf( C )),bind(B,$thf( sk7 @ C ))]]) ).
thf(1271,plain,
! [A: $i] :
( ( sk7 @ A )
= empty_set ),
inference(simp,[status(thm)],[1099]) ).
thf(1426,plain,
! [A: $i] : ( element @ empty_set @ ( powerset @ A ) ),
inference(rewrite,[status(thm)],[90,1271]) ).
thf(14218,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ empty_set @ ( singleton @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[11868,13675]) ).
thf(14233,plain,
! [A: $i] :
( ( A != empty_set )
| ( ( powerset @ A )
!= ( singleton @ sk14 ) ) ),
inference(simp,[status(thm)],[14218]) ).
thf(14247,plain,
( ( powerset @ empty_set )
!= ( singleton @ sk14 ) ),
inference(simp,[status(thm)],[14233]) ).
thf(15005,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( singleton @ A ) )
| ( A
!= ( singleton @ sk14 ) )
| ( B
!= ( powerset @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[168,14247]) ).
thf(15006,plain,
! [A: $i] :
( ~ ( in @ ( powerset @ empty_set ) @ ( singleton @ A ) )
| ( A
!= ( singleton @ sk14 ) ) ),
inference(pattern_uni,[status(thm)],[15005:[bind(A,$thf( A )),bind(B,$thf( powerset @ empty_set ))]]) ).
thf(15072,plain,
~ ( in @ ( powerset @ empty_set ) @ ( singleton @ ( singleton @ sk14 ) ) ),
inference(simp,[status(thm)],[15006]) ).
thf(40,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(185,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(12535,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( singleton @ A ) )
| ( B != empty_set )
| ( A != sk5 ) ),
inference(paramod_ordered,[status(thm)],[168,253]) ).
thf(12536,plain,
! [A: $i] :
( ~ ( in @ A @ ( singleton @ sk5 ) )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[12535:[bind(A,$thf( sk5 ))]]) ).
thf(13378,plain,
~ ( in @ empty_set @ ( singleton @ sk5 ) ),
inference(simp,[status(thm)],[12536]) ).
thf(2560,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( relation_rng @ A ) )
| ( ( relation @ sk1 )
!= ( relation @ A ) ) ),
inference(paramod_ordered,[status(thm)],[50,127]) ).
thf(2561,plain,
( ( empty @ sk1 )
| ~ ( empty @ ( relation_rng @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[2560:[bind(A,$thf( sk1 ))]]) ).
thf(2994,plain,
( ( empty @ sk1 )
| ( ( empty @ ( relation_rng @ sk1 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[70,2561]) ).
thf(3016,plain,
( ( empty @ sk1 )
| ( ( relation_rng @ sk1 )
!= empty_set ) ),
inference(simp,[status(thm)],[2994]) ).
thf(3034,plain,
( ( empty @ sk1 )
| ( ( relation_rng @ sk1 )
!= ( relation_rng @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[1738,3016]) ).
thf(3035,plain,
( ( empty @ sk1 )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[3034]) ).
thf(187,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ),
inference(cnf,[status(esa)],[185]) ).
thf(19418,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( relation @ ( relation_dom @ A ) )
| ( ( empty @ sk1 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3035,187]) ).
thf(19419,plain,
( ( sk1 != empty_set )
| ( relation @ ( relation_dom @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[19418:[bind(A,$thf( sk1 ))]]) ).
thf(51,plain,
! [A: $i] :
( ( one_to_one @ sk1 )
| ( subset @ ( relation_inverse_image @ sk1 @ ( singleton @ A ) ) @ ( singleton @ ( sk3 @ A ) ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(52,plain,
! [A: $i] :
( ( one_to_one @ sk1 )
| ( subset @ ( relation_inverse_image @ sk1 @ ( singleton @ A ) ) @ ( singleton @ ( sk3 @ A ) ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(175,plain,
! [A: $i,B: $i] :
( ( ( subset @ A @ ( singleton @ B ) )
=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) )
& ( ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
=> ( subset @ A @ ( singleton @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(176,plain,
( ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) )
& ! [A: $i,B: $i] :
( ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
=> ( subset @ A @ ( singleton @ B ) ) ) ),
inference(miniscope,[status(thm)],[175]) ).
thf(179,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ ( singleton @ B ) )
| ( A = empty_set )
| ( A
= ( singleton @ B ) ) ),
inference(cnf,[status(esa)],[176]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( A = empty_set )
| ( A
= ( singleton @ B ) )
| ~ ( subset @ A @ ( singleton @ B ) ) ),
inference(lifteq,[status(thm)],[179]) ).
thf(44,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(244,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(246,plain,
relation @ sk26,
inference(cnf,[status(esa)],[244]) ).
thf(2570,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( relation_rng @ A ) )
| ( ( relation @ sk26 )
!= ( relation @ A ) ) ),
inference(paramod_ordered,[status(thm)],[246,127]) ).
thf(2571,plain,
( ( empty @ sk26 )
| ~ ( empty @ ( relation_rng @ sk26 ) ) ),
inference(pattern_uni,[status(thm)],[2570:[bind(A,$thf( sk26 ))]]) ).
thf(186,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) ),
inference(cnf,[status(esa)],[185]) ).
thf(18815,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( empty @ ( relation_dom @ A ) )
| ( ( empty @ sk1 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3035,186]) ).
thf(18816,plain,
( ( sk1 != empty_set )
| ( empty @ ( relation_dom @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[18815:[bind(A,$thf( sk1 ))]]) ).
thf(25472,plain,
( ( sk1 != empty_set )
| ( ( empty @ ( relation_dom @ sk1 ) )
!= ( empty @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[18816,145]) ).
thf(25516,plain,
( ( sk1 != empty_set )
| ( ( relation_dom @ sk1 )
!= sk14 ) ),
inference(simp,[status(thm)],[25472]) ).
thf(28,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ! [B: $i] :
~ ( ( in @ B @ ( relation_rng @ A ) )
& ! [C: $i] :
( ( relation_inverse_image @ A @ ( singleton @ B ) )
!= ( singleton @ C ) ) )
<=> ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_funct_1) ).
thf(118,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( ! [B: $i] :
~ ( ( in @ B @ ( relation_rng @ A ) )
& ! [C: $i] :
( ( relation_inverse_image @ A @ ( singleton @ B ) )
!= ( singleton @ C ) ) )
=> ( one_to_one @ A ) )
& ( ( one_to_one @ A )
=> ! [B: $i] :
~ ( ( in @ B @ ( relation_rng @ A ) )
& ! [C: $i] :
( ( relation_inverse_image @ A @ ( singleton @ B ) )
!= ( singleton @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(119,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ( ~ ? [B: $i] :
( ( in @ B @ ( relation_rng @ A ) )
& ~ ? [C: $i] :
( ( relation_inverse_image @ A @ ( singleton @ B ) )
= ( singleton @ C ) ) )
=> ( one_to_one @ A ) )
& ( ( one_to_one @ A )
=> ~ ? [B: $i] :
( ( in @ B @ ( relation_rng @ A ) )
& ~ ? [C: $i] :
( ( relation_inverse_image @ A @ ( singleton @ B ) )
= ( singleton @ C ) ) ) ) ) ),
inference(miniscope,[status(thm)],[118]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( one_to_one @ A )
| ~ ( in @ B @ ( relation_rng @ A ) )
| ( ( relation_inverse_image @ A @ ( singleton @ B ) )
= ( singleton @ ( sk12 @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[119]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( ( relation_inverse_image @ A @ ( singleton @ B ) )
= ( singleton @ ( sk12 @ B @ A ) ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( one_to_one @ A )
| ~ ( in @ B @ ( relation_rng @ A ) ) ),
inference(lifteq,[status(thm)],[122]) ).
thf(125,plain,
! [B: $i,A: $i] :
( ( ( relation_inverse_image @ A @ ( singleton @ B ) )
= ( singleton @ ( sk12 @ B @ A ) ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( one_to_one @ A )
| ~ ( in @ B @ ( relation_rng @ A ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ~ ( subset @ ( relation_inverse_image @ sk1 @ ( singleton @ sk2 ) ) @ ( singleton @ A ) )
| ( subset @ ( relation_inverse_image @ sk1 @ ( singleton @ B ) ) @ ( singleton @ ( sk3 @ B ) ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(19,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(93,plain,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(152,plain,
one_to_one @ sk15,
inference(cnf,[status(esa)],[151]) ).
thf(12288,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( singleton @ A ) )
| ( B != empty_set )
| ( A
!= ( relation_rng @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[168,10780]) ).
thf(12289,plain,
! [A: $i] :
( ~ ( in @ A @ ( singleton @ ( relation_rng @ sk14 ) ) )
| ( A != empty_set ) ),
inference(pattern_uni,[status(thm)],[12288:[bind(A,$thf( relation_rng @ sk14 )),bind(B,$thf( B ))]]) ).
thf(13265,plain,
~ ( in @ empty_set @ ( singleton @ ( relation_rng @ sk14 ) ) ),
inference(simp,[status(thm)],[12289]) ).
thf(16134,plain,
! [A: $i] :
( ( in @ A @ ( singleton @ A ) )
!= ( in @ empty_set @ ( singleton @ ( relation_rng @ sk14 ) ) ) ),
inference(paramod_ordered,[status(thm)],[164,13265]) ).
thf(16201,plain,
! [A: $i] :
( ( A != empty_set )
| ( ( singleton @ A )
!= ( singleton @ ( relation_rng @ sk14 ) ) ) ),
inference(simp,[status(thm)],[16134]) ).
thf(16223,plain,
( ( singleton @ ( relation_rng @ sk14 ) )
!= ( singleton @ empty_set ) ),
inference(simp,[status(thm)],[16201]) ).
thf(1088,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( one_to_one @ empty_set )
| ( A != sk15 ) ),
inference(paramod_ordered,[status(thm)],[78,152]) ).
thf(1089,plain,
( ~ ( empty @ sk15 )
| ( one_to_one @ empty_set ) ),
inference(pattern_uni,[status(thm)],[1088:[bind(A,$thf( sk15 ))]]) ).
thf(2169,plain,
( ( one_to_one @ empty_set )
| ( ( empty @ sk15 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[70,1089]) ).
thf(2178,plain,
( ( one_to_one @ empty_set )
| ( sk15 != empty_set ) ),
inference(simp,[status(thm)],[2169]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(81,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ),
inference(cnf,[status(esa)],[81]) ).
thf(1459,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( ( in @ A @ ( singleton @ A ) )
!= ( in @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[164,82]) ).
thf(1460,plain,
! [A: $i] :
~ ( in @ ( singleton @ A ) @ A ),
inference(pattern_uni,[status(thm)],[1459:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( singleton @ D ))]]) ).
thf(1465,plain,
! [A: $i] :
~ ( in @ ( singleton @ A ) @ A ),
inference(simp,[status(thm)],[1460]) ).
thf(1487,plain,
! [B: $i,A: $i] :
( ( in @ A @ ( singleton @ A ) )
!= ( in @ ( singleton @ B ) @ B ) ),
inference(paramod_ordered,[status(thm)],[164,1465]) ).
thf(1488,plain,
! [B: $i,A: $i] :
( ( A
!= ( singleton @ B ) )
| ( ( singleton @ A )
!= B ) ),
inference(simp,[status(thm)],[1487]) ).
thf(1489,plain,
! [A: $i] :
( ( singleton @ ( singleton @ A ) )
!= A ),
inference(simp,[status(thm)],[1488]) ).
thf(121,plain,
! [A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ( in @ ( sk11 @ A ) @ ( relation_rng @ A ) )
| ( one_to_one @ A ) ),
inference(cnf,[status(esa)],[119]) ).
thf(23764,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( singleton @ empty_set ) @ ( singleton @ ( singleton @ sk14 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11868,14919]) ).
thf(23781,plain,
! [A: $i] :
( ( A
!= ( singleton @ empty_set ) )
| ( ( powerset @ A )
!= ( singleton @ ( singleton @ sk14 ) ) ) ),
inference(simp,[status(thm)],[23764]) ).
thf(23839,plain,
( ( powerset @ ( singleton @ empty_set ) )
!= ( singleton @ ( singleton @ sk14 ) ) ),
inference(simp,[status(thm)],[23781]) ).
thf(3158,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( empty @ ( relation_rng @ A ) )
| ( ( empty @ sk1 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3035,104]) ).
thf(3159,plain,
( ( sk1 != empty_set )
| ( empty @ ( relation_rng @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[3158:[bind(A,$thf( sk1 ))]]) ).
thf(7583,plain,
( ( sk1 != empty_set )
| ( ( empty @ ( relation_rng @ sk1 ) )
!= ( empty @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[3159,69]) ).
thf(7684,plain,
( ( sk1 != empty_set )
| ( ( relation_rng @ sk1 )
!= sk5 ) ),
inference(simp,[status(thm)],[7583]) ).
thf(11167,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( relation_rng @ sk1 )
!= sk5 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[78,7684]) ).
thf(11168,plain,
( ~ ( empty @ sk1 )
| ( ( relation_rng @ sk1 )
!= sk5 ) ),
inference(pattern_uni,[status(thm)],[11167:[bind(A,$thf( sk1 ))]]) ).
thf(15009,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( singleton @ A ) )
| ( B
!= ( singleton @ sk14 ) )
| ( A
!= ( powerset @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[168,14247]) ).
thf(15010,plain,
! [A: $i] :
( ~ ( in @ A @ ( singleton @ ( powerset @ empty_set ) ) )
| ( A
!= ( singleton @ sk14 ) ) ),
inference(pattern_uni,[status(thm)],[15009:[bind(A,$thf( powerset @ empty_set )),bind(B,$thf( B ))]]) ).
thf(15060,plain,
~ ( in @ ( singleton @ sk14 ) @ ( singleton @ ( powerset @ empty_set ) ) ),
inference(simp,[status(thm)],[15010]) ).
thf(41,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
thf(188,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i] :
( ( ( B
= ( relation_rng @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) )
& ( ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) )
& ( ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) )
=> ( in @ C @ B ) ) )
=> ( B
= ( relation_rng @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(189,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ! [B: $i] :
( ( B
= ( relation_rng @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) )
& ! [C: $i] :
( ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) )
=> ( in @ C @ B ) ) ) )
& ! [B: $i] :
( ( ! [C: $i] :
( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) ) )
& ! [C: $i] :
( ? [D: $i] :
( ( in @ D @ ( relation_dom @ A ) )
& ( C
= ( apply @ A @ D ) ) )
=> ( in @ C @ B ) ) )
=> ( B
= ( relation_rng @ A ) ) ) ) ),
inference(miniscope,[status(thm)],[188]) ).
thf(190,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ( B
!= ( relation_rng @ A ) )
| ~ ( in @ C @ B )
| ( in @ ( sk18 @ C @ B @ A ) @ ( relation_dom @ A ) ) ),
inference(cnf,[status(esa)],[189]) ).
thf(210,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( relation_rng @ A ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ C @ B )
| ( in @ ( sk18 @ C @ B @ A ) @ ( relation_dom @ A ) ) ),
inference(lifteq,[status(thm)],[190]) ).
thf(211,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ B @ ( relation_rng @ A ) )
| ( in @ ( sk18 @ B @ ( relation_rng @ A ) @ A ) @ ( relation_dom @ A ) ) ),
inference(simp,[status(thm)],[210]) ).
thf(13790,plain,
! [A: $i] :
( ( in @ A @ ( singleton @ A ) )
!= ( in @ sk5 @ ( singleton @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[164,13377]) ).
thf(13831,plain,
! [A: $i] :
( ( A != sk5 )
| ( ( singleton @ A )
!= ( singleton @ empty_set ) ) ),
inference(simp,[status(thm)],[13790]) ).
thf(13844,plain,
( ( singleton @ sk5 )
!= ( singleton @ empty_set ) ),
inference(simp,[status(thm)],[13831]) ).
thf(14322,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( singleton @ A ) )
| ( A
!= ( singleton @ empty_set ) )
| ( B
!= ( singleton @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[168,13844]) ).
thf(14323,plain,
! [A: $i] :
( ~ ( in @ ( singleton @ sk5 ) @ ( singleton @ A ) )
| ( A
!= ( singleton @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[14322:[bind(A,$thf( A )),bind(B,$thf( singleton @ sk5 ))]]) ).
thf(14408,plain,
~ ( in @ ( singleton @ sk5 ) @ ( singleton @ ( singleton @ empty_set ) ) ),
inference(simp,[status(thm)],[14323]) ).
thf(23,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(106,plain,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( ( relation_inverse_image @ B @ A )
= empty_set )
<=> ( disjoint @ ( relation_rng @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t173_relat_1) ).
thf(128,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( ( ( ( relation_inverse_image @ B @ A )
= empty_set )
=> ( disjoint @ ( relation_rng @ B ) @ A ) )
& ( ( disjoint @ ( relation_rng @ B ) @ A )
=> ( ( relation_inverse_image @ B @ A )
= empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ~ ( relation @ B )
| ~ ( disjoint @ ( relation_rng @ B ) @ A )
| ( ( relation_inverse_image @ B @ A )
= empty_set ) ),
inference(cnf,[status(esa)],[128]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( ( relation_inverse_image @ B @ A )
= empty_set )
| ~ ( relation @ B )
| ~ ( disjoint @ ( relation_rng @ B ) @ A ) ),
inference(lifteq,[status(thm)],[130]) ).
thf(13952,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ empty_set @ ( singleton @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[11868,13378]) ).
thf(13965,plain,
! [A: $i] :
( ( A != empty_set )
| ( ( powerset @ A )
!= ( singleton @ sk5 ) ) ),
inference(simp,[status(thm)],[13952]) ).
thf(13977,plain,
( ( powerset @ empty_set )
!= ( singleton @ sk5 ) ),
inference(simp,[status(thm)],[13965]) ).
thf(14780,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( singleton @ A ) )
| ( B
!= ( singleton @ sk5 ) )
| ( A
!= ( powerset @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[168,13977]) ).
thf(14781,plain,
! [A: $i] :
( ~ ( in @ A @ ( singleton @ ( powerset @ empty_set ) ) )
| ( A
!= ( singleton @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[14780:[bind(A,$thf( powerset @ empty_set )),bind(B,$thf( B ))]]) ).
thf(14841,plain,
~ ( in @ ( singleton @ sk5 ) @ ( singleton @ ( powerset @ empty_set ) ) ),
inference(simp,[status(thm)],[14781]) ).
thf(23471,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( singleton @ sk5 ) @ ( singleton @ ( powerset @ empty_set ) ) ) ),
inference(paramod_ordered,[status(thm)],[11868,14841]) ).
thf(23505,plain,
! [A: $i] :
( ( A
!= ( singleton @ sk5 ) )
| ( ( powerset @ A )
!= ( singleton @ ( powerset @ empty_set ) ) ) ),
inference(simp,[status(thm)],[23471]) ).
thf(23534,plain,
( ( powerset @ ( singleton @ sk5 ) )
!= ( singleton @ ( powerset @ empty_set ) ) ),
inference(simp,[status(thm)],[23505]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(73,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(74,plain,
! [A: $i] :
( ( empty @ A )
| ( element @ ( sk6 @ A ) @ ( powerset @ A ) ) ),
inference(cnf,[status(esa)],[73]) ).
thf(3122,plain,
( ( sk1 != empty_set )
| ( ( empty @ sk5 )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[3035,69]) ).
thf(3166,plain,
( ( sk1 != empty_set )
| ( sk5 != sk1 ) ),
inference(simp,[status(thm)],[3122]) ).
thf(3183,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk5 != sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[78,3166]) ).
thf(3184,plain,
( ~ ( empty @ sk1 )
| ( sk5 != sk1 ) ),
inference(pattern_uni,[status(thm)],[3183:[bind(A,$thf( sk1 ))]]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(59,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(60,plain,
~ ? [A: $i,B: $i] :
( ( in @ A @ B )
& ? [C: $i] :
( ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) ),
inference(miniscope,[status(thm)],[59]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( element @ B @ ( powerset @ C ) )
| ~ ( empty @ C ) ),
inference(cnf,[status(esa)],[60]) ).
thf(27,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(116,plain,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(678,plain,
! [B: $i,A: $i] :
( ( empty @ ( sk7 @ A ) )
!= ( empty @ ( powerset @ B ) ) ),
inference(paramod_ordered,[status(thm)],[89,85]) ).
thf(684,plain,
! [B: $i,A: $i] :
( ( sk7 @ A )
!= ( powerset @ B ) ),
inference(simp,[status(thm)],[678]) ).
thf(1405,plain,
! [A: $i] :
( ( powerset @ A )
!= empty_set ),
inference(rewrite,[status(thm)],[684,1271]) ).
thf(19372,plain,
! [A: $i] :
( ( relation @ ( relation_dom @ A ) )
| ( ( empty @ ( relation_rng @ empty_set ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1788,187]) ).
thf(19373,plain,
relation @ ( relation_dom @ ( relation_rng @ empty_set ) ),
inference(pattern_uni,[status(thm)],[19372:[bind(A,$thf( relation_rng @ empty_set ))]]) ).
thf(20762,plain,
relation @ ( relation_dom @ empty_set ),
inference(rewrite,[status(thm)],[19373,1738]) ).
thf(117,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ),
inference(cnf,[status(esa)],[116]) ).
thf(21083,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( singleton @ sk5 ) @ ( singleton @ ( singleton @ empty_set ) ) ) ),
inference(paramod_ordered,[status(thm)],[11868,14408]) ).
thf(21099,plain,
! [A: $i] :
( ( A
!= ( singleton @ sk5 ) )
| ( ( powerset @ A )
!= ( singleton @ ( singleton @ empty_set ) ) ) ),
inference(simp,[status(thm)],[21083]) ).
thf(21133,plain,
( ( powerset @ ( singleton @ sk5 ) )
!= ( singleton @ ( singleton @ empty_set ) ) ),
inference(simp,[status(thm)],[21099]) ).
thf(1463,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( ( in @ B @ A )
!= ( in @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[82]) ).
thf(1464,plain,
! [A: $i] :
~ ( in @ A @ A ),
inference(pattern_uni,[status(thm)],[1463:[bind(A,$thf( B ))]]) ).
thf(1467,plain,
! [A: $i] :
~ ( in @ A @ A ),
inference(simp,[status(thm)],[1464]) ).
thf(1468,plain,
! [B: $i,A: $i] :
( ( in @ A @ ( singleton @ A ) )
!= ( in @ B @ B ) ),
inference(paramod_ordered,[status(thm)],[164,1467]) ).
thf(1469,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( singleton @ A )
!= B ) ),
inference(simp,[status(thm)],[1468]) ).
thf(1470,plain,
! [A: $i] :
( ( singleton @ A )
!= A ),
inference(simp,[status(thm)],[1469]) ).
thf(102,plain,
relation @ sk9,
inference(cnf,[status(esa)],[100]) ).
thf(192,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ( sk19 @ A @ B )
| ( ( sk21 @ B @ A )
= ( apply @ A @ ( sk22 @ B @ A ) ) )
| ( B
= ( relation_rng @ A ) ) ),
inference(cnf,[status(esa)],[189]) ).
thf(200,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ B @ A )
= ( apply @ A @ ( sk22 @ B @ A ) ) )
| ( B
= ( relation_rng @ A ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( sk19 @ A @ B ) ),
inference(lifteq,[status(thm)],[192]) ).
thf(201,plain,
! [B: $i,A: $i] :
( ( ( sk21 @ B @ A )
= ( apply @ A @ ( sk22 @ B @ A ) ) )
| ( B
= ( relation_rng @ A ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( sk19 @ A @ B ) ),
inference(simp,[status(thm)],[200]) ).
thf(25191,plain,
! [A: $i] :
( ( in @ A @ ( singleton @ A ) )
!= ( in @ ( singleton @ sk14 ) @ ( singleton @ ( powerset @ empty_set ) ) ) ),
inference(paramod_ordered,[status(thm)],[164,15060]) ).
thf(25291,plain,
! [A: $i] :
( ( A
!= ( singleton @ sk14 ) )
| ( ( singleton @ A )
!= ( singleton @ ( powerset @ empty_set ) ) ) ),
inference(simp,[status(thm)],[25191]) ).
thf(25321,plain,
( ( singleton @ ( powerset @ empty_set ) )
!= ( singleton @ ( singleton @ sk14 ) ) ),
inference(simp,[status(thm)],[25291]) ).
thf(18,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(91,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(92,plain,
! [A: $i] : ( element @ ( sk8 @ A ) @ A ),
inference(cnf,[status(esa)],[91]) ).
thf(42,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ ( relation_dom @ A ) )
& ( in @ ( apply @ A @ D ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
thf(214,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( C
= ( relation_inverse_image @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ ( relation_dom @ A ) )
& ( in @ ( apply @ A @ D ) @ B ) ) )
& ( ( ( in @ D @ ( relation_dom @ A ) )
& ( in @ ( apply @ A @ D ) @ B ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ ( relation_dom @ A ) )
& ( in @ ( apply @ A @ D ) @ B ) ) )
& ( ( ( in @ D @ ( relation_dom @ A ) )
& ( in @ ( apply @ A @ D ) @ B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( relation_inverse_image @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(215,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ! [B: $i,C: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
=> ( ! [D: $i] :
( ( in @ D @ C )
=> ( ( in @ D @ ( relation_dom @ A ) )
& ( in @ ( apply @ A @ D ) @ B ) ) )
& ! [D: $i] :
( ( ( in @ D @ ( relation_dom @ A ) )
& ( in @ ( apply @ A @ D ) @ B ) )
=> ( in @ D @ C ) ) ) )
& ! [B: $i,C: $i] :
( ( ! [D: $i] :
( ( in @ D @ C )
=> ( ( in @ D @ ( relation_dom @ A ) )
& ( in @ ( apply @ A @ D ) @ B ) ) )
& ! [D: $i] :
( ( ( in @ D @ ( relation_dom @ A ) )
& ( in @ ( apply @ A @ D ) @ B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( relation_inverse_image @ A @ B ) ) ) ) ),
inference(miniscope,[status(thm)],[214]) ).
thf(221,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ( in @ ( sk24 @ C @ B @ A ) @ C )
| ~ ( sk23 @ A @ B @ C )
| ( C
= ( relation_inverse_image @ A @ B ) ) ),
inference(cnf,[status(esa)],[215]) ).
thf(228,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( in @ ( sk24 @ C @ B @ A ) @ C )
| ~ ( sk23 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[221]) ).
thf(229,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( in @ ( sk24 @ C @ B @ A ) @ C )
| ~ ( sk23 @ A @ B @ C ) ),
inference(simp,[status(thm)],[228]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(65,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(154,plain,
relation @ sk15,
inference(cnf,[status(esa)],[151]) ).
thf(2564,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( relation_rng @ A ) )
| ( ( relation @ sk15 )
!= ( relation @ A ) ) ),
inference(paramod_ordered,[status(thm)],[154,127]) ).
thf(2565,plain,
( ( empty @ sk15 )
| ~ ( empty @ ( relation_rng @ sk15 ) ) ),
inference(pattern_uni,[status(thm)],[2564:[bind(A,$thf( sk15 ))]]) ).
thf(20,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(97,plain,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(7609,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( A = empty_set )
| ( ( empty @ ( relation_rng @ sk1 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3159,78]) ).
thf(7610,plain,
( ( sk1 != empty_set )
| ( ( relation_rng @ sk1 )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[7609:[bind(A,$thf( relation_rng @ sk1 ))]]) ).
thf(14776,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( singleton @ A ) )
| ( A
!= ( singleton @ sk5 ) )
| ( B
!= ( powerset @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[168,13977]) ).
thf(14777,plain,
! [A: $i] :
( ~ ( in @ ( powerset @ empty_set ) @ ( singleton @ A ) )
| ( A
!= ( singleton @ sk5 ) ) ),
inference(pattern_uni,[status(thm)],[14776:[bind(A,$thf( A )),bind(B,$thf( powerset @ empty_set ))]]) ).
thf(14840,plain,
~ ( in @ ( powerset @ empty_set ) @ ( singleton @ ( singleton @ sk5 ) ) ),
inference(simp,[status(thm)],[14777]) ).
thf(1445,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ C )
| ( in @ B @ C )
| ( ( element @ empty_set @ ( powerset @ A ) )
!= ( element @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[1426,72]) ).
thf(1446,plain,
! [A: $i] :
( ( empty @ ( powerset @ A ) )
| ( in @ empty_set @ ( powerset @ A ) ) ),
inference(pattern_uni,[status(thm)],[1445:[bind(A,$thf( D )),bind(B,$thf( empty_set )),bind(C,$thf( powerset @ D ))]]) ).
thf(1449,plain,
! [A: $i] :
( ( empty @ ( powerset @ A ) )
| ( in @ empty_set @ ( powerset @ A ) ) ),
inference(simp,[status(thm)],[1446]) ).
thf(1495,plain,
! [A: $i] :
( $false
| ( in @ empty_set @ ( powerset @ A ) ) ),
inference(rewrite,[status(thm)],[1449,85]) ).
thf(1496,plain,
! [A: $i] : ( in @ empty_set @ ( powerset @ A ) ),
inference(simp,[status(thm)],[1495]) ).
thf(14220,plain,
! [A: $i] :
( ( in @ empty_set @ ( powerset @ A ) )
!= ( in @ empty_set @ ( singleton @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[1496,13675]) ).
thf(14226,plain,
! [A: $i] :
( ( empty_set != empty_set )
| ( ( powerset @ A )
!= ( singleton @ sk14 ) ) ),
inference(simp,[status(thm)],[14220]) ).
thf(14244,plain,
! [A: $i] :
( ( powerset @ A )
!= ( singleton @ sk14 ) ),
inference(simp,[status(thm)],[14226]) ).
thf(24,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(109,plain,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ( C
!= ( relation_inverse_image @ A @ B ) )
| ~ ( in @ D @ C )
| ( in @ ( apply @ A @ D ) @ B ) ),
inference(cnf,[status(esa)],[215]) ).
thf(224,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( relation_inverse_image @ A @ B ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ D @ C )
| ( in @ ( apply @ A @ D ) @ B ) ),
inference(lifteq,[status(thm)],[217]) ).
thf(225,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ C @ ( relation_inverse_image @ A @ B ) )
| ( in @ ( apply @ A @ C ) @ B ) ),
inference(simp,[status(thm)],[224]) ).
thf(10777,plain,
( ( sk1 != empty_set )
| ( ( empty @ ( relation_rng @ sk14 ) )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[3035,10725]) ).
thf(10778,plain,
( ( sk1 != empty_set )
| ( ( relation_rng @ sk14 )
!= sk1 ) ),
inference(simp,[status(thm)],[10777]) ).
thf(16831,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( relation_rng @ sk14 )
!= sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[78,10778]) ).
thf(16832,plain,
( ~ ( empty @ sk1 )
| ( ( relation_rng @ sk14 )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[16831:[bind(A,$thf( sk1 ))]]) ).
thf(47,plain,
! [A: $i] :
( ~ ( subset @ ( relation_inverse_image @ sk1 @ ( singleton @ sk2 ) ) @ ( singleton @ A ) )
| ~ ( one_to_one @ sk1 ) ),
inference(cnf,[status(esa)],[45]) ).
thf(698,plain,
! [B: $i,A: $i] :
( ~ ( one_to_one @ sk1 )
| ( ( subset @ empty_set @ A )
!= ( subset @ ( relation_inverse_image @ sk1 @ ( singleton @ sk2 ) ) @ ( singleton @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[115,47]) ).
thf(704,plain,
! [B: $i,A: $i] :
( ~ ( one_to_one @ sk1 )
| ( ( relation_inverse_image @ sk1 @ ( singleton @ sk2 ) )
!= empty_set )
| ( A
!= ( singleton @ B ) ) ),
inference(simp,[status(thm)],[698]) ).
thf(706,plain,
( ~ ( one_to_one @ sk1 )
| ( ( relation_inverse_image @ sk1 @ ( singleton @ sk2 ) )
!= empty_set ) ),
inference(simp,[status(thm)],[704]) ).
thf(1926,plain,
( ( ( relation_inverse_image @ sk1 @ ( singleton @ sk2 ) )
!= empty_set )
| ( ( one_to_one @ sk15 )
!= ( one_to_one @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[152,706]) ).
thf(1937,plain,
( ( ( relation_inverse_image @ sk1 @ ( singleton @ sk2 ) )
!= empty_set )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[1926]) ).
thf(25405,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( A = empty_set )
| ( ( empty @ ( relation_dom @ sk1 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18816,78]) ).
thf(25406,plain,
( ( sk1 != empty_set )
| ( ( relation_dom @ sk1 )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[25405:[bind(A,$thf( relation_dom @ sk1 ))]]) ).
thf(96,plain,
! [A: $i] :
( ~ ( relation @ A )
| ~ ( empty @ A )
| ~ ( function @ A )
| ( one_to_one @ A ) ),
inference(cnf,[status(esa)],[93]) ).
thf(14255,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( singleton @ A ) )
| ( A
!= ( singleton @ empty_set ) )
| ( B
!= ( powerset @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[168,13842]) ).
thf(14256,plain,
! [A: $i] :
( ~ ( in @ ( powerset @ sk5 ) @ ( singleton @ A ) )
| ( A
!= ( singleton @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[14255:[bind(A,$thf( A )),bind(B,$thf( powerset @ sk5 ))]]) ).
thf(14313,plain,
~ ( in @ ( powerset @ sk5 ) @ ( singleton @ ( singleton @ empty_set ) ) ),
inference(simp,[status(thm)],[14256]) ).
thf(110,plain,
~ ? [A: $i] : ( empty @ ( singleton @ A ) ),
inference(miniscope,[status(thm)],[109]) ).
thf(111,plain,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
inference(cnf,[status(esa)],[110]) ).
thf(734,plain,
! [A: $i] :
( ( empty @ ( singleton @ A ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[70,111]) ).
thf(738,plain,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
inference(simp,[status(thm)],[734]) ).
thf(24639,plain,
! [A: $i] :
( ( in @ A @ ( singleton @ A ) )
!= ( in @ ( singleton @ empty_set ) @ ( singleton @ ( powerset @ sk14 ) ) ) ),
inference(paramod_ordered,[status(thm)],[164,14992]) ).
thf(24736,plain,
! [A: $i] :
( ( A
!= ( singleton @ empty_set ) )
| ( ( singleton @ A )
!= ( singleton @ ( powerset @ sk14 ) ) ) ),
inference(simp,[status(thm)],[24639]) ).
thf(24758,plain,
( ( singleton @ ( powerset @ sk14 ) )
!= ( singleton @ ( singleton @ empty_set ) ) ),
inference(simp,[status(thm)],[24736]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[147]) ).
thf(10529,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ A )
| ( subset @ B @ C )
| ( ( element @ ( sk6 @ A ) @ ( powerset @ A ) )
!= ( element @ B @ ( powerset @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[74,149]) ).
thf(10530,plain,
! [A: $i] :
( ( empty @ A )
| ( subset @ ( sk6 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[10529:[bind(A,$thf( D )),bind(B,$thf( sk6 @ D )),bind(C,$thf( D ))]]) ).
thf(10550,plain,
! [A: $i] :
( ( empty @ A )
| ( subset @ ( sk6 @ A ) @ A ) ),
inference(simp,[status(thm)],[10530]) ).
thf(1929,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( one_to_one @ sk1 )
| ( A
!= ( relation_inverse_image @ sk1 @ ( singleton @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[78,706]) ).
thf(1930,plain,
( ~ ( empty @ ( relation_inverse_image @ sk1 @ ( singleton @ sk2 ) ) )
| ~ ( one_to_one @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1929:[bind(A,$thf( relation_inverse_image @ sk1 @ ( singleton @ sk2 ) ))]]) ).
thf(1966,plain,
( ~ ( empty @ ( relation_inverse_image @ sk1 @ ( singleton @ sk2 ) ) )
| ( ( one_to_one @ sk15 )
!= ( one_to_one @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[152,1930]) ).
thf(1979,plain,
( ~ ( empty @ ( relation_inverse_image @ sk1 @ ( singleton @ sk2 ) ) )
| ( sk15 != sk1 ) ),
inference(simp,[status(thm)],[1966]) ).
thf(105,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ A ) ) ),
inference(cnf,[status(esa)],[103]) ).
thf(3154,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( relation @ ( relation_rng @ A ) )
| ( ( empty @ sk1 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3035,105]) ).
thf(3155,plain,
( ( sk1 != empty_set )
| ( relation @ ( relation_rng @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[3154:[bind(A,$thf( sk1 ))]]) ).
thf(5478,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_rng @ sk1 ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[78,3155]) ).
thf(5479,plain,
( ~ ( empty @ sk1 )
| ( relation @ ( relation_rng @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[5478:[bind(A,$thf( sk1 ))]]) ).
thf(6,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(62,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(63,plain,
~ ? [A: $i,B: $i] :
( ( in @ A @ B )
& ( empty @ B ) ),
inference(miniscope,[status(thm)],[62]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( empty @ B ) ),
inference(cnf,[status(esa)],[63]) ).
thf(632,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( ( empty @ empty_set )
!= ( empty @ B ) ) ),
inference(paramod_ordered,[status(thm)],[70,64]) ).
thf(633,plain,
! [A: $i] :
~ ( in @ A @ empty_set ),
inference(pattern_uni,[status(thm)],[632:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).
thf(193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ( B
!= ( relation_rng @ A ) )
| ~ ( in @ D @ ( relation_dom @ A ) )
| ( C
!= ( apply @ A @ D ) )
| ( in @ C @ B ) ),
inference(cnf,[status(esa)],[189]) ).
thf(204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( C
!= ( apply @ A @ D ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ D @ ( relation_dom @ A ) )
| ( in @ C @ B ) ),
inference(lifteq,[status(thm)],[193]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ B @ ( relation_dom @ A ) )
| ( in @ ( apply @ A @ B ) @ ( relation_rng @ A ) ) ),
inference(simp,[status(thm)],[204]) ).
thf(25261,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( singleton @ sk14 ) @ ( singleton @ ( powerset @ empty_set ) ) ) ),
inference(paramod_ordered,[status(thm)],[11868,15060]) ).
thf(25286,plain,
! [A: $i] :
( ( A
!= ( singleton @ sk14 ) )
| ( ( powerset @ A )
!= ( singleton @ ( powerset @ empty_set ) ) ) ),
inference(simp,[status(thm)],[25261]) ).
thf(25320,plain,
( ( powerset @ ( singleton @ sk14 ) )
!= ( singleton @ ( powerset @ empty_set ) ) ),
inference(simp,[status(thm)],[25286]) ).
thf(14326,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ ( singleton @ A ) )
| ( B
!= ( singleton @ empty_set ) )
| ( A
!= ( singleton @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[168,13844]) ).
thf(14327,plain,
! [A: $i] :
( ~ ( in @ A @ ( singleton @ ( singleton @ sk5 ) ) )
| ( A
!= ( singleton @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[14326:[bind(A,$thf( singleton @ sk5 )),bind(B,$thf( B ))]]) ).
thf(14412,plain,
~ ( in @ ( singleton @ empty_set ) @ ( singleton @ ( singleton @ sk5 ) ) ),
inference(simp,[status(thm)],[14327]) ).
thf(22917,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( singleton @ empty_set ) @ ( singleton @ ( singleton @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11868,14412]) ).
thf(22948,plain,
! [A: $i] :
( ( A
!= ( singleton @ empty_set ) )
| ( ( powerset @ A )
!= ( singleton @ ( singleton @ sk5 ) ) ) ),
inference(simp,[status(thm)],[22917]) ).
thf(22980,plain,
( ( powerset @ ( singleton @ empty_set ) )
!= ( singleton @ ( singleton @ sk5 ) ) ),
inference(simp,[status(thm)],[22948]) ).
thf(3156,plain,
( ( sk1 != empty_set )
| ( ( empty @ sk14 )
!= ( empty @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[3035,145]) ).
thf(3173,plain,
( ( sk1 != empty_set )
| ( sk14 != sk1 ) ),
inference(simp,[status(thm)],[3156]) ).
thf(16183,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ empty_set @ ( singleton @ ( relation_rng @ sk14 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11868,13265]) ).
thf(16195,plain,
! [A: $i] :
( ( A != empty_set )
| ( ( powerset @ A )
!= ( singleton @ ( relation_rng @ sk14 ) ) ) ),
inference(simp,[status(thm)],[16183]) ).
thf(16220,plain,
( ( powerset @ empty_set )
!= ( singleton @ ( relation_rng @ sk14 ) ) ),
inference(simp,[status(thm)],[16195]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ( ( sk16 @ B @ A )
!= A )
| ~ ( in @ ( sk17 @ B @ A ) @ B )
| ( B
= ( singleton @ A ) ) ),
inference(cnf,[status(esa)],[156]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( ( sk16 @ B @ A )
!= A )
| ( B
= ( singleton @ A ) )
| ~ ( in @ ( sk17 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[160]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( ( sk16 @ B @ A )
!= A )
| ( B
= ( singleton @ A ) )
| ~ ( in @ ( sk17 @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[165]) ).
thf(7638,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( function @ A )
| ( ( empty @ ( relation_rng @ sk1 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[3159,117]) ).
thf(7639,plain,
( ( sk1 != empty_set )
| ( function @ ( relation_rng @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[7638:[bind(A,$thf( relation_rng @ sk1 ))]]) ).
thf(7661,plain,
( ( sk1 != empty_set )
| ( ( empty @ ( relation_rng @ sk1 ) )
!= ( empty @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[3159,145]) ).
thf(7679,plain,
( ( sk1 != empty_set )
| ( ( relation_rng @ sk1 )
!= sk14 ) ),
inference(simp,[status(thm)],[7661]) ).
thf(7735,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( relation_rng @ sk1 )
!= sk14 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[78,7679]) ).
thf(7736,plain,
( ~ ( empty @ sk1 )
| ( ( relation_rng @ sk1 )
!= sk14 ) ),
inference(pattern_uni,[status(thm)],[7735:[bind(A,$thf( sk1 ))]]) ).
thf(49,plain,
function @ sk1,
inference(cnf,[status(esa)],[45]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(86,plain,
! [A: $i,B: $i] :
( ( disjoint @ A @ B )
=> ( disjoint @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(162,plain,
! [B: $i,A: $i] :
( ( in @ ( sk16 @ B @ A ) @ B )
| ~ ( in @ ( sk17 @ B @ A ) @ B )
| ( B
= ( singleton @ A ) ) ),
inference(cnf,[status(esa)],[156]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( B
= ( singleton @ A ) )
| ( in @ ( sk16 @ B @ A ) @ B )
| ~ ( in @ ( sk17 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[162]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ( B
= ( singleton @ A ) )
| ( in @ ( sk16 @ B @ A ) @ B )
| ~ ( in @ ( sk17 @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[171]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_zfmisc_1) ).
thf(112,plain,
! [A: $i,B: $i] :
( ~ ( in @ A @ B )
=> ( disjoint @ ( singleton @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( in @ A @ B )
| ( disjoint @ ( singleton @ A ) @ B ) ),
inference(cnf,[status(esa)],[112]) ).
thf(245,plain,
function @ sk26,
inference(cnf,[status(esa)],[244]) ).
thf(25357,plain,
( ( sk1 != empty_set )
| ( ( empty @ ( relation_dom @ sk1 ) )
!= ( empty @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[18816,69]) ).
thf(25507,plain,
( ( sk1 != empty_set )
| ( ( relation_dom @ sk1 )
!= sk5 ) ),
inference(simp,[status(thm)],[25357]) ).
thf(28528,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( relation_dom @ sk1 )
!= sk5 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[78,25507]) ).
thf(28529,plain,
( ~ ( empty @ sk1 )
| ( ( relation_dom @ sk1 )
!= sk5 ) ),
inference(pattern_uni,[status(thm)],[28528:[bind(A,$thf( sk1 ))]]) ).
thf(98,plain,
relation @ empty_set,
inference(cnf,[status(esa)],[97]) ).
thf(108,plain,
empty @ sk10,
inference(cnf,[status(esa)],[106]) ).
thf(1174,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ sk10 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[108,78]) ).
thf(1175,plain,
sk10 = empty_set,
inference(pattern_uni,[status(thm)],[1174:[bind(A,$thf( sk10 ))]]) ).
thf(11031,plain,
! [C: $i,B: $i,A: $i] :
( ( one_to_one @ sk1 )
| ( element @ B @ ( powerset @ C ) )
| ( ( subset @ ( relation_inverse_image @ sk1 @ ( singleton @ A ) ) @ ( singleton @ ( sk3 @ A ) ) )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[52,150]) ).
thf(11032,plain,
! [A: $i] :
( ( one_to_one @ sk1 )
| ( element @ ( relation_inverse_image @ sk1 @ ( singleton @ A ) ) @ ( powerset @ ( singleton @ ( sk3 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[11031:[bind(A,$thf( H )),bind(B,$thf( relation_inverse_image @ sk1 @ ( singleton @ H ) )),bind(C,$thf( singleton @ ( sk3 @ H ) ))]]) ).
thf(11078,plain,
! [A: $i] :
( ( one_to_one @ sk1 )
| ( element @ ( relation_inverse_image @ sk1 @ ( singleton @ A ) ) @ ( powerset @ ( singleton @ ( sk3 @ A ) ) ) ) ),
inference(simp,[status(thm)],[11032]) ).
thf(195,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ( B
!= ( relation_rng @ A ) )
| ~ ( in @ C @ B )
| ( C
= ( apply @ A @ ( sk18 @ C @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[189]) ).
thf(212,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( relation_rng @ A ) )
| ( ( apply @ A @ ( sk18 @ C @ B @ A ) )
= C )
| ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ C @ B ) ),
inference(lifteq,[status(thm)],[195]) ).
thf(213,plain,
! [B: $i,A: $i] :
( ( ( apply @ A @ ( sk18 @ B @ ( relation_rng @ A ) @ A ) )
= B )
| ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ B @ ( relation_rng @ A ) ) ),
inference(simp,[status(thm)],[212]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ),
inference(cnf,[status(esa)],[65]) ).
thf(43,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(240,plain,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(858,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ A )
| ( empty @ C )
| ( in @ B @ C )
| ( ( element @ ( sk6 @ A ) @ ( powerset @ A ) )
!= ( element @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[74,72]) ).
thf(859,plain,
! [A: $i] :
( ( empty @ A )
| ( empty @ ( powerset @ A ) )
| ( in @ ( sk6 @ A ) @ ( powerset @ A ) ) ),
inference(pattern_uni,[status(thm)],[858:[bind(A,$thf( E )),bind(B,$thf( sk6 @ E )),bind(C,$thf( powerset @ E ))]]) ).
thf(864,plain,
! [A: $i] :
( ( empty @ A )
| ( empty @ ( powerset @ A ) )
| ( in @ ( sk6 @ A ) @ ( powerset @ A ) ) ),
inference(simp,[status(thm)],[859]) ).
thf(2277,plain,
! [A: $i] :
( ( empty @ A )
| $false
| ( in @ ( sk6 @ A ) @ ( powerset @ A ) ) ),
inference(rewrite,[status(thm)],[864,85]) ).
thf(2278,plain,
! [A: $i] :
( ( empty @ A )
| ( in @ ( sk6 @ A ) @ ( powerset @ A ) ) ),
inference(simp,[status(thm)],[2277]) ).
thf(2552,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( relation_rng @ A ) )
| ( ( relation @ sk9 )
!= ( relation @ A ) ) ),
inference(paramod_ordered,[status(thm)],[102,127]) ).
thf(2553,plain,
( ( empty @ sk9 )
| ~ ( empty @ ( relation_rng @ sk9 ) ) ),
inference(pattern_uni,[status(thm)],[2552:[bind(A,$thf( sk9 ))]]) ).
thf(24428,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( singleton @ sk14 ) @ ( singleton @ ( singleton @ empty_set ) ) ) ),
inference(paramod_ordered,[status(thm)],[11868,14937]) ).
thf(24460,plain,
! [A: $i] :
( ( A
!= ( singleton @ sk14 ) )
| ( ( powerset @ A )
!= ( singleton @ ( singleton @ empty_set ) ) ) ),
inference(simp,[status(thm)],[24428]) ).
thf(24488,plain,
( ( powerset @ ( singleton @ sk14 ) )
!= ( singleton @ ( singleton @ empty_set ) ) ),
inference(simp,[status(thm)],[24460]) ).
thf(26941,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ empty_set ) @ ( singleton @ ( singleton @ sk14 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11868,15072]) ).
thf(26962,plain,
! [A: $i] :
( ( A
!= ( powerset @ empty_set ) )
| ( ( powerset @ A )
!= ( singleton @ ( singleton @ sk14 ) ) ) ),
inference(simp,[status(thm)],[26941]) ).
thf(27013,plain,
( ( powerset @ ( powerset @ empty_set ) )
!= ( singleton @ ( singleton @ sk14 ) ) ),
inference(simp,[status(thm)],[26962]) ).
thf(972,plain,
! [C: $i,B: $i,A: $i] :
( ( element @ B @ C )
| ( ( in @ A @ ( singleton @ A ) )
!= ( in @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[164,66]) ).
thf(973,plain,
! [A: $i] : ( element @ A @ ( singleton @ A ) ),
inference(pattern_uni,[status(thm)],[972:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( singleton @ D ))]]) ).
thf(986,plain,
! [A: $i] : ( element @ A @ ( singleton @ A ) ),
inference(simp,[status(thm)],[973]) ).
thf(241,plain,
relation_empty_yielding @ empty_set,
inference(cnf,[status(esa)],[240]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(79,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)],[13]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( element @ B @ ( powerset @ C ) )
| ( element @ A @ C ) ),
inference(cnf,[status(esa)],[79]) ).
thf(18718,plain,
! [A: $i] :
( ( empty @ ( relation_dom @ A ) )
| ( ( empty @ empty_set )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[70,186]) ).
thf(18719,plain,
empty @ ( relation_dom @ empty_set ),
inference(pattern_uni,[status(thm)],[18718:[bind(A,$thf( empty_set ))]]) ).
thf(18917,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ ( relation_dom @ empty_set ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18719,78]) ).
thf(18918,plain,
( ( relation_dom @ empty_set )
= empty_set ),
inference(pattern_uni,[status(thm)],[18917:[bind(A,$thf( relation_dom @ empty_set ))]]) ).
thf(7611,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_rng @ sk1 ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[78,3159]) ).
thf(7612,plain,
( ~ ( empty @ sk1 )
| ( empty @ ( relation_rng @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[7611:[bind(A,$thf( sk1 ))]]) ).
thf(12020,plain,
! [A: $i] :
( ~ ( empty @ sk1 )
| ( function @ A )
| ( ( empty @ ( relation_rng @ sk1 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7612,117]) ).
thf(12021,plain,
( ~ ( empty @ sk1 )
| ( function @ ( relation_rng @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[12020:[bind(A,$thf( relation_rng @ sk1 ))]]) ).
thf(194,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ C @ ( relation_dom @ A ) )
| ( ( sk20 @ B @ A )
!= ( apply @ A @ C ) )
| ~ ( sk19 @ A @ B )
| ( B
= ( relation_rng @ A ) ) ),
inference(cnf,[status(esa)],[189]) ).
thf(208,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk20 @ B @ A )
!= ( apply @ A @ C ) )
| ( B
= ( relation_rng @ A ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ C @ ( relation_dom @ A ) )
| ~ ( sk19 @ A @ B ) ),
inference(lifteq,[status(thm)],[194]) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk20 @ B @ A )
!= ( apply @ A @ C ) )
| ( B
= ( relation_rng @ A ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ C @ ( relation_dom @ A ) )
| ~ ( sk19 @ A @ B ) ),
inference(simp,[status(thm)],[208]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ( ( relation_inverse_image @ A @ ( singleton @ ( sk11 @ A ) ) )
!= ( singleton @ B ) )
| ( one_to_one @ A ) ),
inference(cnf,[status(esa)],[119]) ).
thf(123,plain,
! [B: $i,A: $i] :
( ( ( relation_inverse_image @ A @ ( singleton @ ( sk11 @ A ) ) )
!= ( singleton @ B ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( one_to_one @ A ) ),
inference(lifteq,[status(thm)],[120]) ).
thf(899,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ C )
| ( in @ B @ C )
| ( ( element @ ( sk8 @ A ) @ A )
!= ( element @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[92,72]) ).
thf(900,plain,
! [A: $i] :
( ( empty @ A )
| ( in @ ( sk8 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[899:[bind(A,$thf( D )),bind(B,$thf( sk8 @ D )),bind(C,$thf( D ))]]) ).
thf(903,plain,
! [A: $i] :
( ( empty @ A )
| ( in @ ( sk8 @ A ) @ A ) ),
inference(simp,[status(thm)],[900]) ).
thf(13151,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ A )
| ( C = B )
| ( ( in @ ( sk8 @ A ) @ A )
!= ( in @ C @ ( singleton @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[903,168]) ).
thf(13152,plain,
! [A: $i] :
( ( empty @ ( singleton @ A ) )
| ( ( sk8 @ ( singleton @ A ) )
= A ) ),
inference(pattern_uni,[status(thm)],[13151:[bind(A,$thf( singleton @ E )),bind(B,$thf( E )),bind(C,$thf( sk8 @ ( singleton @ E ) ))]]) ).
thf(13629,plain,
! [A: $i] :
( ( empty @ ( singleton @ A ) )
| ( ( sk8 @ ( singleton @ A ) )
= A ) ),
inference(simp,[status(thm)],[13152]) ).
thf(14416,plain,
! [A: $i] :
( $false
| ( ( sk8 @ ( singleton @ A ) )
= A ) ),
inference(rewrite,[status(thm)],[13629,111]) ).
thf(14417,plain,
! [A: $i] :
( ( sk8 @ ( singleton @ A ) )
= A ),
inference(simp,[status(thm)],[14416]) ).
thf(1586,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ A )
| ( element @ B @ C )
| ( ( in @ ( sk8 @ A ) @ A )
!= ( in @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[903,66]) ).
thf(1587,plain,
! [A: $i] :
( ( empty @ A )
| ( element @ ( sk8 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[1586:[bind(A,$thf( D )),bind(B,$thf( sk8 @ D )),bind(C,$thf( D ))]]) ).
thf(1598,plain,
! [A: $i] :
( ( empty @ A )
| ( element @ ( sk8 @ A ) @ A ) ),
inference(simp,[status(thm)],[1587]) ).
thf(25436,plain,
! [A: $i] :
( ( sk1 != empty_set )
| ( function @ A )
| ( ( empty @ ( relation_dom @ sk1 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18816,117]) ).
thf(25437,plain,
( ( sk1 != empty_set )
| ( function @ ( relation_dom @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[25436:[bind(A,$thf( relation_dom @ sk1 ))]]) ).
thf(17495,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ A )
| ( B = empty_set )
| ( B
= ( singleton @ C ) )
| ( ( subset @ ( sk6 @ A ) @ A )
!= ( subset @ B @ ( singleton @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[10550,184]) ).
thf(17496,plain,
! [A: $i] :
( ( empty @ ( singleton @ A ) )
| ( ( sk6 @ ( singleton @ A ) )
= empty_set )
| ( ( sk6 @ ( singleton @ A ) )
= ( singleton @ A ) ) ),
inference(pattern_uni,[status(thm)],[17495:[bind(A,$thf( singleton @ E )),bind(B,$thf( sk6 @ ( singleton @ E ) )),bind(C,$thf( E ))]]) ).
thf(17827,plain,
! [A: $i] :
( ( empty @ ( singleton @ A ) )
| ( ( sk6 @ ( singleton @ A ) )
= empty_set )
| ( ( sk6 @ ( singleton @ A ) )
= ( singleton @ A ) ) ),
inference(simp,[status(thm)],[17496]) ).
thf(33069,plain,
! [A: $i] :
( $false
| ( ( sk6 @ ( singleton @ A ) )
= empty_set )
| ( ( sk6 @ ( singleton @ A ) )
= ( singleton @ A ) ) ),
inference(rewrite,[status(thm)],[17827,111]) ).
thf(33070,plain,
! [A: $i] :
( ( ( sk6 @ ( singleton @ A ) )
= empty_set )
| ( ( sk6 @ ( singleton @ A ) )
= ( singleton @ A ) ) ),
inference(simp,[status(thm)],[33069]) ).
thf(3201,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk14 != sk1 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[78,3173]) ).
thf(3202,plain,
( ~ ( empty @ sk1 )
| ( sk14 != sk1 ) ),
inference(pattern_uni,[status(thm)],[3201:[bind(A,$thf( sk1 ))]]) ).
thf(13954,plain,
! [A: $i] :
( ( in @ empty_set @ ( powerset @ A ) )
!= ( in @ empty_set @ ( singleton @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[1496,13378]) ).
thf(13969,plain,
! [A: $i] :
( ( empty_set != empty_set )
| ( ( powerset @ A )
!= ( singleton @ sk5 ) ) ),
inference(simp,[status(thm)],[13954]) ).
thf(13978,plain,
! [A: $i] :
( ( powerset @ A )
!= ( singleton @ sk5 ) ),
inference(simp,[status(thm)],[13969]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ~ ( disjoint @ A @ B )
| ( disjoint @ B @ A ) ),
inference(cnf,[status(esa)],[86]) ).
thf(1896,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( in @ A @ B )
| ( disjoint @ D @ C )
| ( ( disjoint @ ( singleton @ A ) @ B )
!= ( disjoint @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[113,87]) ).
thf(1897,plain,
! [B: $i,A: $i] :
( ( in @ B @ A )
| ( disjoint @ A @ ( singleton @ B ) ) ),
inference(pattern_uni,[status(thm)],[1896:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( singleton @ E )),bind(D,$thf( B ))]]) ).
thf(1901,plain,
! [B: $i,A: $i] :
( ( in @ B @ A )
| ( disjoint @ A @ ( singleton @ B ) ) ),
inference(simp,[status(thm)],[1897]) ).
thf(1514,plain,
! [B: $i,A: $i] :
( ( in @ empty_set @ ( powerset @ A ) )
!= ( in @ ( singleton @ B ) @ B ) ),
inference(paramod_ordered,[status(thm)],[1496,1465]) ).
thf(1526,plain,
! [B: $i,A: $i] :
( ( ( singleton @ B )
!= empty_set )
| ( ( powerset @ A )
!= B ) ),
inference(simp,[status(thm)],[1514]) ).
thf(1538,plain,
! [A: $i] :
( ( singleton @ ( powerset @ A ) )
!= empty_set ),
inference(simp,[status(thm)],[1526]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ( sk19 @ A @ B )
| ~ ( in @ ( sk21 @ B @ A ) @ B )
| ( B
= ( relation_rng @ A ) ) ),
inference(cnf,[status(esa)],[189]) ).
thf(198,plain,
! [B: $i,A: $i] :
( ( B
= ( relation_rng @ A ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( sk19 @ A @ B )
| ~ ( in @ ( sk21 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[196]) ).
thf(199,plain,
! [B: $i,A: $i] :
( ( B
= ( relation_rng @ A ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( sk19 @ A @ B )
| ~ ( in @ ( sk21 @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[198]) ).
thf(2087,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( in @ B @ A )
| ( disjoint @ D @ C )
| ( ( disjoint @ A @ ( singleton @ B ) )
!= ( disjoint @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[1901,87]) ).
thf(2088,plain,
! [B: $i,A: $i] :
( ( in @ B @ A )
| ( disjoint @ ( singleton @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[2087:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( A )),bind(D,$thf( singleton @ E ))]]) ).
thf(2092,plain,
! [B: $i,A: $i] :
( ( in @ B @ A )
| ( disjoint @ ( singleton @ B ) @ A ) ),
inference(simp,[status(thm)],[2088]) ).
thf(10537,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ B @ C )
| ( ( element @ ( sk8 @ A ) @ A )
!= ( element @ B @ ( powerset @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,149]) ).
thf(10538,plain,
! [A: $i] : ( subset @ ( sk8 @ ( powerset @ A ) ) @ A ),
inference(pattern_uni,[status(thm)],[10537:[bind(A,$thf( powerset @ E )),bind(B,$thf( sk8 @ ( powerset @ E ) )),bind(C,$thf( E ))]]) ).
thf(10554,plain,
! [A: $i] : ( subset @ ( sk8 @ ( powerset @ A ) ) @ A ),
inference(simp,[status(thm)],[10538]) ).
thf(17765,plain,
! [C: $i,B: $i,A: $i] :
( ( B = empty_set )
| ( B
= ( singleton @ C ) )
| ( ( subset @ ( sk8 @ ( powerset @ A ) ) @ A )
!= ( subset @ B @ ( singleton @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[10554,184]) ).
thf(17766,plain,
! [A: $i] :
( ( ( sk8 @ ( powerset @ ( singleton @ A ) ) )
= empty_set )
| ( ( sk8 @ ( powerset @ ( singleton @ A ) ) )
= ( singleton @ A ) ) ),
inference(pattern_uni,[status(thm)],[17765:[bind(A,$thf( singleton @ F )),bind(B,$thf( sk8 @ ( powerset @ ( singleton @ F ) ) )),bind(C,$thf( F ))]]) ).
thf(17992,plain,
! [A: $i] :
( ( ( sk8 @ ( powerset @ ( singleton @ A ) ) )
= empty_set )
| ( ( sk8 @ ( powerset @ ( singleton @ A ) ) )
= ( singleton @ A ) ) ),
inference(simp,[status(thm)],[17766]) ).
thf(21005,plain,
! [A: $i] :
( ( in @ A @ ( singleton @ A ) )
!= ( in @ ( singleton @ sk5 ) @ ( singleton @ ( singleton @ empty_set ) ) ) ),
inference(paramod_ordered,[status(thm)],[164,14408]) ).
thf(21112,plain,
! [A: $i] :
( ( A
!= ( singleton @ sk5 ) )
| ( ( singleton @ A )
!= ( singleton @ ( singleton @ empty_set ) ) ) ),
inference(simp,[status(thm)],[21005]) ).
thf(21135,plain,
( ( singleton @ ( singleton @ sk5 ) )
!= ( singleton @ ( singleton @ empty_set ) ) ),
inference(simp,[status(thm)],[21112]) ).
thf(10444,plain,
( ( empty @ sk1 )
| ( ( empty @ ( relation_dom @ sk1 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[70,5550]) ).
thf(10496,plain,
( ( empty @ sk1 )
| ( ( relation_dom @ sk1 )
!= empty_set ) ),
inference(simp,[status(thm)],[10444]) ).
thf(16371,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( relation_rng @ sk14 ) @ ( singleton @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[11868,13722]) ).
thf(16383,plain,
! [A: $i] :
( ( A
!= ( relation_rng @ sk14 ) )
| ( ( powerset @ A )
!= ( singleton @ empty_set ) ) ),
inference(simp,[status(thm)],[16371]) ).
thf(16418,plain,
( ( powerset @ ( relation_rng @ sk14 ) )
!= ( singleton @ empty_set ) ),
inference(simp,[status(thm)],[16383]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ( in @ ( sk20 @ B @ A ) @ B )
| ~ ( sk19 @ A @ B )
| ( B
= ( relation_rng @ A ) ) ),
inference(cnf,[status(esa)],[189]) ).
thf(202,plain,
! [B: $i,A: $i] :
( ( B
= ( relation_rng @ A ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( in @ ( sk20 @ B @ A ) @ B )
| ~ ( sk19 @ A @ B ) ),
inference(lifteq,[status(thm)],[197]) ).
thf(203,plain,
! [B: $i,A: $i] :
( ( B
= ( relation_rng @ A ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( in @ ( sk20 @ B @ A ) @ B )
| ~ ( sk19 @ A @ B ) ),
inference(simp,[status(thm)],[202]) ).
thf(1845,plain,
! [A: $i] :
( ( relation @ ( relation_rng @ A ) )
| ( ( empty @ ( relation_rng @ empty_set ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1788,105]) ).
thf(1846,plain,
relation @ ( relation_rng @ ( relation_rng @ empty_set ) ),
inference(pattern_uni,[status(thm)],[1845:[bind(A,$thf( relation_rng @ empty_set ))]]) ).
thf(1866,plain,
relation @ ( relation_rng @ empty_set ),
inference(rewrite,[status(thm)],[1846,1738]) ).
thf(18320,plain,
! [A: $i] :
( ( in @ A @ ( singleton @ A ) )
!= ( in @ ( powerset @ sk5 ) @ ( singleton @ ( singleton @ empty_set ) ) ) ),
inference(paramod_ordered,[status(thm)],[164,14313]) ).
thf(18396,plain,
! [A: $i] :
( ( A
!= ( powerset @ sk5 ) )
| ( ( singleton @ A )
!= ( singleton @ ( singleton @ empty_set ) ) ) ),
inference(simp,[status(thm)],[18320]) ).
thf(18443,plain,
( ( singleton @ ( powerset @ sk5 ) )
!= ( singleton @ ( singleton @ empty_set ) ) ),
inference(simp,[status(thm)],[18396]) ).
thf(220,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ( sk23 @ A @ B @ C )
| ( in @ ( apply @ A @ ( sk25 @ C @ B @ A ) ) @ B )
| ( C
= ( relation_inverse_image @ A @ B ) ) ),
inference(cnf,[status(esa)],[215]) ).
thf(230,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( sk23 @ A @ B @ C )
| ( in @ ( apply @ A @ ( sk25 @ C @ B @ A ) ) @ B ) ),
inference(lifteq,[status(thm)],[220]) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_inverse_image @ A @ B ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( sk23 @ A @ B @ C )
| ( in @ ( apply @ A @ ( sk25 @ C @ B @ A ) ) @ B ) ),
inference(simp,[status(thm)],[230]) ).
thf(23196,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ empty_set ) @ ( singleton @ ( singleton @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[11868,14840]) ).
thf(23223,plain,
! [A: $i] :
( ( A
!= ( powerset @ empty_set ) )
| ( ( powerset @ A )
!= ( singleton @ ( singleton @ sk5 ) ) ) ),
inference(simp,[status(thm)],[23196]) ).
thf(23252,plain,
( ( powerset @ ( powerset @ empty_set ) )
!= ( singleton @ ( singleton @ sk5 ) ) ),
inference(simp,[status(thm)],[23223]) ).
thf(29570,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( relation_dom @ sk1 )
!= sk14 )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[78,25516]) ).
thf(29571,plain,
( ~ ( empty @ sk1 )
| ( ( relation_dom @ sk1 )
!= sk14 ) ),
inference(pattern_uni,[status(thm)],[29570:[bind(A,$thf( sk1 ))]]) ).
thf(18751,plain,
! [A: $i] :
( ( empty @ ( relation_dom @ A ) )
| ( ( empty @ ( relation_rng @ empty_set ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1788,186]) ).
thf(18752,plain,
empty @ ( relation_dom @ ( relation_rng @ empty_set ) ),
inference(pattern_uni,[status(thm)],[18751:[bind(A,$thf( relation_rng @ empty_set ))]]) ).
thf(19196,plain,
empty @ ( relation_dom @ empty_set ),
inference(rewrite,[status(thm)],[18752,1738]) ).
thf(191,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ( sk19 @ A @ B )
| ( in @ ( sk22 @ B @ A ) @ ( relation_dom @ A ) )
| ( B
= ( relation_rng @ A ) ) ),
inference(cnf,[status(esa)],[189]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( B
= ( relation_rng @ A ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( sk19 @ A @ B )
| ( in @ ( sk22 @ B @ A ) @ ( relation_dom @ A ) ) ),
inference(lifteq,[status(thm)],[191]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( B
= ( relation_rng @ A ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( sk19 @ A @ B )
| ( in @ ( sk22 @ B @ A ) @ ( relation_dom @ A ) ) ),
inference(simp,[status(thm)],[206]) ).
thf(75,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( sk6 @ A ) ) ),
inference(cnf,[status(esa)],[73]) ).
thf(10936,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( relation_rng @ sk1 )
= empty_set )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[78,7610]) ).
thf(10937,plain,
( ~ ( empty @ sk1 )
| ( ( relation_rng @ sk1 )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[10936:[bind(A,$thf( sk1 ))]]) ).
thf(18389,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ sk5 ) @ ( singleton @ ( singleton @ empty_set ) ) ) ),
inference(paramod_ordered,[status(thm)],[11868,14313]) ).
thf(18404,plain,
! [A: $i] :
( ( A
!= ( powerset @ sk5 ) )
| ( ( powerset @ A )
!= ( singleton @ ( singleton @ empty_set ) ) ) ),
inference(simp,[status(thm)],[18389]) ).
thf(18447,plain,
( ( powerset @ ( powerset @ sk5 ) )
!= ( singleton @ ( singleton @ empty_set ) ) ),
inference(simp,[status(thm)],[18404]) ).
thf(11425,plain,
! [C: $i,B: $i,A: $i] :
( ( one_to_one @ sk1 )
| ( empty @ C )
| ( in @ B @ C )
| ( ( element @ ( relation_inverse_image @ sk1 @ ( singleton @ A ) ) @ ( powerset @ ( singleton @ ( sk3 @ A ) ) ) )
!= ( element @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[11078,72]) ).
thf(11426,plain,
! [A: $i] :
( ( one_to_one @ sk1 )
| ( empty @ ( powerset @ ( singleton @ ( sk3 @ A ) ) ) )
| ( in @ ( relation_inverse_image @ sk1 @ ( singleton @ A ) ) @ ( powerset @ ( singleton @ ( sk3 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[11425:[bind(A,$thf( I )),bind(B,$thf( relation_inverse_image @ sk1 @ ( singleton @ I ) )),bind(C,$thf( powerset @ ( singleton @ ( sk3 @ I ) ) ))]]) ).
thf(11499,plain,
! [A: $i] :
( ( one_to_one @ sk1 )
| ( empty @ ( powerset @ ( singleton @ ( sk3 @ A ) ) ) )
| ( in @ ( relation_inverse_image @ sk1 @ ( singleton @ A ) ) @ ( powerset @ ( singleton @ ( sk3 @ A ) ) ) ) ),
inference(simp,[status(thm)],[11426]) ).
thf(30702,plain,
! [A: $i] :
( ( one_to_one @ sk1 )
| $false
| ( in @ ( relation_inverse_image @ sk1 @ ( singleton @ A ) ) @ ( powerset @ ( singleton @ ( sk3 @ A ) ) ) ) ),
inference(rewrite,[status(thm)],[11499,85]) ).
thf(30703,plain,
! [A: $i] :
( ( one_to_one @ sk1 )
| ( in @ ( relation_inverse_image @ sk1 @ ( singleton @ A ) ) @ ( powerset @ ( singleton @ ( sk3 @ A ) ) ) ) ),
inference(simp,[status(thm)],[30702]) ).
thf(17250,plain,
! [C: $i,B: $i,A: $i] :
( ( one_to_one @ sk1 )
| ( B = empty_set )
| ( B
= ( singleton @ C ) )
| ( ( subset @ ( relation_inverse_image @ sk1 @ ( singleton @ A ) ) @ ( singleton @ ( sk3 @ A ) ) )
!= ( subset @ B @ ( singleton @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[52,184]) ).
thf(17251,plain,
! [A: $i] :
( ( one_to_one @ sk1 )
| ( ( relation_inverse_image @ sk1 @ ( singleton @ A ) )
= empty_set )
| ( ( relation_inverse_image @ sk1 @ ( singleton @ A ) )
= ( singleton @ ( sk3 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[17250:[bind(A,$thf( G )),bind(B,$thf( relation_inverse_image @ sk1 @ ( singleton @ G ) )),bind(C,$thf( sk3 @ G ))]]) ).
thf(17989,plain,
! [A: $i] :
( ( one_to_one @ sk1 )
| ( ( relation_inverse_image @ sk1 @ ( singleton @ A ) )
= empty_set )
| ( ( relation_inverse_image @ sk1 @ ( singleton @ A ) )
= ( singleton @ ( sk3 @ A ) ) ) ),
inference(simp,[status(thm)],[17251]) ).
thf(23127,plain,
! [A: $i] :
( ( in @ A @ ( singleton @ A ) )
!= ( in @ ( powerset @ empty_set ) @ ( singleton @ ( singleton @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[164,14840]) ).
thf(23212,plain,
! [A: $i] :
( ( A
!= ( powerset @ empty_set ) )
| ( ( singleton @ A )
!= ( singleton @ ( singleton @ sk5 ) ) ) ),
inference(simp,[status(thm)],[23127]) ).
thf(23247,plain,
( ( singleton @ ( powerset @ empty_set ) )
!= ( singleton @ ( singleton @ sk5 ) ) ),
inference(simp,[status(thm)],[23212]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ~ ( relation @ B )
| ( ( relation_inverse_image @ B @ A )
!= empty_set )
| ( disjoint @ ( relation_rng @ B ) @ A ) ),
inference(cnf,[status(esa)],[128]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ( ( relation_inverse_image @ B @ A )
!= empty_set )
| ~ ( relation @ B )
| ( disjoint @ ( relation_rng @ B ) @ A ) ),
inference(lifteq,[status(thm)],[129]) ).
thf(653,plain,
! [A: $i] :
( ( empty @ ( powerset @ A ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[70,85]) ).
thf(659,plain,
! [A: $i] :
( ( powerset @ A )
!= empty_set ),
inference(simp,[status(thm)],[653]) ).
thf(25407,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ sk1 ) )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[78,18816]) ).
thf(25408,plain,
( ~ ( empty @ sk1 )
| ( empty @ ( relation_dom @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[25407:[bind(A,$thf( sk1 ))]]) ).
thf(733,plain,
! [B: $i,A: $i] :
( ( empty @ ( sk7 @ A ) )
!= ( empty @ ( singleton @ B ) ) ),
inference(paramod_ordered,[status(thm)],[89,111]) ).
thf(739,plain,
! [B: $i,A: $i] :
( ( sk7 @ A )
!= ( singleton @ B ) ),
inference(simp,[status(thm)],[733]) ).
thf(1416,plain,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
inference(rewrite,[status(thm)],[739,1271]) ).
thf(216,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ( C
!= ( relation_inverse_image @ A @ B ) )
| ~ ( in @ D @ C )
| ( in @ D @ ( relation_dom @ A ) ) ),
inference(cnf,[status(esa)],[215]) ).
thf(226,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( relation_inverse_image @ A @ B ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ D @ C )
| ( in @ D @ ( relation_dom @ A ) ) ),
inference(lifteq,[status(thm)],[216]) ).
thf(227,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ C @ ( relation_inverse_image @ A @ B ) )
| ( in @ C @ ( relation_dom @ A ) ) ),
inference(simp,[status(thm)],[226]) ).
thf(59442,plain,
$false,
inference(e,[status(thm)],[69,3944,101,23842,88,170,1211,24759,115,10780,18706,14937,7208,1305,25039,5550,56,13675,13722,142,153,1788,1426,174,15072,185,13378,19419,52,184,2571,25516,125,46,93,152,16223,57,78,2178,1489,121,2540,23839,11168,15060,164,1465,211,253,14408,106,14113,132,133,23534,74,3184,5220,61,116,1405,20762,10725,117,13265,21133,1470,102,85,201,25321,70,92,3166,229,65,2565,97,18816,1089,11056,1121,53,141,188,7610,14840,14244,109,14841,225,16832,1937,25406,706,96,2561,14313,738,24758,10550,1979,5479,134,73,128,633,205,13844,25320,22980,105,244,3173,16220,166,45,64,2894,149,7639,7736,14247,59,118,71,1271,144,49,86,187,172,113,3155,81,76,245,28529,98,1175,11078,11868,103,140,213,91,10778,66,240,2278,2553,155,24488,27013,14412,3159,986,1496,135,3016,241,80,18918,12021,1467,209,112,7679,123,145,14417,1598,150,25437,33070,14919,50,67,3202,13978,127,1901,1538,1738,199,2092,154,72,175,7612,13674,14992,143,17992,21135,10496,16418,87,203,903,104,1866,18443,231,23252,186,114,139,29571,19196,207,25507,82,214,75,10937,246,18447,151,168,146,30703,17989,23247,126,14315,79,13842,13377,7684,1930,13977,10554,62,14114,131,47,111,83,659,25408,1416,3035,100,15003,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU078+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n005.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 13:04:09 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.98/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.32/1.07 % [INFO] Parsing done (155ms).
% 1.32/1.08 % [INFO] Running in sequential loop mode.
% 1.79/1.28 % [INFO] eprover registered as external prover.
% 1.79/1.28 % [INFO] cvc4 registered as external prover.
% 1.79/1.29 % [INFO] Scanning for conjecture ...
% 1.99/1.35 % [INFO] Found a conjecture and 42 axioms. Running axiom selection ...
% 2.14/1.40 % [INFO] Axiom selection finished. Selected 42 axioms (removed 0 axioms).
% 2.14/1.44 % [INFO] Problem is first-order (TPTP FOF).
% 2.14/1.44 % [INFO] Type checking passed.
% 2.14/1.45 % [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 ...
% 181.48/37.40 % External prover 'e' found a proof!
% 181.48/37.40 % [INFO] Killing All external provers ...
% 181.48/37.40 % Time passed: 36880ms (effective reasoning time: 36318ms)
% 181.48/37.40 % 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)>
% 181.48/37.40 % Axioms used in derivation (42): d1_tarski, rc3_funct_1, cc1_relat_1, rc1_funct_1, t173_relat_1, t5_subset, fc2_subset_1, fc5_relat_1, rc2_relat_1, d5_funct_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_xboole_0, fc4_relat_1, t1_subset, rc3_relat_1, t56_zfmisc_1, t6_boole, rc2_subset_1, d13_funct_1, t4_subset, t7_boole, cc1_funct_1, fc1_subset_1, rc2_funct_1, rc1_subset_1, cc2_funct_1, t3_subset, existence_m1_subset_1, t39_zfmisc_1, rc1_relat_1, reflexivity_r1_tarski, t144_funct_1, t2_xboole_1, fc6_relat_1, t8_boole, rc1_xboole_0, t2_subset, fc7_relat_1, fc12_relat_1, symmetry_r1_xboole_0, fc8_relat_1
% 181.48/37.40 % No. of inferences in proof: 590
% 181.48/37.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 36880 ms resp. 36318 ms w/o parsing
% 182.10/37.53 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 182.10/37.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------