TSTP Solution File: SEU214+3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU214+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 11:57:35 EDT 2023
% Result : Theorem 254.00s 53.69s
% Output : Refutation 254.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 78
% Syntax : Number of formulae : 1043 ( 149 unt; 38 typ; 0 def)
% Number of atoms : 2879 (1081 equ; 0 cnn)
% Maximal formula atoms : 17 ( 2 avg)
% Number of connectives : 9210 (1565 ~;1279 |; 96 &;6169 @)
% ( 7 <=>; 94 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 56 ( 56 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 38 usr; 12 con; 0-5 aty)
% Number of variables : 821 ( 0 ^; 772 !; 49 ?; 821 :)
% Comments :
%------------------------------------------------------------------------------
thf(relation_type,type,
relation: $i > $o ).
thf(function_type,type,
function: $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(relation_dom_type,type,
relation_dom: $i > $i ).
thf(relation_composition_type,type,
relation_composition: $i > $i > $i ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(unordered_pair_type,type,
unordered_pair: $i > $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(element_type,type,
element: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(relation_empty_yielding_type,type,
relation_empty_yielding: $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $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 ).
thf(sk12_type,type,
sk12: $i > $i > $i > $i ).
thf(sk13_type,type,
sk13: $i > $i > $i ).
thf(sk14_type,type,
sk14: $i > $i > $i ).
thf(sk15_type,type,
sk15: $i > $i > $i ).
thf(sk16_type,type,
sk16: $i > $i > $i > $i > $i > $i ).
thf(sk17_type,type,
sk17: $i > $i > $i > $o ).
thf(sk18_type,type,
sk18: $i > $i > $i > $i ).
thf(sk19_type,type,
sk19: $i > $i > $i > $i ).
thf(sk20_type,type,
sk20: $i > $i > $i > $i ).
thf(sk21_type,type,
sk21: $i > $i > $i > $i ).
thf(sk22_type,type,
sk22: $i > $i > $i > $i ).
thf(sk23_type,type,
sk23: $i ).
thf(15,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
thf(85,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(86,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ),
inference(cnf,[status(esa)],[85]) ).
thf(87,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( empty @ A ) ),
inference(lifteq,[status(thm)],[86]) ).
thf(9,axiom,
empty @ empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(67,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(35,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(150,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(151,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) ),
inference(cnf,[status(esa)],[150]) ).
thf(6978,plain,
! [A: $i] :
( ( empty @ ( relation_dom @ A ) )
| ( ( empty @ empty_set )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[67,151]) ).
thf(6979,plain,
empty @ ( relation_dom @ empty_set ),
inference(pattern_uni,[status(thm)],[6978:[bind(A,$thf( empty_set ))]]) ).
thf(7105,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ ( relation_dom @ empty_set ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6979,87]) ).
thf(7106,plain,
( ( relation_dom @ empty_set )
= empty_set ),
inference(pattern_uni,[status(thm)],[7105:[bind(A,$thf( relation_dom @ empty_set ))]]) ).
thf(41,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(202,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(204,plain,
relation @ sk23,
inference(cnf,[status(esa)],[202]) ).
thf(39,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(178,plain,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(179,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ),
inference(cnf,[status(esa)],[178]) ).
thf(13407,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( relation_dom @ A ) )
| ( ( relation @ sk23 )
!= ( relation @ A ) ) ),
inference(paramod_ordered,[status(thm)],[204,179]) ).
thf(13408,plain,
( ( empty @ sk23 )
| ~ ( empty @ ( relation_dom @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[13407:[bind(A,$thf( sk23 ))]]) ).
thf(27814,plain,
( ( empty @ sk23 )
| ( ( empty @ ( relation_dom @ sk23 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[67,13408]) ).
thf(27837,plain,
( ( empty @ sk23 )
| ( ( relation_dom @ sk23 )
!= empty_set ) ),
inference(simp,[status(thm)],[27814]) ).
thf(30869,plain,
( ( empty @ sk23 )
| ( ( relation_dom @ sk23 )
!= ( relation_dom @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[7106,27837]) ).
thf(30977,plain,
( ( empty @ sk23 )
| ( sk23 != empty_set ) ),
inference(simp,[status(thm)],[30869]) ).
thf(31082,plain,
! [A: $i] :
( ( sk23 != empty_set )
| ( empty @ ( relation_dom @ A ) )
| ( ( empty @ sk23 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30977,151]) ).
thf(31083,plain,
( ( sk23 != empty_set )
| ( empty @ ( relation_dom @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[31082:[bind(A,$thf( sk23 ))]]) ).
thf(36251,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ sk23 ) )
| ( A != sk23 ) ),
inference(paramod_ordered,[status(thm)],[87,31083]) ).
thf(36252,plain,
( ~ ( empty @ sk23 )
| ( empty @ ( relation_dom @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[36251:[bind(A,$thf( sk23 ))]]) ).
thf(45337,plain,
! [A: $i] :
( ~ ( empty @ sk23 )
| ( empty @ ( relation_dom @ A ) )
| ( ( empty @ ( relation_dom @ sk23 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[36252,151]) ).
thf(45338,plain,
( ~ ( empty @ sk23 )
| ( empty @ ( relation_dom @ ( relation_dom @ sk23 ) ) ) ),
inference(pattern_uni,[status(thm)],[45337:[bind(A,$thf( relation_dom @ sk23 ))]]) ).
thf(26,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(115,plain,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(116,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ),
inference(cnf,[status(esa)],[115]) ).
thf(66591,plain,
! [A: $i] :
( ~ ( empty @ sk23 )
| ( function @ A )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk23 ) ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45338,116]) ).
thf(66592,plain,
( ~ ( empty @ sk23 )
| ( function @ ( relation_dom @ ( relation_dom @ sk23 ) ) ) ),
inference(pattern_uni,[status(thm)],[66591:[bind(A,$thf( relation_dom @ ( relation_dom @ sk23 ) ))]]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(50,plain,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(cnf,[status(esa)],[50]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(lifteq,[status(thm)],[51]) ).
thf(33,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(145,plain,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(147,plain,
relation @ sk11,
inference(cnf,[status(esa)],[145]) ).
thf(37,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
thf(155,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( ( B
= ( relation_dom @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) )
& ( ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) )
& ( ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ C @ B ) ) )
=> ( B
= ( relation_dom @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(156,plain,
! [A: $i] :
( ( relation @ A )
=> ( ! [B: $i] :
( ( B
= ( relation_dom @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) )
& ! [C: $i] :
( ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ C @ B ) ) ) )
& ! [B: $i] :
( ( ! [C: $i] :
( ( in @ C @ B )
=> ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A ) )
& ! [C: $i] :
( ? [D: $i] : ( in @ ( ordered_pair @ C @ D ) @ A )
=> ( in @ C @ B ) ) )
=> ( B
= ( relation_dom @ A ) ) ) ) ),
inference(miniscope,[status(thm)],[155]) ).
thf(159,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ( in @ ( sk13 @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sk14 @ B @ A ) @ ( sk15 @ B @ A ) ) @ A )
| ( B
= ( relation_dom @ A ) ) ),
inference(cnf,[status(esa)],[156]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ( in @ ( sk13 @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sk14 @ B @ A ) @ ( sk15 @ B @ A ) ) @ A ) ),
inference(lifteq,[status(thm)],[159]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ( in @ ( sk13 @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sk14 @ B @ A ) @ ( sk15 @ B @ A ) ) @ A ) ),
inference(simp,[status(thm)],[169]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(76,plain,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
inference(cnf,[status(esa)],[76]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(1469,plain,
! [B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ( in @ ( sk13 @ B @ A ) @ B )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ B @ A ) @ ( sk15 @ B @ A ) ) @ ( singleton @ ( sk14 @ B @ A ) ) ) @ A ) ),
inference(rewrite,[status(thm)],[170,78]) ).
thf(1543,plain,
! [B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ( in @ ( sk13 @ B @ A ) @ B )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ B @ A ) @ ( sk15 @ B @ A ) ) @ ( singleton @ ( sk14 @ B @ A ) ) ) @ A )
| ( ( relation @ sk11 )
!= ( relation @ A ) ) ),
inference(paramod_ordered,[status(thm)],[147,1469]) ).
thf(1544,plain,
! [A: $i] :
( ( A
= ( relation_dom @ sk11 ) )
| ( in @ ( sk13 @ A @ sk11 ) @ A )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ A @ sk11 ) @ ( sk15 @ A @ sk11 ) ) @ ( singleton @ ( sk14 @ A @ sk11 ) ) ) @ sk11 ) ),
inference(pattern_uni,[status(thm)],[1543:[bind(A,$thf( sk11 ))]]) ).
thf(1690,plain,
! [A: $i] :
( ( A
= ( relation_dom @ sk11 ) )
| ( in @ ( sk13 @ A @ sk11 ) @ A )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ A @ sk11 ) @ ( sk15 @ A @ sk11 ) ) @ ( singleton @ ( sk14 @ A @ sk11 ) ) ) @ sk11 ) ),
inference(simp,[status(thm)],[1544]) ).
thf(20,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
thf(99,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(100,plain,
~ ? [A: $i,B: $i] :
( ( in @ A @ B )
& ( empty @ B ) ),
inference(miniscope,[status(thm)],[99]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( empty @ B ) ),
inference(cnf,[status(esa)],[100]) ).
thf(1376,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( ( empty @ empty_set )
!= ( empty @ B ) ) ),
inference(paramod_ordered,[status(thm)],[67,101]) ).
thf(1377,plain,
! [A: $i] :
~ ( in @ A @ empty_set ),
inference(pattern_uni,[status(thm)],[1376:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).
thf(2085,plain,
! [B: $i,A: $i] :
( ( A
= ( relation_dom @ sk11 ) )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ A @ sk11 ) @ ( sk15 @ A @ sk11 ) ) @ ( singleton @ ( sk14 @ A @ sk11 ) ) ) @ sk11 )
| ( ( in @ ( sk13 @ A @ sk11 ) @ A )
!= ( in @ B @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[1690,1377]) ).
thf(2086,plain,
( ( ( relation_dom @ sk11 )
= empty_set )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 ) ),
inference(pattern_uni,[status(thm)],[2085:[bind(A,$thf( empty_set )),bind(B,$thf( sk13 @ empty_set @ sk11 ))]]) ).
thf(2727,plain,
! [B: $i,A: $i] :
( ( ( relation_dom @ sk11 )
= empty_set )
| ( in @ ( unordered_pair @ B @ A ) @ sk11 )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[52,2086]) ).
thf(2728,plain,
( ( ( relation_dom @ sk11 )
= empty_set )
| ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 ) ),
inference(pattern_uni,[status(thm)],[2727:[bind(A,$thf( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) )),bind(B,$thf( singleton @ ( sk14 @ empty_set @ sk11 ) ))]]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
thf(102,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ),
inference(cnf,[status(esa)],[102]) ).
thf(3208,plain,
! [B: $i,A: $i] :
( ( ( relation_dom @ sk11 )
= empty_set )
| ( element @ A @ B )
| ( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2728,103]) ).
thf(3209,plain,
( ( ( relation_dom @ sk11 )
= empty_set )
| ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 ) ),
inference(pattern_uni,[status(thm)],[3208:[bind(A,$thf( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) )),bind(B,$thf( sk11 ))]]) ).
thf(13392,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( relation_dom @ A ) )
| ( ( relation @ sk11 )
!= ( relation @ A ) ) ),
inference(paramod_ordered,[status(thm)],[147,179]) ).
thf(13393,plain,
( ( empty @ sk11 )
| ~ ( empty @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[13392:[bind(A,$thf( sk11 ))]]) ).
thf(27739,plain,
( ( empty @ sk11 )
| ( ( empty @ ( relation_dom @ sk11 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[67,13393]) ).
thf(27767,plain,
( ( empty @ sk11 )
| ( ( relation_dom @ sk11 )
!= empty_set ) ),
inference(simp,[status(thm)],[27739]) ).
thf(28842,plain,
! [A: $i] :
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( A = empty_set )
| ( ( empty @ sk11 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27767,87]) ).
thf(28843,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( sk11 = empty_set ) ),
inference(pattern_uni,[status(thm)],[28842:[bind(A,$thf( sk11 ))]]) ).
thf(32991,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( sk11 = empty_set )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[3209,28843]) ).
thf(32992,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( sk11 = empty_set ) ),
inference(pattern_uni,[status(thm)],[32991:[]]) ).
thf(2764,plain,
! [A: $i] :
( ( ( relation_dom @ sk11 )
= empty_set )
| ( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
!= ( in @ A @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[2086,1377]) ).
thf(2902,plain,
! [A: $i] :
( ( ( relation_dom @ sk11 )
= empty_set )
| ( ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) )
!= A )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[2764]) ).
thf(2921,plain,
( ( ( relation_dom @ sk11 )
= empty_set )
| ( sk11 != empty_set ) ),
inference(simp,[status(thm)],[2902]) ).
thf(28755,plain,
( ( sk11 != empty_set )
| ( empty @ sk11 )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[2921,27767]) ).
thf(28756,plain,
( ( sk11 != empty_set )
| ( empty @ sk11 ) ),
inference(pattern_uni,[status(thm)],[28755:[]]) ).
thf(29566,plain,
! [A: $i] :
( ( sk11 != empty_set )
| ( empty @ ( relation_dom @ A ) )
| ( ( empty @ sk11 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28756,151]) ).
thf(29567,plain,
( ( sk11 != empty_set )
| ( empty @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[29566:[bind(A,$thf( sk11 ))]]) ).
thf(33978,plain,
! [A: $i] :
( ( sk11 != empty_set )
| ( empty @ ( relation_dom @ A ) )
| ( ( empty @ ( relation_dom @ sk11 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29567,151]) ).
thf(33979,plain,
( ( sk11 != empty_set )
| ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[33978:[bind(A,$thf( relation_dom @ sk11 ))]]) ).
thf(53683,plain,
! [A: $i] :
( ( sk11 != empty_set )
| ( A = empty_set )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33979,87]) ).
thf(53684,plain,
( ( sk11 != empty_set )
| ( ( relation_dom @ ( relation_dom @ sk11 ) )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[53683:[bind(A,$thf( relation_dom @ ( relation_dom @ sk11 ) ))]]) ).
thf(73812,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( ( relation_dom @ ( relation_dom @ sk11 ) )
= empty_set )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32992,53684]) ).
thf(73813,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( ( relation_dom @ ( relation_dom @ sk11 ) )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[73812:[]]) ).
thf(32980,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( sk11 = empty_set )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[2086,28843]) ).
thf(32981,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( sk11 = empty_set ) ),
inference(pattern_uni,[status(thm)],[32980:[]]) ).
thf(152,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ),
inference(cnf,[status(esa)],[150]) ).
thf(33859,plain,
! [A: $i] :
( ( sk11 != empty_set )
| ( relation @ ( relation_dom @ A ) )
| ( ( empty @ ( relation_dom @ sk11 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29567,152]) ).
thf(33860,plain,
( ( sk11 != empty_set )
| ( relation @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[33859:[bind(A,$thf( relation_dom @ sk11 ))]]) ).
thf(53036,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32981,33860]) ).
thf(53037,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[53036:[]]) ).
thf(2759,plain,
! [B: $i,A: $i] :
( ( ( relation_dom @ sk11 )
= empty_set )
| ~ ( empty @ B )
| ( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2086,101]) ).
thf(2760,plain,
( ( ( relation_dom @ sk11 )
= empty_set )
| ~ ( empty @ sk11 ) ),
inference(pattern_uni,[status(thm)],[2759:[bind(A,$thf( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) )),bind(B,$thf( sk11 ))]]) ).
thf(32995,plain,
( ~ ( empty @ sk11 )
| ( sk11 = empty_set )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[2760,28843]) ).
thf(32996,plain,
( ~ ( empty @ sk11 )
| ( sk11 = empty_set ) ),
inference(pattern_uni,[status(thm)],[32995:[]]) ).
thf(33919,plain,
( ~ ( empty @ sk11 )
| ( empty @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32996,29567]) ).
thf(33920,plain,
( ~ ( empty @ sk11 )
| ( empty @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[33919:[]]) ).
thf(42551,plain,
! [A: $i] :
( ~ ( empty @ sk11 )
| ( empty @ ( relation_dom @ A ) )
| ( ( empty @ ( relation_dom @ sk11 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33920,151]) ).
thf(42552,plain,
( ~ ( empty @ sk11 )
| ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[42551:[bind(A,$thf( relation_dom @ sk11 ))]]) ).
thf(28,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(131,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(133,plain,
~ ( empty @ sk10 ),
inference(cnf,[status(esa)],[131]) ).
thf(62009,plain,
( ~ ( empty @ sk11 )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
!= ( empty @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[42552,133]) ).
thf(62305,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ ( relation_dom @ sk11 ) )
!= sk10 ) ),
inference(simp,[status(thm)],[62009]) ).
thf(85284,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ ( relation_dom @ empty_set ) )
!= sk10 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32996,62305]) ).
thf(85285,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ ( relation_dom @ empty_set ) )
!= sk10 ) ),
inference(pattern_uni,[status(thm)],[85284:[]]) ).
thf(90180,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ empty_set )
!= sk10 ) ),
inference(rewrite,[status(thm)],[85285,7106]) ).
thf(30,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(136,plain,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(138,plain,
relation @ empty_set,
inference(cnf,[status(esa)],[136]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
=> ( ( apply @ ( relation_composition @ C @ B ) @ A )
= ( apply @ B @ ( apply @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
=> ( ( apply @ ( relation_composition @ C @ B ) @ A )
= ( apply @ B @ ( apply @ C @ A ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(42,plain,
~ ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ A @ ( relation_dom @ ( relation_composition @ C @ B ) ) )
=> ( ( apply @ ( relation_composition @ C @ B ) @ A )
= ( apply @ B @ ( apply @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(46,plain,
in @ sk1 @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ),
inference(cnf,[status(esa)],[42]) ).
thf(1766,plain,
! [B: $i,A: $i] :
( ( element @ A @ B )
| ( ( in @ sk1 @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[46,103]) ).
thf(1767,plain,
element @ sk1 @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1766:[bind(A,$thf( sk1 )),bind(B,$thf( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ))]]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ B @ A ) )
& ( relation @ ( relation_composition @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(107,plain,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ B @ A ) )
& ( relation @ ( relation_composition @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( empty @ ( relation_composition @ B @ A ) ) ),
inference(cnf,[status(esa)],[107]) ).
thf(1374,plain,
! [B: $i,A: $i] :
( ~ ( empty @ B )
| ( ( in @ sk1 @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[46,101]) ).
thf(1375,plain,
~ ( empty @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[1374:[bind(A,$thf( sk1 )),bind(B,$thf( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ))]]) ).
thf(1383,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ ( relation_dom @ empty_set ) )
| ( A
!= ( relation_composition @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[87,1375]) ).
thf(1384,plain,
( ~ ( empty @ ( relation_composition @ sk3 @ sk2 ) )
| ~ ( empty @ ( relation_dom @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[1383:[bind(A,$thf( relation_composition @ sk3 @ sk2 ))]]) ).
thf(2610,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ~ ( empty @ ( relation_dom @ empty_set ) )
| ( ( empty @ ( relation_composition @ B @ A ) )
!= ( empty @ ( relation_composition @ sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[108,1384]) ).
thf(2611,plain,
( ~ ( empty @ sk2 )
| ~ ( relation @ sk3 )
| ~ ( empty @ ( relation_dom @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[2610:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(44,plain,
relation @ sk3,
inference(cnf,[status(esa)],[42]) ).
thf(3936,plain,
( ~ ( empty @ sk2 )
| ~ $true
| ~ ( empty @ ( relation_dom @ empty_set ) ) ),
inference(rewrite,[status(thm)],[2611,44]) ).
thf(3937,plain,
( ~ ( empty @ sk2 )
| ~ ( empty @ ( relation_dom @ empty_set ) ) ),
inference(simp,[status(thm)],[3936]) ).
thf(7048,plain,
( ~ ( empty @ sk2 )
| ~ $true ),
inference(rewrite,[status(thm)],[3937,6979]) ).
thf(7049,plain,
~ ( empty @ sk2 ),
inference(simp,[status(thm)],[7048]) ).
thf(36225,plain,
( ( sk23 != empty_set )
| ( ( empty @ ( relation_dom @ sk23 ) )
!= ( empty @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[31083,7049]) ).
thf(36300,plain,
( ( sk23 != empty_set )
| ( ( relation_dom @ sk23 )
!= sk2 ) ),
inference(simp,[status(thm)],[36225]) ).
thf(42326,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( relation_dom @ sk23 )
!= sk2 )
| ( A != sk23 ) ),
inference(paramod_ordered,[status(thm)],[87,36300]) ).
thf(42327,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ sk23 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[42326:[bind(A,$thf( sk23 ))]]) ).
thf(44288,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( ( relation_dom @ sk23 )
!= sk2 )
| ( ( empty @ sk23 )
!= ( empty @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[27837,42327]) ).
thf(44289,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( ( relation_dom @ sk23 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[44288:[]]) ).
thf(29503,plain,
! [A: $i] :
( ( sk11 != empty_set )
| ( function @ A )
| ( ( empty @ sk11 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28756,116]) ).
thf(29504,plain,
( ( sk11 != empty_set )
| ( function @ sk11 ) ),
inference(pattern_uni,[status(thm)],[29503:[bind(A,$thf( sk11 ))]]) ).
thf(29615,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( function @ sk11 )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[87,29504]) ).
thf(29616,plain,
( ~ ( empty @ sk11 )
| ( function @ sk11 ) ),
inference(pattern_uni,[status(thm)],[29615:[bind(A,$thf( sk11 ))]]) ).
thf(13405,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( relation_dom @ A ) )
| ( ( relation @ sk3 )
!= ( relation @ A ) ) ),
inference(paramod_ordered,[status(thm)],[44,179]) ).
thf(13406,plain,
( ( empty @ sk3 )
| ~ ( empty @ ( relation_dom @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[13405:[bind(A,$thf( sk3 ))]]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ A @ B ) )
& ( relation @ ( relation_composition @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(175,plain,
! [A: $i,B: $i] :
( ( ( empty @ A )
& ( relation @ B ) )
=> ( ( empty @ ( relation_composition @ A @ B ) )
& ( relation @ ( relation_composition @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( empty @ ( relation_composition @ A @ B ) ) ),
inference(cnf,[status(esa)],[175]) ).
thf(6936,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( empty @ ( relation_dom @ A ) )
!= ( empty @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[151,1375]) ).
thf(6937,plain,
~ ( empty @ ( relation_composition @ sk3 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[6936:[bind(A,$thf( relation_composition @ sk3 @ sk2 ))]]) ).
thf(12290,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( ( empty @ ( relation_composition @ A @ B ) )
!= ( empty @ ( relation_composition @ sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[176,6937]) ).
thf(12291,plain,
( ~ ( empty @ sk3 )
| ~ ( relation @ sk2 ) ),
inference(pattern_uni,[status(thm)],[12290:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 ))]]) ).
thf(45,plain,
relation @ sk2,
inference(cnf,[status(esa)],[42]) ).
thf(12482,plain,
( ~ ( empty @ sk3 )
| ~ $true ),
inference(rewrite,[status(thm)],[12291,45]) ).
thf(12483,plain,
~ ( empty @ sk3 ),
inference(simp,[status(thm)],[12482]) ).
thf(18066,plain,
( $false
| ~ ( empty @ ( relation_dom @ sk3 ) ) ),
inference(rewrite,[status(thm)],[13406,12483]) ).
thf(18067,plain,
~ ( empty @ ( relation_dom @ sk3 ) ),
inference(simp,[status(thm)],[18066]) ).
thf(36204,plain,
( ( sk23 != empty_set )
| ( ( empty @ ( relation_dom @ sk23 ) )
!= ( empty @ ( relation_dom @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[31083,18067]) ).
thf(36290,plain,
( ( sk23 != empty_set )
| ( ( relation_dom @ sk23 )
!= ( relation_dom @ sk3 ) ) ),
inference(simp,[status(thm)],[36204]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(148,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ),
inference(cnf,[status(esa)],[148]) ).
thf(6565,plain,
! [B: $i,A: $i] :
( ~ ( in @ B @ A )
| ( ( in @ sk1 @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[46,149]) ).
thf(6566,plain,
~ ( in @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ) @ sk1 ),
inference(pattern_uni,[status(thm)],[6565:[bind(A,$thf( sk1 )),bind(B,$thf( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ))]]) ).
thf(14,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(82,plain,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(83,plain,
~ ? [A: $i,B: $i] : ( empty @ ( unordered_pair @ A @ B ) ),
inference(miniscope,[status(thm)],[82]) ).
thf(84,plain,
! [B: $i,A: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
inference(cnf,[status(esa)],[83]) ).
thf(655,plain,
! [B: $i,A: $i] :
( ( empty @ ( unordered_pair @ A @ B ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[67,84]) ).
thf(666,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
!= empty_set ),
inference(simp,[status(thm)],[655]) ).
thf(16,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox/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)],[16]) ).
thf(2796,plain,
! [B: $i,A: $i] :
( ( ( relation_dom @ sk11 )
= empty_set )
| ( element @ A @ B )
| ( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2086,103]) ).
thf(2797,plain,
( ( ( relation_dom @ sk11 )
= empty_set )
| ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 ) ),
inference(pattern_uni,[status(thm)],[2796:[bind(A,$thf( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) )),bind(B,$thf( sk11 ))]]) ).
thf(32982,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( sk11 = empty_set )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[2797,28843]) ).
thf(32983,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( sk11 = empty_set ) ),
inference(pattern_uni,[status(thm)],[32982:[]]) ).
thf(29498,plain,
! [A: $i] :
( ( sk11 != empty_set )
| ( relation @ ( relation_dom @ A ) )
| ( ( empty @ sk11 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[28756,152]) ).
thf(29499,plain,
( ( sk11 != empty_set )
| ( relation @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[29498:[bind(A,$thf( sk11 ))]]) ).
thf(39120,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32983,29499]) ).
thf(39121,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[39120:[]]) ).
thf(30923,plain,
! [A: $i] :
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( A = empty_set )
| ( ( empty @ sk23 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27837,87]) ).
thf(30924,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( sk23 = empty_set ) ),
inference(pattern_uni,[status(thm)],[30923:[bind(A,$thf( sk23 ))]]) ).
thf(35447,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk23 = empty_set )
| ( A
!= ( relation_dom @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[87,30924]) ).
thf(35448,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( sk23 = empty_set ) ),
inference(pattern_uni,[status(thm)],[35447:[bind(A,$thf( relation_dom @ sk23 ))]]) ).
thf(43388,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk23 = empty_set )
| ( ( empty @ ( relation_dom @ A ) )
!= ( empty @ ( relation_dom @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[151,35448]) ).
thf(43389,plain,
( ~ ( empty @ sk23 )
| ( sk23 = empty_set ) ),
inference(pattern_uni,[status(thm)],[43388:[bind(A,$thf( sk23 ))]]) ).
thf(7,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(61,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(62,plain,
~ ! [A: $i] : ( empty @ A ),
inference(miniscope,[status(thm)],[61]) ).
thf(63,plain,
~ ( empty @ sk5 ),
inference(cnf,[status(esa)],[62]) ).
thf(36230,plain,
( ( sk23 != empty_set )
| ( ( empty @ ( relation_dom @ sk23 ) )
!= ( empty @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[31083,63]) ).
thf(36294,plain,
( ( sk23 != empty_set )
| ( ( relation_dom @ sk23 )
!= sk5 ) ),
inference(simp,[status(thm)],[36230]) ).
thf(43774,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ sk23 )
!= sk5 )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[43389,36294]) ).
thf(43775,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ sk23 )
!= sk5 ) ),
inference(pattern_uni,[status(thm)],[43774:[]]) ).
thf(46194,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( ( relation_dom @ sk23 )
!= sk5 )
| ( ( empty @ sk23 )
!= ( empty @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[27837,43775]) ).
thf(46195,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( ( relation_dom @ sk23 )
!= sk5 ) ),
inference(pattern_uni,[status(thm)],[46194:[]]) ).
thf(36249,plain,
! [A: $i] :
( ( sk23 != empty_set )
| ( A = empty_set )
| ( ( empty @ ( relation_dom @ sk23 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31083,87]) ).
thf(36250,plain,
( ( sk23 != empty_set )
| ( ( relation_dom @ sk23 )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[36249:[bind(A,$thf( relation_dom @ sk23 ))]]) ).
thf(44429,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ sk23 )
= empty_set )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[43389,36250]) ).
thf(44430,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ sk23 )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[44429:[]]) ).
thf(132,plain,
relation @ sk10,
inference(cnf,[status(esa)],[131]) ).
thf(13390,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( relation_dom @ A ) )
| ( ( relation @ sk10 )
!= ( relation @ A ) ) ),
inference(paramod_ordered,[status(thm)],[132,179]) ).
thf(13391,plain,
( ( empty @ sk10 )
| ~ ( empty @ ( relation_dom @ sk10 ) ) ),
inference(pattern_uni,[status(thm)],[13390:[bind(A,$thf( sk10 ))]]) ).
thf(24637,plain,
( $false
| ~ ( empty @ ( relation_dom @ sk10 ) ) ),
inference(rewrite,[status(thm)],[13391,133]) ).
thf(24638,plain,
~ ( empty @ ( relation_dom @ sk10 ) ),
inference(simp,[status(thm)],[24637]) ).
thf(24677,plain,
( ( empty @ ( relation_dom @ sk10 ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[67,24638]) ).
thf(24708,plain,
( ( relation_dom @ sk10 )
!= empty_set ),
inference(simp,[status(thm)],[24677]) ).
thf(24754,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[2760,24708]) ).
thf(24770,plain,
( ~ ( empty @ sk11 )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[24754]) ).
thf(28793,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( sk11 != sk10 )
| ( ( empty @ sk11 )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[27767,24770]) ).
thf(28794,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( sk11 != sk10 ) ),
inference(pattern_uni,[status(thm)],[28793:[]]) ).
thf(46642,plain,
( ~ ( empty @ sk23 )
| ( sk11 != sk10 )
| ( ( relation_dom @ sk23 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[44430,28794]) ).
thf(46946,plain,
( ~ ( empty @ sk23 )
| ( sk11 != sk10 )
| ( sk23 != sk11 ) ),
inference(simp,[status(thm)],[46642]) ).
thf(5,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
thf(55,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(56,plain,
~ ? [A: $i] :
( ( empty @ A )
& ? [B: $i] :
( ( A != B )
& ( empty @ B ) ) ),
inference(miniscope,[status(thm)],[55]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( A = B )
| ~ ( empty @ B ) ),
inference(cnf,[status(esa)],[56]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(47,plain,
( ( apply @ ( relation_composition @ sk3 @ sk2 ) @ sk1 )
!= ( apply @ sk2 @ ( apply @ sk3 @ sk1 ) ) ),
inference(cnf,[status(esa)],[42]) ).
thf(49,plain,
( ( apply @ ( relation_composition @ sk3 @ sk2 ) @ sk1 )
!= ( apply @ sk2 @ ( apply @ sk3 @ sk1 ) ) ),
inference(lifteq,[status(thm)],[47]) ).
thf(209,plain,
( ( ( relation_composition @ sk3 @ sk2 )
!= sk2 )
| ( ( apply @ sk3 @ sk1 )
!= sk1 ) ),
inference(simp,[status(thm)],[49]) ).
thf(299,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( ( relation_composition @ sk3 @ sk2 )
!= sk2 )
| ( B != sk1 )
| ( A
!= ( apply @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[58,209]) ).
thf(300,plain,
! [A: $i] :
( ~ ( empty @ ( apply @ sk3 @ sk1 ) )
| ~ ( empty @ A )
| ( ( relation_composition @ sk3 @ sk2 )
!= sk2 )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[299:[bind(A,$thf( apply @ sk3 @ sk1 )),bind(B,$thf( B ))]]) ).
thf(408,plain,
( ~ ( empty @ ( apply @ sk3 @ sk1 ) )
| ~ ( empty @ sk1 )
| ( ( relation_composition @ sk3 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[300]) ).
thf(36279,plain,
! [A: $i] :
( ( sk23 != empty_set )
| ( empty @ ( relation_dom @ A ) )
| ( ( empty @ ( relation_dom @ sk23 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31083,151]) ).
thf(36280,plain,
( ( sk23 != empty_set )
| ( empty @ ( relation_dom @ ( relation_dom @ sk23 ) ) ) ),
inference(pattern_uni,[status(thm)],[36279:[bind(A,$thf( relation_dom @ sk23 ))]]) ).
thf(56063,plain,
( ( sk23 != empty_set )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk23 ) ) )
!= ( empty @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[36280,7049]) ).
thf(56176,plain,
( ( sk23 != empty_set )
| ( ( relation_dom @ ( relation_dom @ sk23 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[56063]) ).
thf(40,axiom,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_composition @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
thf(180,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( ( C
= ( relation_composition @ A @ B ) )
=> ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) )
& ( ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) )
& ( ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) )
=> ( C
= ( relation_composition @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(181,plain,
! [A: $i] :
( ( relation @ A )
=> ! [B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( ( C
= ( relation_composition @ A @ B ) )
=> ( ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) ) )
& ( ( ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) ) )
& ! [D: $i,E: $i] :
( ? [F: $i] :
( ( in @ ( ordered_pair @ D @ F ) @ A )
& ( in @ ( ordered_pair @ F @ E ) @ B ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) )
=> ( C
= ( relation_composition @ A @ B ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[180]) ).
thf(182,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ( C
!= ( relation_composition @ A @ B ) )
| ~ ( in @ ( ordered_pair @ D @ F ) @ A )
| ~ ( in @ ( ordered_pair @ F @ E ) @ B )
| ( in @ ( ordered_pair @ D @ E ) @ C ) ),
inference(cnf,[status(esa)],[181]) ).
thf(197,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( relation_composition @ A @ B ) )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ D @ F ) @ A )
| ~ ( in @ ( ordered_pair @ F @ E ) @ B )
| ( in @ ( ordered_pair @ D @ E ) @ C ) ),
inference(lifteq,[status(thm)],[182]) ).
thf(198,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ ( relation_composition @ A @ B ) )
| ~ ( in @ ( ordered_pair @ C @ E ) @ A )
| ~ ( in @ ( ordered_pair @ E @ D ) @ B )
| ( in @ ( ordered_pair @ C @ D ) @ ( relation_composition @ A @ B ) ) ),
inference(simp,[status(thm)],[197]) ).
thf(22333,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ ( relation_composition @ A @ B ) )
| ~ ( in @ ( unordered_pair @ ( unordered_pair @ C @ E ) @ ( singleton @ C ) ) @ A )
| ~ ( in @ ( unordered_pair @ ( unordered_pair @ E @ D ) @ ( singleton @ E ) ) @ B )
| ( in @ ( unordered_pair @ ( unordered_pair @ C @ D ) @ ( singleton @ C ) ) @ ( relation_composition @ A @ B ) ) ),
inference(rewrite,[status(thm)],[198,78]) ).
thf(66750,plain,
! [A: $i] :
( ~ ( empty @ sk23 )
| ( A = empty_set )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk23 ) ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45338,87]) ).
thf(66751,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ ( relation_dom @ sk23 ) )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[66750:[bind(A,$thf( relation_dom @ ( relation_dom @ sk23 ) ))]]) ).
thf(30858,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( ( empty @ sk23 )
!= ( empty @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[27837,133]) ).
thf(30987,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( sk23 != sk10 ) ),
inference(simp,[status(thm)],[30858]) ).
thf(34696,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk23 != sk10 )
| ( A
!= ( relation_dom @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[87,30987]) ).
thf(34697,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( sk23 != sk10 ) ),
inference(pattern_uni,[status(thm)],[34696:[bind(A,$thf( relation_dom @ sk23 ))]]) ).
thf(3911,plain,
! [A: $i] :
( ( function @ A )
| ( ( empty @ empty_set )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[67,116]) ).
thf(3912,plain,
function @ empty_set,
inference(pattern_uni,[status(thm)],[3911:[bind(A,$thf( empty_set ))]]) ).
thf(137,plain,
relation_empty_yielding @ empty_set,
inference(cnf,[status(esa)],[136]) ).
thf(271,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( relation_empty_yielding @ A )
| ( B != empty_set ) ),
inference(paramod_ordered,[status(thm)],[58,137]) ).
thf(272,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ empty_set )
| ( relation_empty_yielding @ A ) ),
inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).
thf(32556,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ $true
| ( relation_empty_yielding @ A ) ),
inference(rewrite,[status(thm)],[272,67]) ).
thf(32557,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( relation_empty_yielding @ A ) ),
inference(simp,[status(thm)],[32556]) ).
thf(32558,plain,
! [A: $i] :
( ( sk23 != empty_set )
| ( relation_empty_yielding @ A )
| ( ( empty @ sk23 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30977,32557]) ).
thf(32559,plain,
( ( sk23 != empty_set )
| ( relation_empty_yielding @ sk23 ) ),
inference(pattern_uni,[status(thm)],[32558:[bind(A,$thf( sk23 ))]]) ).
thf(32598,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( relation_empty_yielding @ sk23 )
| ( A != sk23 ) ),
inference(paramod_ordered,[status(thm)],[87,32559]) ).
thf(32599,plain,
( ~ ( empty @ sk23 )
| ( relation_empty_yielding @ sk23 ) ),
inference(pattern_uni,[status(thm)],[32598:[bind(A,$thf( sk23 ))]]) ).
thf(29507,plain,
( ( sk11 != empty_set )
| ( ( empty @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ) )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[28756,1375]) ).
thf(29584,plain,
( ( sk11 != empty_set )
| ( ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) )
!= sk11 ) ),
inference(simp,[status(thm)],[29507]) ).
thf(42451,plain,
( ~ ( empty @ sk11 )
| ( ( empty @ ( relation_dom @ sk11 ) )
!= ( empty @ ( relation_dom @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[33920,18067]) ).
thf(42583,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk3 ) ) ),
inference(simp,[status(thm)],[42451]) ).
thf(22,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(104,plain,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(106,plain,
empty @ sk9,
inference(cnf,[status(esa)],[104]) ).
thf(18,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(93,plain,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(94,plain,
~ ? [A: $i,B: $i] : ( empty @ ( ordered_pair @ A @ B ) ),
inference(miniscope,[status(thm)],[93]) ).
thf(95,plain,
! [B: $i,A: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
inference(cnf,[status(esa)],[94]) ).
thf(674,plain,
! [B: $i,A: $i] :
( ( empty @ ( ordered_pair @ A @ B ) )
!= ( empty @ sk9 ) ),
inference(paramod_ordered,[status(thm)],[106,95]) ).
thf(680,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
!= sk9 ),
inference(simp,[status(thm)],[674]) ).
thf(842,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) )
!= sk9 ),
inference(rewrite,[status(thm)],[680,78]) ).
thf(845,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ ( unordered_pair @ B @ A ) @ ( singleton @ C ) )
!= sk9 )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[52,842]) ).
thf(846,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ B @ A ) @ ( singleton @ A ) )
!= sk9 ),
inference(pattern_uni,[status(thm)],[845:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1024,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ sk9 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[106,87]) ).
thf(1025,plain,
sk9 = empty_set,
inference(pattern_uni,[status(thm)],[1024:[bind(A,$thf( sk9 ))]]) ).
thf(1875,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ B @ A ) @ ( singleton @ A ) )
!= empty_set ),
inference(rewrite,[status(thm)],[846,1025]) ).
thf(1878,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ B @ A )
!= empty_set )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ ( unordered_pair @ D @ C ) @ ( singleton @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[52,1875]) ).
thf(1879,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ A @ B ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[1878:[bind(A,$thf( unordered_pair @ E @ G )),bind(B,$thf( singleton @ G )),bind(C,$thf( G )),bind(D,$thf( E ))]]) ).
thf(1918,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ A @ B ) )
!= empty_set ),
inference(simp,[status(thm)],[1879]) ).
thf(3793,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ ( singleton @ D ) @ ( unordered_pair @ A @ B ) )
!= empty_set )
| ( ( unordered_pair @ B @ A )
!= ( unordered_pair @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[52,1918]) ).
thf(3794,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ B ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[3793:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(32,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(142,plain,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(13,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(79,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(80,plain,
~ ? [A: $i] : ( empty @ ( powerset @ A ) ),
inference(miniscope,[status(thm)],[79]) ).
thf(81,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(cnf,[status(esa)],[80]) ).
thf(465,plain,
! [A: $i] :
( ( empty @ ( powerset @ A ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[67,81]) ).
thf(472,plain,
! [A: $i] :
( ( powerset @ A )
!= empty_set ),
inference(simp,[status(thm)],[465]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
thf(153,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)],[36]) ).
thf(62063,plain,
( ~ ( empty @ sk11 )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
!= ( empty @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[42552,12483]) ).
thf(62309,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ ( relation_dom @ sk11 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[62063]) ).
thf(83878,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ ( relation_dom @ empty_set ) )
!= sk3 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32996,62309]) ).
thf(83879,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ ( relation_dom @ empty_set ) )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[83878:[]]) ).
thf(89659,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ empty_set )
!= sk3 ) ),
inference(rewrite,[status(thm)],[83879,7106]) ).
thf(33927,plain,
( ( sk11 != empty_set )
| ( ( empty @ ( relation_dom @ sk11 ) )
!= ( empty @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[29567,63]) ).
thf(33990,plain,
( ( sk11 != empty_set )
| ( ( relation_dom @ sk11 )
!= sk5 ) ),
inference(simp,[status(thm)],[33927]) ).
thf(40054,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ sk11 )
!= sk5 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32996,33990]) ).
thf(40055,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ sk11 )
!= sk5 ) ),
inference(pattern_uni,[status(thm)],[40054:[]]) ).
thf(13402,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( relation_dom @ A ) )
| ( ( relation @ sk2 )
!= ( relation @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45,179]) ).
thf(13403,plain,
( ( empty @ sk2 )
| ~ ( empty @ ( relation_dom @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[13402:[bind(A,$thf( sk2 ))]]) ).
thf(14157,plain,
( $false
| ~ ( empty @ ( relation_dom @ sk2 ) ) ),
inference(rewrite,[status(thm)],[13403,7049]) ).
thf(14158,plain,
~ ( empty @ ( relation_dom @ sk2 ) ),
inference(simp,[status(thm)],[14157]) ).
thf(14191,plain,
( ( empty @ ( relation_dom @ sk2 ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[67,14158]) ).
thf(14214,plain,
( ( relation_dom @ sk2 )
!= empty_set ),
inference(simp,[status(thm)],[14191]) ).
thf(14260,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[2760,14214]) ).
thf(14273,plain,
( ~ ( empty @ sk11 )
| ( sk11 != sk2 ) ),
inference(simp,[status(thm)],[14260]) ).
thf(18104,plain,
( ( empty @ ( relation_dom @ sk3 ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[67,18067]) ).
thf(18122,plain,
( ( relation_dom @ sk3 )
!= empty_set ),
inference(simp,[status(thm)],[18104]) ).
thf(18177,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[2760,18122]) ).
thf(18190,plain,
( ~ ( empty @ sk11 )
| ( sk11 != sk3 ) ),
inference(simp,[status(thm)],[18177]) ).
thf(31009,plain,
( ( sk23 != empty_set )
| ( sk11 != sk3 )
| ( ( empty @ sk23 )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[30977,18190]) ).
thf(31097,plain,
( ( sk23 != empty_set )
| ( sk11 != sk3 )
| ( sk23 != sk11 ) ),
inference(simp,[status(thm)],[31009]) ).
thf(28768,plain,
! [A: $i] :
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( relation @ ( relation_dom @ A ) )
| ( ( empty @ sk11 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27767,152]) ).
thf(28769,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( relation @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[28768:[bind(A,$thf( sk11 ))]]) ).
thf(62109,plain,
( ~ ( empty @ sk11 )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
!= ( empty @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[42552,7049]) ).
thf(62259,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ ( relation_dom @ sk11 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[62109]) ).
thf(82440,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ ( relation_dom @ empty_set ) )
!= sk2 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32996,62259]) ).
thf(82441,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ ( relation_dom @ empty_set ) )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[82440:[]]) ).
thf(89485,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ empty_set )
!= sk2 ) ),
inference(rewrite,[status(thm)],[82441,7106]) ).
thf(28792,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( ( empty @ ( relation_composition @ sk3 @ sk2 ) )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[27767,6937]) ).
thf(28879,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( ( relation_composition @ sk3 @ sk2 )
!= sk11 ) ),
inference(simp,[status(thm)],[28792]) ).
thf(33865,plain,
! [A: $i] :
( ( sk11 != empty_set )
| ( function @ A )
| ( ( empty @ ( relation_dom @ sk11 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29567,116]) ).
thf(33866,plain,
( ( sk11 != empty_set )
| ( function @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[33865:[bind(A,$thf( relation_dom @ sk11 ))]]) ).
thf(41131,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32983,33866]) ).
thf(41132,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[41131:[]]) ).
thf(53735,plain,
! [A: $i] :
( ( sk11 != empty_set )
| ( relation_empty_yielding @ A )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33979,32557]) ).
thf(53736,plain,
( ( sk11 != empty_set )
| ( relation_empty_yielding @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[53735:[bind(A,$thf( relation_dom @ ( relation_dom @ sk11 ) ))]]) ).
thf(1378,plain,
( ( empty @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[67,1375]) ).
thf(1403,plain,
( ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) )
!= empty_set ),
inference(simp,[status(thm)],[1378]) ).
thf(6230,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[2760,1403]) ).
thf(6291,plain,
( ~ ( empty @ sk11 )
| ( ( relation_composition @ sk3 @ sk2 )
!= sk11 ) ),
inference(simp,[status(thm)],[6230]) ).
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(1038,plain,
! [B: $i,A: $i] :
( ( B = empty_set )
| ( ( empty @ ( sk7 @ A ) )
!= ( empty @ B ) ) ),
inference(paramod_ordered,[status(thm)],[89,87]) ).
thf(1039,plain,
! [A: $i] :
( ( sk7 @ A )
= empty_set ),
inference(pattern_uni,[status(thm)],[1038:[bind(A,$thf( C )),bind(B,$thf( sk7 @ C ))]]) ).
thf(1172,plain,
! [A: $i] :
( ( sk7 @ A )
= empty_set ),
inference(simp,[status(thm)],[1039]) ).
thf(1254,plain,
! [A: $i] : ( element @ empty_set @ ( powerset @ A ) ),
inference(rewrite,[status(thm)],[90,1172]) ).
thf(28757,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( sk11 != sk2 )
| ( ( empty @ sk11 )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[27767,14273]) ).
thf(28758,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( sk11 != sk2 ) ),
inference(pattern_uni,[status(thm)],[28757:[]]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
thf(110,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(56105,plain,
! [A: $i] :
( ( sk23 != empty_set )
| ( A = empty_set )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk23 ) ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[36280,87]) ).
thf(56106,plain,
( ( sk23 != empty_set )
| ( ( relation_dom @ ( relation_dom @ sk23 ) )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[56105:[bind(A,$thf( relation_dom @ ( relation_dom @ sk23 ) ))]]) ).
thf(66810,plain,
! [A: $i] :
( ~ ( empty @ sk23 )
| ( relation_empty_yielding @ A )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk23 ) ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[45338,32557]) ).
thf(66811,plain,
( ~ ( empty @ sk23 )
| ( relation_empty_yielding @ ( relation_dom @ ( relation_dom @ sk23 ) ) ) ),
inference(pattern_uni,[status(thm)],[66810:[bind(A,$thf( relation_dom @ ( relation_dom @ sk23 ) ))]]) ).
thf(28814,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ sk11 )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[2086,27767]) ).
thf(28815,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ sk11 ) ),
inference(pattern_uni,[status(thm)],[28814:[]]) ).
thf(32993,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( sk11 = empty_set )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[2728,28843]) ).
thf(32994,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( sk11 = empty_set ) ),
inference(pattern_uni,[status(thm)],[32993:[]]) ).
thf(41443,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32994,29499]) ).
thf(41444,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[41443:[]]) ).
thf(30951,plain,
! [A: $i] :
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( empty @ ( relation_dom @ A ) )
| ( ( empty @ sk23 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27837,151]) ).
thf(30952,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( empty @ ( relation_dom @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[30951:[bind(A,$thf( sk23 ))]]) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( in @ ( ordered_pair @ ( sk13 @ B @ A ) @ C ) @ A )
| ~ ( in @ ( sk14 @ B @ A ) @ B )
| ( B
= ( relation_dom @ A ) ) ),
inference(cnf,[status(esa)],[156]) ).
thf(167,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ~ ( in @ ( ordered_pair @ ( sk13 @ B @ A ) @ C ) @ A )
| ~ ( in @ ( sk14 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[161]) ).
thf(168,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ~ ( in @ ( ordered_pair @ ( sk13 @ B @ A ) @ C ) @ A )
| ~ ( in @ ( sk14 @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[167]) ).
thf(9240,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ~ ( in @ ( unordered_pair @ ( unordered_pair @ ( sk13 @ B @ A ) @ C ) @ ( singleton @ ( sk13 @ B @ A ) ) ) @ A )
| ~ ( in @ ( sk14 @ B @ A ) @ B ) ),
inference(rewrite,[status(thm)],[168,78]) ).
thf(28773,plain,
! [A: $i] :
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( function @ A )
| ( ( empty @ sk11 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27767,116]) ).
thf(28774,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( function @ sk11 ) ),
inference(pattern_uni,[status(thm)],[28773:[bind(A,$thf( sk11 ))]]) ).
thf(32327,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( function @ sk11 )
| ( A
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[87,28774]) ).
thf(32328,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( function @ sk11 ) ),
inference(pattern_uni,[status(thm)],[32327:[bind(A,$thf( relation_dom @ sk11 ))]]) ).
thf(31037,plain,
( ( sk23 != empty_set )
| ( ( empty @ ( relation_dom @ sk3 ) )
!= ( empty @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[30977,18067]) ).
thf(31107,plain,
( ( sk23 != empty_set )
| ( ( relation_dom @ sk3 )
!= sk23 ) ),
inference(simp,[status(thm)],[31037]) ).
thf(315,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( ( relation_composition @ sk3 @ sk2 )
!= sk2 )
| ( ( apply @ sk3 @ A )
!= sk1 )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[58,209]) ).
thf(316,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ( ( relation_composition @ sk3 @ sk2 )
!= sk2 )
| ( ( apply @ sk3 @ A )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[315:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(32560,plain,
! [A: $i] :
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( relation_empty_yielding @ A )
| ( ( empty @ sk23 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27837,32557]) ).
thf(32561,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( relation_empty_yielding @ sk23 ) ),
inference(pattern_uni,[status(thm)],[32560:[bind(A,$thf( sk23 ))]]) ).
thf(66649,plain,
( ~ ( empty @ sk23 )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk23 ) ) )
!= ( empty @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[45338,12483]) ).
thf(66853,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ ( relation_dom @ sk23 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[66649]) ).
thf(87404,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ ( relation_dom @ empty_set ) )
!= sk3 )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[43389,66853]) ).
thf(87405,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ ( relation_dom @ empty_set ) )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[87404:[]]) ).
thf(90351,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ empty_set )
!= sk3 ) ),
inference(rewrite,[status(thm)],[87405,7106]) ).
thf(31023,plain,
( ( sk23 != empty_set )
| ( ( empty @ ( relation_dom @ sk10 ) )
!= ( empty @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[30977,24638]) ).
thf(31092,plain,
( ( sk23 != empty_set )
| ( ( relation_dom @ sk10 )
!= sk23 ) ),
inference(simp,[status(thm)],[31023]) ).
thf(37236,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( relation_empty_yielding @ sk23 )
| ( A
!= ( relation_dom @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[87,32561]) ).
thf(37237,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( relation_empty_yielding @ sk23 ) ),
inference(pattern_uni,[status(thm)],[37236:[bind(A,$thf( relation_dom @ sk23 ))]]) ).
thf(45291,plain,
( ~ ( empty @ sk23 )
| ( ( empty @ ( relation_dom @ sk23 ) )
!= ( empty @ ( relation_dom @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[36252,14158]) ).
thf(45374,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ sk23 )
!= ( relation_dom @ sk2 ) ) ),
inference(simp,[status(thm)],[45291]) ).
thf(28779,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( ( empty @ ( relation_dom @ sk10 ) )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[27767,24638]) ).
thf(28875,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( ( relation_dom @ sk10 )
!= sk11 ) ),
inference(simp,[status(thm)],[28779]) ).
thf(3951,plain,
( ~ ( empty @ ( relation_dom @ empty_set ) )
| ( ( empty @ sk2 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[67,3937]) ).
thf(3976,plain,
( ~ ( empty @ ( relation_dom @ empty_set ) )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[3951]) ).
thf(7046,plain,
( ~ $true
| ( sk2 != empty_set ) ),
inference(rewrite,[status(thm)],[3976,6979]) ).
thf(7047,plain,
sk2 != empty_set,
inference(simp,[status(thm)],[7046]) ).
thf(31008,plain,
( ( sk23 != empty_set )
| ( sk11 != sk2 )
| ( ( empty @ sk23 )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[30977,14273]) ).
thf(31103,plain,
( ( sk23 != empty_set )
| ( sk11 != sk2 )
| ( sk23 != sk11 ) ),
inference(simp,[status(thm)],[31008]) ).
thf(41139,plain,
( ~ ( empty @ sk11 )
| ( function @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32996,33866]) ).
thf(41140,plain,
( ~ ( empty @ sk11 )
| ( function @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[41139:[]]) ).
thf(28821,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( ( empty @ sk11 )
!= ( empty @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[27767,63]) ).
thf(28885,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( sk11 != sk5 ) ),
inference(simp,[status(thm)],[28821]) ).
thf(375,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( ( apply @ ( relation_composition @ sk3 @ sk2 ) @ A )
!= ( apply @ sk2 @ ( apply @ sk3 @ sk1 ) ) )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[58,49]) ).
thf(376,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ( ( apply @ ( relation_composition @ sk3 @ sk2 ) @ A )
!= ( apply @ sk2 @ ( apply @ sk3 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[375:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(42405,plain,
! [A: $i] :
( ~ ( empty @ sk11 )
| ( relation @ ( relation_dom @ A ) )
| ( ( empty @ ( relation_dom @ sk11 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33920,152]) ).
thf(42406,plain,
( ~ ( empty @ sk11 )
| ( relation @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[42405:[bind(A,$thf( relation_dom @ sk11 ))]]) ).
thf(17,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/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)],[17]) ).
thf(92,plain,
! [A: $i] : ( element @ ( sk8 @ A ) @ A ),
inference(cnf,[status(esa)],[91]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ),
inference(cnf,[status(esa)],[110]) ).
thf(3339,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ C )
| ( in @ B @ C )
| ( ( element @ ( sk8 @ A ) @ A )
!= ( element @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[92,111]) ).
thf(3340,plain,
! [A: $i] :
( ( empty @ A )
| ( in @ ( sk8 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[3339:[bind(A,$thf( D )),bind(B,$thf( sk8 @ D )),bind(C,$thf( D ))]]) ).
thf(3357,plain,
! [A: $i] :
( ( empty @ A )
| ( in @ ( sk8 @ A ) @ A ) ),
inference(simp,[status(thm)],[3340]) ).
thf(30917,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( ( empty @ ( relation_dom @ sk2 ) )
!= ( empty @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[27837,14158]) ).
thf(30962,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( ( relation_dom @ sk2 )
!= sk23 ) ),
inference(simp,[status(thm)],[30917]) ).
thf(41429,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32994,33866]) ).
thf(41430,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[41429:[]]) ).
thf(36200,plain,
( ( sk23 != empty_set )
| ( ( empty @ ( relation_dom @ sk23 ) )
!= ( empty @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[31083,12483]) ).
thf(36303,plain,
( ( sk23 != empty_set )
| ( ( relation_dom @ sk23 )
!= sk3 ) ),
inference(simp,[status(thm)],[36200]) ).
thf(42913,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( relation_dom @ sk23 )
!= sk3 )
| ( A != sk23 ) ),
inference(paramod_ordered,[status(thm)],[87,36303]) ).
thf(42914,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ sk23 )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[42913:[bind(A,$thf( sk23 ))]]) ).
thf(44788,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( ( relation_dom @ sk23 )
!= sk3 )
| ( ( empty @ sk23 )
!= ( empty @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[27837,42914]) ).
thf(44789,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( ( relation_dom @ sk23 )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[44788:[]]) ).
thf(847,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ A @ B )
!= sk9 )
| ( ( unordered_pair @ B @ A )
!= ( unordered_pair @ ( unordered_pair @ C @ D ) @ ( singleton @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[52,842]) ).
thf(848,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ B @ A ) )
!= sk9 ),
inference(pattern_uni,[status(thm)],[847:[bind(A,$thf( singleton @ G )),bind(B,$thf( unordered_pair @ G @ F )),bind(C,$thf( G )),bind(D,$thf( F ))]]) ).
thf(863,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ B @ A ) )
!= sk9 ),
inference(simp,[status(thm)],[848]) ).
thf(2540,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ B @ A ) )
!= empty_set ),
inference(rewrite,[status(thm)],[863,1025]) ).
thf(30905,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( ( empty @ sk23 )
!= ( empty @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[27837,63]) ).
thf(30974,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( sk23 != sk5 ) ),
inference(simp,[status(thm)],[30905]) ).
thf(43224,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( ( relation_dom @ sk10 )
!= sk23 )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[35448,31092]) ).
thf(43225,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( ( relation_dom @ sk10 )
!= sk23 ) ),
inference(pattern_uni,[status(thm)],[43224:[]]) ).
thf(12492,plain,
( ( empty @ sk3 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[67,12483]) ).
thf(12504,plain,
sk3 != empty_set,
inference(simp,[status(thm)],[12492]) ).
thf(37557,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32981,29567]) ).
thf(37558,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[37557:[]]) ).
thf(359,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( B
!= ( apply @ sk2 @ ( apply @ sk3 @ sk1 ) ) )
| ( A
!= ( apply @ ( relation_composition @ sk3 @ sk2 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[58,49]) ).
thf(360,plain,
! [A: $i] :
( ~ ( empty @ ( apply @ ( relation_composition @ sk3 @ sk2 ) @ sk1 ) )
| ~ ( empty @ A )
| ( A
!= ( apply @ sk2 @ ( apply @ sk3 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[359:[bind(A,$thf( apply @ ( relation_composition @ sk3 @ sk2 ) @ sk1 )),bind(B,$thf( B ))]]) ).
thf(428,plain,
( ~ ( empty @ ( apply @ ( relation_composition @ sk3 @ sk2 ) @ sk1 ) )
| ~ ( empty @ ( apply @ sk2 @ ( apply @ sk3 @ sk1 ) ) ) ),
inference(simp,[status(thm)],[360]) ).
thf(2613,plain,
( ~ ( empty @ ( relation_dom @ empty_set ) )
| ( ( empty @ ( relation_composition @ sk3 @ sk2 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[67,1384]) ).
thf(2648,plain,
( ~ ( empty @ ( relation_dom @ empty_set ) )
| ( ( relation_composition @ sk3 @ sk2 )
!= empty_set ) ),
inference(simp,[status(thm)],[2613]) ).
thf(7050,plain,
( ~ $true
| ( ( relation_composition @ sk3 @ sk2 )
!= empty_set ) ),
inference(rewrite,[status(thm)],[2648,6979]) ).
thf(7051,plain,
( ( relation_composition @ sk3 @ sk2 )
!= empty_set ),
inference(simp,[status(thm)],[7050]) ).
thf(32323,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ sk11 )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[2728,28774]) ).
thf(32324,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ sk11 ) ),
inference(pattern_uni,[status(thm)],[32323:[]]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox/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(27,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( in @ ( ordered_pair @ B @ C ) @ A ) ) )
& ( ~ ( in @ B @ ( relation_dom @ A ) )
=> ( ( C
= ( apply @ A @ B ) )
<=> ( C = empty_set ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
thf(117,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ! [B: $i,C: $i] :
( ( ( in @ B @ ( relation_dom @ A ) )
=> ( ( ( C
= ( apply @ A @ B ) )
=> ( in @ ( ordered_pair @ B @ C ) @ A ) )
& ( ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( C
= ( apply @ A @ B ) ) ) ) )
& ( ~ ( in @ B @ ( relation_dom @ A ) )
=> ( ( ( C
= ( apply @ A @ B ) )
=> ( C = empty_set ) )
& ( ( C = empty_set )
=> ( C
= ( apply @ A @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(45347,plain,
! [A: $i] :
( ~ ( empty @ sk23 )
| ( relation_empty_yielding @ A )
| ( ( empty @ ( relation_dom @ sk23 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[36252,32557]) ).
thf(45348,plain,
( ~ ( empty @ sk23 )
| ( relation_empty_yielding @ ( relation_dom @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[45347:[bind(A,$thf( relation_dom @ sk23 ))]]) ).
thf(33984,plain,
! [A: $i] :
( ( sk11 != empty_set )
| ( relation_empty_yielding @ A )
| ( ( empty @ ( relation_dom @ sk11 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29567,32557]) ).
thf(33985,plain,
( ( sk11 != empty_set )
| ( relation_empty_yielding @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[33984:[bind(A,$thf( relation_dom @ sk11 ))]]) ).
thf(43059,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32981,33985]) ).
thf(43060,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[43059:[]]) ).
thf(32997,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk11 = empty_set )
| ( A
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[87,28843]) ).
thf(32998,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( sk11 = empty_set ) ),
inference(pattern_uni,[status(thm)],[32997:[bind(A,$thf( relation_dom @ sk11 ))]]) ).
thf(38426,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( relation @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32998,29499]) ).
thf(38427,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( relation @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[38426:[]]) ).
thf(62123,plain,
( ~ ( empty @ sk11 )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
!= ( empty @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[42552,63]) ).
thf(62263,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ ( relation_dom @ sk11 ) )
!= sk5 ) ),
inference(simp,[status(thm)],[62123]) ).
thf(31051,plain,
( ( sk23 != empty_set )
| ( ( empty @ sk23 )
!= ( empty @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[30977,63]) ).
thf(31100,plain,
( ( sk23 != empty_set )
| ( sk23 != sk5 ) ),
inference(simp,[status(thm)],[31051]) ).
thf(31173,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk23 != sk5 )
| ( A != sk23 ) ),
inference(paramod_ordered,[status(thm)],[87,31100]) ).
thf(31174,plain,
( ~ ( empty @ sk23 )
| ( sk23 != sk5 ) ),
inference(pattern_uni,[status(thm)],[31173:[bind(A,$thf( sk23 ))]]) ).
thf(32027,plain,
( ( sk11 != empty_set )
| ( sk23 != sk5 )
| ( ( empty @ sk23 )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[28756,31174]) ).
thf(32059,plain,
( ( sk11 != empty_set )
| ( sk23 != sk5 )
| ( sk23 != sk11 ) ),
inference(simp,[status(thm)],[32027]) ).
thf(62010,plain,
! [A: $i] :
( ~ ( empty @ sk11 )
| ( function @ A )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[42552,116]) ).
thf(62011,plain,
( ~ ( empty @ sk11 )
| ( function @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[62010:[bind(A,$thf( relation_dom @ ( relation_dom @ sk11 ) ))]]) ).
thf(33892,plain,
( ( sk11 != empty_set )
| ( ( empty @ ( relation_composition @ sk3 @ sk2 ) )
!= ( empty @ ( relation_dom @ sk11 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29567,6937]) ).
thf(34012,plain,
( ( sk11 != empty_set )
| ( ( relation_composition @ sk3 @ sk2 )
!= ( relation_dom @ sk11 ) ) ),
inference(simp,[status(thm)],[33892]) ).
thf(4,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(53,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(54,plain,
! [A: $i] : ( subset @ A @ A ),
inference(cnf,[status(esa)],[53]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(68,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)],[10]) ).
thf(69,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)],[68]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ),
inference(simp,[status(thm)],[70]) ).
thf(583,plain,
! [C: $i,B: $i,A: $i] :
( ( element @ B @ ( powerset @ C ) )
| ( ( subset @ A @ A )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[54,72]) ).
thf(584,plain,
! [A: $i] : ( element @ A @ ( powerset @ A ) ),
inference(pattern_uni,[status(thm)],[583:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(3347,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ C )
| ( in @ B @ C )
| ( ( element @ A @ ( powerset @ A ) )
!= ( element @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[584,111]) ).
thf(3348,plain,
! [A: $i] :
( ( empty @ ( powerset @ A ) )
| ( in @ A @ ( powerset @ A ) ) ),
inference(pattern_uni,[status(thm)],[3347:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( powerset @ D ))]]) ).
thf(3355,plain,
! [A: $i] :
( ( empty @ ( powerset @ A ) )
| ( in @ A @ ( powerset @ A ) ) ),
inference(simp,[status(thm)],[3348]) ).
thf(6491,plain,
! [A: $i] :
( $false
| ( in @ A @ ( powerset @ A ) ) ),
inference(rewrite,[status(thm)],[3355,81]) ).
thf(6492,plain,
! [A: $i] : ( in @ A @ ( powerset @ A ) ),
inference(simp,[status(thm)],[6491]) ).
thf(6601,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( ( in @ B @ A )
!= ( in @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[149]) ).
thf(6602,plain,
! [A: $i] :
~ ( in @ A @ A ),
inference(pattern_uni,[status(thm)],[6601:[bind(A,$thf( B ))]]) ).
thf(6609,plain,
! [A: $i] :
~ ( in @ A @ A ),
inference(simp,[status(thm)],[6602]) ).
thf(11377,plain,
! [B: $i,A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ B @ B ) ),
inference(paramod_ordered,[status(thm)],[6492,6609]) ).
thf(11396,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( powerset @ A )
!= B ) ),
inference(simp,[status(thm)],[11377]) ).
thf(11402,plain,
! [A: $i] :
( ( powerset @ A )
!= A ),
inference(simp,[status(thm)],[11396]) ).
thf(11420,plain,
! [B: $i,A: $i] :
( ( in @ ( sk13 @ A @ sk11 ) @ A )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ A @ sk11 ) @ ( sk15 @ A @ sk11 ) ) @ ( singleton @ ( sk14 @ A @ sk11 ) ) ) @ sk11 )
| ( ( relation_dom @ sk11 )
!= B )
| ( A
!= ( powerset @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1690,11402]) ).
thf(11421,plain,
! [A: $i] :
( ( in @ ( sk13 @ ( powerset @ A ) @ sk11 ) @ ( powerset @ A ) )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ ( powerset @ A ) @ sk11 ) @ ( sk15 @ ( powerset @ A ) @ sk11 ) ) @ ( singleton @ ( sk14 @ ( powerset @ A ) @ sk11 ) ) ) @ sk11 )
| ( ( relation_dom @ sk11 )
!= A ) ),
inference(pattern_uni,[status(thm)],[11420:[bind(A,$thf( powerset @ C )),bind(B,$thf( C ))]]) ).
thf(11437,plain,
( ( in @ ( sk13 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( powerset @ ( relation_dom @ sk11 ) ) )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) @ ( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) ) @ sk11 ) ),
inference(simp,[status(thm)],[11421]) ).
thf(11822,plain,
! [B: $i,A: $i] :
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) @ ( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) ) @ sk11 )
| ( element @ A @ B )
| ( ( in @ ( sk13 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( powerset @ ( relation_dom @ sk11 ) ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11437,103]) ).
thf(11823,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) @ ( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) ) @ sk11 )
| ( element @ ( sk13 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( powerset @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[11822:[bind(A,$thf( sk13 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 )),bind(B,$thf( powerset @ ( relation_dom @ sk11 ) ))]]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[69]) ).
thf(13655,plain,
! [B: $i,A: $i] :
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) @ ( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) ) @ sk11 )
| ( subset @ A @ B )
| ( ( element @ ( sk13 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( powerset @ ( relation_dom @ sk11 ) ) )
!= ( element @ A @ ( powerset @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[11823,71]) ).
thf(13656,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) @ ( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) ) @ sk11 )
| ( subset @ ( sk13 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[13655:[bind(A,$thf( sk13 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 )),bind(B,$thf( relation_dom @ sk11 ))]]) ).
thf(15433,plain,
! [B: $i,A: $i] :
( ( in @ ( unordered_pair @ B @ A ) @ sk11 )
| ( subset @ ( sk13 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( relation_dom @ sk11 ) )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ ( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) @ ( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[52,13656]) ).
thf(15434,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) ) @ sk11 )
| ( subset @ ( sk13 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[15433:[bind(A,$thf( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) )),bind(B,$thf( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ))]]) ).
thf(53737,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32992,33979]) ).
thf(53738,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[53737:[]]) ).
thf(73445,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( ( relation_dom @ ( relation_dom @ sk11 ) )
= empty_set )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32994,53684]) ).
thf(73446,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( ( relation_dom @ ( relation_dom @ sk11 ) )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[73445:[]]) ).
thf(3345,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)],[74,111]) ).
thf(3346,plain,
! [A: $i] :
( ( empty @ A )
| ( empty @ ( powerset @ A ) )
| ( in @ ( sk6 @ A ) @ ( powerset @ A ) ) ),
inference(pattern_uni,[status(thm)],[3345:[bind(A,$thf( E )),bind(B,$thf( sk6 @ E )),bind(C,$thf( powerset @ E ))]]) ).
thf(3354,plain,
! [A: $i] :
( ( empty @ A )
| ( empty @ ( powerset @ A ) )
| ( in @ ( sk6 @ A ) @ ( powerset @ A ) ) ),
inference(simp,[status(thm)],[3346]) ).
thf(11105,plain,
! [A: $i] :
( ( empty @ A )
| $false
| ( in @ ( sk6 @ A ) @ ( powerset @ A ) ) ),
inference(rewrite,[status(thm)],[3354,81]) ).
thf(11106,plain,
! [A: $i] :
( ( empty @ A )
| ( in @ ( sk6 @ A ) @ ( powerset @ A ) ) ),
inference(simp,[status(thm)],[11105]) ).
thf(158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ( B
!= ( relation_dom @ A ) )
| ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) ),
inference(cnf,[status(esa)],[156]) ).
thf(173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
!= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ~ ( in @ ( ordered_pair @ C @ D ) @ A )
| ( in @ C @ B ) ),
inference(lifteq,[status(thm)],[158]) ).
thf(174,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ( in @ B @ ( relation_dom @ A ) ) ),
inference(simp,[status(thm)],[173]) ).
thf(11212,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( in @ ( unordered_pair @ ( unordered_pair @ B @ C ) @ ( singleton @ B ) ) @ A )
| ( in @ B @ ( relation_dom @ A ) ) ),
inference(rewrite,[status(thm)],[174,78]) ).
thf(5908,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ A )
| ( element @ B @ C )
| ( ( in @ ( sk8 @ A ) @ A )
!= ( in @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[3357,103]) ).
thf(5909,plain,
! [A: $i] :
( ( empty @ A )
| ( element @ ( sk8 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[5908:[bind(A,$thf( D )),bind(B,$thf( sk8 @ D )),bind(C,$thf( D ))]]) ).
thf(5924,plain,
! [A: $i] :
( ( empty @ A )
| ( element @ ( sk8 @ A ) @ A ) ),
inference(simp,[status(thm)],[5909]) ).
thf(42559,plain,
! [A: $i] :
( ~ ( empty @ sk11 )
| ( relation_empty_yielding @ A )
| ( ( empty @ ( relation_dom @ sk11 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33920,32557]) ).
thf(42560,plain,
( ~ ( empty @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[42559:[bind(A,$thf( relation_dom @ sk11 ))]]) ).
thf(46096,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( relation_empty_yielding @ ( relation_dom @ sk11 ) )
| ( ( empty @ sk11 )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[27767,42560]) ).
thf(46097,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( relation_empty_yielding @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[46096:[]]) ).
thf(43801,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( ( relation_dom @ sk23 )
!= sk5 )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[35448,36294]) ).
thf(43802,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( ( relation_dom @ sk23 )
!= sk5 ) ),
inference(pattern_uni,[status(thm)],[43801:[]]) ).
thf(251,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( in @ A @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ) )
| ( B != sk1 ) ),
inference(paramod_ordered,[status(thm)],[58,46]) ).
thf(252,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk1 )
| ( in @ A @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[251:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(73616,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( ( relation_dom @ ( relation_dom @ sk11 ) )
= empty_set )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32983,53684]) ).
thf(73617,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( ( relation_dom @ ( relation_dom @ sk11 ) )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[73616:[]]) ).
thf(43000,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32983,33985]) ).
thf(43001,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[43000:[]]) ).
thf(185,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ( in @ ( ordered_pair @ ( sk18 @ C @ B @ A ) @ ( sk19 @ C @ B @ A ) ) @ C )
| ~ ( sk17 @ B @ A @ C )
| ( C
= ( relation_composition @ A @ B ) ) ),
inference(cnf,[status(esa)],[181]) ).
thf(190,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_composition @ A @ B ) )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ( in @ ( ordered_pair @ ( sk18 @ C @ B @ A ) @ ( sk19 @ C @ B @ A ) ) @ C )
| ~ ( sk17 @ B @ A @ C ) ),
inference(lifteq,[status(thm)],[185]) ).
thf(14291,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_composition @ A @ B ) )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk18 @ C @ B @ A ) @ ( sk19 @ C @ B @ A ) ) @ ( singleton @ ( sk18 @ C @ B @ A ) ) ) @ C )
| ~ ( sk17 @ B @ A @ C ) ),
inference(rewrite,[status(thm)],[190,78]) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ( B
!= ( relation_dom @ A ) )
| ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sk12 @ C @ B @ A ) ) @ A ) ),
inference(cnf,[status(esa)],[156]) ).
thf(163,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sk12 @ C @ B @ A ) ) @ A ) ),
inference(lifteq,[status(thm)],[157]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( in @ B @ ( relation_dom @ A ) )
| ( in @ ( ordered_pair @ B @ ( sk12 @ B @ ( relation_dom @ A ) @ A ) ) @ A ) ),
inference(simp,[status(thm)],[163]) ).
thf(7891,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( in @ B @ ( relation_dom @ A ) )
| ( in @ ( unordered_pair @ ( unordered_pair @ B @ ( sk12 @ B @ ( relation_dom @ A ) @ A ) ) @ ( singleton @ B ) ) @ A ) ),
inference(rewrite,[status(thm)],[164,78]) ).
thf(36242,plain,
( ( sk23 != empty_set )
| ( ( empty @ ( relation_dom @ sk23 ) )
!= ( empty @ ( relation_dom @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[31083,14158]) ).
thf(36297,plain,
( ( sk23 != empty_set )
| ( ( relation_dom @ sk23 )
!= ( relation_dom @ sk2 ) ) ),
inference(simp,[status(thm)],[36242]) ).
thf(45614,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( ( relation_dom @ sk11 )
!= sk5 )
| ( ( empty @ sk11 )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[27767,40055]) ).
thf(45615,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( ( relation_dom @ sk11 )
!= sk5 ) ),
inference(pattern_uni,[status(thm)],[45614:[]]) ).
thf(36174,plain,
( ( sk23 != empty_set )
| ( ( empty @ ( relation_dom @ sk23 ) )
!= ( empty @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[31083,133]) ).
thf(36317,plain,
( ( sk23 != empty_set )
| ( ( relation_dom @ sk23 )
!= sk10 ) ),
inference(simp,[status(thm)],[36174]) ).
thf(44204,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( ( relation_dom @ sk23 )
!= sk10 )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[35448,36317]) ).
thf(44205,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( ( relation_dom @ sk23 )
!= sk10 ) ),
inference(pattern_uni,[status(thm)],[44204:[]]) ).
thf(714,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ B @ C )
| ( ( element @ ( sk7 @ A ) @ ( powerset @ A ) )
!= ( element @ B @ ( powerset @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[90,71]) ).
thf(715,plain,
! [A: $i] : ( subset @ ( sk7 @ A ) @ A ),
inference(pattern_uni,[status(thm)],[714:[bind(A,$thf( D )),bind(B,$thf( sk7 @ D )),bind(C,$thf( D ))]]) ).
thf(726,plain,
! [A: $i] : ( subset @ ( sk7 @ A ) @ A ),
inference(simp,[status(thm)],[715]) ).
thf(1259,plain,
! [A: $i] : ( subset @ empty_set @ A ),
inference(rewrite,[status(thm)],[726,1172]) ).
thf(29535,plain,
( ( sk11 != empty_set )
| ( ( empty @ sk11 )
!= ( empty @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[28756,63]) ).
thf(29573,plain,
( ( sk11 != empty_set )
| ( sk11 != sk5 ) ),
inference(simp,[status(thm)],[29535]) ).
thf(29660,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk11 != sk5 )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[87,29573]) ).
thf(29661,plain,
( ~ ( empty @ sk11 )
| ( sk11 != sk5 ) ),
inference(pattern_uni,[status(thm)],[29660:[bind(A,$thf( sk11 ))]]) ).
thf(31052,plain,
( ( sk23 != empty_set )
| ( sk11 != sk5 )
| ( ( empty @ sk23 )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[30977,29661]) ).
thf(31093,plain,
( ( sk23 != empty_set )
| ( sk11 != sk5 )
| ( sk23 != sk11 ) ),
inference(simp,[status(thm)],[31052]) ).
thf(24722,plain,
( ( sk11 != empty_set )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[2921,24708]) ).
thf(24771,plain,
( ( sk11 != empty_set )
| ( sk11 != sk10 ) ),
inference(simp,[status(thm)],[24722]) ).
thf(33790,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( relation_dom @ sk3 )
!= sk23 )
| ( A != sk23 ) ),
inference(paramod_ordered,[status(thm)],[87,31107]) ).
thf(33791,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ sk3 )
!= sk23 ) ),
inference(pattern_uni,[status(thm)],[33790:[bind(A,$thf( sk23 ))]]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(140,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( relation @ B ) )
=> ( relation @ ( relation_composition @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ),
inference(cnf,[status(esa)],[140]) ).
thf(30865,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( ( empty @ ( relation_dom @ sk10 ) )
!= ( empty @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[27837,24638]) ).
thf(30969,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( ( relation_dom @ sk10 )
!= sk23 ) ),
inference(simp,[status(thm)],[30865]) ).
thf(30854,plain,
! [A: $i] :
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( relation @ ( relation_dom @ A ) )
| ( ( empty @ sk23 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27837,152]) ).
thf(30855,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( relation @ ( relation_dom @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[30854:[bind(A,$thf( sk23 ))]]) ).
thf(45261,plain,
( ~ ( empty @ sk23 )
| ( ( empty @ ( relation_dom @ sk23 ) )
!= ( empty @ ( relation_dom @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[36252,18067]) ).
thf(45415,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ sk23 )
!= ( relation_dom @ sk3 ) ) ),
inference(simp,[status(thm)],[45261]) ).
thf(42968,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32994,33985]) ).
thf(42969,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[42968:[]]) ).
thf(33895,plain,
( ( sk11 != empty_set )
| ( ( empty @ ( relation_dom @ sk11 ) )
!= ( empty @ ( relation_dom @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29567,18067]) ).
thf(33989,plain,
( ( sk11 != empty_set )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk3 ) ) ),
inference(simp,[status(thm)],[33895]) ).
thf(62221,plain,
! [A: $i] :
( ~ ( empty @ sk11 )
| ( relation_empty_yielding @ A )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[42552,32557]) ).
thf(62222,plain,
( ~ ( empty @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[62221:[bind(A,$thf( relation_dom @ ( relation_dom @ sk11 ) ))]]) ).
thf(85986,plain,
( ~ ( empty @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ ( relation_dom @ empty_set ) ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32996,62222]) ).
thf(85987,plain,
( ~ ( empty @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ ( relation_dom @ empty_set ) ) ) ),
inference(pattern_uni,[status(thm)],[85986:[]]) ).
thf(90518,plain,
( ~ ( empty @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ empty_set ) ) ),
inference(rewrite,[status(thm)],[85987,7106]) ).
thf(53555,plain,
! [A: $i] :
( ( sk11 != empty_set )
| ( function @ A )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33979,116]) ).
thf(53556,plain,
( ( sk11 != empty_set )
| ( function @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[53555:[bind(A,$thf( relation_dom @ ( relation_dom @ sk11 ) ))]]) ).
thf(72789,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32992,53556]) ).
thf(72790,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[72789:[]]) ).
thf(30901,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( ( empty @ sk23 )
!= ( empty @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[27837,7049]) ).
thf(30976,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( sk23 != sk2 ) ),
inference(simp,[status(thm)],[30901]) ).
thf(32813,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk23 != sk2 )
| ( A
!= ( relation_dom @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[87,30976]) ).
thf(32814,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( sk23 != sk2 ) ),
inference(pattern_uni,[status(thm)],[32813:[bind(A,$thf( relation_dom @ sk23 ))]]) ).
thf(14234,plain,
( ( sk11 != empty_set )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[2921,14214]) ).
thf(14276,plain,
( ( sk11 != empty_set )
| ( sk11 != sk2 ) ),
inference(simp,[status(thm)],[14234]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ B @ A ) ) ),
inference(cnf,[status(esa)],[107]) ).
thf(33917,plain,
( ( sk11 != empty_set )
| ( ( empty @ ( relation_dom @ sk11 ) )
!= ( empty @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[29567,7049]) ).
thf(33992,plain,
( ( sk11 != empty_set )
| ( ( relation_dom @ sk11 )
!= sk2 ) ),
inference(simp,[status(thm)],[33917]) ).
thf(39896,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ sk11 )
!= sk2 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32996,33992]) ).
thf(39897,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ sk11 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[39896:[]]) ).
thf(43691,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( ( relation_dom @ sk11 )
!= sk2 )
| ( ( empty @ sk11 )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[27767,39897]) ).
thf(43692,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( ( relation_dom @ sk11 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[43691:[]]) ).
thf(31035,plain,
( ( sk23 != empty_set )
| ( ( empty @ ( relation_composition @ sk3 @ sk2 ) )
!= ( empty @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[30977,6937]) ).
thf(31108,plain,
( ( sk23 != empty_set )
| ( ( relation_composition @ sk3 @ sk2 )
!= sk23 ) ),
inference(simp,[status(thm)],[31035]) ).
thf(28833,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( ( empty @ ( relation_dom @ sk2 ) )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[27767,14158]) ).
thf(28881,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( ( relation_dom @ sk2 )
!= sk11 ) ),
inference(simp,[status(thm)],[28833]) ).
thf(37501,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32981,29499]) ).
thf(37502,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[37501:[]]) ).
thf(3343,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)],[1254,111]) ).
thf(3344,plain,
! [A: $i] :
( ( empty @ ( powerset @ A ) )
| ( in @ empty_set @ ( powerset @ A ) ) ),
inference(pattern_uni,[status(thm)],[3343:[bind(A,$thf( D )),bind(B,$thf( empty_set )),bind(C,$thf( powerset @ D ))]]) ).
thf(3353,plain,
! [A: $i] :
( ( empty @ ( powerset @ A ) )
| ( in @ empty_set @ ( powerset @ A ) ) ),
inference(simp,[status(thm)],[3344]) ).
thf(3595,plain,
! [A: $i] :
( $false
| ( in @ empty_set @ ( powerset @ A ) ) ),
inference(rewrite,[status(thm)],[3353,81]) ).
thf(3596,plain,
! [A: $i] : ( in @ empty_set @ ( powerset @ A ) ),
inference(simp,[status(thm)],[3595]) ).
thf(53523,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32994,33979]) ).
thf(53524,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[53523:[]]) ).
thf(210,plain,
( ( empty @ sk10 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[67,133]) ).
thf(212,plain,
sk10 != empty_set,
inference(simp,[status(thm)],[210]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
thf(96,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(66692,plain,
( ~ ( empty @ sk23 )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk23 ) ) )
!= ( empty @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[45338,7049]) ).
thf(66877,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ ( relation_dom @ sk23 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[66692]) ).
thf(87642,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ ( relation_dom @ empty_set ) )
!= sk2 )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[43389,66877]) ).
thf(87643,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ ( relation_dom @ empty_set ) )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[87642:[]]) ).
thf(90688,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ empty_set )
!= sk2 ) ),
inference(rewrite,[status(thm)],[87643,7106]) ).
thf(36201,plain,
( ( sk23 != empty_set )
| ( ( empty @ ( relation_composition @ sk3 @ sk2 ) )
!= ( empty @ ( relation_dom @ sk23 ) ) ) ),
inference(paramod_ordered,[status(thm)],[31083,6937]) ).
thf(36301,plain,
( ( sk23 != empty_set )
| ( ( relation_composition @ sk3 @ sk2 )
!= ( relation_dom @ sk23 ) ) ),
inference(simp,[status(thm)],[36201]) ).
thf(189,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ( C
!= ( relation_composition @ A @ B ) )
| ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ ( ordered_pair @ D @ ( sk16 @ E @ D @ C @ B @ A ) ) @ A ) ),
inference(cnf,[status(esa)],[181]) ).
thf(192,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( relation_composition @ A @ B ) )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ ( ordered_pair @ D @ ( sk16 @ E @ D @ C @ B @ A ) ) @ A ) ),
inference(lifteq,[status(thm)],[189]) ).
thf(193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ ( relation_composition @ A @ B ) )
| ~ ( in @ ( ordered_pair @ C @ D ) @ ( relation_composition @ A @ B ) )
| ( in @ ( ordered_pair @ C @ ( sk16 @ D @ C @ ( relation_composition @ A @ B ) @ B @ A ) ) @ A ) ),
inference(simp,[status(thm)],[192]) ).
thf(18208,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ ( relation_composition @ A @ B ) )
| ~ ( in @ ( unordered_pair @ ( unordered_pair @ C @ D ) @ ( singleton @ C ) ) @ ( relation_composition @ A @ B ) )
| ( in @ ( unordered_pair @ ( unordered_pair @ C @ ( sk16 @ D @ C @ ( relation_composition @ A @ B ) @ B @ A ) ) @ ( singleton @ C ) ) @ A ) ),
inference(rewrite,[status(thm)],[193,78]) ).
thf(31013,plain,
! [A: $i] :
( ( sk23 != empty_set )
| ( relation @ ( relation_dom @ A ) )
| ( ( empty @ sk23 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[30977,152]) ).
thf(31014,plain,
( ( sk23 != empty_set )
| ( relation @ ( relation_dom @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[31013:[bind(A,$thf( sk23 ))]]) ).
thf(35594,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ sk23 ) )
| ( A != sk23 ) ),
inference(paramod_ordered,[status(thm)],[87,31014]) ).
thf(35595,plain,
( ~ ( empty @ sk23 )
| ( relation @ ( relation_dom @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[35594:[bind(A,$thf( sk23 ))]]) ).
thf(661,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ ( sk7 @ A ) )
!= ( empty @ ( unordered_pair @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[89,84]) ).
thf(668,plain,
! [C: $i,B: $i,A: $i] :
( ( sk7 @ A )
!= ( unordered_pair @ B @ C ) ),
inference(simp,[status(thm)],[661]) ).
thf(1451,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
!= empty_set ),
inference(rewrite,[status(thm)],[668,1172]) ).
thf(33864,plain,
( ( sk11 != empty_set )
| ( ( empty @ ( relation_dom @ sk11 ) )
!= ( empty @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[29567,133]) ).
thf(34004,plain,
( ( sk11 != empty_set )
| ( ( relation_dom @ sk11 )
!= sk10 ) ),
inference(simp,[status(thm)],[33864]) ).
thf(32310,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ sk11 )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[2086,28774]) ).
thf(32311,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ sk11 ) ),
inference(pattern_uni,[status(thm)],[32310:[]]) ).
thf(43368,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( ( relation_dom @ sk23 )
!= sk3 )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[35448,36303]) ).
thf(43369,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( ( relation_dom @ sk23 )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[43368:[]]) ).
thf(45987,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( function @ ( relation_dom @ sk11 ) )
| ( ( empty @ sk11 )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[27767,41140]) ).
thf(45988,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( function @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[45987:[]]) ).
thf(53626,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32983,33979]) ).
thf(53627,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[53626:[]]) ).
thf(29,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(134,plain,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(28759,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( sk11 != sk3 )
| ( ( empty @ sk11 )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[27767,18190]) ).
thf(28760,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( sk11 != sk3 ) ),
inference(pattern_uni,[status(thm)],[28759:[]]) ).
thf(29053,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk11 != sk3 )
| ( A
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[87,28760]) ).
thf(29054,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( sk11 != sk3 ) ),
inference(pattern_uni,[status(thm)],[29053:[bind(A,$thf( relation_dom @ sk11 ))]]) ).
thf(118,plain,
! [A: $i] :
( ( ( relation @ A )
& ( function @ A ) )
=> ( ! [B: $i] :
( ( in @ B @ ( relation_dom @ A ) )
=> ( ! [C: $i] :
( ( C
= ( apply @ A @ B ) )
=> ( in @ ( ordered_pair @ B @ C ) @ A ) )
& ! [C: $i] :
( ( in @ ( ordered_pair @ B @ C ) @ A )
=> ( C
= ( apply @ A @ B ) ) ) ) )
& ! [B: $i] :
( ~ ( in @ B @ ( relation_dom @ A ) )
=> ( ! [C: $i] :
( ( C
= ( apply @ A @ B ) )
=> ( C = empty_set ) )
& ! [C: $i] :
( ( C = empty_set )
=> ( C
= ( apply @ A @ B ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[117]) ).
thf(121,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ( in @ B @ ( relation_dom @ A ) )
| ( C != empty_set )
| ( C
= ( apply @ A @ B ) ) ),
inference(cnf,[status(esa)],[118]) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ( C != empty_set )
| ( C
= ( apply @ A @ B ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( in @ B @ ( relation_dom @ A ) ) ),
inference(lifteq,[status(thm)],[121]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( ( apply @ A @ B )
= empty_set )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( in @ B @ ( relation_dom @ A ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(28819,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ sk11 )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[2797,27767]) ).
thf(28820,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ sk11 ) ),
inference(pattern_uni,[status(thm)],[28819:[]]) ).
thf(32812,plain,
( ~ ( empty @ sk11 )
| ( sk23 != sk2 )
| ( ( relation_dom @ sk23 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[2760,30976]) ).
thf(32843,plain,
( ~ ( empty @ sk11 )
| ( sk23 != sk2 )
| ( sk23 != sk11 ) ),
inference(simp,[status(thm)],[32812]) ).
thf(66590,plain,
( ~ ( empty @ sk23 )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk23 ) ) )
!= ( empty @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[45338,133]) ).
thf(66897,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ ( relation_dom @ sk23 ) )
!= sk10 ) ),
inference(simp,[status(thm)],[66590]) ).
thf(53554,plain,
( ( sk11 != empty_set )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
!= ( empty @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[33979,133]) ).
thf(53825,plain,
( ( sk11 != empty_set )
| ( ( relation_dom @ ( relation_dom @ sk11 ) )
!= sk10 ) ),
inference(simp,[status(thm)],[53554]) ).
thf(53649,plain,
( ( sk11 != empty_set )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
!= ( empty @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[33979,63]) ).
thf(53808,plain,
( ( sk11 != empty_set )
| ( ( relation_dom @ ( relation_dom @ sk11 ) )
!= sk5 ) ),
inference(simp,[status(thm)],[53649]) ).
thf(7384,plain,
! [A: $i] :
( ( relation @ ( relation_dom @ A ) )
| ( ( empty @ ( relation_dom @ empty_set ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6979,152]) ).
thf(7385,plain,
relation @ ( relation_dom @ ( relation_dom @ empty_set ) ),
inference(pattern_uni,[status(thm)],[7384:[bind(A,$thf( relation_dom @ empty_set ))]]) ).
thf(7817,plain,
relation @ ( relation_dom @ empty_set ),
inference(rewrite,[status(thm)],[7385,7106]) ).
thf(74634,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32992,53736]) ).
thf(74635,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[74634:[]]) ).
thf(36186,plain,
( ( sk23 != empty_set )
| ( ( empty @ ( relation_dom @ sk23 ) )
!= ( empty @ ( relation_dom @ sk10 ) ) ) ),
inference(paramod_ordered,[status(thm)],[31083,24638]) ).
thf(36326,plain,
( ( sk23 != empty_set )
| ( ( relation_dom @ sk23 )
!= ( relation_dom @ sk10 ) ) ),
inference(simp,[status(thm)],[36186]) ).
thf(188,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ( C
!= ( relation_composition @ A @ B ) )
| ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ ( ordered_pair @ ( sk16 @ E @ D @ C @ B @ A ) @ E ) @ B ) ),
inference(cnf,[status(esa)],[181]) ).
thf(194,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( relation_composition @ A @ B ) )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ ( ordered_pair @ ( sk16 @ E @ D @ C @ B @ A ) @ E ) @ B ) ),
inference(lifteq,[status(thm)],[188]) ).
thf(195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ ( relation_composition @ A @ B ) )
| ~ ( in @ ( ordered_pair @ C @ D ) @ ( relation_composition @ A @ B ) )
| ( in @ ( ordered_pair @ ( sk16 @ D @ C @ ( relation_composition @ A @ B ) @ B @ A ) @ D ) @ B ) ),
inference(simp,[status(thm)],[194]) ).
thf(18853,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ ( relation_composition @ A @ B ) )
| ~ ( in @ ( unordered_pair @ ( unordered_pair @ C @ D ) @ ( singleton @ C ) ) @ ( relation_composition @ A @ B ) )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk16 @ D @ C @ ( relation_composition @ A @ B ) @ B @ A ) @ D ) @ ( singleton @ ( sk16 @ D @ C @ ( relation_composition @ A @ B ) @ B @ A ) ) ) @ B ) ),
inference(rewrite,[status(thm)],[195,78]) ).
thf(18147,plain,
( ( sk11 != empty_set )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[2921,18122]) ).
thf(18196,plain,
( ( sk11 != empty_set )
| ( sk11 != sk3 ) ),
inference(simp,[status(thm)],[18147]) ).
thf(31048,plain,
( ( sk23 != empty_set )
| ( ( empty @ sk23 )
!= ( empty @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[30977,7049]) ).
thf(31086,plain,
( ( sk23 != empty_set )
| ( sk23 != sk2 ) ),
inference(simp,[status(thm)],[31048]) ).
thf(31135,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk23 != sk2 )
| ( A != sk23 ) ),
inference(paramod_ordered,[status(thm)],[87,31086]) ).
thf(31136,plain,
( ~ ( empty @ sk23 )
| ( sk23 != sk2 ) ),
inference(pattern_uni,[status(thm)],[31135:[bind(A,$thf( sk23 ))]]) ).
thf(31641,plain,
( ( sk11 != empty_set )
| ( sk23 != sk2 )
| ( ( empty @ sk23 )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[28756,31136]) ).
thf(31673,plain,
( ( sk11 != empty_set )
| ( sk23 != sk2 )
| ( sk23 != sk11 ) ),
inference(simp,[status(thm)],[31641]) ).
thf(184,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ( sk17 @ B @ A @ C )
| ( in @ ( ordered_pair @ ( sk22 @ C @ B @ A ) @ ( sk21 @ C @ B @ A ) ) @ B )
| ( C
= ( relation_composition @ A @ B ) ) ),
inference(cnf,[status(esa)],[181]) ).
thf(191,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_composition @ A @ B ) )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ( sk17 @ B @ A @ C )
| ( in @ ( ordered_pair @ ( sk22 @ C @ B @ A ) @ ( sk21 @ C @ B @ A ) ) @ B ) ),
inference(lifteq,[status(thm)],[184]) ).
thf(16152,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_composition @ A @ B ) )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ( sk17 @ B @ A @ C )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk22 @ C @ B @ A ) @ ( sk21 @ C @ B @ A ) ) @ ( singleton @ ( sk22 @ C @ B @ A ) ) ) @ B ) ),
inference(rewrite,[status(thm)],[191,78]) ).
thf(28870,plain,
! [A: $i] :
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( empty @ ( relation_dom @ A ) )
| ( ( empty @ sk11 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27767,151]) ).
thf(28871,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( empty @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[28870:[bind(A,$thf( sk11 ))]]) ).
thf(31057,plain,
( ( sk23 != empty_set )
| ( ( empty @ ( relation_dom @ sk2 ) )
!= ( empty @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[30977,14158]) ).
thf(31087,plain,
( ( sk23 != empty_set )
| ( ( relation_dom @ sk2 )
!= sk23 ) ),
inference(simp,[status(thm)],[31057]) ).
thf(29540,plain,
( ( sk11 != empty_set )
| ( ( empty @ ( relation_dom @ sk2 ) )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[28756,14158]) ).
thf(29579,plain,
( ( sk11 != empty_set )
| ( ( relation_dom @ sk2 )
!= sk11 ) ),
inference(simp,[status(thm)],[29540]) ).
thf(8,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(64,plain,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(88782,plain,
( ~ ( empty @ sk23 )
| ( relation_empty_yielding @ ( relation_dom @ ( relation_dom @ empty_set ) ) )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[43389,66811]) ).
thf(88783,plain,
( ~ ( empty @ sk23 )
| ( relation_empty_yielding @ ( relation_dom @ ( relation_dom @ empty_set ) ) ) ),
inference(pattern_uni,[status(thm)],[88782:[]]) ).
thf(90857,plain,
( ~ ( empty @ sk23 )
| ( relation_empty_yielding @ ( relation_dom @ empty_set ) ) ),
inference(rewrite,[status(thm)],[88783,7106]) ).
thf(11513,plain,
! [B: $i,A: $i] :
( ( in @ ( sk13 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( powerset @ ( relation_dom @ sk11 ) ) )
| ( in @ ( unordered_pair @ B @ A ) @ sk11 )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ ( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) @ ( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[52,11437]) ).
thf(11514,plain,
( ( in @ ( sk13 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( powerset @ ( relation_dom @ sk11 ) ) )
| ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) ) @ sk11 ) ),
inference(pattern_uni,[status(thm)],[11513:[bind(A,$thf( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) )),bind(B,$thf( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ))]]) ).
thf(12826,plain,
! [B: $i,A: $i] :
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) ) @ sk11 )
| ( element @ A @ B )
| ( ( in @ ( sk13 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( powerset @ ( relation_dom @ sk11 ) ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11514,103]) ).
thf(12827,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) ) @ sk11 )
| ( element @ ( sk13 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( powerset @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[12826:[bind(A,$thf( sk13 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 )),bind(B,$thf( powerset @ ( relation_dom @ sk11 ) ))]]) ).
thf(28961,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk11 != sk2 )
| ( A
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[87,28758]) ).
thf(28962,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( sk11 != sk2 ) ),
inference(pattern_uni,[status(thm)],[28961:[bind(A,$thf( relation_dom @ sk11 ))]]) ).
thf(39941,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( ( relation_dom @ sk11 )
!= sk2 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32998,33992]) ).
thf(39942,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( ( relation_dom @ sk11 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[39941:[]]) ).
thf(572,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( element @ B @ C )
| ( A
!= ( sk8 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[58,92]) ).
thf(573,plain,
! [B: $i,A: $i] :
( ~ ( empty @ ( sk8 @ B ) )
| ~ ( empty @ A )
| ( element @ A @ B ) ),
inference(pattern_uni,[status(thm)],[572:[bind(A,$thf( sk8 @ D )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(577,plain,
! [B: $i,A: $i] :
( ~ ( empty @ ( sk8 @ B ) )
| ~ ( empty @ A )
| ( element @ A @ B ) ),
inference(simp,[status(thm)],[573]) ).
thf(74558,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32983,53736]) ).
thf(74559,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[74558:[]]) ).
thf(29521,plain,
( ( sk11 != empty_set )
| ( ( empty @ ( relation_dom @ sk3 ) )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[28756,18067]) ).
thf(29570,plain,
( ( sk11 != empty_set )
| ( ( relation_dom @ sk3 )
!= sk11 ) ),
inference(simp,[status(thm)],[29521]) ).
thf(34787,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( relation_dom @ sk10 )
!= sk23 )
| ( A != sk23 ) ),
inference(paramod_ordered,[status(thm)],[87,31092]) ).
thf(34788,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ sk10 )
!= sk23 ) ),
inference(pattern_uni,[status(thm)],[34787:[bind(A,$thf( sk23 ))]]) ).
thf(119,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ B @ ( relation_dom @ A ) )
| ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ( C
= ( apply @ A @ B ) ) ),
inference(cnf,[status(esa)],[118]) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( apply @ A @ B ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ B @ ( relation_dom @ A ) )
| ~ ( in @ ( ordered_pair @ B @ C ) @ A ) ),
inference(lifteq,[status(thm)],[119]) ).
thf(124,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( apply @ A @ B ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ B @ ( relation_dom @ A ) )
| ~ ( in @ ( ordered_pair @ B @ C ) @ A ) ),
inference(simp,[status(thm)],[123]) ).
thf(4341,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( apply @ A @ B ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ B @ ( relation_dom @ A ) )
| ~ ( in @ ( unordered_pair @ ( unordered_pair @ B @ C ) @ ( singleton @ B ) ) @ A ) ),
inference(rewrite,[status(thm)],[124,78]) ).
thf(33891,plain,
( ( sk11 != empty_set )
| ( ( empty @ ( relation_dom @ sk11 ) )
!= ( empty @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[29567,12483]) ).
thf(34002,plain,
( ( sk11 != empty_set )
| ( ( relation_dom @ sk11 )
!= sk3 ) ),
inference(simp,[status(thm)],[33891]) ).
thf(41020,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ sk11 )
!= sk3 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32996,34002]) ).
thf(41021,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ sk11 )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[41020:[]]) ).
thf(39172,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32983,29567]) ).
thf(39173,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[39172:[]]) ).
thf(41258,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ sk11 )
!= sk10 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32996,34004]) ).
thf(41259,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ sk11 )
!= sk10 ) ),
inference(pattern_uni,[status(thm)],[41258:[]]) ).
thf(6,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(59,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(43218,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( ( relation_dom @ sk3 )
!= sk23 )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[35448,31107]) ).
thf(43219,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( ( relation_dom @ sk3 )
!= sk23 ) ),
inference(pattern_uni,[status(thm)],[43218:[]]) ).
thf(34191,plain,
( ~ ( empty @ sk11 )
| ( sk23 != sk5 )
| ( ( relation_dom @ sk23 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[2760,30974]) ).
thf(34218,plain,
( ~ ( empty @ sk11 )
| ( sk23 != sk5 )
| ( sk23 != sk11 ) ),
inference(simp,[status(thm)],[34191]) ).
thf(31034,plain,
( ( sk23 != empty_set )
| ( ( empty @ sk23 )
!= ( empty @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[30977,12483]) ).
thf(31105,plain,
( ( sk23 != empty_set )
| ( sk23 != sk3 ) ),
inference(simp,[status(thm)],[31034]) ).
thf(31606,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk23 != sk3 )
| ( A != sk23 ) ),
inference(paramod_ordered,[status(thm)],[87,31105]) ).
thf(31607,plain,
( ~ ( empty @ sk23 )
| ( sk23 != sk3 ) ),
inference(pattern_uni,[status(thm)],[31606:[bind(A,$thf( sk23 ))]]) ).
thf(32083,plain,
( ( sk11 != empty_set )
| ( sk23 != sk3 )
| ( ( empty @ sk23 )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[28756,31607]) ).
thf(32113,plain,
( ( sk11 != empty_set )
| ( sk23 != sk3 )
| ( sk23 != sk11 ) ),
inference(simp,[status(thm)],[32083]) ).
thf(45216,plain,
( ~ ( empty @ sk23 )
| ( ( empty @ ( relation_dom @ sk23 ) )
!= ( empty @ ( relation_dom @ sk10 ) ) ) ),
inference(paramod_ordered,[status(thm)],[36252,24638]) ).
thf(45375,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ sk23 )
!= ( relation_dom @ sk10 ) ) ),
inference(simp,[status(thm)],[45216]) ).
thf(45182,plain,
! [A: $i] :
( ~ ( empty @ sk23 )
| ( relation @ ( relation_dom @ A ) )
| ( ( empty @ ( relation_dom @ sk23 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[36252,152]) ).
thf(45183,plain,
( ~ ( empty @ sk23 )
| ( relation @ ( relation_dom @ ( relation_dom @ sk23 ) ) ) ),
inference(pattern_uni,[status(thm)],[45182:[bind(A,$thf( relation_dom @ sk23 ))]]) ).
thf(673,plain,
! [B: $i,A: $i] :
( ( empty @ ( ordered_pair @ A @ B ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[67,95]) ).
thf(683,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
!= empty_set ),
inference(simp,[status(thm)],[673]) ).
thf(900,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) )
!= empty_set ),
inference(rewrite,[status(thm)],[683,78]) ).
thf(162,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ( in @ ( sk13 @ B @ A ) @ B )
| ~ ( in @ ( sk14 @ B @ A ) @ B )
| ( B
= ( relation_dom @ A ) ) ),
inference(cnf,[status(esa)],[156]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ( in @ ( sk13 @ B @ A ) @ B )
| ~ ( in @ ( sk14 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[162]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ( in @ ( sk13 @ B @ A ) @ B )
| ~ ( in @ ( sk14 @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[171]) ).
thf(36169,plain,
! [A: $i] :
( ( sk23 != empty_set )
| ( relation @ ( relation_dom @ A ) )
| ( ( empty @ ( relation_dom @ sk23 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31083,152]) ).
thf(36170,plain,
( ( sk23 != empty_set )
| ( relation @ ( relation_dom @ ( relation_dom @ sk23 ) ) ) ),
inference(pattern_uni,[status(thm)],[36169:[bind(A,$thf( relation_dom @ sk23 ))]]) ).
thf(33875,plain,
( ( sk11 != empty_set )
| ( ( empty @ ( relation_dom @ sk11 ) )
!= ( empty @ ( relation_dom @ sk10 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29567,24638]) ).
thf(33996,plain,
( ( sk11 != empty_set )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk10 ) ) ),
inference(simp,[status(thm)],[33875]) ).
thf(74509,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32994,53736]) ).
thf(74510,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[74509:[]]) ).
thf(30369,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk11 != sk10 )
| ( A
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[87,28794]) ).
thf(30370,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( sk11 != sk10 ) ),
inference(pattern_uni,[status(thm)],[30369:[bind(A,$thf( relation_dom @ sk11 ))]]) ).
thf(31022,plain,
( ( sk23 != empty_set )
| ( ( empty @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ) )
!= ( empty @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[30977,1375]) ).
thf(31109,plain,
( ( sk23 != empty_set )
| ( ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) )
!= sk23 ) ),
inference(simp,[status(thm)],[31022]) ).
thf(97,plain,
~ ? [A: $i,B: $i] :
( ( in @ A @ B )
& ? [C: $i] :
( ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) ),
inference(miniscope,[status(thm)],[96]) ).
thf(98,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( element @ B @ ( powerset @ C ) )
| ~ ( empty @ C ) ),
inference(cnf,[status(esa)],[97]) ).
thf(72707,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32983,53556]) ).
thf(72708,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[72707:[]]) ).
thf(34192,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk23 != sk5 )
| ( A
!= ( relation_dom @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[87,30974]) ).
thf(34193,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( sk23 != sk5 ) ),
inference(pattern_uni,[status(thm)],[34192:[bind(A,$thf( relation_dom @ sk23 ))]]) ).
thf(6577,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ B )
| ( ( in @ A @ ( powerset @ A ) )
!= ( in @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[6492,149]) ).
thf(6578,plain,
! [A: $i] :
~ ( in @ ( powerset @ A ) @ A ),
inference(pattern_uni,[status(thm)],[6577:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( powerset @ D ))]]) ).
thf(6613,plain,
! [A: $i] :
~ ( in @ ( powerset @ A ) @ A ),
inference(simp,[status(thm)],[6578]) ).
thf(42426,plain,
( ~ ( empty @ sk11 )
| ( ( empty @ ( relation_dom @ sk11 ) )
!= ( empty @ ( relation_dom @ sk10 ) ) ) ),
inference(paramod_ordered,[status(thm)],[33920,24638]) ).
thf(42618,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk10 ) ) ),
inference(simp,[status(thm)],[42426]) ).
thf(62165,plain,
! [A: $i] :
( ~ ( empty @ sk11 )
| ( A = empty_set )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[42552,87]) ).
thf(62166,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ ( relation_dom @ sk11 ) )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[62165:[bind(A,$thf( relation_dom @ ( relation_dom @ sk11 ) ))]]) ).
thf(639,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)],[74,71]) ).
thf(640,plain,
! [A: $i] :
( ( empty @ A )
| ( subset @ ( sk6 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[639:[bind(A,$thf( D )),bind(B,$thf( sk6 @ D )),bind(C,$thf( D ))]]) ).
thf(649,plain,
! [A: $i] :
( ( empty @ A )
| ( subset @ ( sk6 @ A ) @ A ) ),
inference(simp,[status(thm)],[640]) ).
thf(43935,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( ( relation_dom @ sk11 )
!= sk3 )
| ( ( empty @ sk11 )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[27767,41021]) ).
thf(43936,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( ( relation_dom @ sk11 )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[43935:[]]) ).
thf(1876,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ ( unordered_pair @ B @ A ) @ ( singleton @ C ) )
!= empty_set )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[52,1875]) ).
thf(1877,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ B @ A ) @ ( singleton @ B ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[1876:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(211,plain,
( ( empty @ sk5 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[67,63]) ).
thf(213,plain,
sk5 != empty_set,
inference(simp,[status(thm)],[211]) ).
thf(40215,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32992,29499]) ).
thf(40216,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[40215:[]]) ).
thf(46665,plain,
( ~ ( empty @ sk23 )
| ( sk11 != sk5 )
| ( ( relation_dom @ sk23 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[44430,28885]) ).
thf(46989,plain,
( ~ ( empty @ sk23 )
| ( sk11 != sk5 )
| ( sk23 != sk11 ) ),
inference(simp,[status(thm)],[46665]) ).
thf(65,plain,
~ ? [A: $i] : ( empty @ ( singleton @ A ) ),
inference(miniscope,[status(thm)],[64]) ).
thf(66,plain,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
inference(cnf,[status(esa)],[65]) ).
thf(41188,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32992,33866]) ).
thf(41189,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[41188:[]]) ).
thf(32312,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ sk11 )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[2797,28774]) ).
thf(32313,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ sk11 ) ),
inference(pattern_uni,[status(thm)],[32312:[]]) ).
thf(32321,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ sk11 )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[3209,28774]) ).
thf(32322,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ sk11 ) ),
inference(pattern_uni,[status(thm)],[32321:[]]) ).
thf(40099,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( ( relation_dom @ sk11 )
!= sk5 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32998,33990]) ).
thf(40100,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( ( relation_dom @ sk11 )
!= sk5 ) ),
inference(pattern_uni,[status(thm)],[40099:[]]) ).
thf(135,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ),
inference(cnf,[status(esa)],[134]) ).
thf(120,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ B @ ( relation_dom @ A ) )
| ( C
!= ( apply @ A @ B ) )
| ( in @ ( ordered_pair @ B @ C ) @ A ) ),
inference(cnf,[status(esa)],[118]) ).
thf(125,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( apply @ A @ B ) )
| ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ B @ ( relation_dom @ A ) )
| ( in @ ( ordered_pair @ B @ C ) @ A ) ),
inference(lifteq,[status(thm)],[120]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ B @ ( relation_dom @ A ) )
| ( in @ ( ordered_pair @ B @ ( apply @ A @ B ) ) @ A ) ),
inference(simp,[status(thm)],[125]) ).
thf(5326,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( in @ B @ ( relation_dom @ A ) )
| ( in @ ( unordered_pair @ ( unordered_pair @ B @ ( apply @ A @ B ) ) @ ( singleton @ B ) ) @ A ) ),
inference(rewrite,[status(thm)],[126,78]) ).
thf(74642,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32981,53736]) ).
thf(74643,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[74642:[]]) ).
thf(34695,plain,
( ~ ( empty @ sk11 )
| ( sk23 != sk10 )
| ( ( relation_dom @ sk23 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[2760,30987]) ).
thf(34724,plain,
( ~ ( empty @ sk11 )
| ( sk23 != sk10 )
| ( sk23 != sk11 ) ),
inference(simp,[status(thm)],[34695]) ).
thf(6346,plain,
( ( sk11 != empty_set )
| ( ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[2921,1403]) ).
thf(6417,plain,
( ( sk11 != empty_set )
| ( ( relation_composition @ sk3 @ sk2 )
!= sk11 ) ),
inference(simp,[status(thm)],[6346]) ).
thf(72654,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32994,53556]) ).
thf(72655,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[72654:[]]) ).
thf(44530,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( ( relation_dom @ sk23 )
= empty_set )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[35448,36250]) ).
thf(44531,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( ( relation_dom @ sk23 )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[44530:[]]) ).
thf(46641,plain,
( ~ ( empty @ sk23 )
| ( sk11 != sk2 )
| ( ( relation_dom @ sk23 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[44430,28758]) ).
thf(46977,plain,
( ~ ( empty @ sk23 )
| ( sk11 != sk2 )
| ( sk23 != sk11 ) ),
inference(simp,[status(thm)],[46641]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_composition @ A @ B ) )
& ( function @ ( relation_composition @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(112,plain,
! [A: $i,B: $i] :
( ( ( relation @ A )
& ( function @ A )
& ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_composition @ A @ B ) )
& ( function @ ( relation_composition @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(89267,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ ( relation_dom @ empty_set ) )
!= sk10 )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[43389,66897]) ).
thf(89268,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ ( relation_dom @ empty_set ) )
!= sk10 ) ),
inference(pattern_uni,[status(thm)],[89267:[]]) ).
thf(91188,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ empty_set )
!= sk10 ) ),
inference(rewrite,[status(thm)],[89268,7106]) ).
thf(53596,plain,
( ( sk11 != empty_set )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
!= ( empty @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[33979,12483]) ).
thf(53777,plain,
( ( sk11 != empty_set )
| ( ( relation_dom @ ( relation_dom @ sk11 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[53596]) ).
thf(6632,plain,
( ( in @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ) @ sk1 )
!= ( in @ sk1 @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[46,6566]) ).
thf(6706,plain,
( ( ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) )
!= sk1 )
| ( ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) )
!= sk1 ) ),
inference(simp,[status(thm)],[6632]) ).
thf(6719,plain,
( ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) )
!= sk1 ),
inference(simp,[status(thm)],[6706]) ).
thf(38528,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( ( relation_dom @ sk3 )
!= sk11 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32998,29570]) ).
thf(38529,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( ( relation_dom @ sk3 )
!= sk11 ) ),
inference(pattern_uni,[status(thm)],[38528:[]]) ).
thf(28831,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ sk11 )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[3209,27767]) ).
thf(28832,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ sk11 ) ),
inference(pattern_uni,[status(thm)],[28831:[]]) ).
thf(66705,plain,
( ~ ( empty @ sk23 )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk23 ) ) )
!= ( empty @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[45338,63]) ).
thf(66839,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ ( relation_dom @ sk23 ) )
!= sk5 ) ),
inference(simp,[status(thm)],[66705]) ).
thf(48,plain,
function @ sk3,
inference(cnf,[status(esa)],[42]) ).
thf(160,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( in @ ( ordered_pair @ ( sk13 @ B @ A ) @ C ) @ A )
| ( in @ ( ordered_pair @ ( sk14 @ B @ A ) @ ( sk15 @ B @ A ) ) @ A )
| ( B
= ( relation_dom @ A ) ) ),
inference(cnf,[status(esa)],[156]) ).
thf(165,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ~ ( in @ ( ordered_pair @ ( sk13 @ B @ A ) @ C ) @ A )
| ( in @ ( ordered_pair @ ( sk14 @ B @ A ) @ ( sk15 @ B @ A ) ) @ A ) ),
inference(lifteq,[status(thm)],[160]) ).
thf(166,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ~ ( in @ ( ordered_pair @ ( sk13 @ B @ A ) @ C ) @ A )
| ( in @ ( ordered_pair @ ( sk14 @ B @ A ) @ ( sk15 @ B @ A ) ) @ A ) ),
inference(simp,[status(thm)],[165]) ).
thf(8163,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ~ ( in @ ( unordered_pair @ ( unordered_pair @ ( sk13 @ B @ A ) @ C ) @ ( singleton @ ( sk13 @ B @ A ) ) ) @ A )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ B @ A ) @ ( sk15 @ B @ A ) ) @ ( singleton @ ( sk14 @ B @ A ) ) ) @ A ) ),
inference(rewrite,[status(thm)],[166,78]) ).
thf(186,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ( sk17 @ B @ A @ C )
| ( in @ ( ordered_pair @ ( sk20 @ C @ B @ A ) @ ( sk22 @ C @ B @ A ) ) @ A )
| ( C
= ( relation_composition @ A @ B ) ) ),
inference(cnf,[status(esa)],[181]) ).
thf(199,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_composition @ A @ B ) )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ( sk17 @ B @ A @ C )
| ( in @ ( ordered_pair @ ( sk20 @ C @ B @ A ) @ ( sk22 @ C @ B @ A ) ) @ A ) ),
inference(lifteq,[status(thm)],[186]) ).
thf(23104,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_composition @ A @ B ) )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ( sk17 @ B @ A @ C )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk20 @ C @ B @ A ) @ ( sk22 @ C @ B @ A ) ) @ ( singleton @ ( sk20 @ C @ B @ A ) ) ) @ A ) ),
inference(rewrite,[status(thm)],[199,78]) ).
thf(52834,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32994,33860]) ).
thf(52835,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[52834:[]]) ).
thf(43055,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( relation_empty_yielding @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32998,33985]) ).
thf(43056,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( relation_empty_yielding @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[43055:[]]) ).
thf(55986,plain,
! [A: $i] :
( ( sk23 != empty_set )
| ( function @ A )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk23 ) ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[36280,116]) ).
thf(55987,plain,
( ( sk23 != empty_set )
| ( function @ ( relation_dom @ ( relation_dom @ sk23 ) ) ) ),
inference(pattern_uni,[status(thm)],[55986:[bind(A,$thf( relation_dom @ ( relation_dom @ sk23 ) ))]]) ).
thf(56157,plain,
! [A: $i] :
( ( sk23 != empty_set )
| ( relation_empty_yielding @ A )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk23 ) ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[36280,32557]) ).
thf(56158,plain,
( ( sk23 != empty_set )
| ( relation_empty_yielding @ ( relation_dom @ ( relation_dom @ sk23 ) ) ) ),
inference(pattern_uni,[status(thm)],[56157:[bind(A,$thf( relation_dom @ ( relation_dom @ sk23 ) ))]]) ).
thf(45888,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( ( relation_dom @ sk11 )
!= sk10 )
| ( ( empty @ sk11 )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[27767,41259]) ).
thf(45889,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( ( relation_dom @ sk11 )
!= sk10 ) ),
inference(pattern_uni,[status(thm)],[45888:[]]) ).
thf(36175,plain,
! [A: $i] :
( ( sk23 != empty_set )
| ( function @ A )
| ( ( empty @ ( relation_dom @ sk23 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31083,116]) ).
thf(36176,plain,
( ( sk23 != empty_set )
| ( function @ ( relation_dom @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[36175:[bind(A,$thf( relation_dom @ sk23 ))]]) ).
thf(44096,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( function @ ( relation_dom @ sk23 ) )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[35448,36176]) ).
thf(44097,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( function @ ( relation_dom @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[44096:[]]) ).
thf(44063,plain,
( ~ ( empty @ sk23 )
| ( function @ ( relation_dom @ sk23 ) )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[43389,36176]) ).
thf(44064,plain,
( ~ ( empty @ sk23 )
| ( function @ ( relation_dom @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[44063:[]]) ).
thf(46585,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( function @ ( relation_dom @ sk23 ) )
| ( ( empty @ sk23 )
!= ( empty @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[27837,44064]) ).
thf(46586,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( function @ ( relation_dom @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[46585:[]]) ).
thf(56028,plain,
( ( sk23 != empty_set )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk23 ) ) )
!= ( empty @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[36280,12483]) ).
thf(56165,plain,
( ( sk23 != empty_set )
| ( ( relation_dom @ ( relation_dom @ sk23 ) )
!= sk3 ) ),
inference(simp,[status(thm)],[56028]) ).
thf(30879,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( ( empty @ sk23 )
!= ( empty @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[27837,12483]) ).
thf(30978,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( sk23 != sk3 ) ),
inference(simp,[status(thm)],[30879]) ).
thf(32905,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk23 != sk3 )
| ( A
!= ( relation_dom @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[87,30978]) ).
thf(32906,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( sk23 != sk3 ) ),
inference(pattern_uni,[status(thm)],[32905:[bind(A,$thf( relation_dom @ sk23 ))]]) ).
thf(6635,plain,
! [A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ) @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[6492,6566]) ).
thf(6699,plain,
! [A: $i] :
( ( A
!= ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ) )
| ( ( powerset @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[6635]) ).
thf(6715,plain,
( ( powerset @ ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) ) )
!= sk1 ),
inference(simp,[status(thm)],[6699]) ).
thf(55985,plain,
( ( sk23 != empty_set )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk23 ) ) )
!= ( empty @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[36280,133]) ).
thf(56200,plain,
( ( sk23 != empty_set )
| ( ( relation_dom @ ( relation_dom @ sk23 ) )
!= sk10 ) ),
inference(simp,[status(thm)],[55985]) ).
thf(46808,plain,
( ~ ( empty @ sk23 )
| ( sk11 != sk3 )
| ( ( relation_dom @ sk23 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[44430,28760]) ).
thf(47000,plain,
( ~ ( empty @ sk23 )
| ( sk11 != sk3 )
| ( sk23 != sk11 ) ),
inference(simp,[status(thm)],[46808]) ).
thf(720,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ( element @ A @ ( powerset @ C ) )
| ( B
!= ( sk7 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[58,90]) ).
thf(721,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ ( sk7 @ B ) )
| ( element @ A @ ( powerset @ B ) ) ),
inference(pattern_uni,[status(thm)],[720:[bind(A,$thf( A )),bind(B,$thf( sk7 @ D )),bind(C,$thf( D ))]]) ).
thf(724,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ ( sk7 @ B ) )
| ( element @ A @ ( powerset @ B ) ) ),
inference(simp,[status(thm)],[721]) ).
thf(89832,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ empty_set )
| ( element @ A @ ( powerset @ B ) ) ),
inference(rewrite,[status(thm)],[724,1172]) ).
thf(177,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( relation @ B )
| ( relation @ ( relation_composition @ A @ B ) ) ),
inference(cnf,[status(esa)],[175]) ).
thf(28795,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( ( empty @ ( relation_dom @ sk3 ) )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[27767,18067]) ).
thf(28887,plain,
( ( ( relation_dom @ sk11 )
!= empty_set )
| ( ( relation_dom @ sk3 )
!= sk11 ) ),
inference(simp,[status(thm)],[28795]) ).
thf(32235,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( relation_dom @ sk2 )
!= sk11 )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[87,29579]) ).
thf(32236,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ sk2 )
!= sk11 ) ),
inference(pattern_uni,[status(thm)],[32235:[bind(A,$thf( sk11 ))]]) ).
thf(570,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ B @ C )
| ( ( element @ ( sk8 @ A ) @ A )
!= ( element @ B @ ( powerset @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[92,71]) ).
thf(571,plain,
! [A: $i] : ( subset @ ( sk8 @ ( powerset @ A ) ) @ A ),
inference(pattern_uni,[status(thm)],[570:[bind(A,$thf( powerset @ E )),bind(B,$thf( sk8 @ ( powerset @ E ) )),bind(C,$thf( E ))]]) ).
thf(576,plain,
! [A: $i] : ( subset @ ( sk8 @ ( powerset @ A ) ) @ A ),
inference(simp,[status(thm)],[571]) ).
thf(36285,plain,
! [A: $i] :
( ( sk23 != empty_set )
| ( relation_empty_yielding @ A )
| ( ( empty @ ( relation_dom @ sk23 ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31083,32557]) ).
thf(36286,plain,
( ( sk23 != empty_set )
| ( relation_empty_yielding @ ( relation_dom @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[36285:[bind(A,$thf( relation_dom @ sk23 ))]]) ).
thf(45477,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( relation_empty_yielding @ ( relation_dom @ sk23 ) )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[35448,36286]) ).
thf(45478,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( relation_empty_yielding @ ( relation_dom @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[45477:[]]) ).
thf(33488,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( relation_dom @ sk2 )
!= sk23 )
| ( A != sk23 ) ),
inference(paramod_ordered,[status(thm)],[87,31087]) ).
thf(33489,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ sk2 )
!= sk23 ) ),
inference(pattern_uni,[status(thm)],[33488:[bind(A,$thf( sk23 ))]]) ).
thf(73828,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( ( relation_dom @ ( relation_dom @ sk11 ) )
= empty_set )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32981,53684]) ).
thf(73829,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( ( relation_dom @ ( relation_dom @ sk11 ) )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[73828:[]]) ).
thf(32410,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk11 != sk5 )
| ( A
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[87,28885]) ).
thf(32411,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( sk11 != sk5 ) ),
inference(pattern_uni,[status(thm)],[32410:[bind(A,$thf( relation_dom @ sk11 ))]]) ).
thf(29508,plain,
( ( sk11 != empty_set )
| ( ( empty @ ( relation_dom @ sk10 ) )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[28756,24638]) ).
thf(29581,plain,
( ( sk11 != empty_set )
| ( ( relation_dom @ sk10 )
!= sk11 ) ),
inference(simp,[status(thm)],[29508]) ).
thf(2542,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ ( singleton @ D ) @ ( unordered_pair @ B @ A ) )
!= empty_set )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[52,2540]) ).
thf(2543,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ B @ A ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[2542:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(154,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( element @ B @ ( powerset @ C ) )
| ( element @ A @ C ) ),
inference(cnf,[status(esa)],[153]) ).
thf(41196,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32981,33866]) ).
thf(41197,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[41196:[]]) ).
thf(11824,plain,
! [B: $i,A: $i] :
( ( in @ ( sk13 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( powerset @ ( relation_dom @ sk11 ) ) )
| ( element @ A @ B )
| ( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) @ ( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) ) @ sk11 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11437,103]) ).
thf(11825,plain,
( ( in @ ( sk13 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( powerset @ ( relation_dom @ sk11 ) ) )
| ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) @ ( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) ) @ sk11 ) ),
inference(pattern_uni,[status(thm)],[11824:[bind(A,$thf( unordered_pair @ ( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) @ ( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) )),bind(B,$thf( sk11 ))]]) ).
thf(32904,plain,
( ~ ( empty @ sk11 )
| ( sk23 != sk3 )
| ( ( relation_dom @ sk23 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[2760,30978]) ).
thf(32934,plain,
( ~ ( empty @ sk11 )
| ( sk23 != sk3 )
| ( sk23 != sk11 ) ),
inference(simp,[status(thm)],[32904]) ).
thf(38371,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( ( relation_dom @ sk11 )
= empty_set )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32998,2921]) ).
thf(38372,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( ( relation_dom @ sk11 )
= empty_set ) ),
inference(pattern_uni,[status(thm)],[38371:[]]) ).
thf(43,plain,
function @ sk2,
inference(cnf,[status(esa)],[42]) ).
thf(52927,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32983,33860]) ).
thf(52928,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[52927:[]]) ).
thf(43208,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( ( relation_dom @ sk23 )
!= sk2 )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[35448,36300]) ).
thf(43209,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( ( relation_dom @ sk23 )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[43208:[]]) ).
thf(47188,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( relation_empty_yielding @ ( relation_dom @ sk23 ) )
| ( ( empty @ sk23 )
!= ( empty @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[27837,45348]) ).
thf(47189,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( relation_empty_yielding @ ( relation_dom @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[47188:[]]) ).
thf(203,plain,
function @ sk23,
inference(cnf,[status(esa)],[202]) ).
thf(15748,plain,
! [B: $i,A: $i] :
( ( subset @ ( sk13 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( relation_dom @ sk11 ) )
| ( element @ A @ B )
| ( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) @ ( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) ) @ sk11 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[13656,103]) ).
thf(15749,plain,
( ( subset @ ( sk13 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( relation_dom @ sk11 ) )
| ( element @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) @ ( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) ) @ sk11 ) ),
inference(pattern_uni,[status(thm)],[15748:[bind(A,$thf( unordered_pair @ ( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) @ ( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) )),bind(B,$thf( sk11 ))]]) ).
thf(75,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( sk6 @ A ) ) ),
inference(cnf,[status(esa)],[73]) ).
thf(751,plain,
! [A: $i] :
( ( empty @ A )
| ( ( empty @ ( sk6 @ A ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[67,75]) ).
thf(759,plain,
! [A: $i] :
( ( empty @ A )
| ( ( sk6 @ A )
!= empty_set ) ),
inference(simp,[status(thm)],[751]) ).
thf(42446,plain,
( ~ ( empty @ sk11 )
| ( ( empty @ ( relation_composition @ sk3 @ sk2 ) )
!= ( empty @ ( relation_dom @ sk11 ) ) ) ),
inference(paramod_ordered,[status(thm)],[33920,6937]) ).
thf(42575,plain,
( ~ ( empty @ sk11 )
| ( ( relation_composition @ sk3 @ sk2 )
!= ( relation_dom @ sk11 ) ) ),
inference(simp,[status(thm)],[42446]) ).
thf(7128,plain,
! [A: $i] :
( ( empty @ ( relation_dom @ A ) )
| ( ( empty @ ( relation_dom @ empty_set ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6979,151]) ).
thf(7129,plain,
empty @ ( relation_dom @ ( relation_dom @ empty_set ) ),
inference(pattern_uni,[status(thm)],[7128:[bind(A,$thf( relation_dom @ empty_set ))]]) ).
thf(7589,plain,
empty @ ( relation_dom @ empty_set ),
inference(rewrite,[status(thm)],[7129,7106]) ).
thf(753,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ( ( empty @ ( sk7 @ A ) )
!= ( empty @ ( sk6 @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[89,75]) ).
thf(760,plain,
! [B: $i,A: $i] :
( ( empty @ B )
| ( ( sk7 @ A )
!= ( sk6 @ B ) ) ),
inference(simp,[status(thm)],[753]) ).
thf(91398,plain,
! [A: $i] :
( ( empty @ A )
| ( ( sk6 @ A )
!= empty_set ) ),
inference(rewrite,[status(thm)],[760,1172]) ).
thf(31017,plain,
( ( sk23 != empty_set )
| ( ( empty @ sk23 )
!= ( empty @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[30977,133]) ).
thf(31106,plain,
( ( sk23 != empty_set )
| ( sk23 != sk10 ) ),
inference(simp,[status(thm)],[31017]) ).
thf(31992,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk23 != sk10 )
| ( A != sk23 ) ),
inference(paramod_ordered,[status(thm)],[87,31106]) ).
thf(31993,plain,
( ~ ( empty @ sk23 )
| ( sk23 != sk10 ) ),
inference(pattern_uni,[status(thm)],[31992:[bind(A,$thf( sk23 ))]]) ).
thf(32143,plain,
( ( sk11 != empty_set )
| ( sk23 != sk10 )
| ( ( empty @ sk23 )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[28756,31993]) ).
thf(32178,plain,
( ( sk11 != empty_set )
| ( sk23 != sk10 )
| ( sk23 != sk11 ) ),
inference(simp,[status(thm)],[32143]) ).
thf(28836,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ sk11 )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[2728,27767]) ).
thf(28837,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ sk11 ) ),
inference(pattern_uni,[status(thm)],[28836:[]]) ).
thf(43322,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( relation @ ( relation_dom @ sk23 ) )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[35448,31014]) ).
thf(43323,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( relation @ ( relation_dom @ sk23 ) ) ),
inference(pattern_uni,[status(thm)],[43322:[]]) ).
thf(41498,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32994,29567]) ).
thf(41499,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[41498:[]]) ).
thf(187,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ( sk17 @ B @ A @ C )
| ~ ( in @ ( ordered_pair @ ( sk20 @ C @ B @ A ) @ ( sk21 @ C @ B @ A ) ) @ C )
| ( C
= ( relation_composition @ A @ B ) ) ),
inference(cnf,[status(esa)],[181]) ).
thf(196,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_composition @ A @ B ) )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ( sk17 @ B @ A @ C )
| ~ ( in @ ( ordered_pair @ ( sk20 @ C @ B @ A ) @ ( sk21 @ C @ B @ A ) ) @ C ) ),
inference(lifteq,[status(thm)],[187]) ).
thf(20195,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_composition @ A @ B ) )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ( sk17 @ B @ A @ C )
| ~ ( in @ ( unordered_pair @ ( unordered_pair @ ( sk20 @ C @ B @ A ) @ ( sk21 @ C @ B @ A ) ) @ ( singleton @ ( sk20 @ C @ B @ A ) ) ) @ C ) ),
inference(rewrite,[status(thm)],[196,78]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( function @ A )
| ~ ( relation @ B )
| ~ ( function @ B )
| ( function @ ( relation_composition @ A @ B ) ) ),
inference(cnf,[status(esa)],[112]) ).
thf(44177,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ sk23 )
!= sk10 )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[43389,36317]) ).
thf(44178,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ sk23 )
!= sk10 ) ),
inference(pattern_uni,[status(thm)],[44177:[]]) ).
thf(11450,plain,
! [B: $i,A: $i] :
( ( in @ empty_set @ ( powerset @ A ) )
!= ( in @ ( powerset @ B ) @ B ) ),
inference(paramod_ordered,[status(thm)],[3596,6613]) ).
thf(11477,plain,
! [B: $i,A: $i] :
( ( ( powerset @ B )
!= empty_set )
| ( ( powerset @ A )
!= B ) ),
inference(simp,[status(thm)],[11450]) ).
thf(11497,plain,
! [A: $i] :
( ( powerset @ ( powerset @ A ) )
!= empty_set ),
inference(simp,[status(thm)],[11477]) ).
thf(32721,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( relation_dom @ sk10 )
!= sk11 )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[87,29581]) ).
thf(32722,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ sk10 )
!= sk11 ) ),
inference(pattern_uni,[status(thm)],[32721:[bind(A,$thf( sk11 ))]]) ).
thf(30882,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( ( empty @ ( relation_dom @ sk3 ) )
!= ( empty @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[27837,18067]) ).
thf(30986,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( ( relation_dom @ sk3 )
!= sk23 ) ),
inference(simp,[status(thm)],[30882]) ).
thf(43277,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( ( relation_dom @ sk2 )
!= sk23 )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[35448,31087]) ).
thf(43278,plain,
( ~ ( empty @ ( relation_dom @ sk23 ) )
| ( ( relation_dom @ sk2 )
!= sk23 ) ),
inference(pattern_uni,[status(thm)],[43277:[]]) ).
thf(41069,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( ( relation_dom @ sk11 )
!= sk3 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32998,34002]) ).
thf(41070,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( ( relation_dom @ sk11 )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[41069:[]]) ).
thf(42503,plain,
( ~ ( empty @ sk11 )
| ( ( empty @ ( relation_dom @ sk11 ) )
!= ( empty @ ( relation_dom @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[33920,14158]) ).
thf(42605,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk2 ) ) ),
inference(simp,[status(thm)],[42503]) ).
thf(46329,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( ( relation_dom @ sk23 )
!= sk10 )
| ( ( empty @ sk23 )
!= ( empty @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[27837,44178]) ).
thf(46330,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( ( relation_dom @ sk23 )
!= sk10 ) ),
inference(pattern_uni,[status(thm)],[46329:[]]) ).
thf(40267,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32992,29567]) ).
thf(40268,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[40267:[]]) ).
thf(60,plain,
empty @ sk4,
inference(cnf,[status(esa)],[59]) ).
thf(1044,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ sk4 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[60,87]) ).
thf(1045,plain,
sk4 = empty_set,
inference(pattern_uni,[status(thm)],[1044:[bind(A,$thf( sk4 ))]]) ).
thf(33628,plain,
( ~ ( empty @ sk11 )
| ( relation @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32996,29499]) ).
thf(33629,plain,
( ~ ( empty @ sk11 )
| ( relation @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[33628:[]]) ).
thf(43051,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32992,33985]) ).
thf(43052,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation_empty_yielding @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[43051:[]]) ).
thf(30880,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( ( empty @ ( relation_composition @ sk3 @ sk2 ) )
!= ( empty @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[27837,6937]) ).
thf(30958,plain,
( ( ( relation_dom @ sk23 )
!= empty_set )
| ( ( relation_composition @ sk3 @ sk2 )
!= sk23 ) ),
inference(simp,[status(thm)],[30880]) ).
thf(31036,plain,
( ( sk23 != empty_set )
| ( sk11 != sk10 )
| ( ( empty @ sk23 )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[30977,24770]) ).
thf(31091,plain,
( ( sk23 != empty_set )
| ( sk11 != sk10 )
| ( sk23 != sk11 ) ),
inference(simp,[status(thm)],[31036]) ).
thf(30789,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( ( relation_dom @ sk3 )
!= sk11 )
| ( A != sk11 ) ),
inference(paramod_ordered,[status(thm)],[87,29570]) ).
thf(30790,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ sk3 )
!= sk11 ) ),
inference(pattern_uni,[status(thm)],[30789:[bind(A,$thf( sk11 ))]]) ).
thf(38688,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( ( relation_dom @ sk10 )
!= sk11 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32998,29581]) ).
thf(38689,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( ( relation_dom @ sk10 )
!= sk11 ) ),
inference(pattern_uni,[status(thm)],[38688:[]]) ).
thf(38521,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( ( relation_dom @ sk2 )
!= sk11 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32998,29579]) ).
thf(38522,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( ( relation_dom @ sk2 )
!= sk11 ) ),
inference(pattern_uni,[status(thm)],[38521:[]]) ).
thf(146,plain,
relation_empty_yielding @ sk11,
inference(cnf,[status(esa)],[145]) ).
thf(85024,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ ( relation_dom @ empty_set ) )
!= sk5 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32996,62263]) ).
thf(85025,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ ( relation_dom @ empty_set ) )
!= sk5 ) ),
inference(pattern_uni,[status(thm)],[85024:[]]) ).
thf(90007,plain,
( ~ ( empty @ sk11 )
| ( ( relation_dom @ empty_set )
!= sk5 ) ),
inference(rewrite,[status(thm)],[85025,7106]) ).
thf(11451,plain,
! [B: $i,A: $i] :
( ( in @ A @ ( powerset @ A ) )
!= ( in @ ( powerset @ B ) @ B ) ),
inference(paramod_ordered,[status(thm)],[6492,6613]) ).
thf(11474,plain,
! [B: $i,A: $i] :
( ( A
!= ( powerset @ B ) )
| ( ( powerset @ A )
!= B ) ),
inference(simp,[status(thm)],[11451]) ).
thf(11494,plain,
! [A: $i] :
( ( powerset @ ( powerset @ A ) )
!= A ),
inference(simp,[status(thm)],[11474]) ).
thf(766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ B @ A )
!= empty_set )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[52,666]) ).
thf(767,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ B @ A )
!= empty_set ),
inference(pattern_uni,[status(thm)],[766:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(89026,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ ( relation_dom @ empty_set ) )
!= sk5 )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[43389,66839]) ).
thf(89027,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ ( relation_dom @ empty_set ) )
!= sk5 ) ),
inference(pattern_uni,[status(thm)],[89026:[]]) ).
thf(91022,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ empty_set )
!= sk5 ) ),
inference(rewrite,[status(thm)],[89027,7106]) ).
thf(41192,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( function @ ( relation_dom @ sk11 ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32998,33866]) ).
thf(41193,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( function @ ( relation_dom @ sk11 ) ) ),
inference(pattern_uni,[status(thm)],[41192:[]]) ).
thf(453,plain,
! [A: $i] :
( ( empty @ ( singleton @ A ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[67,66]) ).
thf(459,plain,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
inference(simp,[status(thm)],[453]) ).
thf(675,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ ( sk7 @ A ) )
!= ( empty @ ( ordered_pair @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[89,95]) ).
thf(682,plain,
! [C: $i,B: $i,A: $i] :
( ( sk7 @ A )
!= ( ordered_pair @ B @ C ) ),
inference(simp,[status(thm)],[675]) ).
thf(1827,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) )
!= empty_set ),
inference(rewrite,[status(thm)],[682,1172,78]) ).
thf(183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ ( sk18 @ C @ B @ A ) @ D ) @ A )
| ~ ( in @ ( ordered_pair @ D @ ( sk19 @ C @ B @ A ) ) @ B )
| ~ ( sk17 @ B @ A @ C )
| ( C
= ( relation_composition @ A @ B ) ) ),
inference(cnf,[status(esa)],[181]) ).
thf(200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( relation_composition @ A @ B ) )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ ( sk18 @ C @ B @ A ) @ D ) @ A )
| ~ ( in @ ( ordered_pair @ D @ ( sk19 @ C @ B @ A ) ) @ B )
| ~ ( sk17 @ B @ A @ C ) ),
inference(lifteq,[status(thm)],[183]) ).
thf(201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( relation_composition @ A @ B ) )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ ( sk18 @ C @ B @ A ) @ D ) @ A )
| ~ ( in @ ( ordered_pair @ D @ ( sk19 @ C @ B @ A ) ) @ B )
| ~ ( sk17 @ B @ A @ C ) ),
inference(simp,[status(thm)],[200]) ).
thf(24792,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( relation_composition @ A @ B ) )
| ~ ( relation @ A )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ~ ( in @ ( unordered_pair @ ( unordered_pair @ ( sk18 @ C @ B @ A ) @ D ) @ ( singleton @ ( sk18 @ C @ B @ A ) ) ) @ A )
| ~ ( in @ ( unordered_pair @ ( unordered_pair @ D @ ( sk19 @ C @ B @ A ) ) @ ( singleton @ D ) ) @ B )
| ~ ( sk17 @ B @ A @ C ) ),
inference(rewrite,[status(thm)],[201,78]) ).
thf(53637,plain,
( ( sk11 != empty_set )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
!= ( empty @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[33979,7049]) ).
thf(53774,plain,
( ( sk11 != empty_set )
| ( ( relation_dom @ ( relation_dom @ sk11 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[53637]) ).
thf(849,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ C ) )
!= sk9 )
| ( ( unordered_pair @ B @ A )
!= ( unordered_pair @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[52,842]) ).
thf(850,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ B ) )
!= sk9 ),
inference(pattern_uni,[status(thm)],[849:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(2484,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ B ) )
!= empty_set ),
inference(rewrite,[status(thm)],[850,1025]) ).
thf(46739,plain,
( ~ ( empty @ sk23 )
| ( ( relation_dom @ ( relation_composition @ sk3 @ sk2 ) )
!= ( relation_dom @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[44430,1403]) ).
thf(46995,plain,
( ~ ( empty @ sk23 )
| ( ( relation_composition @ sk3 @ sk2 )
!= sk23 ) ),
inference(simp,[status(thm)],[46739]) ).
thf(33940,plain,
( ( sk11 != empty_set )
| ( ( empty @ ( relation_dom @ sk11 ) )
!= ( empty @ ( relation_dom @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[29567,14158]) ).
thf(33999,plain,
( ( sk11 != empty_set )
| ( ( relation_dom @ sk11 )
!= ( relation_dom @ sk2 ) ) ),
inference(simp,[status(thm)],[33940]) ).
thf(41307,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( ( relation_dom @ sk11 )
!= sk10 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32998,34004]) ).
thf(41308,plain,
( ~ ( empty @ ( relation_dom @ sk11 ) )
| ( ( relation_dom @ sk11 )
!= sk10 ) ),
inference(pattern_uni,[status(thm)],[41307:[]]) ).
thf(53028,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32992,33860]) ).
thf(53029,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( relation @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[53028:[]]) ).
thf(17689,plain,
! [B: $i,A: $i] :
( ( subset @ ( sk13 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( relation_dom @ sk11 ) )
| ( element @ A @ B )
| ( ( in @ ( unordered_pair @ ( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) ) @ sk11 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[15434,103]) ).
thf(17690,plain,
( ( subset @ ( sk13 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( relation_dom @ sk11 ) )
| ( element @ ( unordered_pair @ ( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) ) @ sk11 ) ),
inference(pattern_uni,[status(thm)],[17689:[bind(A,$thf( unordered_pair @ ( singleton @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) @ ( unordered_pair @ ( sk14 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) @ ( sk15 @ ( powerset @ ( relation_dom @ sk11 ) ) @ sk11 ) ) )),bind(B,$thf( sk11 ))]]) ).
thf(72797,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32981,53556]) ).
thf(72798,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( function @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[72797:[]]) ).
thf(53746,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[32981,33979]) ).
thf(53747,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk14 @ empty_set @ sk11 ) @ ( sk15 @ empty_set @ sk11 ) ) @ ( singleton @ ( sk14 @ empty_set @ sk11 ) ) ) @ sk11 )
| ( empty @ ( relation_dom @ ( relation_dom @ sk11 ) ) ) ),
inference(pattern_uni,[status(thm)],[53746:[]]) ).
thf(56070,plain,
( ( sk23 != empty_set )
| ( ( empty @ ( relation_dom @ ( relation_dom @ sk23 ) ) )
!= ( empty @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[36280,63]) ).
thf(56186,plain,
( ( sk23 != empty_set )
| ( ( relation_dom @ ( relation_dom @ sk23 ) )
!= sk5 ) ),
inference(simp,[status(thm)],[56070]) ).
thf(163319,plain,
$false,
inference(cvc4,[status(thm)],[66592,73813,53037,90180,1469,138,101,1767,44289,29616,36290,2921,6566,666,88,39121,46195,46946,408,56176,115,53684,36280,22333,66751,34697,3912,32599,202,29584,42583,3794,142,472,153,89659,40055,14273,31097,28769,89485,42,28879,41132,53736,28843,6291,1254,52,28758,28794,110,36300,56106,66811,28815,41444,32994,46,93,24708,30952,9240,32328,31107,316,32561,90351,31092,18190,37237,45374,13393,28875,152,7047,31103,78,1875,41140,179,28885,376,42406,43389,36294,3357,30962,41430,44789,2540,30977,84,30974,1377,61,132,33866,43225,133,116,147,12504,37558,428,7051,32324,74,30987,42327,117,45348,13408,29499,43060,85,38427,62263,102,31083,32059,62011,34012,15434,53738,73446,11106,137,11212,31100,5924,46097,92,43802,30924,252,73617,43001,14291,7891,36297,62259,45615,44205,1259,1375,27837,31093,24771,33791,141,30969,30855,45415,42969,33989,90518,72790,32814,53,24638,14276,109,43692,31108,28881,37502,3596,53524,44430,212,96,90688,36301,18208,35595,32559,1451,29567,34004,36252,29573,32311,43369,45988,53627,134,29054,73,128,28820,32843,66897,53825,53808,7817,74635,36326,7106,18853,18196,42914,31673,148,45,33920,180,16152,6492,149,53556,28871,31087,29579,64,62222,90857,12827,584,28962,176,39942,44,577,74559,29570,204,34788,4341,41021,12483,39173,41259,1403,59,71,43219,54,6937,28756,42552,34218,32113,45375,49,31607,24770,45183,30976,900,172,36170,33996,81,74510,76,30370,31109,98,1690,72708,34193,18067,6613,42618,62166,649,32983,43936,1877,33990,140,213,91,31136,155,108,40216,103,46989,66,66877,2086,41189,32313,32322,11402,7049,62309,40100,6609,32996,135,2797,31105,33979,5326,36317,31014,74643,34724,6417,72655,44531,46977,209,112,42560,91188,53777,6719,145,38529,28832,66839,48,35448,1025,150,31086,8163,23104,3209,14158,63,52835,29661,43056,55987,56158,50,45889,67,44097,46586,28760,56165,32906,6715,56200,47000,89832,11823,177,28887,32236,27767,576,45478,33489,73829,32411,29581,2543,154,41197,34002,72,175,11825,32934,2728,38372,43,52928,43209,2760,1918,99,47189,203,29504,15749,759,104,42575,36176,87,66853,7589,43775,91398,11514,31174,32178,28837,43323,41499,20195,36286,55,114,44178,75,11497,13656,58,32722,39897,30986,43278,31993,41070,36303,42605,46330,40268,82,1045,151,33860,33629,33992,43052,11437,30958,18122,31091,36250,30790,38689,38522,146,107,136,31106,79,28774,90007,14214,11494,1172,767,62305,91022,41193,459,131,68,178,33985,32557,1827,24792,53774,2484,46995,44064,33999,30978,32992,32998,41308,53029,17690,72798,53747,56186,32981,111,45338]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU214+3 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n015.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 13:25:38 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.82/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.15/1.00 % [INFO] Parsing done (134ms).
% 1.41/1.00 % [INFO] Running in sequential loop mode.
% 1.74/1.21 % [INFO] eprover registered as external prover.
% 1.74/1.21 % [INFO] cvc4 registered as external prover.
% 1.82/1.21 % [INFO] Scanning for conjecture ...
% 1.90/1.28 % [INFO] Found a conjecture and 39 axioms. Running axiom selection ...
% 1.90/1.33 % [INFO] Axiom selection finished. Selected 39 axioms (removed 0 axioms).
% 2.16/1.37 % [INFO] Problem is first-order (TPTP FOF).
% 2.16/1.38 % [INFO] Type checking passed.
% 2.16/1.38 % [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 ...
% 254.00/53.69 % External prover 'cvc4' found a proof!
% 254.00/53.69 % [INFO] Killing All external provers ...
% 254.00/53.69 % Time passed: 53159ms (effective reasoning time: 52680ms)
% 254.00/53.69 % 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)>
% 254.00/53.69 % Axioms used in derivation (39): fc9_relat_1, fc1_funct_1, cc1_relat_1, rc1_funct_1, t4_subset, fc5_relat_1, d8_relat_1, rc2_relat_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_zfmisc_1, d4_funct_1, fc1_xboole_0, d5_tarski, fc4_relat_1, t1_subset, rc3_relat_1, t6_boole, rc2_subset_1, fc3_subset_1, t5_subset, d4_relat_1, fc2_subset_1, t7_boole, cc1_funct_1, fc1_subset_1, fc10_relat_1, rc1_subset_1, t3_subset, existence_m1_subset_1, commutativity_k2_tarski, rc1_relat_1, dt_k5_relat_1, reflexivity_r1_tarski, t8_boole, rc1_xboole_0, t2_subset, fc7_relat_1, fc12_relat_1
% 254.00/53.69 % No. of inferences in proof: 1005
% 254.00/53.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 53159 ms resp. 52680 ms w/o parsing
% 254.35/53.83 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 254.35/53.83 % [INFO] Killing All external provers ...
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