TSTP Solution File: SEU043+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU043+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:56:53 EDT 2023
% Result : Theorem 280.05s 56.48s
% Output : Refutation 280.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 87
% Syntax : Number of formulae : 774 ( 223 unt; 45 typ; 0 def)
% Number of atoms : 2156 ( 579 equ; 0 cnn)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 7318 ( 956 ~; 875 |; 128 &;5237 @)
% ( 12 <=>; 110 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 49 ( 49 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 45 usr; 20 con; 0-3 aty)
% Number of variables : 1540 ( 0 ^;1496 !; 44 ?;1540 :)
% Comments :
%------------------------------------------------------------------------------
thf(relation_type,type,
relation: $i > $o ).
thf(function_type,type,
function: $i > $o ).
thf(relation_rng_restriction_type,type,
relation_rng_restriction: $i > $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(relation_dom_type,type,
relation_dom: $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(one_to_one_type,type,
one_to_one: $i > $o ).
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: $o ).
thf(sk5_type,type,
sk5: $o ).
thf(sk6_type,type,
sk6: $o ).
thf(sk7_type,type,
sk7: $i ).
thf(sk8_type,type,
sk8: $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 ).
thf(sk13_type,type,
sk13: $i > $i ).
thf(sk14_type,type,
sk14: $i > $i ).
thf(sk15_type,type,
sk15: $i ).
thf(sk16_type,type,
sk16: $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 > $i > $i ).
thf(sk24_type,type,
sk24: $i > $i > $i ).
thf(sk25_type,type,
sk25: $i > $i > $i ).
thf(sk26_type,type,
sk26: $i ).
thf(sk27_type,type,
sk27: $i ).
thf(sk28_type,type,
sk28: $i ).
thf(sk29_type,type,
sk29: $i ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(69,plain,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(cnf,[status(esa)],[69]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
inference(lifteq,[status(thm)],[70]) ).
thf(6,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(78,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(79,plain,
empty @ sk10,
inference(cnf,[status(esa)],[78]) ).
thf(18,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(112,plain,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(113,plain,
~ ? [A: $i,B: $i] : ( empty @ ( ordered_pair @ A @ B ) ),
inference(miniscope,[status(thm)],[112]) ).
thf(114,plain,
! [B: $i,A: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
inference(cnf,[status(esa)],[113]) ).
thf(457,plain,
! [B: $i,A: $i] :
( ( empty @ ( ordered_pair @ A @ B ) )
!= ( empty @ sk10 ) ),
inference(paramod_ordered,[status(thm)],[79,114]) ).
thf(460,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
!= sk10 ),
inference(simp,[status(thm)],[457]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(95,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(96,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
inference(cnf,[status(esa)],[95]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
inference(lifteq,[status(thm)],[96]) ).
thf(1585,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) )
!= sk10 ),
inference(rewrite,[status(thm)],[460,97]) ).
thf(15,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(104,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(105,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( A = empty_set ) ),
inference(cnf,[status(esa)],[104]) ).
thf(106,plain,
! [A: $i] :
( ( A = empty_set )
| ~ ( empty @ A ) ),
inference(lifteq,[status(thm)],[105]) ).
thf(2567,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ sk10 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[79,106]) ).
thf(2568,plain,
sk10 = empty_set,
inference(pattern_uni,[status(thm)],[2567:[bind(A,$thf( sk10 ))]]) ).
thf(2845,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) )
!= empty_set ),
inference(rewrite,[status(thm)],[1585,2568]) ).
thf(2872,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 @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[71,2845]) ).
thf(2873,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ B @ A ) @ ( singleton @ A ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[2872:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(3929,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)],[71,2873]) ).
thf(3930,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ B @ A ) @ ( singleton @ B ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[3929:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( B
= ( relation_rng_restriction @ A @ C ) )
<=> ( ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
<=> ( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ D ) @ A ) ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( B
= ( relation_rng_restriction @ A @ C ) )
<=> ( ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
<=> ( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ D ) @ A ) ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(44,plain,
~ ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( ( B
= ( relation_rng_restriction @ A @ C ) )
=> ( ! [D: $i] :
( ( ( in @ D @ ( relation_dom @ B ) )
=> ( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ D ) @ A ) ) )
& ( ( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ D ) @ A ) )
=> ( in @ D @ ( relation_dom @ B ) ) ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) ) )
& ( ( ! [D: $i] :
( ( ( in @ D @ ( relation_dom @ B ) )
=> ( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ D ) @ A ) ) )
& ( ( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ D ) @ A ) )
=> ( in @ D @ ( relation_dom @ B ) ) ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) )
=> ( B
= ( relation_rng_restriction @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(45,plain,
~ ! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ! [C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( ( B
= ( relation_rng_restriction @ A @ C ) )
=> ( ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ D ) @ A ) ) )
& ! [D: $i] :
( ( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ D ) @ A ) )
=> ( in @ D @ ( relation_dom @ B ) ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) ) )
& ( ( ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ D ) @ A ) ) )
& ! [D: $i] :
( ( ( in @ D @ ( relation_dom @ C ) )
& ( in @ ( apply @ C @ D ) @ A ) )
=> ( in @ D @ ( relation_dom @ B ) ) )
& ! [D: $i] :
( ( in @ D @ ( relation_dom @ B ) )
=> ( ( apply @ B @ D )
= ( apply @ C @ D ) ) ) )
=> ( B
= ( relation_rng_restriction @ A @ C ) ) ) ) ) ),
inference(miniscope,[status(thm)],[44]) ).
thf(54,plain,
relation @ sk3,
inference(cnf,[status(esa)],[45]) ).
thf(30,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/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
thf(169,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)],[30]) ).
thf(170,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)],[169]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ( in @ ( sk23 @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sk24 @ B @ A ) @ ( sk25 @ B @ A ) ) @ A )
| ( B
= ( relation_dom @ A ) ) ),
inference(cnf,[status(esa)],[170]) ).
thf(179,plain,
! [B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ( in @ ( sk23 @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sk24 @ B @ A ) @ ( sk25 @ B @ A ) ) @ A ) ),
inference(lifteq,[status(thm)],[173]) ).
thf(180,plain,
! [B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ( in @ ( sk23 @ B @ A ) @ B )
| ( in @ ( ordered_pair @ ( sk24 @ B @ A ) @ ( sk25 @ B @ A ) ) @ A ) ),
inference(simp,[status(thm)],[179]) ).
thf(1671,plain,
! [B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ( in @ ( sk23 @ B @ A ) @ B )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ B @ A ) @ ( sk25 @ B @ A ) ) @ ( singleton @ ( sk24 @ B @ A ) ) ) @ A ) ),
inference(rewrite,[status(thm)],[180,97]) ).
thf(1842,plain,
! [B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ( in @ ( sk23 @ B @ A ) @ B )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ B @ A ) @ ( sk25 @ B @ A ) ) @ ( singleton @ ( sk24 @ B @ A ) ) ) @ A )
| ( ( relation @ sk3 )
!= ( relation @ A ) ) ),
inference(paramod_ordered,[status(thm)],[54,1671]) ).
thf(1843,plain,
! [A: $i] :
( ( A
= ( relation_dom @ sk3 ) )
| ( in @ ( sk23 @ A @ sk3 ) @ A )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ A @ sk3 ) @ ( sk25 @ A @ sk3 ) ) @ ( singleton @ ( sk24 @ A @ sk3 ) ) ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[1842:[bind(A,$thf( sk3 ))]]) ).
thf(2078,plain,
! [A: $i] :
( ( A
= ( relation_dom @ sk3 ) )
| ( in @ ( sk23 @ A @ sk3 ) @ A )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ A @ sk3 ) @ ( sk25 @ A @ sk3 ) ) @ ( singleton @ ( sk24 @ A @ sk3 ) ) ) @ sk3 ) ),
inference(simp,[status(thm)],[1843]) ).
thf(9,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(86,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(22,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(125,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(126,plain,
~ ? [A: $i,B: $i] :
( ( in @ A @ B )
& ( empty @ B ) ),
inference(miniscope,[status(thm)],[125]) ).
thf(127,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( empty @ B ) ),
inference(cnf,[status(esa)],[126]) ).
thf(3835,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( ( empty @ empty_set )
!= ( empty @ B ) ) ),
inference(paramod_ordered,[status(thm)],[86,127]) ).
thf(3836,plain,
! [A: $i] :
~ ( in @ A @ empty_set ),
inference(pattern_uni,[status(thm)],[3835:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).
thf(3873,plain,
! [B: $i,A: $i] :
( ( A
= ( relation_dom @ sk3 ) )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ A @ sk3 ) @ ( sk25 @ A @ sk3 ) ) @ ( singleton @ ( sk24 @ A @ sk3 ) ) ) @ sk3 )
| ( ( in @ ( sk23 @ A @ sk3 ) @ A )
!= ( in @ B @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[2078,3836]) ).
thf(3874,plain,
( ( ( relation_dom @ sk3 )
= empty_set )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[3873:[bind(A,$thf( empty_set )),bind(B,$thf( sk23 @ empty_set @ sk3 ))]]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(128,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( element @ A @ B ) ),
inference(cnf,[status(esa)],[128]) ).
thf(4322,plain,
! [B: $i,A: $i] :
( ( ( relation_dom @ sk3 )
= empty_set )
| ( element @ A @ B )
| ( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) ) @ sk3 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3874,129]) ).
thf(4323,plain,
( ( ( relation_dom @ sk3 )
= empty_set )
| ( element @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[4322:[bind(A,$thf( unordered_pair @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) )),bind(B,$thf( sk3 ))]]) ).
thf(31,axiom,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
thf(189,plain,
! [A: $i] :
( ( ~ ( empty @ A )
& ( relation @ A ) )
=> ~ ( empty @ ( relation_dom @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(190,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( relation @ A )
| ~ ( empty @ ( relation_dom @ A ) ) ),
inference(cnf,[status(esa)],[189]) ).
thf(19574,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( relation_dom @ A ) )
| ( ( relation @ sk3 )
!= ( relation @ A ) ) ),
inference(paramod_ordered,[status(thm)],[54,190]) ).
thf(19575,plain,
( ( empty @ sk3 )
| ~ ( empty @ ( relation_dom @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[19574:[bind(A,$thf( sk3 ))]]) ).
thf(19745,plain,
( ( empty @ sk3 )
| ( ( empty @ ( relation_dom @ sk3 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,19575]) ).
thf(19770,plain,
( ( empty @ sk3 )
| ( ( relation_dom @ sk3 )
!= empty_set ) ),
inference(simp,[status(thm)],[19745]) ).
thf(19935,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) ) @ sk3 )
| ( empty @ sk3 )
| ( ( relation_dom @ sk3 )
!= ( relation_dom @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[4323,19770]) ).
thf(19936,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) ) @ sk3 )
| ( empty @ sk3 ) ),
inference(pattern_uni,[status(thm)],[19935:[]]) ).
thf(4046,plain,
! [A: $i] :
( ( ( relation_dom @ sk3 )
= empty_set )
| ( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) ) @ sk3 )
!= ( in @ A @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[3874,3836]) ).
thf(4230,plain,
! [A: $i] :
( ( ( relation_dom @ sk3 )
= empty_set )
| ( ( unordered_pair @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) )
!= A )
| ( sk3 != empty_set ) ),
inference(simp,[status(thm)],[4046]) ).
thf(4250,plain,
( ( ( relation_dom @ sk3 )
= empty_set )
| ( sk3 != empty_set ) ),
inference(simp,[status(thm)],[4230]) ).
thf(20024,plain,
( ( sk3 != empty_set )
| ( empty @ sk3 )
| ( ( relation_dom @ sk3 )
!= ( relation_dom @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[4250,19770]) ).
thf(20025,plain,
( ( sk3 != empty_set )
| ( empty @ sk3 ) ),
inference(pattern_uni,[status(thm)],[20024:[]]) ).
thf(34,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(209,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(211,plain,
~ ( empty @ sk27 ),
inference(cnf,[status(esa)],[209]) ).
thf(20081,plain,
( ( sk3 != empty_set )
| ( ( empty @ sk27 )
!= ( empty @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[20025,211]) ).
thf(20162,plain,
( ( sk3 != empty_set )
| ( sk27 != sk3 ) ),
inference(simp,[status(thm)],[20081]) ).
thf(43,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(233,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(235,plain,
relation @ sk29,
inference(cnf,[status(esa)],[233]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
thf(219,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(220,plain,
! [B: $i,A: $i] :
( ~ ( relation @ B )
| ( relation @ ( relation_rng_restriction @ A @ B ) ) ),
inference(cnf,[status(esa)],[219]) ).
thf(25959,plain,
! [B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ A @ B ) )
| ( ( relation @ sk29 )
!= ( relation @ B ) ) ),
inference(paramod_ordered,[status(thm)],[235,220]) ).
thf(25960,plain,
! [A: $i] : ( relation @ ( relation_rng_restriction @ A @ sk29 ) ),
inference(pattern_uni,[status(thm)],[25959:[bind(A,$thf( A )),bind(B,$thf( sk29 ))]]) ).
thf(48,plain,
relation @ sk2,
inference(cnf,[status(esa)],[45]) ).
thf(19583,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( relation_dom @ A ) )
| ( ( relation @ sk2 )
!= ( relation @ A ) ) ),
inference(paramod_ordered,[status(thm)],[48,190]) ).
thf(19584,plain,
( ( empty @ sk2 )
| ~ ( empty @ ( relation_dom @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[19583:[bind(A,$thf( sk2 ))]]) ).
thf(19818,plain,
( ( empty @ sk2 )
| ( ( empty @ ( relation_dom @ sk2 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,19584]) ).
thf(19841,plain,
( ( empty @ sk2 )
| ( ( relation_dom @ sk2 )
!= empty_set ) ),
inference(simp,[status(thm)],[19818]) ).
thf(8,axiom,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(83,plain,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(84,plain,
~ ? [A: $i] : ( empty @ ( singleton @ A ) ),
inference(miniscope,[status(thm)],[83]) ).
thf(85,plain,
! [A: $i] :
~ ( empty @ ( singleton @ A ) ),
inference(cnf,[status(esa)],[84]) ).
thf(358,plain,
! [A: $i] :
( ( empty @ ( singleton @ A ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[86,85]) ).
thf(365,plain,
! [A: $i] :
( ( singleton @ A )
!= empty_set ),
inference(simp,[status(thm)],[358]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(137,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ~ ( element @ A @ B )
| ( empty @ B )
| ( in @ A @ B ) ),
inference(cnf,[status(esa)],[137]) ).
thf(2870,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ B @ A )
!= empty_set )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ ( unordered_pair @ C @ D ) @ ( singleton @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[71,2845]) ).
thf(2871,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ B @ A ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[2870:[bind(A,$thf( unordered_pair @ G @ F )),bind(B,$thf( singleton @ G )),bind(C,$thf( G )),bind(D,$thf( F ))]]) ).
thf(2889,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ B @ A ) )
!= empty_set ),
inference(simp,[status(thm)],[2871]) ).
thf(14,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(101,plain,
! [A: $i,B: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(107,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(109,plain,
! [A: $i] : ( element @ ( sk13 @ A ) @ ( powerset @ A ) ),
inference(cnf,[status(esa)],[107]) ).
thf(108,plain,
! [A: $i] : ( empty @ ( sk13 @ A ) ),
inference(cnf,[status(esa)],[107]) ).
thf(2463,plain,
! [B: $i,A: $i] :
( ( B = empty_set )
| ( ( empty @ ( sk13 @ A ) )
!= ( empty @ B ) ) ),
inference(paramod_ordered,[status(thm)],[108,106]) ).
thf(2464,plain,
! [A: $i] :
( ( sk13 @ A )
= empty_set ),
inference(pattern_uni,[status(thm)],[2463:[bind(A,$thf( C )),bind(B,$thf( sk13 @ C ))]]) ).
thf(2650,plain,
! [A: $i] :
( ( sk13 @ A )
= empty_set ),
inference(simp,[status(thm)],[2464]) ).
thf(2752,plain,
! [A: $i] : ( element @ empty_set @ ( powerset @ A ) ),
inference(rewrite,[status(thm)],[109,2650]) ).
thf(4758,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)],[2752,138]) ).
thf(4759,plain,
! [A: $i] :
( ( empty @ ( powerset @ A ) )
| ( in @ empty_set @ ( powerset @ A ) ) ),
inference(pattern_uni,[status(thm)],[4758:[bind(A,$thf( D )),bind(B,$thf( empty_set )),bind(C,$thf( powerset @ D ))]]) ).
thf(4764,plain,
! [A: $i] :
( ( empty @ ( powerset @ A ) )
| ( in @ empty_set @ ( powerset @ A ) ) ),
inference(simp,[status(thm)],[4759]) ).
thf(13,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(98,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(99,plain,
~ ? [A: $i] : ( empty @ ( powerset @ A ) ),
inference(miniscope,[status(thm)],[98]) ).
thf(100,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(cnf,[status(esa)],[99]) ).
thf(4823,plain,
! [A: $i] :
( $false
| ( in @ empty_set @ ( powerset @ A ) ) ),
inference(rewrite,[status(thm)],[4764,100]) ).
thf(4824,plain,
! [A: $i] : ( in @ empty_set @ ( powerset @ A ) ),
inference(simp,[status(thm)],[4823]) ).
thf(57,plain,
( sk5
| ( in @ sk9 @ ( relation_dom @ sk2 ) )
| ~ sk4 ),
inference(cnf,[status(esa)],[45]) ).
thf(3829,plain,
! [B: $i,A: $i] :
( sk5
| ~ sk4
| ~ ( empty @ B )
| ( ( in @ sk9 @ ( relation_dom @ sk2 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[57,127]) ).
thf(3830,plain,
( sk5
| ~ sk4
| ~ ( empty @ ( relation_dom @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[3829:[bind(A,$thf( sk9 )),bind(B,$thf( relation_dom @ sk2 ))]]) ).
thf(4171,plain,
! [B: $i,A: $i] :
( ( ( relation_dom @ sk3 )
= empty_set )
| ~ ( empty @ B )
| ( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) ) @ sk3 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3874,127]) ).
thf(4172,plain,
( ( ( relation_dom @ sk3 )
= empty_set )
| ~ ( empty @ sk3 ) ),
inference(pattern_uni,[status(thm)],[4171:[bind(A,$thf( unordered_pair @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) )),bind(B,$thf( sk3 ))]]) ).
thf(60,plain,
( sk5
| ( ( apply @ sk2 @ sk9 )
!= ( apply @ sk3 @ sk9 ) )
| ~ sk4 ),
inference(cnf,[status(esa)],[45]) ).
thf(63,plain,
( ( ( apply @ sk3 @ sk9 )
!= ( apply @ sk2 @ sk9 ) )
| sk5
| ~ sk4 ),
inference(lifteq,[status(thm)],[60]) ).
thf(319,plain,
( sk5
| ( sk3 != sk2 )
| ( sk9 != sk9 )
| ~ sk4 ),
inference(simp,[status(thm)],[63]) ).
thf(320,plain,
( sk5
| ( sk3 != sk2 )
| ~ sk4 ),
inference(simp,[status(thm)],[319]) ).
thf(58,plain,
( sk6
| ( in @ sk8 @ ( relation_dom @ sk3 ) )
| ~ sk5
| ~ sk4 ),
inference(cnf,[status(esa)],[45]) ).
thf(47,plain,
( sk6
| ~ ( in @ sk8 @ ( relation_dom @ sk2 ) )
| ~ sk5
| ~ sk4 ),
inference(cnf,[status(esa)],[45]) ).
thf(269,plain,
( sk6
| ~ sk5
| ~ sk4
| ( ( in @ sk8 @ ( relation_dom @ sk3 ) )
!= ( in @ sk8 @ ( relation_dom @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[58,47]) ).
thf(270,plain,
( sk6
| ~ sk5
| ~ sk4
| ( sk8 != sk8 )
| ( ( relation_dom @ sk3 )
!= ( relation_dom @ sk2 ) ) ),
inference(simp,[status(thm)],[269]) ).
thf(271,plain,
( sk6
| ~ sk5
| ~ sk4
| ( ( relation_dom @ sk3 )
!= ( relation_dom @ sk2 ) ) ),
inference(simp,[status(thm)],[270]) ).
thf(272,plain,
( sk6
| ~ sk5
| ~ sk4
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[271]) ).
thf(55,plain,
( ( in @ sk7 @ ( relation_dom @ sk2 ) )
| ~ sk6
| ~ sk5
| ~ sk4 ),
inference(cnf,[status(esa)],[45]) ).
thf(285,plain,
( ~ sk5
| ~ sk4
| ( sk3 != sk2 )
| ( in @ sk7 @ ( relation_dom @ sk2 ) )
| ( sk6 != sk6 ) ),
inference(paramod_ordered,[status(thm)],[272,55]) ).
thf(286,plain,
( ~ sk5
| ~ sk4
| ( sk3 != sk2 )
| ( in @ sk7 @ ( relation_dom @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[285:[]]) ).
thf(382,plain,
( ( sk3 != sk2 )
| ~ sk4
| ( in @ sk7 @ ( relation_dom @ sk2 ) )
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[320,286]) ).
thf(383,plain,
( ( sk3 != sk2 )
| ~ sk4
| ( in @ sk7 @ ( relation_dom @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[382:[]]) ).
thf(3878,plain,
! [A: $i] :
( ( sk3 != sk2 )
| ~ sk4
| ( ( in @ sk7 @ ( relation_dom @ sk2 ) )
!= ( in @ A @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[383,3836]) ).
thf(3880,plain,
! [A: $i] :
( ( sk3 != sk2 )
| ~ sk4
| ( sk7 != A )
| ( ( relation_dom @ sk2 )
!= empty_set ) ),
inference(simp,[status(thm)],[3878]) ).
thf(3890,plain,
( ( sk3 != sk2 )
| ~ sk4
| ( ( relation_dom @ sk2 )
!= empty_set ) ),
inference(simp,[status(thm)],[3880]) ).
thf(6394,plain,
( ~ ( empty @ sk3 )
| ( sk3 != sk2 )
| ~ sk4
| ( ( relation_dom @ sk3 )
!= ( relation_dom @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[4172,3890]) ).
thf(6421,plain,
( ~ ( empty @ sk3 )
| ( sk3 != sk2 )
| ~ sk4
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[6394]) ).
thf(6431,plain,
( ~ ( empty @ sk3 )
| ( sk3 != sk2 )
| ~ sk4 ),
inference(simp,[status(thm)],[6421]) ).
thf(36,axiom,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
thf(214,plain,
? [A: $i] :
( ( relation @ A )
& ( relation_empty_yielding @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(216,plain,
relation @ sk28,
inference(cnf,[status(esa)],[214]) ).
thf(19542,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( relation_dom @ A ) )
| ( ( relation @ sk28 )
!= ( relation @ A ) ) ),
inference(paramod_ordered,[status(thm)],[216,190]) ).
thf(19543,plain,
( ( empty @ sk28 )
| ~ ( empty @ ( relation_dom @ sk28 ) ) ),
inference(pattern_uni,[status(thm)],[19542:[bind(A,$thf( sk28 ))]]) ).
thf(234,plain,
function @ sk29,
inference(cnf,[status(esa)],[233]) ).
thf(19,axiom,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(115,plain,
! [A: $i] :
( ( ( relation @ A )
& ( empty @ A )
& ( function @ A ) )
=> ( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(217,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(25,axiom,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(133,plain,
? [A: $i] :
( ( relation @ A )
& ( function @ A )
& ( one_to_one @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(136,plain,
relation @ sk16,
inference(cnf,[status(esa)],[133]) ).
thf(25967,plain,
! [B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ A @ B ) )
| ( ( relation @ sk16 )
!= ( relation @ B ) ) ),
inference(paramod_ordered,[status(thm)],[136,220]) ).
thf(25968,plain,
! [A: $i] : ( relation @ ( relation_rng_restriction @ A @ sk16 ) ),
inference(pattern_uni,[status(thm)],[25967:[bind(A,$thf( A )),bind(B,$thf( sk16 ))]]) ).
thf(28567,plain,
! [C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ B @ C ) )
| ( ( relation @ ( relation_rng_restriction @ A @ sk16 ) )
!= ( relation @ C ) ) ),
inference(paramod_ordered,[status(thm)],[25968,220]) ).
thf(28568,plain,
! [B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[28567:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( relation_rng_restriction @ D @ sk16 ))]]) ).
thf(28678,plain,
! [B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ sk16 ) ) ),
inference(simp,[status(thm)],[28568]) ).
thf(31305,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ C @ D ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ sk16 ) ) )
!= ( relation @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28678,220]) ).
thf(31306,plain,
! [C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ sk16 ) ) ) ),
inference(pattern_uni,[status(thm)],[31305:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( relation_rng_restriction @ E @ ( relation_rng_restriction @ G @ sk16 ) ))]]) ).
thf(31474,plain,
! [C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ sk16 ) ) ) ),
inference(simp,[status(thm)],[31306]) ).
thf(33643,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ D @ E ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ sk16 ) ) ) )
!= ( relation @ E ) ) ),
inference(paramod_ordered,[status(thm)],[31474,220]) ).
thf(33644,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ sk16 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[33643:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( J )),bind(D,$thf( D )),bind(E,$thf( relation_rng_restriction @ F @ ( relation_rng_restriction @ H @ ( relation_rng_restriction @ J @ sk16 ) ) ))]]) ).
thf(33870,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ sk16 ) ) ) ) ),
inference(simp,[status(thm)],[33644]) ).
thf(20,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(119,plain,
( ( empty @ empty_set )
& ( relation @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(120,plain,
relation @ empty_set,
inference(cnf,[status(esa)],[119]) ).
thf(39,axiom,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
thf(221,plain,
! [A: $i] :
( ( empty @ A )
=> ( ( empty @ ( relation_dom @ A ) )
& ( relation @ ( relation_dom @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(222,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( empty @ ( relation_dom @ A ) ) ),
inference(cnf,[status(esa)],[221]) ).
thf(27107,plain,
! [A: $i] :
( ( empty @ ( relation_dom @ A ) )
| ( ( empty @ empty_set )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[86,222]) ).
thf(27108,plain,
empty @ ( relation_dom @ empty_set ),
inference(pattern_uni,[status(thm)],[27107:[bind(A,$thf( empty_set ))]]) ).
thf(27229,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ ( relation_dom @ empty_set ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27108,106]) ).
thf(27230,plain,
( ( relation_dom @ empty_set )
= empty_set ),
inference(pattern_uni,[status(thm)],[27229:[bind(A,$thf( relation_dom @ empty_set ))]]) ).
thf(19599,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( relation_dom @ A ) )
| ( ( relation @ sk29 )
!= ( relation @ A ) ) ),
inference(paramod_ordered,[status(thm)],[235,190]) ).
thf(19600,plain,
( ( empty @ sk29 )
| ~ ( empty @ ( relation_dom @ sk29 ) ) ),
inference(pattern_uni,[status(thm)],[19599:[bind(A,$thf( sk29 ))]]) ).
thf(21354,plain,
( ( empty @ sk29 )
| ( ( empty @ ( relation_dom @ sk29 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,19600]) ).
thf(21376,plain,
( ( empty @ sk29 )
| ( ( relation_dom @ sk29 )
!= empty_set ) ),
inference(simp,[status(thm)],[21354]) ).
thf(7,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(80,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(81,plain,
~ ! [A: $i] : ( empty @ A ),
inference(miniscope,[status(thm)],[80]) ).
thf(82,plain,
~ ( empty @ sk11 ),
inference(cnf,[status(esa)],[81]) ).
thf(23574,plain,
( ( ( relation_dom @ sk29 )
!= empty_set )
| ( ( empty @ sk29 )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[21376,82]) ).
thf(23604,plain,
( ( ( relation_dom @ sk29 )
!= empty_set )
| ( sk29 != sk11 ) ),
inference(simp,[status(thm)],[23574]) ).
thf(27431,plain,
( ( sk29 != sk11 )
| ( ( relation_dom @ sk29 )
!= ( relation_dom @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[27230,23604]) ).
thf(27579,plain,
( ( sk29 != sk11 )
| ( sk29 != empty_set ) ),
inference(simp,[status(thm)],[27431]) ).
thf(28717,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk29 != sk11 )
| ( A != sk29 ) ),
inference(paramod_ordered,[status(thm)],[106,27579]) ).
thf(28718,plain,
( ~ ( empty @ sk29 )
| ( sk29 != sk11 ) ),
inference(pattern_uni,[status(thm)],[28717:[bind(A,$thf( sk29 ))]]) ).
thf(56,plain,
! [A: $i] :
( sk4
| ~ ( in @ A @ ( relation_dom @ sk2 ) )
| ( in @ ( apply @ sk3 @ A ) @ sk1 ) ),
inference(cnf,[status(esa)],[45]) ).
thf(19924,plain,
! [A: $i] :
( ( ( relation_dom @ sk3 )
!= empty_set )
| ( A = empty_set )
| ( ( empty @ sk3 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19770,106]) ).
thf(19925,plain,
( ( ( relation_dom @ sk3 )
!= empty_set )
| ( sk3 = empty_set ) ),
inference(pattern_uni,[status(thm)],[19924:[bind(A,$thf( sk3 ))]]) ).
thf(22075,plain,
( ~ ( empty @ sk3 )
| ( sk3 = empty_set )
| ( ( relation_dom @ sk3 )
!= ( relation_dom @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[4172,19925]) ).
thf(22076,plain,
( ~ ( empty @ sk3 )
| ( sk3 = empty_set ) ),
inference(pattern_uni,[status(thm)],[22075:[]]) ).
thf(3876,plain,
! [A: $i] :
( ~ sk6
| ~ sk5
| ~ sk4
| ( ( in @ sk7 @ ( relation_dom @ sk2 ) )
!= ( in @ A @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[55,3836]) ).
thf(3885,plain,
! [A: $i] :
( ~ sk6
| ~ sk5
| ~ sk4
| ( sk7 != A )
| ( ( relation_dom @ sk2 )
!= empty_set ) ),
inference(simp,[status(thm)],[3876]) ).
thf(3895,plain,
( ~ sk6
| ~ sk5
| ~ sk4
| ( ( relation_dom @ sk2 )
!= empty_set ) ),
inference(simp,[status(thm)],[3885]) ).
thf(19666,plain,
( ( empty @ sk28 )
| ( ( empty @ ( relation_dom @ sk28 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,19543]) ).
thf(19688,plain,
( ( empty @ sk28 )
| ( ( relation_dom @ sk28 )
!= empty_set ) ),
inference(simp,[status(thm)],[19666]) ).
thf(22693,plain,
( ( ( relation_dom @ sk28 )
!= empty_set )
| ( ( empty @ sk28 )
!= ( empty @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[19688,82]) ).
thf(22704,plain,
( ( ( relation_dom @ sk28 )
!= empty_set )
| ( sk28 != sk11 ) ),
inference(simp,[status(thm)],[22693]) ).
thf(61,plain,
( sk6
| ( in @ ( apply @ sk3 @ sk8 ) @ sk1 )
| ~ sk5
| ~ sk4 ),
inference(cnf,[status(esa)],[45]) ).
thf(3854,plain,
! [A: $i] :
( sk6
| ~ sk5
| ~ sk4
| ( ( in @ ( apply @ sk3 @ sk8 ) @ sk1 )
!= ( in @ A @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[61,3836]) ).
thf(3888,plain,
! [A: $i] :
( sk6
| ~ sk5
| ~ sk4
| ( ( apply @ sk3 @ sk8 )
!= A )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[3854]) ).
thf(3898,plain,
( sk6
| ~ sk5
| ~ sk4
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[3888]) ).
thf(17,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(110,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(111,plain,
! [A: $i] : ( element @ ( sk14 @ A ) @ A ),
inference(cnf,[status(esa)],[110]) ).
thf(4760,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ C )
| ( in @ B @ C )
| ( ( element @ ( sk14 @ A ) @ A )
!= ( element @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[111,138]) ).
thf(4761,plain,
! [A: $i] :
( ( empty @ A )
| ( in @ ( sk14 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[4760:[bind(A,$thf( D )),bind(B,$thf( sk14 @ D )),bind(C,$thf( D ))]]) ).
thf(4765,plain,
! [A: $i] :
( ( empty @ A )
| ( in @ ( sk14 @ A ) @ A ) ),
inference(simp,[status(thm)],[4761]) ).
thf(9012,plain,
! [B: $i,A: $i] :
( ( empty @ A )
| sk4
| ( in @ ( apply @ sk3 @ B ) @ sk1 )
| ( ( in @ ( sk14 @ A ) @ A )
!= ( in @ B @ ( relation_dom @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[4765,56]) ).
thf(9013,plain,
( ( empty @ ( relation_dom @ sk2 ) )
| sk4
| ( in @ ( apply @ sk3 @ ( sk14 @ ( relation_dom @ sk2 ) ) ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[9012:[bind(A,$thf( relation_dom @ sk2 )),bind(B,$thf( sk14 @ ( relation_dom @ sk2 ) ))]]) ).
thf(26887,plain,
! [C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ B @ C ) )
| ( ( relation @ ( relation_rng_restriction @ A @ sk29 ) )
!= ( relation @ C ) ) ),
inference(paramod_ordered,[status(thm)],[25960,220]) ).
thf(26888,plain,
! [B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ sk29 ) ) ),
inference(pattern_uni,[status(thm)],[26887:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( relation_rng_restriction @ D @ sk29 ))]]) ).
thf(26986,plain,
! [B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ sk29 ) ) ),
inference(simp,[status(thm)],[26888]) ).
thf(30489,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ C @ D ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ sk29 ) ) )
!= ( relation @ D ) ) ),
inference(paramod_ordered,[status(thm)],[26986,220]) ).
thf(30490,plain,
! [C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ sk29 ) ) ) ),
inference(pattern_uni,[status(thm)],[30489:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( relation_rng_restriction @ E @ ( relation_rng_restriction @ G @ sk29 ) ))]]) ).
thf(30636,plain,
! [C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ sk29 ) ) ) ),
inference(simp,[status(thm)],[30490]) ).
thf(33073,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ D @ E ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ sk29 ) ) ) )
!= ( relation @ E ) ) ),
inference(paramod_ordered,[status(thm)],[30636,220]) ).
thf(33074,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ sk29 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[33073:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( J )),bind(D,$thf( D )),bind(E,$thf( relation_rng_restriction @ F @ ( relation_rng_restriction @ H @ ( relation_rng_restriction @ J @ sk29 ) ) ))]]) ).
thf(33269,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ sk29 ) ) ) ) ),
inference(simp,[status(thm)],[33074]) ).
thf(35858,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ E @ F ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ sk29 ) ) ) ) )
!= ( relation @ F ) ) ),
inference(paramod_ordered,[status(thm)],[33269,220]) ).
thf(35859,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ sk29 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[35858:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( M )),bind(E,$thf( E )),bind(F,$thf( relation_rng_restriction @ G @ ( relation_rng_restriction @ I @ ( relation_rng_restriction @ K @ ( relation_rng_restriction @ M @ sk29 ) ) ) ))]]) ).
thf(36055,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ sk29 ) ) ) ) ) ),
inference(simp,[status(thm)],[35859]) ).
thf(20788,plain,
( ( ( relation_dom @ sk2 )
!= empty_set )
| ( ( empty @ sk11 )
!= ( empty @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[19841,82]) ).
thf(20803,plain,
( ( ( relation_dom @ sk2 )
!= empty_set )
| ( sk11 != sk2 ) ),
inference(simp,[status(thm)],[20788]) ).
thf(39340,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ F @ G ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ sk29 ) ) ) ) ) )
!= ( relation @ G ) ) ),
inference(paramod_ordered,[status(thm)],[36055,220]) ).
thf(39341,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ sk29 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[39340:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( L )),bind(D,$thf( N )),bind(E,$thf( P )),bind(F,$thf( F )),bind(G,$thf( relation_rng_restriction @ H @ ( relation_rng_restriction @ J @ ( relation_rng_restriction @ L @ ( relation_rng_restriction @ N @ ( relation_rng_restriction @ P @ sk29 ) ) ) ) ))]]) ).
thf(39650,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ sk29 ) ) ) ) ) ) ),
inference(simp,[status(thm)],[39341]) ).
thf(44405,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ G @ H ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ sk29 ) ) ) ) ) ) )
!= ( relation @ H ) ) ),
inference(paramod_ordered,[status(thm)],[39650,220]) ).
thf(44406,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ sk29 ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[44405:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( O )),bind(E,$thf( Q )),bind(F,$thf( S )),bind(G,$thf( G )),bind(H,$thf( relation_rng_restriction @ I @ ( relation_rng_restriction @ K @ ( relation_rng_restriction @ M @ ( relation_rng_restriction @ O @ ( relation_rng_restriction @ Q @ ( relation_rng_restriction @ S @ sk29 ) ) ) ) ) ))]]) ).
thf(44743,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ sk29 ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[44406]) ).
thf(49363,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ H @ I ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ sk29 ) ) ) ) ) ) ) )
!= ( relation @ I ) ) ),
inference(paramod_ordered,[status(thm)],[44743,220]) ).
thf(49364,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ ( relation_rng_restriction @ H @ sk29 ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[49363:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( P )),bind(E,$thf( R )),bind(F,$thf( T )),bind(G,$thf( V )),bind(H,$thf( H )),bind(I,$thf( relation_rng_restriction @ J @ ( relation_rng_restriction @ L @ ( relation_rng_restriction @ N @ ( relation_rng_restriction @ P @ ( relation_rng_restriction @ R @ ( relation_rng_restriction @ T @ ( relation_rng_restriction @ V @ sk29 ) ) ) ) ) ) ))]]) ).
thf(49777,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ ( relation_rng_restriction @ H @ sk29 ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[49364]) ).
thf(49,plain,
( ~ ( in @ sk7 @ ( relation_dom @ sk3 ) )
| ~ ( in @ ( apply @ sk3 @ sk7 ) @ sk1 )
| ~ sk6
| ~ sk5
| ~ sk4 ),
inference(cnf,[status(esa)],[45]) ).
thf(287,plain,
( ~ sk5
| ~ sk4
| ( sk3 != sk2 )
| ~ ( in @ sk7 @ ( relation_dom @ sk3 ) )
| ~ ( in @ ( apply @ sk3 @ sk7 ) @ sk1 )
| ( sk6 != sk6 ) ),
inference(paramod_ordered,[status(thm)],[272,49]) ).
thf(288,plain,
( ~ sk5
| ~ sk4
| ( sk3 != sk2 )
| ~ ( in @ sk7 @ ( relation_dom @ sk3 ) )
| ~ ( in @ ( apply @ sk3 @ sk7 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[287:[]]) ).
thf(52,plain,
function @ sk2,
inference(cnf,[status(esa)],[45]) ).
thf(210,plain,
relation @ sk27,
inference(cnf,[status(esa)],[209]) ).
thf(25965,plain,
! [B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ A @ B ) )
| ( ( relation @ sk27 )
!= ( relation @ B ) ) ),
inference(paramod_ordered,[status(thm)],[210,220]) ).
thf(25966,plain,
! [A: $i] : ( relation @ ( relation_rng_restriction @ A @ sk27 ) ),
inference(pattern_uni,[status(thm)],[25965:[bind(A,$thf( A )),bind(B,$thf( sk27 ))]]) ).
thf(28367,plain,
! [C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ B @ C ) )
| ( ( relation @ ( relation_rng_restriction @ A @ sk27 ) )
!= ( relation @ C ) ) ),
inference(paramod_ordered,[status(thm)],[25966,220]) ).
thf(28368,plain,
! [B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ sk27 ) ) ),
inference(pattern_uni,[status(thm)],[28367:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( relation_rng_restriction @ D @ sk27 ))]]) ).
thf(28473,plain,
! [B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ sk27 ) ) ),
inference(simp,[status(thm)],[28368]) ).
thf(30752,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ C @ D ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ sk27 ) ) )
!= ( relation @ D ) ) ),
inference(paramod_ordered,[status(thm)],[28473,220]) ).
thf(30753,plain,
! [C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ sk27 ) ) ) ),
inference(pattern_uni,[status(thm)],[30752:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( relation_rng_restriction @ E @ ( relation_rng_restriction @ G @ sk27 ) ))]]) ).
thf(30905,plain,
! [C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ sk27 ) ) ) ),
inference(simp,[status(thm)],[30753]) ).
thf(33358,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ D @ E ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ sk27 ) ) ) )
!= ( relation @ E ) ) ),
inference(paramod_ordered,[status(thm)],[30905,220]) ).
thf(33359,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ sk27 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[33358:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( J )),bind(D,$thf( D )),bind(E,$thf( relation_rng_restriction @ F @ ( relation_rng_restriction @ H @ ( relation_rng_restriction @ J @ sk27 ) ) ))]]) ).
thf(33566,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ sk27 ) ) ) ) ),
inference(simp,[status(thm)],[33359]) ).
thf(36203,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ E @ F ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ sk27 ) ) ) ) )
!= ( relation @ F ) ) ),
inference(paramod_ordered,[status(thm)],[33566,220]) ).
thf(36204,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ sk27 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[36203:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( M )),bind(E,$thf( E )),bind(F,$thf( relation_rng_restriction @ G @ ( relation_rng_restriction @ I @ ( relation_rng_restriction @ K @ ( relation_rng_restriction @ M @ sk27 ) ) ) ))]]) ).
thf(36434,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ sk27 ) ) ) ) ) ),
inference(simp,[status(thm)],[36204]) ).
thf(41022,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ F @ G ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ sk27 ) ) ) ) ) )
!= ( relation @ G ) ) ),
inference(paramod_ordered,[status(thm)],[36434,220]) ).
thf(41023,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ sk27 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[41022:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( L )),bind(D,$thf( N )),bind(E,$thf( P )),bind(F,$thf( F )),bind(G,$thf( relation_rng_restriction @ H @ ( relation_rng_restriction @ J @ ( relation_rng_restriction @ L @ ( relation_rng_restriction @ N @ ( relation_rng_restriction @ P @ sk27 ) ) ) ) ))]]) ).
thf(41285,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ sk27 ) ) ) ) ) ) ),
inference(simp,[status(thm)],[41023]) ).
thf(44870,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ G @ H ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ sk27 ) ) ) ) ) ) )
!= ( relation @ H ) ) ),
inference(paramod_ordered,[status(thm)],[41285,220]) ).
thf(44871,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ sk27 ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[44870:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( O )),bind(E,$thf( Q )),bind(F,$thf( S )),bind(G,$thf( G )),bind(H,$thf( relation_rng_restriction @ I @ ( relation_rng_restriction @ K @ ( relation_rng_restriction @ M @ ( relation_rng_restriction @ O @ ( relation_rng_restriction @ Q @ ( relation_rng_restriction @ S @ sk27 ) ) ) ) ) ))]]) ).
thf(45187,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ sk27 ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[44871]) ).
thf(19603,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( relation_dom @ A ) )
| ( ( relation @ sk16 )
!= ( relation @ A ) ) ),
inference(paramod_ordered,[status(thm)],[136,190]) ).
thf(19604,plain,
( ( empty @ sk16 )
| ~ ( empty @ ( relation_dom @ sk16 ) ) ),
inference(pattern_uni,[status(thm)],[19603:[bind(A,$thf( sk16 ))]]) ).
thf(22543,plain,
( ( empty @ sk16 )
| ( ( empty @ ( relation_dom @ sk16 ) )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,19604]) ).
thf(22569,plain,
( ( empty @ sk16 )
| ( ( relation_dom @ sk16 )
!= empty_set ) ),
inference(simp,[status(thm)],[22543]) ).
thf(23478,plain,
( ( ( relation_dom @ sk29 )
!= empty_set )
| ( ( empty @ sk29 )
!= ( empty @ sk27 ) ) ),
inference(paramod_ordered,[status(thm)],[21376,211]) ).
thf(23587,plain,
( ( ( relation_dom @ sk29 )
!= empty_set )
| ( sk29 != sk27 ) ),
inference(simp,[status(thm)],[23478]) ).
thf(49888,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ H @ I ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ sk27 ) ) ) ) ) ) ) )
!= ( relation @ I ) ) ),
inference(paramod_ordered,[status(thm)],[45187,220]) ).
thf(49889,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ ( relation_rng_restriction @ H @ sk27 ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[49888:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( P )),bind(E,$thf( R )),bind(F,$thf( T )),bind(G,$thf( V )),bind(H,$thf( H )),bind(I,$thf( relation_rng_restriction @ J @ ( relation_rng_restriction @ L @ ( relation_rng_restriction @ N @ ( relation_rng_restriction @ P @ ( relation_rng_restriction @ R @ ( relation_rng_restriction @ T @ ( relation_rng_restriction @ V @ sk27 ) ) ) ) ) ) ))]]) ).
thf(50309,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ ( relation_rng_restriction @ H @ sk27 ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[49889]) ).
thf(19601,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( relation_dom @ A ) )
| ( ( relation @ sk27 )
!= ( relation @ A ) ) ),
inference(paramod_ordered,[status(thm)],[210,190]) ).
thf(19602,plain,
( ( empty @ sk27 )
| ~ ( empty @ ( relation_dom @ sk27 ) ) ),
inference(pattern_uni,[status(thm)],[19601:[bind(A,$thf( sk27 ))]]) ).
thf(21395,plain,
( $false
| ~ ( empty @ ( relation_dom @ sk27 ) ) ),
inference(rewrite,[status(thm)],[19602,211]) ).
thf(21396,plain,
~ ( empty @ ( relation_dom @ sk27 ) ),
inference(simp,[status(thm)],[21395]) ).
thf(21410,plain,
( ( sk3 != empty_set )
| ( ( empty @ ( relation_dom @ sk27 ) )
!= ( empty @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[20025,21396]) ).
thf(21465,plain,
( ( sk3 != empty_set )
| ( ( relation_dom @ sk27 )
!= sk3 ) ),
inference(simp,[status(thm)],[21410]) ).
thf(23646,plain,
( ~ ( empty @ sk3 )
| ( ( relation_dom @ sk27 )
!= sk3 )
| ( sk3 != sk3 ) ),
inference(paramod_ordered,[status(thm)],[22076,21465]) ).
thf(23647,plain,
( ~ ( empty @ sk3 )
| ( ( relation_dom @ sk27 )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[23646:[]]) ).
thf(20144,plain,
( ( sk3 != empty_set )
| ( ( empty @ sk11 )
!= ( empty @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[20025,82]) ).
thf(20156,plain,
( ( sk3 != empty_set )
| ( sk11 != sk3 ) ),
inference(simp,[status(thm)],[20144]) ).
thf(20180,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk11 != sk3 )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[106,20156]) ).
thf(20181,plain,
( ~ ( empty @ sk3 )
| ( sk11 != sk3 ) ),
inference(pattern_uni,[status(thm)],[20180:[bind(A,$thf( sk3 ))]]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(92,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(93,plain,
! [A: $i] :
( ( empty @ A )
| ( element @ ( sk12 @ A ) @ ( powerset @ A ) ) ),
inference(cnf,[status(esa)],[92]) ).
thf(4156,plain,
! [B: $i,A: $i] :
( ( ( relation_dom @ sk3 )
= empty_set )
| ( in @ ( unordered_pair @ B @ A ) @ sk3 )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[71,3874]) ).
thf(4157,plain,
( ( ( relation_dom @ sk3 )
= empty_set )
| ( in @ ( unordered_pair @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[4156:[bind(A,$thf( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) )),bind(B,$thf( singleton @ ( sk24 @ empty_set @ sk3 ) ))]]) ).
thf(4590,plain,
! [B: $i,A: $i] :
( ( ( relation_dom @ sk3 )
= empty_set )
| ( element @ A @ B )
| ( ( in @ ( unordered_pair @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) ) @ sk3 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[4157,129]) ).
thf(4591,plain,
( ( ( relation_dom @ sk3 )
= empty_set )
| ( element @ ( unordered_pair @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[4590:[bind(A,$thf( unordered_pair @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) )),bind(B,$thf( sk3 ))]]) ).
thf(20026,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) ) @ sk3 )
| ( empty @ sk3 )
| ( ( relation_dom @ sk3 )
!= ( relation_dom @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[4591,19770]) ).
thf(20027,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) ) @ sk3 )
| ( empty @ sk3 ) ),
inference(pattern_uni,[status(thm)],[20026:[]]) ).
thf(4367,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)],[71,2889]) ).
thf(4368,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ B @ A ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[4367:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_rng_restriction @ A @ B ) )
& ( function @ ( relation_rng_restriction @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
thf(226,plain,
! [A: $i,B: $i] :
( ( ( relation @ B )
& ( function @ B ) )
=> ( ( relation @ ( relation_rng_restriction @ A @ B ) )
& ( function @ ( relation_rng_restriction @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(228,plain,
! [B: $i,A: $i] :
( ~ ( relation @ B )
| ~ ( function @ B )
| ( function @ ( relation_rng_restriction @ A @ B ) ) ),
inference(cnf,[status(esa)],[226]) ).
thf(23281,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk11 != sk2 )
| ( A
!= ( relation_dom @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[106,20803]) ).
thf(23282,plain,
( ~ ( empty @ ( relation_dom @ sk2 ) )
| ( sk11 != sk2 ) ),
inference(pattern_uni,[status(thm)],[23281:[bind(A,$thf( relation_dom @ sk2 ))]]) ).
thf(27066,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk11 != sk2 )
| ( ( empty @ ( relation_dom @ A ) )
!= ( empty @ ( relation_dom @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[222,23282]) ).
thf(27067,plain,
( ~ ( empty @ sk2 )
| ( sk11 != sk2 ) ),
inference(pattern_uni,[status(thm)],[27066:[bind(A,$thf( sk2 ))]]) ).
thf(19923,plain,
( ( ( relation_dom @ sk3 )
!= empty_set )
| ( ( empty @ sk27 )
!= ( empty @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[19770,211]) ).
thf(20042,plain,
( ( ( relation_dom @ sk3 )
!= empty_set )
| ( sk27 != sk3 ) ),
inference(simp,[status(thm)],[19923]) ).
thf(25943,plain,
! [B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ A @ B ) )
| ( ( relation @ sk2 )
!= ( relation @ B ) ) ),
inference(paramod_ordered,[status(thm)],[48,220]) ).
thf(25944,plain,
! [A: $i] : ( relation @ ( relation_rng_restriction @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[25943:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(26531,plain,
! [C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ B @ C ) )
| ( ( relation @ ( relation_rng_restriction @ A @ sk2 ) )
!= ( relation @ C ) ) ),
inference(paramod_ordered,[status(thm)],[25944,220]) ).
thf(26532,plain,
! [B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[26531:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( relation_rng_restriction @ D @ sk2 ))]]) ).
thf(26637,plain,
! [B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ sk2 ) ) ),
inference(simp,[status(thm)],[26532]) ).
thf(30260,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ C @ D ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ sk2 ) ) )
!= ( relation @ D ) ) ),
inference(paramod_ordered,[status(thm)],[26637,220]) ).
thf(30261,plain,
! [C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[30260:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( relation_rng_restriction @ E @ ( relation_rng_restriction @ G @ sk2 ) ))]]) ).
thf(30426,plain,
! [C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ sk2 ) ) ) ),
inference(simp,[status(thm)],[30261]) ).
thf(32784,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ D @ E ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ sk2 ) ) ) )
!= ( relation @ E ) ) ),
inference(paramod_ordered,[status(thm)],[30426,220]) ).
thf(32785,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ sk2 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[32784:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( J )),bind(D,$thf( D )),bind(E,$thf( relation_rng_restriction @ F @ ( relation_rng_restriction @ H @ ( relation_rng_restriction @ J @ sk2 ) ) ))]]) ).
thf(32960,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ sk2 ) ) ) ) ),
inference(simp,[status(thm)],[32785]) ).
thf(35037,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ E @ F ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ sk2 ) ) ) ) )
!= ( relation @ F ) ) ),
inference(paramod_ordered,[status(thm)],[32960,220]) ).
thf(35038,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ sk2 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[35037:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( M )),bind(E,$thf( E )),bind(F,$thf( relation_rng_restriction @ G @ ( relation_rng_restriction @ I @ ( relation_rng_restriction @ K @ ( relation_rng_restriction @ M @ sk2 ) ) ) ))]]) ).
thf(35321,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ sk2 ) ) ) ) ) ),
inference(simp,[status(thm)],[35038]) ).
thf(7155,plain,
! [A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ sk3 )
| ( sk2 != empty_set )
| ~ sk4
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[106,6431]) ).
thf(7156,plain,
( ~ ( empty @ sk3 )
| ~ ( empty @ sk3 )
| ( sk2 != empty_set )
| ~ sk4 ),
inference(pattern_uni,[status(thm)],[7155:[bind(A,$thf( sk3 ))]]) ).
thf(7171,plain,
( ~ ( empty @ sk3 )
| ( sk2 != empty_set )
| ~ sk4 ),
inference(simp,[status(thm)],[7156]) ).
thf(7314,plain,
( ( sk2 != empty_set )
| ~ sk4
| ( ( empty @ sk3 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,7171]) ).
thf(7317,plain,
( ( sk2 != empty_set )
| ~ sk4
| ( sk3 != empty_set ) ),
inference(simp,[status(thm)],[7314]) ).
thf(36548,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ E @ F ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ sk16 ) ) ) ) )
!= ( relation @ F ) ) ),
inference(paramod_ordered,[status(thm)],[33870,220]) ).
thf(36549,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ sk16 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[36548:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( M )),bind(E,$thf( E )),bind(F,$thf( relation_rng_restriction @ G @ ( relation_rng_restriction @ I @ ( relation_rng_restriction @ K @ ( relation_rng_restriction @ M @ sk16 ) ) ) ))]]) ).
thf(36817,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ sk16 ) ) ) ) ) ),
inference(simp,[status(thm)],[36549]) ).
thf(41427,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ F @ G ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ sk16 ) ) ) ) ) )
!= ( relation @ G ) ) ),
inference(paramod_ordered,[status(thm)],[36817,220]) ).
thf(41428,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ sk16 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[41427:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( L )),bind(D,$thf( N )),bind(E,$thf( P )),bind(F,$thf( F )),bind(G,$thf( relation_rng_restriction @ H @ ( relation_rng_restriction @ J @ ( relation_rng_restriction @ L @ ( relation_rng_restriction @ N @ ( relation_rng_restriction @ P @ sk16 ) ) ) ) ))]]) ).
thf(41755,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ sk16 ) ) ) ) ) ) ),
inference(simp,[status(thm)],[41428]) ).
thf(25925,plain,
! [B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ A @ B ) )
| ( ( relation @ sk3 )
!= ( relation @ B ) ) ),
inference(paramod_ordered,[status(thm)],[54,220]) ).
thf(25926,plain,
! [A: $i] : ( relation @ ( relation_rng_restriction @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[25925:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(26368,plain,
! [C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ B @ C ) )
| ( ( relation @ ( relation_rng_restriction @ A @ sk3 ) )
!= ( relation @ C ) ) ),
inference(paramod_ordered,[status(thm)],[25926,220]) ).
thf(26369,plain,
! [B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[26368:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( relation_rng_restriction @ D @ sk3 ))]]) ).
thf(26463,plain,
! [B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ sk3 ) ) ),
inference(simp,[status(thm)],[26369]) ).
thf(30034,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ C @ D ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ sk3 ) ) )
!= ( relation @ D ) ) ),
inference(paramod_ordered,[status(thm)],[26463,220]) ).
thf(30035,plain,
! [C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[30034:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( relation_rng_restriction @ E @ ( relation_rng_restriction @ G @ sk3 ) ))]]) ).
thf(30208,plain,
! [C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ sk3 ) ) ) ),
inference(simp,[status(thm)],[30035]) ).
thf(46770,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ G @ H ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ sk16 ) ) ) ) ) ) )
!= ( relation @ H ) ) ),
inference(paramod_ordered,[status(thm)],[41755,220]) ).
thf(46771,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ sk16 ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[46770:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( O )),bind(E,$thf( Q )),bind(F,$thf( S )),bind(G,$thf( G )),bind(H,$thf( relation_rng_restriction @ I @ ( relation_rng_restriction @ K @ ( relation_rng_restriction @ M @ ( relation_rng_restriction @ O @ ( relation_rng_restriction @ Q @ ( relation_rng_restriction @ S @ sk16 ) ) ) ) ) ))]]) ).
thf(47134,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ sk16 ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[46771]) ).
thf(292,plain,
( sk6
| ~ sk5
| ~ sk4
| ( ( in @ ( apply @ sk3 @ sk8 ) @ sk1 )
!= ( in @ sk8 @ ( relation_dom @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[61,47]) ).
thf(293,plain,
( sk6
| ~ sk5
| ~ sk4
| ( ( apply @ sk3 @ sk8 )
!= sk8 )
| ( ( relation_dom @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[292]) ).
thf(38931,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ F @ G ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ sk2 ) ) ) ) ) )
!= ( relation @ G ) ) ),
inference(paramod_ordered,[status(thm)],[35321,220]) ).
thf(38932,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ sk2 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[38931:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( L )),bind(D,$thf( N )),bind(E,$thf( P )),bind(F,$thf( F )),bind(G,$thf( relation_rng_restriction @ H @ ( relation_rng_restriction @ J @ ( relation_rng_restriction @ L @ ( relation_rng_restriction @ N @ ( relation_rng_restriction @ P @ sk2 ) ) ) ) ))]]) ).
thf(39164,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ sk2 ) ) ) ) ) ) ),
inference(simp,[status(thm)],[38932]) ).
thf(43936,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ G @ H ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ sk2 ) ) ) ) ) ) )
!= ( relation @ H ) ) ),
inference(paramod_ordered,[status(thm)],[39164,220]) ).
thf(43937,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ sk2 ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[43936:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( O )),bind(E,$thf( Q )),bind(F,$thf( S )),bind(G,$thf( G )),bind(H,$thf( relation_rng_restriction @ I @ ( relation_rng_restriction @ K @ ( relation_rng_restriction @ M @ ( relation_rng_restriction @ O @ ( relation_rng_restriction @ Q @ ( relation_rng_restriction @ S @ sk2 ) ) ) ) ) ))]]) ).
thf(44296,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ sk2 ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[43937]) ).
thf(48834,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ H @ I ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ sk2 ) ) ) ) ) ) ) )
!= ( relation @ I ) ) ),
inference(paramod_ordered,[status(thm)],[44296,220]) ).
thf(48835,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ ( relation_rng_restriction @ H @ sk2 ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[48834:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( P )),bind(E,$thf( R )),bind(F,$thf( T )),bind(G,$thf( V )),bind(H,$thf( H )),bind(I,$thf( relation_rng_restriction @ J @ ( relation_rng_restriction @ L @ ( relation_rng_restriction @ N @ ( relation_rng_restriction @ P @ ( relation_rng_restriction @ R @ ( relation_rng_restriction @ T @ ( relation_rng_restriction @ V @ sk2 ) ) ) ) ) ) ))]]) ).
thf(49243,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ ( relation_rng_restriction @ H @ sk2 ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[48835]) ).
thf(294,plain,
! [B: $i,A: $i] :
( sk4
| ~ ( in @ A @ ( relation_dom @ sk2 ) )
| ( in @ ( apply @ sk3 @ B ) @ sk1 )
| ( ( in @ ( apply @ sk3 @ A ) @ sk1 )
!= ( in @ B @ ( relation_dom @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[56,56]) ).
thf(309,plain,
! [B: $i,A: $i] :
( sk4
| ( in @ ( apply @ sk3 @ B ) @ sk1 )
| ~ ( in @ A @ ( relation_dom @ sk2 ) )
| ( ( apply @ sk3 @ A )
!= B )
| ( ( relation_dom @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[294]) ).
thf(312,plain,
! [A: $i] :
( sk4
| ( in @ ( apply @ sk3 @ ( apply @ sk3 @ A ) ) @ sk1 )
| ~ ( in @ A @ ( relation_dom @ sk2 ) )
| ( ( relation_dom @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[309]) ).
thf(5,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(74,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(33,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/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
thf(195,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)],[33]) ).
thf(196,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)],[195]) ).
thf(199,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)],[196]) ).
thf(205,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)],[199]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( ( apply @ A @ B )
= empty_set )
| ~ ( relation @ A )
| ~ ( function @ A )
| ( in @ B @ ( relation_dom @ A ) ) ),
inference(simp,[status(thm)],[205]) ).
thf(174,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ( B
!= ( relation_dom @ A ) )
| ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sk22 @ C @ B @ A ) ) @ A ) ),
inference(cnf,[status(esa)],[170]) ).
thf(177,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ~ ( in @ C @ B )
| ( in @ ( ordered_pair @ C @ ( sk22 @ C @ B @ A ) ) @ A ) ),
inference(lifteq,[status(thm)],[174]) ).
thf(178,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( in @ B @ ( relation_dom @ A ) )
| ( in @ ( ordered_pair @ B @ ( sk22 @ B @ ( relation_dom @ A ) @ A ) ) @ A ) ),
inference(simp,[status(thm)],[177]) ).
thf(13838,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( in @ B @ ( relation_dom @ A ) )
| ( in @ ( unordered_pair @ ( unordered_pair @ B @ ( sk22 @ B @ ( relation_dom @ A ) @ A ) ) @ ( singleton @ B ) ) @ A ) ),
inference(rewrite,[status(thm)],[178,97]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( C
= ( relation_rng_restriction @ A @ B ) )
<=> ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
<=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_relat_1) ).
thf(148,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( ( C
= ( relation_rng_restriction @ A @ B ) )
=> ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) )
& ( ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) ) )
& ( ! [D: $i,E: $i] :
( ( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) )
& ( ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) )
=> ( C
= ( relation_rng_restriction @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(149,plain,
! [A: $i,B: $i] :
( ( relation @ B )
=> ! [C: $i] :
( ( relation @ C )
=> ( ( ( C
= ( relation_rng_restriction @ A @ B ) )
=> ( ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) )
& ! [D: $i,E: $i] :
( ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) ) )
& ( ( ! [D: $i,E: $i] :
( ( in @ ( ordered_pair @ D @ E ) @ C )
=> ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) ) )
& ! [D: $i,E: $i] :
( ( ( in @ E @ A )
& ( in @ ( ordered_pair @ D @ E ) @ B ) )
=> ( in @ ( ordered_pair @ D @ E ) @ C ) ) )
=> ( C
= ( relation_rng_restriction @ A @ B ) ) ) ) ) ),
inference(miniscope,[status(thm)],[148]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ B )
| ~ ( relation @ C )
| ( in @ ( ordered_pair @ ( sk18 @ C @ B @ A ) @ ( sk19 @ C @ B @ A ) ) @ C )
| ~ ( sk17 @ B @ A @ C )
| ( C
= ( relation_rng_restriction @ A @ B ) ) ),
inference(cnf,[status(esa)],[149]) ).
thf(158,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_rng_restriction @ A @ B ) )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ( in @ ( ordered_pair @ ( sk18 @ C @ B @ A ) @ ( sk19 @ C @ B @ A ) ) @ C )
| ~ ( sk17 @ B @ A @ C ) ),
inference(lifteq,[status(thm)],[153]) ).
thf(7321,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_rng_restriction @ A @ B ) )
| ~ ( 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)],[158,97]) ).
thf(25863,plain,
! [B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ A @ B ) )
| ( ( relation @ empty_set )
!= ( relation @ B ) ) ),
inference(paramod_ordered,[status(thm)],[120,220]) ).
thf(25864,plain,
! [A: $i] : ( relation @ ( relation_rng_restriction @ A @ empty_set ) ),
inference(pattern_uni,[status(thm)],[25863:[bind(A,$thf( A )),bind(B,$thf( empty_set ))]]) ).
thf(26042,plain,
! [C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ B @ C ) )
| ( ( relation @ ( relation_rng_restriction @ A @ empty_set ) )
!= ( relation @ C ) ) ),
inference(paramod_ordered,[status(thm)],[25864,220]) ).
thf(26043,plain,
! [B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ empty_set ) ) ),
inference(pattern_uni,[status(thm)],[26042:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( relation_rng_restriction @ D @ empty_set ))]]) ).
thf(26154,plain,
! [B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ empty_set ) ) ),
inference(simp,[status(thm)],[26043]) ).
thf(29147,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ C @ D ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ empty_set ) ) )
!= ( relation @ D ) ) ),
inference(paramod_ordered,[status(thm)],[26154,220]) ).
thf(29148,plain,
! [C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ empty_set ) ) ) ),
inference(pattern_uni,[status(thm)],[29147:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( relation_rng_restriction @ E @ ( relation_rng_restriction @ G @ empty_set ) ))]]) ).
thf(29323,plain,
! [C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ empty_set ) ) ) ),
inference(simp,[status(thm)],[29148]) ).
thf(31540,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ D @ E ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ empty_set ) ) ) )
!= ( relation @ E ) ) ),
inference(paramod_ordered,[status(thm)],[29323,220]) ).
thf(31541,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ empty_set ) ) ) ) ),
inference(pattern_uni,[status(thm)],[31540:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( J )),bind(D,$thf( D )),bind(E,$thf( relation_rng_restriction @ F @ ( relation_rng_restriction @ H @ ( relation_rng_restriction @ J @ empty_set ) ) ))]]) ).
thf(31737,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ empty_set ) ) ) ) ),
inference(simp,[status(thm)],[31541]) ).
thf(33999,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ E @ F ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ empty_set ) ) ) ) )
!= ( relation @ F ) ) ),
inference(paramod_ordered,[status(thm)],[31737,220]) ).
thf(34000,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ empty_set ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[33999:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( M )),bind(E,$thf( E )),bind(F,$thf( relation_rng_restriction @ G @ ( relation_rng_restriction @ I @ ( relation_rng_restriction @ K @ ( relation_rng_restriction @ M @ empty_set ) ) ) ))]]) ).
thf(34273,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ empty_set ) ) ) ) ) ),
inference(simp,[status(thm)],[34000]) ).
thf(36903,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ F @ G ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ empty_set ) ) ) ) ) )
!= ( relation @ G ) ) ),
inference(paramod_ordered,[status(thm)],[34273,220]) ).
thf(36904,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ empty_set ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[36903:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( L )),bind(D,$thf( N )),bind(E,$thf( P )),bind(F,$thf( F )),bind(G,$thf( relation_rng_restriction @ H @ ( relation_rng_restriction @ J @ ( relation_rng_restriction @ L @ ( relation_rng_restriction @ N @ ( relation_rng_restriction @ P @ empty_set ) ) ) ) ))]]) ).
thf(37145,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ empty_set ) ) ) ) ) ) ),
inference(simp,[status(thm)],[36904]) ).
thf(41842,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ G @ H ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ empty_set ) ) ) ) ) ) )
!= ( relation @ H ) ) ),
inference(paramod_ordered,[status(thm)],[37145,220]) ).
thf(41843,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ empty_set ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[41842:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( O )),bind(E,$thf( Q )),bind(F,$thf( S )),bind(G,$thf( G )),bind(H,$thf( relation_rng_restriction @ I @ ( relation_rng_restriction @ K @ ( relation_rng_restriction @ M @ ( relation_rng_restriction @ O @ ( relation_rng_restriction @ Q @ ( relation_rng_restriction @ S @ empty_set ) ) ) ) ) ))]]) ).
thf(42180,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ empty_set ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[41843]) ).
thf(47245,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ H @ I ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ empty_set ) ) ) ) ) ) ) )
!= ( relation @ I ) ) ),
inference(paramod_ordered,[status(thm)],[42180,220]) ).
thf(47246,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ ( relation_rng_restriction @ H @ empty_set ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[47245:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( P )),bind(E,$thf( R )),bind(F,$thf( T )),bind(G,$thf( V )),bind(H,$thf( H )),bind(I,$thf( relation_rng_restriction @ J @ ( relation_rng_restriction @ L @ ( relation_rng_restriction @ N @ ( relation_rng_restriction @ P @ ( relation_rng_restriction @ R @ ( relation_rng_restriction @ T @ ( relation_rng_restriction @ V @ empty_set ) ) ) ) ) ) ))]]) ).
thf(47627,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ ( relation_rng_restriction @ H @ empty_set ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[47246]) ).
thf(25869,plain,
! [B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ A @ B ) )
| ( ( relation @ sk28 )
!= ( relation @ B ) ) ),
inference(paramod_ordered,[status(thm)],[216,220]) ).
thf(25870,plain,
! [A: $i] : ( relation @ ( relation_rng_restriction @ A @ sk28 ) ),
inference(pattern_uni,[status(thm)],[25869:[bind(A,$thf( A )),bind(B,$thf( sk28 ))]]) ).
thf(26204,plain,
! [C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ B @ C ) )
| ( ( relation @ ( relation_rng_restriction @ A @ sk28 ) )
!= ( relation @ C ) ) ),
inference(paramod_ordered,[status(thm)],[25870,220]) ).
thf(26205,plain,
! [B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ sk28 ) ) ),
inference(pattern_uni,[status(thm)],[26204:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( relation_rng_restriction @ D @ sk28 ))]]) ).
thf(26317,plain,
! [B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ sk28 ) ) ),
inference(simp,[status(thm)],[26205]) ).
thf(29807,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ C @ D ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ sk28 ) ) )
!= ( relation @ D ) ) ),
inference(paramod_ordered,[status(thm)],[26317,220]) ).
thf(29808,plain,
! [C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ sk28 ) ) ) ),
inference(pattern_uni,[status(thm)],[29807:[bind(A,$thf( E )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( relation_rng_restriction @ E @ ( relation_rng_restriction @ G @ sk28 ) ))]]) ).
thf(29992,plain,
! [C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ sk28 ) ) ) ),
inference(simp,[status(thm)],[29808]) ).
thf(31825,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ D @ E ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ sk28 ) ) ) )
!= ( relation @ E ) ) ),
inference(paramod_ordered,[status(thm)],[29992,220]) ).
thf(31826,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ sk28 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[31825:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( J )),bind(D,$thf( D )),bind(E,$thf( relation_rng_restriction @ F @ ( relation_rng_restriction @ H @ ( relation_rng_restriction @ J @ sk28 ) ) ))]]) ).
thf(32033,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ sk28 ) ) ) ) ),
inference(simp,[status(thm)],[31826]) ).
thf(34344,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ E @ F ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ sk28 ) ) ) ) )
!= ( relation @ F ) ) ),
inference(paramod_ordered,[status(thm)],[32033,220]) ).
thf(34345,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ sk28 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[34344:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( M )),bind(E,$thf( E )),bind(F,$thf( relation_rng_restriction @ G @ ( relation_rng_restriction @ I @ ( relation_rng_restriction @ K @ ( relation_rng_restriction @ M @ sk28 ) ) ) ))]]) ).
thf(34551,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ sk28 ) ) ) ) ) ),
inference(simp,[status(thm)],[34345]) ).
thf(38116,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ F @ G ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ sk28 ) ) ) ) ) )
!= ( relation @ G ) ) ),
inference(paramod_ordered,[status(thm)],[34551,220]) ).
thf(38117,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ sk28 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[38116:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( L )),bind(D,$thf( N )),bind(E,$thf( P )),bind(F,$thf( F )),bind(G,$thf( relation_rng_restriction @ H @ ( relation_rng_restriction @ J @ ( relation_rng_restriction @ L @ ( relation_rng_restriction @ N @ ( relation_rng_restriction @ P @ sk28 ) ) ) ) ))]]) ).
thf(38452,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ sk28 ) ) ) ) ) ) ),
inference(simp,[status(thm)],[38117]) ).
thf(42307,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ G @ H ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ sk28 ) ) ) ) ) ) )
!= ( relation @ H ) ) ),
inference(paramod_ordered,[status(thm)],[38452,220]) ).
thf(42308,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ sk28 ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[42307:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( O )),bind(E,$thf( Q )),bind(F,$thf( S )),bind(G,$thf( G )),bind(H,$thf( relation_rng_restriction @ I @ ( relation_rng_restriction @ K @ ( relation_rng_restriction @ M @ ( relation_rng_restriction @ O @ ( relation_rng_restriction @ Q @ ( relation_rng_restriction @ S @ sk28 ) ) ) ) ) ))]]) ).
thf(42623,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ sk28 ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[42308]) ).
thf(47770,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ H @ I ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ sk28 ) ) ) ) ) ) ) )
!= ( relation @ I ) ) ),
inference(paramod_ordered,[status(thm)],[42623,220]) ).
thf(47771,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ ( relation_rng_restriction @ H @ sk28 ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[47770:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( P )),bind(E,$thf( R )),bind(F,$thf( T )),bind(G,$thf( V )),bind(H,$thf( H )),bind(I,$thf( relation_rng_restriction @ J @ ( relation_rng_restriction @ L @ ( relation_rng_restriction @ N @ ( relation_rng_restriction @ P @ ( relation_rng_restriction @ R @ ( relation_rng_restriction @ T @ ( relation_rng_restriction @ V @ sk28 ) ) ) ) ) ) ))]]) ).
thf(48158,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ ( relation_rng_restriction @ H @ sk28 ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[47771]) ).
thf(218,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ),
inference(cnf,[status(esa)],[217]) ).
thf(25036,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ B )
| ( ( in @ B @ A )
!= ( in @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[218]) ).
thf(25037,plain,
! [A: $i] :
~ ( in @ A @ A ),
inference(pattern_uni,[status(thm)],[25036:[bind(A,$thf( B ))]]) ).
thf(25056,plain,
! [A: $i] :
~ ( in @ A @ A ),
inference(simp,[status(thm)],[25037]) ).
thf(25076,plain,
! [A: $i] :
( sk5
| ~ sk4
| ( ( in @ sk9 @ ( relation_dom @ sk2 ) )
!= ( in @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[57,25056]) ).
thf(25127,plain,
! [A: $i] :
( sk5
| ~ sk4
| ( sk9 != A )
| ( ( relation_dom @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[25076]) ).
thf(25156,plain,
( sk5
| ~ sk4
| ( ( relation_dom @ sk2 )
!= sk9 ) ),
inference(simp,[status(thm)],[25127]) ).
thf(75,plain,
~ ? [A: $i] :
( ( empty @ A )
& ? [B: $i] :
( ( A != B )
& ( empty @ B ) ) ),
inference(miniscope,[status(thm)],[74]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ( A = B )
| ~ ( empty @ B ) ),
inference(cnf,[status(esa)],[75]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( empty @ A )
| ~ ( empty @ B ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(7159,plain,
! [B: $i,A: $i] :
( ~ ( empty @ A )
| ~ ( empty @ B )
| ~ ( empty @ sk3 )
| ( B != sk2 )
| ~ sk4
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[77,6431]) ).
thf(7160,plain,
! [A: $i] :
( ~ ( empty @ sk3 )
| ~ ( empty @ A )
| ~ ( empty @ sk3 )
| ( A != sk2 )
| ~ sk4 ),
inference(pattern_uni,[status(thm)],[7159:[bind(A,$thf( sk3 ))]]) ).
thf(7173,plain,
( ~ ( empty @ sk3 )
| ~ ( empty @ sk2 )
| ~ sk4 ),
inference(simp,[status(thm)],[7160]) ).
thf(8105,plain,
( ~ ( empty @ sk2 )
| ~ sk4
| ( ( empty @ sk3 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,7173]) ).
thf(8113,plain,
( ~ ( empty @ sk2 )
| ~ sk4
| ( sk3 != empty_set ) ),
inference(simp,[status(thm)],[8105]) ).
thf(32,axiom,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(191,plain,
? [A: $i] :
( ( relation @ A )
& ( empty @ A )
& ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(192,plain,
function @ sk26,
inference(cnf,[status(esa)],[191]) ).
thf(193,plain,
empty @ sk26,
inference(cnf,[status(esa)],[191]) ).
thf(2365,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ sk26 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[193,106]) ).
thf(2366,plain,
sk26 = empty_set,
inference(pattern_uni,[status(thm)],[2365:[bind(A,$thf( sk26 ))]]) ).
thf(2705,plain,
function @ empty_set,
inference(rewrite,[status(thm)],[192,2366]) ).
thf(32112,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ D @ E ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ sk3 ) ) ) )
!= ( relation @ E ) ) ),
inference(paramod_ordered,[status(thm)],[30208,220]) ).
thf(32113,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ sk3 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[32112:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( J )),bind(D,$thf( D )),bind(E,$thf( relation_rng_restriction @ F @ ( relation_rng_restriction @ H @ ( relation_rng_restriction @ J @ sk3 ) ) ))]]) ).
thf(32345,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ sk3 ) ) ) ) ),
inference(simp,[status(thm)],[32113]) ).
thf(34691,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ E @ F ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ sk3 ) ) ) ) )
!= ( relation @ F ) ) ),
inference(paramod_ordered,[status(thm)],[32345,220]) ).
thf(34692,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ sk3 ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[34691:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( K )),bind(D,$thf( M )),bind(E,$thf( E )),bind(F,$thf( relation_rng_restriction @ G @ ( relation_rng_restriction @ I @ ( relation_rng_restriction @ K @ ( relation_rng_restriction @ M @ sk3 ) ) ) ))]]) ).
thf(34936,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ sk3 ) ) ) ) ) ),
inference(simp,[status(thm)],[34692]) ).
thf(38523,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ F @ G ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ sk3 ) ) ) ) ) )
!= ( relation @ G ) ) ),
inference(paramod_ordered,[status(thm)],[34936,220]) ).
thf(38524,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ sk3 ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[38523:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( L )),bind(D,$thf( N )),bind(E,$thf( P )),bind(F,$thf( F )),bind(G,$thf( relation_rng_restriction @ H @ ( relation_rng_restriction @ J @ ( relation_rng_restriction @ L @ ( relation_rng_restriction @ N @ ( relation_rng_restriction @ P @ sk3 ) ) ) ) ))]]) ).
thf(38818,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ sk3 ) ) ) ) ) ) ),
inference(simp,[status(thm)],[38524]) ).
thf(134,plain,
one_to_one @ sk16,
inference(cnf,[status(esa)],[133]) ).
thf(2377,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( one_to_one @ empty_set )
| ( A != sk16 ) ),
inference(paramod_ordered,[status(thm)],[106,134]) ).
thf(2378,plain,
( ~ ( empty @ sk16 )
| ( one_to_one @ empty_set ) ),
inference(pattern_uni,[status(thm)],[2377:[bind(A,$thf( sk16 ))]]) ).
thf(10092,plain,
( ( one_to_one @ empty_set )
| ( ( empty @ sk16 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,2378]) ).
thf(10099,plain,
( ( one_to_one @ empty_set )
| ( sk16 != empty_set ) ),
inference(simp,[status(thm)],[10092]) ).
thf(20691,plain,
( ( ( relation_dom @ sk2 )
!= empty_set )
| ( ( empty @ sk27 )
!= ( empty @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[19841,211]) ).
thf(20829,plain,
( ( ( relation_dom @ sk2 )
!= empty_set )
| ( sk27 != sk2 ) ),
inference(simp,[status(thm)],[20691]) ).
thf(256,plain,
( ~ sk6
| ~ sk5
| ~ sk4
| ~ ( in @ sk7 @ ( relation_dom @ sk3 ) )
| ( ( in @ ( apply @ sk3 @ sk7 ) @ sk1 )
!= ( in @ sk7 @ ( relation_dom @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[55,49]) ).
thf(260,plain,
( ~ sk6
| ~ sk5
| ~ sk4
| ~ ( in @ sk7 @ ( relation_dom @ sk3 ) )
| ( ( apply @ sk3 @ sk7 )
!= sk7 )
| ( ( relation_dom @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[256]) ).
thf(20028,plain,
( ( ( relation_dom @ sk3 )
!= empty_set )
| ( ( empty @ sk11 )
!= ( empty @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[19770,82]) ).
thf(20039,plain,
( ( ( relation_dom @ sk3 )
!= empty_set )
| ( sk11 != sk3 ) ),
inference(simp,[status(thm)],[20028]) ).
thf(21563,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk11 != sk3 )
| ( A
!= ( relation_dom @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[106,20039]) ).
thf(21564,plain,
( ~ ( empty @ ( relation_dom @ sk3 ) )
| ( sk11 != sk3 ) ),
inference(pattern_uni,[status(thm)],[21563:[bind(A,$thf( relation_dom @ sk3 ))]]) ).
thf(3861,plain,
! [A: $i] :
( sk5
| ~ sk4
| ( ( in @ sk9 @ ( relation_dom @ sk2 ) )
!= ( in @ A @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[57,3836]) ).
thf(3884,plain,
! [A: $i] :
( sk5
| ~ sk4
| ( sk9 != A )
| ( ( relation_dom @ sk2 )
!= empty_set ) ),
inference(simp,[status(thm)],[3861]) ).
thf(3894,plain,
( sk5
| ~ sk4
| ( ( relation_dom @ sk2 )
!= empty_set ) ),
inference(simp,[status(thm)],[3884]) ).
thf(22597,plain,
( ( ( relation_dom @ sk28 )
!= empty_set )
| ( ( empty @ sk28 )
!= ( empty @ sk27 ) ) ),
inference(paramod_ordered,[status(thm)],[19688,211]) ).
thf(22731,plain,
( ( ( relation_dom @ sk28 )
!= empty_set )
| ( sk28 != sk27 ) ),
inference(simp,[status(thm)],[22597]) ).
thf(27467,plain,
( ( sk28 != sk27 )
| ( ( relation_dom @ sk28 )
!= ( relation_dom @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[27230,22731]) ).
thf(27576,plain,
( ( sk28 != sk27 )
| ( sk28 != empty_set ) ),
inference(simp,[status(thm)],[27467]) ).
thf(40,axiom,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(224,plain,
! [A: $i] :
( ( empty @ A )
=> ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(42,axiom,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
thf(229,plain,
( ( empty @ empty_set )
& ( relation @ empty_set )
& ( relation_empty_yielding @ empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(24288,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk28 != sk11 )
| ( A
!= ( relation_dom @ sk28 ) ) ),
inference(paramod_ordered,[status(thm)],[106,22704]) ).
thf(24289,plain,
( ~ ( empty @ ( relation_dom @ sk28 ) )
| ( sk28 != sk11 ) ),
inference(pattern_uni,[status(thm)],[24288:[bind(A,$thf( relation_dom @ sk28 ))]]) ).
thf(20692,plain,
! [A: $i] :
( ( ( relation_dom @ sk2 )
!= empty_set )
| ( A = empty_set )
| ( ( empty @ sk2 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[19841,106]) ).
thf(20693,plain,
( ( ( relation_dom @ sk2 )
!= empty_set )
| ( sk2 = empty_set ) ),
inference(pattern_uni,[status(thm)],[20692:[bind(A,$thf( sk2 ))]]) ).
thf(171,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ( in @ ( sk23 @ B @ A ) @ B )
| ~ ( in @ ( sk24 @ B @ A ) @ B )
| ( B
= ( relation_dom @ A ) ) ),
inference(cnf,[status(esa)],[170]) ).
thf(187,plain,
! [B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ( in @ ( sk23 @ B @ A ) @ B )
| ~ ( in @ ( sk24 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[171]) ).
thf(188,plain,
! [B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ( in @ ( sk23 @ B @ A ) @ B )
| ~ ( in @ ( sk24 @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[187]) ).
thf(27328,plain,
! [A: $i] :
( ( empty @ ( relation_dom @ A ) )
| ( ( empty @ ( relation_dom @ empty_set ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27108,222]) ).
thf(27329,plain,
empty @ ( relation_dom @ ( relation_dom @ empty_set ) ),
inference(pattern_uni,[status(thm)],[27328:[bind(A,$thf( relation_dom @ empty_set ))]]) ).
thf(27678,plain,
empty @ ( relation_dom @ empty_set ),
inference(rewrite,[status(thm)],[27329,27230]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( in @ ( ordered_pair @ A @ B ) @ C )
<=> ( ( in @ A @ ( relation_dom @ C ) )
& ( B
= ( apply @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_funct_1) ).
thf(141,plain,
! [A: $i,B: $i,C: $i] :
( ( ( relation @ C )
& ( function @ C ) )
=> ( ( ( in @ ( ordered_pair @ A @ B ) @ C )
=> ( ( in @ A @ ( relation_dom @ C ) )
& ( B
= ( apply @ C @ A ) ) ) )
& ( ( ( in @ A @ ( relation_dom @ C ) )
& ( B
= ( apply @ C @ A ) ) )
=> ( in @ ( ordered_pair @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(22123,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) ) @ sk3 )
| ( sk3 = empty_set )
| ( ( relation_dom @ sk3 )
!= ( relation_dom @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[4591,19925]) ).
thf(22124,plain,
( ( element @ ( unordered_pair @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) ) @ sk3 )
| ( sk3 = empty_set ) ),
inference(pattern_uni,[status(thm)],[22123:[]]) ).
thf(2876,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ C ) )
!= empty_set )
| ( ( unordered_pair @ B @ A )
!= ( unordered_pair @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[71,2845]) ).
thf(2877,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ B ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[2876:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(3845,plain,
! [B: $i,A: $i] :
( ( sk3 != sk2 )
| ~ sk4
| ~ ( empty @ B )
| ( ( in @ sk7 @ ( relation_dom @ sk2 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[383,127]) ).
thf(3846,plain,
( ( sk3 != sk2 )
| ~ sk4
| ~ ( empty @ ( relation_dom @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[3845:[bind(A,$thf( sk7 )),bind(B,$thf( relation_dom @ sk2 ))]]) ).
thf(175,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( in @ ( ordered_pair @ ( sk23 @ B @ A ) @ C ) @ A )
| ~ ( in @ ( sk24 @ B @ A ) @ B )
| ( B
= ( relation_dom @ A ) ) ),
inference(cnf,[status(esa)],[170]) ).
thf(185,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ~ ( in @ ( ordered_pair @ ( sk23 @ B @ A ) @ C ) @ A )
| ~ ( in @ ( sk24 @ B @ A ) @ B ) ),
inference(lifteq,[status(thm)],[175]) ).
thf(186,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ~ ( in @ ( ordered_pair @ ( sk23 @ B @ A ) @ C ) @ A )
| ~ ( in @ ( sk24 @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[185]) ).
thf(16683,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ~ ( in @ ( unordered_pair @ ( unordered_pair @ ( sk23 @ B @ A ) @ C ) @ ( singleton @ ( sk23 @ B @ A ) ) ) @ A )
| ~ ( in @ ( sk24 @ B @ A ) @ B ) ),
inference(rewrite,[status(thm)],[186,97]) ).
thf(35,axiom,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(212,plain,
! [A: $i] :
( ( empty @ A )
=> ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(122,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(123,plain,
~ ? [A: $i,B: $i] :
( ( in @ A @ B )
& ? [C: $i] :
( ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ) ),
inference(miniscope,[status(thm)],[122]) ).
thf(124,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( element @ B @ ( powerset @ C ) )
| ~ ( empty @ C ) ),
inference(cnf,[status(esa)],[123]) ).
thf(225,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( function @ A ) ),
inference(cnf,[status(esa)],[224]) ).
thf(27030,plain,
! [A: $i] :
( ~ ( empty @ A )
| sk5
| ~ sk4
| ( ( empty @ ( relation_dom @ A ) )
!= ( empty @ ( relation_dom @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[222,3830]) ).
thf(27031,plain,
( ~ ( empty @ sk2 )
| sk5
| ~ sk4 ),
inference(pattern_uni,[status(thm)],[27030:[bind(A,$thf( sk2 ))]]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(87,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(88,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)],[87]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ~ ( element @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) ),
inference(cnf,[status(esa)],[88]) ).
thf(1291,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ B @ C )
| ( ( element @ ( sk14 @ A ) @ A )
!= ( element @ B @ ( powerset @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[111,90]) ).
thf(1292,plain,
! [A: $i] : ( subset @ ( sk14 @ ( powerset @ A ) ) @ A ),
inference(pattern_uni,[status(thm)],[1291:[bind(A,$thf( powerset @ E )),bind(B,$thf( sk14 @ ( powerset @ E ) )),bind(C,$thf( E ))]]) ).
thf(1297,plain,
! [A: $i] : ( subset @ ( sk14 @ ( powerset @ A ) ) @ A ),
inference(simp,[status(thm)],[1292]) ).
thf(154,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ B )
| ~ ( relation @ C )
| ( sk17 @ B @ A @ C )
| ~ ( in @ ( ordered_pair @ ( sk20 @ C @ B @ A ) @ ( sk21 @ C @ B @ A ) ) @ C )
| ( C
= ( relation_rng_restriction @ A @ B ) ) ),
inference(cnf,[status(esa)],[149]) ).
thf(166,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_rng_restriction @ A @ B ) )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ( sk17 @ B @ A @ C )
| ~ ( in @ ( ordered_pair @ ( sk20 @ C @ B @ A ) @ ( sk21 @ C @ B @ A ) ) @ C ) ),
inference(lifteq,[status(thm)],[154]) ).
thf(12218,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_rng_restriction @ A @ B ) )
| ~ ( 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)],[166,97]) ).
thf(51,plain,
! [A: $i] :
( sk4
| ~ ( in @ A @ ( relation_dom @ sk2 ) )
| ( in @ A @ ( relation_dom @ sk3 ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(3221,plain,
! [B: $i,A: $i] :
( ( A
= ( relation_dom @ sk3 ) )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ A @ sk3 ) @ ( sk25 @ A @ sk3 ) ) @ ( singleton @ ( sk24 @ A @ sk3 ) ) ) @ sk3 )
| sk4
| ( in @ B @ ( relation_dom @ sk3 ) )
| ( ( in @ ( sk23 @ A @ sk3 ) @ A )
!= ( in @ B @ ( relation_dom @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2078,51]) ).
thf(3222,plain,
( ( ( relation_dom @ sk3 )
= ( relation_dom @ sk2 ) )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ ( relation_dom @ sk2 ) @ sk3 ) @ ( sk25 @ ( relation_dom @ sk2 ) @ sk3 ) ) @ ( singleton @ ( sk24 @ ( relation_dom @ sk2 ) @ sk3 ) ) ) @ sk3 )
| sk4
| ( in @ ( sk23 @ ( relation_dom @ sk2 ) @ sk3 ) @ ( relation_dom @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[3221:[bind(A,$thf( relation_dom @ sk2 )),bind(B,$thf( sk23 @ ( relation_dom @ sk2 ) @ sk3 ))]]) ).
thf(28511,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk28 != sk27 )
| ( A != sk28 ) ),
inference(paramod_ordered,[status(thm)],[106,27576]) ).
thf(28512,plain,
( ~ ( empty @ sk28 )
| ( sk28 != sk27 ) ),
inference(pattern_uni,[status(thm)],[28511:[bind(A,$thf( sk28 ))]]) ).
thf(4,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(72,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(73,plain,
! [A: $i] : ( subset @ A @ A ),
inference(cnf,[status(esa)],[72]) ).
thf(242,plain,
( ( empty @ sk27 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[86,211]) ).
thf(244,plain,
sk27 != empty_set,
inference(simp,[status(thm)],[242]) ).
thf(142,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ C )
| ~ ( function @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C )
| ( B
= ( apply @ C @ A ) ) ),
inference(cnf,[status(esa)],[141]) ).
thf(145,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( apply @ C @ A ) )
| ~ ( relation @ C )
| ~ ( function @ C )
| ~ ( in @ ( ordered_pair @ A @ B ) @ C ) ),
inference(lifteq,[status(thm)],[142]) ).
thf(5737,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( apply @ C @ A ) )
| ~ ( relation @ C )
| ~ ( function @ C )
| ~ ( in @ ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) @ C ) ),
inference(rewrite,[status(thm)],[145,97]) ).
thf(172,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)],[170]) ).
thf(183,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)],[172]) ).
thf(184,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( in @ ( ordered_pair @ B @ C ) @ A )
| ( in @ B @ ( relation_dom @ A ) ) ),
inference(simp,[status(thm)],[183]) ).
thf(16296,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)],[184,97]) ).
thf(22067,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk3 = empty_set )
| ( A
!= ( relation_dom @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[106,19925]) ).
thf(22068,plain,
( ~ ( empty @ ( relation_dom @ sk3 ) )
| ( sk3 = empty_set ) ),
inference(pattern_uni,[status(thm)],[22067:[bind(A,$thf( relation_dom @ sk3 ))]]) ).
thf(8109,plain,
( ~ ( empty @ sk2 )
| ~ sk4
| ( ( empty @ sk3 )
!= ( empty @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[7173]) ).
thf(8110,plain,
( ~ ( empty @ sk2 )
| ~ sk4
| ( ( empty @ sk3 )
!= ( empty @ sk2 ) ) ),
inference(simp,[status(thm)],[8109]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ B )
| ~ ( relation @ C )
| ( sk17 @ B @ A @ C )
| ( in @ ( sk21 @ C @ B @ A ) @ A )
| ( C
= ( relation_rng_restriction @ A @ B ) ) ),
inference(cnf,[status(esa)],[149]) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_rng_restriction @ A @ B ) )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ( sk17 @ B @ A @ C )
| ( in @ ( sk21 @ C @ B @ A ) @ A ) ),
inference(lifteq,[status(thm)],[156]) ).
thf(53,plain,
( ( sk2
= ( relation_rng_restriction @ sk1 @ sk3 ) )
| ~ sk4 ),
inference(cnf,[status(esa)],[45]) ).
thf(64,plain,
( ( ( relation_rng_restriction @ sk1 @ sk3 )
= sk2 )
| ~ sk4 ),
inference(lifteq,[status(thm)],[53]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ),
inference(cnf,[status(esa)],[88]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( element @ A @ ( powerset @ B ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(1373,plain,
! [C: $i,B: $i,A: $i] :
( ( element @ B @ ( powerset @ C ) )
| ( ( subset @ A @ A )
!= ( subset @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[73,91]) ).
thf(1374,plain,
! [A: $i] : ( element @ A @ ( powerset @ A ) ),
inference(pattern_uni,[status(thm)],[1373:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(27389,plain,
( ( empty @ sk2 )
| ( ( relation_dom @ sk2 )
!= ( relation_dom @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[27230,19841]) ).
thf(27582,plain,
( ( empty @ sk2 )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[27389]) ).
thf(27402,plain,
( ( sk28 != sk11 )
| ( ( relation_dom @ sk28 )
!= ( relation_dom @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[27230,22704]) ).
thf(27590,plain,
( ( sk28 != sk11 )
| ( sk28 != empty_set ) ),
inference(simp,[status(thm)],[27402]) ).
thf(257,plain,
( ~ ( in @ sk7 @ ( relation_dom @ sk3 ) )
| ~ sk6
| ~ sk5
| ~ sk4
| ( ( in @ ( apply @ sk3 @ sk7 ) @ sk1 )
!= ( in @ sk7 @ ( relation_dom @ sk3 ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[49]) ).
thf(259,plain,
( ~ ( in @ sk7 @ ( relation_dom @ sk3 ) )
| ~ sk6
| ~ sk5
| ~ sk4
| ( ( apply @ sk3 @ sk7 )
!= sk7 )
| ( ( relation_dom @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[257]) ).
thf(27403,plain,
( ( sk11 != sk2 )
| ( ( relation_dom @ sk2 )
!= ( relation_dom @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[27230,20803]) ).
thf(27549,plain,
( ( sk11 != sk2 )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[27403]) ).
thf(59,plain,
function @ sk3,
inference(cnf,[status(esa)],[45]) ).
thf(118,plain,
! [A: $i] :
( ~ ( relation @ A )
| ~ ( empty @ A )
| ~ ( function @ A )
| ( one_to_one @ A ) ),
inference(cnf,[status(esa)],[115]) ).
thf(50,plain,
! [A: $i] :
( sk4
| ~ ( in @ A @ ( relation_dom @ sk2 ) )
| ( ( apply @ sk2 @ A )
= ( apply @ sk3 @ A ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(65,plain,
! [A: $i] :
( ( ( apply @ sk3 @ A )
= ( apply @ sk2 @ A ) )
| sk4
| ~ ( in @ A @ ( relation_dom @ sk2 ) ) ),
inference(lifteq,[status(thm)],[50]) ).
thf(66,plain,
! [A: $i] :
( ( ( apply @ sk3 @ A )
= ( apply @ sk2 @ A ) )
| sk4
| ~ ( in @ A @ ( relation_dom @ sk2 ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(9036,plain,
! [B: $i,A: $i] :
( ( empty @ A )
| ( ( apply @ sk3 @ B )
= ( apply @ sk2 @ B ) )
| sk4
| ( ( in @ ( sk14 @ A ) @ A )
!= ( in @ B @ ( relation_dom @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[4765,66]) ).
thf(9037,plain,
( ( empty @ ( relation_dom @ sk2 ) )
| ( ( apply @ sk3 @ ( sk14 @ ( relation_dom @ sk2 ) ) )
= ( apply @ sk2 @ ( sk14 @ ( relation_dom @ sk2 ) ) ) )
| sk4 ),
inference(pattern_uni,[status(thm)],[9036:[bind(A,$thf( relation_dom @ sk2 )),bind(B,$thf( sk14 @ ( relation_dom @ sk2 ) ))]]) ).
thf(11685,plain,
! [B: $i,A: $i] :
( ( empty @ ( relation_dom @ sk2 ) )
| sk4
| ( element @ A @ B )
| ( ( in @ ( apply @ sk3 @ ( sk14 @ ( relation_dom @ sk2 ) ) ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9013,129]) ).
thf(11686,plain,
( ( empty @ ( relation_dom @ sk2 ) )
| sk4
| ( element @ ( apply @ sk3 @ ( sk14 @ ( relation_dom @ sk2 ) ) ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[11685:[bind(A,$thf( apply @ sk3 @ ( sk14 @ ( relation_dom @ sk2 ) ) )),bind(B,$thf( sk1 ))]]) ).
thf(14359,plain,
( ( empty @ ( relation_dom @ sk2 ) )
| sk4
| ( element @ ( apply @ sk2 @ ( sk14 @ ( relation_dom @ sk2 ) ) ) @ sk1 )
| ( ( apply @ sk3 @ ( sk14 @ ( relation_dom @ sk2 ) ) )
!= ( apply @ sk3 @ ( sk14 @ ( relation_dom @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[9037,11686]) ).
thf(14360,plain,
( ( empty @ ( relation_dom @ sk2 ) )
| sk4
| ( element @ ( apply @ sk2 @ ( sk14 @ ( relation_dom @ sk2 ) ) ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[14359:[]]) ).
thf(1285,plain,
! [C: $i,B: $i,A: $i] :
( ( subset @ B @ C )
| ( ( element @ ( sk13 @ A ) @ ( powerset @ A ) )
!= ( element @ B @ ( powerset @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,90]) ).
thf(1286,plain,
! [A: $i] : ( subset @ ( sk13 @ A ) @ A ),
inference(pattern_uni,[status(thm)],[1285:[bind(A,$thf( D )),bind(B,$thf( sk13 @ D )),bind(C,$thf( D ))]]) ).
thf(1294,plain,
! [A: $i] : ( subset @ ( sk13 @ A ) @ A ),
inference(simp,[status(thm)],[1286]) ).
thf(2759,plain,
! [A: $i] : ( subset @ empty_set @ A ),
inference(rewrite,[status(thm)],[1294,2650]) ).
thf(27430,plain,
( sk5
| ~ sk4
| ( ( relation_dom @ sk2 )
!= ( relation_dom @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[27230,3894]) ).
thf(27594,plain,
( sk5
| ~ sk4
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[27430]) ).
thf(9046,plain,
! [B: $i,A: $i] :
( ( empty @ A )
| sk4
| ( in @ B @ ( relation_dom @ sk3 ) )
| ( ( in @ ( sk14 @ A ) @ A )
!= ( in @ B @ ( relation_dom @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[4765,51]) ).
thf(9047,plain,
( ( empty @ ( relation_dom @ sk2 ) )
| sk4
| ( in @ ( sk14 @ ( relation_dom @ sk2 ) ) @ ( relation_dom @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[9046:[bind(A,$thf( relation_dom @ sk2 )),bind(B,$thf( sk14 @ ( relation_dom @ sk2 ) ))]]) ).
thf(230,plain,
relation_empty_yielding @ empty_set,
inference(cnf,[status(esa)],[229]) ).
thf(243,plain,
( ( empty @ sk11 )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[86,82]) ).
thf(245,plain,
sk11 != empty_set,
inference(simp,[status(thm)],[243]) ).
thf(22119,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) ) @ sk3 )
| ( sk3 = empty_set )
| ( ( relation_dom @ sk3 )
!= ( relation_dom @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[3874,19925]) ).
thf(22120,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) ) @ sk3 )
| ( sk3 = empty_set ) ),
inference(pattern_uni,[status(thm)],[22119:[]]) ).
thf(102,plain,
~ ? [A: $i,B: $i] : ( empty @ ( unordered_pair @ A @ B ) ),
inference(miniscope,[status(thm)],[101]) ).
thf(103,plain,
! [B: $i,A: $i] :
~ ( empty @ ( unordered_pair @ A @ B ) ),
inference(cnf,[status(esa)],[102]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(139,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)],[27]) ).
thf(140,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ A @ B )
| ~ ( element @ B @ ( powerset @ C ) )
| ( element @ A @ C ) ),
inference(cnf,[status(esa)],[139]) ).
thf(213,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( relation @ A ) ),
inference(cnf,[status(esa)],[212]) ).
thf(6416,plain,
( ( sk3 != empty_set )
| ( sk3 != sk2 )
| ~ sk4
| ( ( relation_dom @ sk3 )
!= ( relation_dom @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[4250,3890]) ).
thf(6418,plain,
( ( sk3 != empty_set )
| ( sk3 != sk2 )
| ~ sk4
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[6416]) ).
thf(6429,plain,
( ( sk3 != empty_set )
| ( sk3 != sk2 )
| ~ sk4 ),
inference(simp,[status(thm)],[6418]) ).
thf(1283,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ A )
| ( subset @ B @ C )
| ( ( element @ ( sk12 @ A ) @ ( powerset @ A ) )
!= ( element @ B @ ( powerset @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[93,90]) ).
thf(1284,plain,
! [A: $i] :
( ( empty @ A )
| ( subset @ ( sk12 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[1283:[bind(A,$thf( D )),bind(B,$thf( sk12 @ D )),bind(C,$thf( D ))]]) ).
thf(1293,plain,
! [A: $i] :
( ( empty @ A )
| ( subset @ ( sk12 @ A ) @ A ) ),
inference(simp,[status(thm)],[1284]) ).
thf(23204,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk2 = empty_set )
| ( A
!= ( relation_dom @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[106,20693]) ).
thf(23205,plain,
( ~ ( empty @ ( relation_dom @ sk2 ) )
| ( sk2 = empty_set ) ),
inference(pattern_uni,[status(thm)],[23204:[bind(A,$thf( relation_dom @ sk2 ))]]) ).
thf(27148,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk2 = empty_set )
| ( ( empty @ ( relation_dom @ A ) )
!= ( empty @ ( relation_dom @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[222,23205]) ).
thf(27149,plain,
( ~ ( empty @ sk2 )
| ( sk2 = empty_set ) ),
inference(pattern_uni,[status(thm)],[27148:[bind(A,$thf( sk2 ))]]) ).
thf(22073,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) ) @ sk3 )
| ( sk3 = empty_set )
| ( ( relation_dom @ sk3 )
!= ( relation_dom @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[4323,19925]) ).
thf(22074,plain,
( ( element @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) ) @ sk3 )
| ( sk3 = empty_set ) ),
inference(pattern_uni,[status(thm)],[22073:[]]) ).
thf(24,axiom,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(130,plain,
? [A: $i] :
( ( empty @ A )
& ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(23376,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk27 != sk2 )
| ( A
!= ( relation_dom @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[106,20829]) ).
thf(23377,plain,
( ~ ( empty @ ( relation_dom @ sk2 ) )
| ( sk27 != sk2 ) ),
inference(pattern_uni,[status(thm)],[23376:[bind(A,$thf( relation_dom @ sk2 ))]]) ).
thf(14293,plain,
( ( empty @ ( relation_dom @ sk2 ) )
| sk4
| ( in @ ( apply @ sk2 @ ( sk14 @ ( relation_dom @ sk2 ) ) ) @ sk1 )
| ( ( apply @ sk3 @ ( sk14 @ ( relation_dom @ sk2 ) ) )
!= ( apply @ sk3 @ ( sk14 @ ( relation_dom @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[9037,9013]) ).
thf(14294,plain,
( ( empty @ ( relation_dom @ sk2 ) )
| sk4
| ( in @ ( apply @ sk2 @ ( sk14 @ ( relation_dom @ sk2 ) ) ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[14293:[]]) ).
thf(223,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( relation @ ( relation_dom @ A ) ) ),
inference(cnf,[status(esa)],[221]) ).
thf(135,plain,
function @ sk16,
inference(cnf,[status(esa)],[133]) ).
thf(27113,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk27 != sk2 )
| ( ( empty @ ( relation_dom @ A ) )
!= ( empty @ ( relation_dom @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[222,23377]) ).
thf(27114,plain,
( ~ ( empty @ sk2 )
| ( sk27 != sk2 ) ),
inference(pattern_uni,[status(thm)],[27113:[bind(A,$thf( sk2 ))]]) ).
thf(152,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ B )
| ~ ( relation @ C )
| ~ ( in @ ( sk19 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sk18 @ C @ B @ A ) @ ( sk19 @ C @ B @ A ) ) @ B )
| ~ ( sk17 @ B @ A @ C )
| ( C
= ( relation_rng_restriction @ A @ B ) ) ),
inference(cnf,[status(esa)],[149]) ).
thf(160,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_rng_restriction @ A @ B ) )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ~ ( in @ ( sk19 @ C @ B @ A ) @ A )
| ~ ( in @ ( ordered_pair @ ( sk18 @ C @ B @ A ) @ ( sk19 @ C @ B @ A ) ) @ B )
| ~ ( sk17 @ B @ A @ C ) ),
inference(lifteq,[status(thm)],[152]) ).
thf(9111,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_rng_restriction @ A @ B ) )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ~ ( in @ ( sk19 @ C @ B @ A ) @ A )
| ~ ( in @ ( unordered_pair @ ( unordered_pair @ ( sk18 @ C @ B @ A ) @ ( sk19 @ C @ B @ A ) ) @ ( singleton @ ( sk18 @ C @ B @ A ) ) ) @ B )
| ~ ( sk17 @ B @ A @ C ) ),
inference(rewrite,[status(thm)],[160,97]) ).
thf(22764,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk27 != sk3 )
| ( A
!= ( relation_dom @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[106,20042]) ).
thf(22765,plain,
( ~ ( empty @ ( relation_dom @ sk3 ) )
| ( sk27 != sk3 ) ),
inference(pattern_uni,[status(thm)],[22764:[bind(A,$thf( relation_dom @ sk3 ))]]) ).
thf(8111,plain,
( ~ ( empty @ sk2 )
| ~ sk4
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[8109]) ).
thf(8974,plain,
( ~ sk4
| ( sk3 != sk2 )
| ( ( empty @ sk2 )
!= ( empty @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[86,8111]) ).
thf(8979,plain,
( ~ sk4
| ( sk3 != sk2 )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[8974]) ).
thf(368,plain,
! [A: $i] :
( ( empty @ ( powerset @ A ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[86,100]) ).
thf(374,plain,
! [A: $i] :
( ( powerset @ A )
!= empty_set ),
inference(simp,[status(thm)],[368]) ).
thf(27951,plain,
! [A: $i] :
( ( relation @ ( relation_dom @ A ) )
| ( ( empty @ ( relation_dom @ empty_set ) )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[27678,223]) ).
thf(27952,plain,
relation @ ( relation_dom @ ( relation_dom @ empty_set ) ),
inference(pattern_uni,[status(thm)],[27951:[bind(A,$thf( relation_dom @ empty_set ))]]) ).
thf(28195,plain,
relation @ ( relation_dom @ empty_set ),
inference(rewrite,[status(thm)],[27952,27230]) ).
thf(27406,plain,
( ( sk29 != sk27 )
| ( ( relation_dom @ sk29 )
!= ( relation_dom @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[27230,23587]) ).
thf(27603,plain,
( ( sk29 != sk27 )
| ( sk29 != empty_set ) ),
inference(simp,[status(thm)],[27406]) ).
thf(150,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ B )
| ~ ( relation @ C )
| ( C
!= ( relation_rng_restriction @ A @ B ) )
| ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ E @ A ) ),
inference(cnf,[status(esa)],[149]) ).
thf(164,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( relation_rng_restriction @ A @ B ) )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ E @ A ) ),
inference(lifteq,[status(thm)],[150]) ).
thf(165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ B )
| ~ ( relation @ ( relation_rng_restriction @ A @ B ) )
| ~ ( in @ ( ordered_pair @ C @ D ) @ ( relation_rng_restriction @ A @ B ) )
| ( in @ D @ A ) ),
inference(simp,[status(thm)],[164]) ).
thf(11795,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ B )
| ~ ( relation @ ( relation_rng_restriction @ A @ B ) )
| ~ ( in @ ( unordered_pair @ ( unordered_pair @ C @ D ) @ ( singleton @ C ) ) @ ( relation_rng_restriction @ A @ B ) )
| ( in @ D @ A ) ),
inference(rewrite,[status(thm)],[165,97]) ).
thf(29077,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk28 != sk11 )
| ( A != sk28 ) ),
inference(paramod_ordered,[status(thm)],[106,27590]) ).
thf(29078,plain,
( ~ ( empty @ sk28 )
| ( sk28 != sk11 ) ),
inference(pattern_uni,[status(thm)],[29077:[bind(A,$thf( sk28 ))]]) ).
thf(176,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( in @ ( ordered_pair @ ( sk23 @ B @ A ) @ C ) @ A )
| ( in @ ( ordered_pair @ ( sk24 @ B @ A ) @ ( sk25 @ B @ A ) ) @ A )
| ( B
= ( relation_dom @ A ) ) ),
inference(cnf,[status(esa)],[170]) ).
thf(181,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ~ ( in @ ( ordered_pair @ ( sk23 @ B @ A ) @ C ) @ A )
| ( in @ ( ordered_pair @ ( sk24 @ B @ A ) @ ( sk25 @ B @ A ) ) @ A ) ),
inference(lifteq,[status(thm)],[176]) ).
thf(182,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ~ ( in @ ( ordered_pair @ ( sk23 @ B @ A ) @ C ) @ A )
| ( in @ ( ordered_pair @ ( sk24 @ B @ A ) @ ( sk25 @ B @ A ) ) @ A ) ),
inference(simp,[status(thm)],[181]) ).
thf(14417,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( relation_dom @ A ) )
| ~ ( relation @ A )
| ~ ( in @ ( unordered_pair @ ( unordered_pair @ ( sk23 @ B @ A ) @ C ) @ ( singleton @ ( sk23 @ B @ A ) ) ) @ A )
| ( in @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ B @ A ) @ ( sk25 @ B @ A ) ) @ ( singleton @ ( sk24 @ B @ A ) ) ) @ A ) ),
inference(rewrite,[status(thm)],[182,97]) ).
thf(3841,plain,
! [B: $i,A: $i] :
( ~ sk6
| ~ sk5
| ~ sk4
| ~ ( empty @ B )
| ( ( in @ sk7 @ ( relation_dom @ sk2 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[55,127]) ).
thf(3842,plain,
( ~ sk6
| ~ sk5
| ~ sk4
| ~ ( empty @ ( relation_dom @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[3841:[bind(A,$thf( sk7 )),bind(B,$thf( relation_dom @ sk2 ))]]) ).
thf(43464,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ G @ H ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ sk3 ) ) ) ) ) ) )
!= ( relation @ H ) ) ),
inference(paramod_ordered,[status(thm)],[38818,220]) ).
thf(43465,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ sk3 ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[43464:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( O )),bind(E,$thf( Q )),bind(F,$thf( S )),bind(G,$thf( G )),bind(H,$thf( relation_rng_restriction @ I @ ( relation_rng_restriction @ K @ ( relation_rng_restriction @ M @ ( relation_rng_restriction @ O @ ( relation_rng_restriction @ Q @ ( relation_rng_restriction @ S @ sk3 ) ) ) ) ) ))]]) ).
thf(43842,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ sk3 ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[43465]) ).
thf(299,plain,
! [B: $i,A: $i] :
( sk4
| ~ ( in @ A @ ( relation_dom @ sk2 ) )
| ( in @ B @ ( relation_dom @ sk3 ) )
| ( ( in @ ( apply @ sk3 @ A ) @ sk1 )
!= ( in @ B @ ( relation_dom @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[56,51]) ).
thf(307,plain,
! [B: $i,A: $i] :
( sk4
| ( in @ B @ ( relation_dom @ sk3 ) )
| ~ ( in @ A @ ( relation_dom @ sk2 ) )
| ( ( apply @ sk3 @ A )
!= B )
| ( ( relation_dom @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[299]) ).
thf(310,plain,
! [A: $i] :
( sk4
| ( in @ ( apply @ sk3 @ A ) @ ( relation_dom @ sk3 ) )
| ~ ( in @ A @ ( relation_dom @ sk2 ) )
| ( ( relation_dom @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[307]) ).
thf(46,plain,
( sk4
| ( sk2
!= ( relation_rng_restriction @ sk1 @ sk3 ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(67,plain,
( ( ( relation_rng_restriction @ sk1 @ sk3 )
!= sk2 )
| sk4 ),
inference(lifteq,[status(thm)],[46]) ).
thf(20022,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) ) @ sk3 )
| ( empty @ sk3 )
| ( ( relation_dom @ sk3 )
!= ( relation_dom @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[3874,19770]) ).
thf(20023,plain,
( ( in @ ( unordered_pair @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) ) @ sk3 )
| ( empty @ sk3 ) ),
inference(pattern_uni,[status(thm)],[20022:[]]) ).
thf(21438,plain,
( ( empty @ ( relation_dom @ sk27 ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[86,21396]) ).
thf(21464,plain,
( ( relation_dom @ sk27 )
!= empty_set ),
inference(simp,[status(thm)],[21438]) ).
thf(255,plain,
( ~ sk6
| ~ sk5
| ~ sk4
| ~ ( in @ ( apply @ sk3 @ sk7 ) @ sk1 )
| ( ( in @ sk7 @ ( relation_dom @ sk3 ) )
!= ( in @ sk7 @ ( relation_dom @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[55,49]) ).
thf(261,plain,
( ~ sk6
| ~ sk5
| ~ sk4
| ~ ( in @ ( apply @ sk3 @ sk7 ) @ sk1 )
| ( sk7 != sk7 )
| ( ( relation_dom @ sk3 )
!= ( relation_dom @ sk2 ) ) ),
inference(simp,[status(thm)],[255]) ).
thf(262,plain,
( ~ sk6
| ~ sk5
| ~ sk4
| ~ ( in @ ( apply @ sk3 @ sk7 ) @ sk1 )
| ( ( relation_dom @ sk3 )
!= ( relation_dom @ sk2 ) ) ),
inference(simp,[status(thm)],[261]) ).
thf(463,plain,
( ~ sk6
| ~ sk5
| ~ sk4
| ~ ( in @ ( apply @ sk3 @ sk7 ) @ sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[262]) ).
thf(3935,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ A @ B )
!= empty_set )
| ( ( unordered_pair @ B @ A )
!= ( unordered_pair @ ( unordered_pair @ D @ C ) @ ( singleton @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[71,2873]) ).
thf(3936,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ A @ B ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[3935:[bind(A,$thf( singleton @ G )),bind(B,$thf( unordered_pair @ E @ G )),bind(C,$thf( G )),bind(D,$thf( E ))]]) ).
thf(3943,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ A @ B ) )
!= empty_set ),
inference(simp,[status(thm)],[3936]) ).
thf(51341,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ I @ J ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ ( relation_rng_restriction @ H @ empty_set ) ) ) ) ) ) ) ) )
!= ( relation @ J ) ) ),
inference(paramod_ordered,[status(thm)],[47627,220]) ).
thf(51342,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ ( relation_rng_restriction @ H @ ( relation_rng_restriction @ I @ empty_set ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[51341:[bind(A,$thf( K )),bind(B,$thf( M )),bind(C,$thf( O )),bind(D,$thf( Q )),bind(E,$thf( S )),bind(F,$thf( U )),bind(G,$thf( W )),bind(H,$thf( Y )),bind(I,$thf( I )),bind(J,$thf( relation_rng_restriction @ K @ ( relation_rng_restriction @ M @ ( relation_rng_restriction @ O @ ( relation_rng_restriction @ Q @ ( relation_rng_restriction @ S @ ( relation_rng_restriction @ U @ ( relation_rng_restriction @ W @ ( relation_rng_restriction @ Y @ empty_set ) ) ) ) ) ) ) ))]]) ).
thf(51758,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ ( relation_rng_restriction @ H @ ( relation_rng_restriction @ I @ empty_set ) ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[51342]) ).
thf(4794,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)],[71,3943]) ).
thf(4795,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ A ) @ ( unordered_pair @ A @ B ) )
!= empty_set ),
inference(pattern_uni,[status(thm)],[4794:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ B )
| ~ ( relation @ C )
| ( sk17 @ B @ A @ C )
| ( in @ ( ordered_pair @ ( sk20 @ C @ B @ A ) @ ( sk21 @ C @ B @ A ) ) @ B )
| ( C
= ( relation_rng_restriction @ A @ B ) ) ),
inference(cnf,[status(esa)],[149]) ).
thf(159,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_rng_restriction @ A @ B ) )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ( sk17 @ B @ A @ C )
| ( in @ ( ordered_pair @ ( sk20 @ C @ B @ A ) @ ( sk21 @ C @ B @ A ) ) @ B ) ),
inference(lifteq,[status(thm)],[157]) ).
thf(8140,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( relation_rng_restriction @ A @ B ) )
| ~ ( 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 ) ) ) @ B ) ),
inference(rewrite,[status(thm)],[159,97]) ).
thf(456,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ ( sk13 @ A ) )
!= ( empty @ ( ordered_pair @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[108,114]) ).
thf(459,plain,
! [C: $i,B: $i,A: $i] :
( ( sk13 @ A )
!= ( ordered_pair @ B @ C ) ),
inference(simp,[status(thm)],[456]) ).
thf(1596,plain,
! [C: $i,B: $i,A: $i] :
( ( sk13 @ A )
!= ( unordered_pair @ ( unordered_pair @ B @ C ) @ ( singleton @ B ) ) ),
inference(rewrite,[status(thm)],[459,97]) ).
thf(1615,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( unordered_pair @ B @ A )
!= ( sk13 @ C ) )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ ( unordered_pair @ D @ E ) @ ( singleton @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[71,1596]) ).
thf(1616,plain,
! [C: $i,B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ C ) @ ( unordered_pair @ C @ B ) )
!= ( sk13 @ A ) ),
inference(pattern_uni,[status(thm)],[1615:[bind(A,$thf( unordered_pair @ H @ G )),bind(B,$thf( singleton @ H )),bind(C,$thf( C )),bind(D,$thf( H )),bind(E,$thf( G ))]]) ).
thf(1628,plain,
! [C: $i,B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ C ) @ ( unordered_pair @ C @ B ) )
!= ( sk13 @ A ) ),
inference(simp,[status(thm)],[1616]) ).
thf(7089,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ ( singleton @ B ) @ ( unordered_pair @ B @ A ) )
!= empty_set ),
inference(rewrite,[status(thm)],[1628,2650]) ).
thf(445,plain,
! [B: $i,A: $i] :
( ( empty @ ( unordered_pair @ A @ B ) )
!= ( empty @ empty_set ) ),
inference(paramod_ordered,[status(thm)],[86,103]) ).
thf(450,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ A @ B )
!= empty_set ),
inference(simp,[status(thm)],[445]) ).
thf(20034,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) ) @ sk3 )
| ( empty @ sk3 )
| ( ( relation_dom @ sk3 )
!= ( relation_dom @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[4157,19770]) ).
thf(20035,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) ) @ sk3 )
| ( empty @ sk3 ) ),
inference(pattern_uni,[status(thm)],[20034:[]]) ).
thf(27427,plain,
( ( sk27 != sk2 )
| ( ( relation_dom @ sk2 )
!= ( relation_dom @ empty_set ) ) ),
inference(paramod_ordered,[status(thm)],[27230,20829]) ).
thf(27587,plain,
( ( sk27 != sk2 )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[27427]) ).
thf(10224,plain,
! [B: $i,A: $i] :
( ( empty @ ( relation_dom @ sk2 ) )
| sk4
| ( element @ A @ B )
| ( ( in @ ( sk14 @ ( relation_dom @ sk2 ) ) @ ( relation_dom @ sk3 ) )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9047,129]) ).
thf(10225,plain,
( ( empty @ ( relation_dom @ sk2 ) )
| sk4
| ( element @ ( sk14 @ ( relation_dom @ sk2 ) ) @ ( relation_dom @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[10224:[bind(A,$thf( sk14 @ ( relation_dom @ sk2 ) )),bind(B,$thf( relation_dom @ sk3 ))]]) ).
thf(258,plain,
( ~ ( in @ sk7 @ ( relation_dom @ sk3 ) )
| ~ sk6
| ~ sk5
| ~ sk4
| ( ( in @ ( apply @ sk3 @ sk7 ) @ sk1 )
!= ( in @ sk7 @ ( relation_dom @ sk3 ) ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(151,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ B )
| ~ ( relation @ C )
| ( C
!= ( relation_rng_restriction @ A @ B ) )
| ~ ( in @ E @ A )
| ~ ( in @ ( ordered_pair @ D @ E ) @ B )
| ( in @ ( ordered_pair @ D @ E ) @ C ) ),
inference(cnf,[status(esa)],[149]) ).
thf(167,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( relation_rng_restriction @ A @ B ) )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ~ ( in @ E @ A )
| ~ ( in @ ( ordered_pair @ D @ E ) @ B )
| ( in @ ( ordered_pair @ D @ E ) @ C ) ),
inference(lifteq,[status(thm)],[151]) ).
thf(168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ B )
| ~ ( relation @ ( relation_rng_restriction @ A @ B ) )
| ~ ( in @ D @ A )
| ~ ( in @ ( ordered_pair @ C @ D ) @ B )
| ( in @ ( ordered_pair @ C @ D ) @ ( relation_rng_restriction @ A @ B ) ) ),
inference(simp,[status(thm)],[167]) ).
thf(13267,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ B )
| ~ ( relation @ ( relation_rng_restriction @ A @ B ) )
| ~ ( in @ D @ A )
| ~ ( in @ ( unordered_pair @ ( unordered_pair @ C @ D ) @ ( singleton @ C ) ) @ B )
| ( in @ ( unordered_pair @ ( unordered_pair @ C @ D ) @ ( singleton @ C ) ) @ ( relation_rng_restriction @ A @ B ) ) ),
inference(rewrite,[status(thm)],[168,97]) ).
thf(30686,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk29 != sk27 )
| ( A != sk29 ) ),
inference(paramod_ordered,[status(thm)],[106,27603]) ).
thf(30687,plain,
( ~ ( empty @ sk29 )
| ( sk29 != sk27 ) ),
inference(pattern_uni,[status(thm)],[30686:[bind(A,$thf( sk29 ))]]) ).
thf(5407,plain,
( ~ sk5
| ~ sk4
| ( sk1 != empty_set )
| ~ ( empty @ ( relation_dom @ sk2 ) )
| ( sk6 != sk6 ) ),
inference(paramod_ordered,[status(thm)],[3898,3842]) ).
thf(5408,plain,
( ~ sk5
| ~ sk4
| ( sk1 != empty_set )
| ~ ( empty @ ( relation_dom @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[5407:[]]) ).
thf(198,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)],[196]) ).
thf(203,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)],[198]) ).
thf(204,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)],[203]) ).
thf(20842,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)],[204,97]) ).
thf(20218,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk27 != sk3 )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[106,20162]) ).
thf(20219,plain,
( ~ ( empty @ sk3 )
| ( sk27 != sk3 ) ),
inference(pattern_uni,[status(thm)],[20218:[bind(A,$thf( sk3 ))]]) ).
thf(50413,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ H @ I ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ sk16 ) ) ) ) ) ) ) )
!= ( relation @ I ) ) ),
inference(paramod_ordered,[status(thm)],[47134,220]) ).
thf(50414,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ ( relation_rng_restriction @ H @ sk16 ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[50413:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( P )),bind(E,$thf( R )),bind(F,$thf( T )),bind(G,$thf( V )),bind(H,$thf( H )),bind(I,$thf( relation_rng_restriction @ J @ ( relation_rng_restriction @ L @ ( relation_rng_restriction @ N @ ( relation_rng_restriction @ P @ ( relation_rng_restriction @ R @ ( relation_rng_restriction @ T @ ( relation_rng_restriction @ V @ sk16 ) ) ) ) ) ) ))]]) ).
thf(50848,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ ( relation_rng_restriction @ H @ sk16 ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[50414]) ).
thf(1228,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)],[71,450]) ).
thf(1229,plain,
! [B: $i,A: $i] :
( ( unordered_pair @ B @ A )
!= empty_set ),
inference(pattern_uni,[status(thm)],[1228:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(3821,plain,
! [B: $i,A: $i] :
( sk6
| ~ sk5
| ~ sk4
| ~ ( empty @ B )
| ( ( in @ ( apply @ sk3 @ sk8 ) @ sk1 )
!= ( in @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[61,127]) ).
thf(3822,plain,
( sk6
| ~ sk5
| ~ sk4
| ~ ( empty @ sk1 ) ),
inference(pattern_uni,[status(thm)],[3821:[bind(A,$thf( apply @ sk3 @ sk8 )),bind(B,$thf( sk1 ))]]) ).
thf(132,plain,
empty @ sk15,
inference(cnf,[status(esa)],[130]) ).
thf(2333,plain,
! [A: $i] :
( ( A = empty_set )
| ( ( empty @ sk15 )
!= ( empty @ A ) ) ),
inference(paramod_ordered,[status(thm)],[132,106]) ).
thf(2334,plain,
sk15 = empty_set,
inference(pattern_uni,[status(thm)],[2333:[bind(A,$thf( sk15 ))]]) ).
thf(94,plain,
! [A: $i] :
( ( empty @ A )
| ~ ( empty @ ( sk12 @ A ) ) ),
inference(cnf,[status(esa)],[92]) ).
thf(325,plain,
( ( sk3 != sk2 )
| ~ sk4
| ~ ( in @ sk7 @ ( relation_dom @ sk3 ) )
| ~ ( in @ ( apply @ sk3 @ sk7 ) @ sk1 )
| ~ sk6
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[320,49]) ).
thf(326,plain,
( ( sk3 != sk2 )
| ~ sk4
| ~ ( in @ sk7 @ ( relation_dom @ sk3 ) )
| ~ ( in @ ( apply @ sk3 @ sk7 ) @ sk1 )
| ~ sk6 ),
inference(pattern_uni,[status(thm)],[325:[]]) ).
thf(331,plain,
( ( sk3 != sk2 )
| ~ sk4
| sk6
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[320,272]) ).
thf(332,plain,
( ( sk3 != sk2 )
| ~ sk4
| sk6 ),
inference(pattern_uni,[status(thm)],[331:[]]) ).
thf(24384,plain,
! [A: $i] :
( ~ ( empty @ A )
| ( sk28 != sk27 )
| ( A
!= ( relation_dom @ sk28 ) ) ),
inference(paramod_ordered,[status(thm)],[106,22731]) ).
thf(24385,plain,
( ~ ( empty @ ( relation_dom @ sk28 ) )
| ( sk28 != sk27 ) ),
inference(pattern_uni,[status(thm)],[24384:[bind(A,$thf( relation_dom @ sk28 ))]]) ).
thf(62,plain,
! [A: $i] :
( sk4
| ~ ( in @ A @ ( relation_dom @ sk3 ) )
| ~ ( in @ ( apply @ sk3 @ A ) @ sk1 )
| ( in @ A @ ( relation_dom @ sk2 ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(68,plain,
! [A: $i] :
( sk4
| ~ ( in @ A @ ( relation_dom @ sk3 ) )
| ~ ( in @ ( apply @ sk3 @ A ) @ sk1 )
| ( in @ A @ ( relation_dom @ sk2 ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(22125,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) ) @ sk3 )
| ( sk3 = empty_set )
| ( ( relation_dom @ sk3 )
!= ( relation_dom @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[4157,19925]) ).
thf(22126,plain,
( ( in @ ( unordered_pair @ ( singleton @ ( sk24 @ empty_set @ sk3 ) ) @ ( unordered_pair @ ( sk24 @ empty_set @ sk3 ) @ ( sk25 @ empty_set @ sk3 ) ) ) @ sk3 )
| ( sk3 = empty_set ) ),
inference(pattern_uni,[status(thm)],[22125:[]]) ).
thf(155,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ B )
| ~ ( relation @ C )
| ( C
!= ( relation_rng_restriction @ A @ B ) )
| ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ ( ordered_pair @ D @ E ) @ B ) ),
inference(cnf,[status(esa)],[149]) ).
thf(162,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( relation_rng_restriction @ A @ B ) )
| ~ ( relation @ B )
| ~ ( relation @ C )
| ~ ( in @ ( ordered_pair @ D @ E ) @ C )
| ( in @ ( ordered_pair @ D @ E ) @ B ) ),
inference(lifteq,[status(thm)],[155]) ).
thf(163,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ B )
| ~ ( relation @ ( relation_rng_restriction @ A @ B ) )
| ~ ( in @ ( ordered_pair @ C @ D ) @ ( relation_rng_restriction @ A @ B ) )
| ( in @ ( ordered_pair @ C @ D ) @ B ) ),
inference(simp,[status(thm)],[162]) ).
thf(11309,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( relation @ B )
| ~ ( relation @ ( relation_rng_restriction @ A @ B ) )
| ~ ( in @ ( unordered_pair @ ( unordered_pair @ C @ D ) @ ( singleton @ C ) ) @ ( relation_rng_restriction @ A @ B ) )
| ( in @ ( unordered_pair @ ( unordered_pair @ C @ D ) @ ( singleton @ C ) ) @ B ) ),
inference(rewrite,[status(thm)],[163,97]) ).
thf(9027,plain,
! [C: $i,B: $i,A: $i] :
( ( empty @ A )
| ( element @ B @ C )
| ( ( in @ ( sk14 @ A ) @ A )
!= ( in @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[4765,129]) ).
thf(9028,plain,
! [A: $i] :
( ( empty @ A )
| ( element @ ( sk14 @ A ) @ A ) ),
inference(pattern_uni,[status(thm)],[9027:[bind(A,$thf( D )),bind(B,$thf( sk14 @ D )),bind(C,$thf( D ))]]) ).
thf(9066,plain,
! [A: $i] :
( ( empty @ A )
| ( element @ ( sk14 @ A ) @ A ) ),
inference(simp,[status(thm)],[9028]) ).
thf(48297,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( relation @ ( relation_rng_restriction @ H @ I ) )
| ( ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ sk3 ) ) ) ) ) ) ) )
!= ( relation @ I ) ) ),
inference(paramod_ordered,[status(thm)],[43842,220]) ).
thf(48298,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ ( relation_rng_restriction @ H @ sk3 ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[48297:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( N )),bind(D,$thf( P )),bind(E,$thf( R )),bind(F,$thf( T )),bind(G,$thf( V )),bind(H,$thf( H )),bind(I,$thf( relation_rng_restriction @ J @ ( relation_rng_restriction @ L @ ( relation_rng_restriction @ N @ ( relation_rng_restriction @ P @ ( relation_rng_restriction @ R @ ( relation_rng_restriction @ T @ ( relation_rng_restriction @ V @ sk3 ) ) ) ) ) ) ))]]) ).
thf(48697,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( relation @ ( relation_rng_restriction @ A @ ( relation_rng_restriction @ B @ ( relation_rng_restriction @ C @ ( relation_rng_restriction @ D @ ( relation_rng_restriction @ E @ ( relation_rng_restriction @ F @ ( relation_rng_restriction @ G @ ( relation_rng_restriction @ H @ sk3 ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[48298]) ).
thf(144,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( relation @ C )
| ~ ( function @ C )
| ~ ( in @ A @ ( relation_dom @ C ) )
| ( B
!= ( apply @ C @ A ) )
| ( in @ ( ordered_pair @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[141]) ).
thf(146,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( apply @ C @ A ) )
| ~ ( relation @ C )
| ~ ( function @ C )
| ~ ( in @ A @ ( relation_dom @ C ) )
| ( in @ ( ordered_pair @ A @ B ) @ C ) ),
inference(lifteq,[status(thm)],[144]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ~ ( relation @ B )
| ~ ( function @ B )
| ~ ( in @ A @ ( relation_dom @ B ) )
| ( in @ ( ordered_pair @ A @ ( apply @ B @ A ) ) @ B ) ),
inference(simp,[status(thm)],[146]) ).
thf(6842,plain,
! [B: $i,A: $i] :
( ~ ( relation @ B )
| ~ ( function @ B )
| ~ ( in @ A @ ( relation_dom @ B ) )
| ( in @ ( unordered_pair @ ( unordered_pair @ A @ ( apply @ B @ A ) ) @ ( singleton @ A ) ) @ B ) ),
inference(rewrite,[status(thm)],[147,97]) ).
thf(215,plain,
relation_empty_yielding @ sk28,
inference(cnf,[status(esa)],[214]) ).
thf(68936,plain,
$false,
inference(cvc4,[status(thm)],[69,3930,19936,20162,25960,19841,365,138,2889,101,4824,3830,6431,19543,234,115,217,33870,120,28718,1671,56,22076,3895,3836,19575,27230,22704,3898,320,9013,36055,20803,49777,288,52,45187,22569,23587,110,125,50309,189,19604,23647,20181,57,78,93,20027,4368,228,216,27067,20042,35321,2650,211,106,7317,41755,30208,61,221,133,20156,47134,293,49243,312,74,206,13838,7321,233,47627,4323,28473,39650,20025,85,48158,220,4172,25156,8113,2705,38818,10099,20829,260,21564,25944,137,92,26637,32345,23282,3894,27576,23604,224,229,2873,97,24289,7173,20693,188,27678,169,141,37145,22124,2877,3846,77,30905,25968,16683,212,124,225,27031,28678,25926,1297,12218,2845,34273,33269,3222,129,28512,31474,134,73,128,244,4765,41285,5737,26986,16296,22731,22068,31737,27579,42623,3890,148,8110,161,64,1374,25864,27582,21465,191,2568,27590,25870,259,44,27549,59,118,71,54,34936,14360,86,49,2759,11686,219,27594,9047,230,245,98,22120,2378,271,103,29992,140,213,6429,26463,1293,91,27149,22074,66,130,23377,14294,223,135,2752,27114,226,39164,80,9111,22765,19770,8979,374,209,112,28195,27603,11795,44296,29078,44743,36434,14417,63,3842,43842,25056,310,19584,21396,48,19925,95,9037,32033,67,8111,20023,33566,21464,463,127,30636,32960,3943,51758,4795,8140,19688,72,7089,450,87,2078,3874,20035,104,23205,38452,21376,218,34551,27587,10225,55,139,4250,258,4591,26317,13267,19600,383,30687,30426,82,214,119,58,5408,235,20842,262,51,20219,50848,190,29323,1229,7171,3822,210,136,42180,2334,195,4157,2366,36817,94,326,107,332,24385,68,22126,11309,47,9066,26154,48697,122,83,6842,25966,215,222,20039,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU043+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 12:54:16 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.91/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/0.97 % [INFO] Parsing done (133ms).
% 1.18/0.98 % [INFO] Running in sequential loop mode.
% 1.76/1.18 % [INFO] eprover registered as external prover.
% 1.76/1.18 % [INFO] cvc4 registered as external prover.
% 1.76/1.18 % [INFO] Scanning for conjecture ...
% 1.93/1.25 % [INFO] Found a conjecture and 41 axioms. Running axiom selection ...
% 2.08/1.30 % [INFO] Axiom selection finished. Selected 41 axioms (removed 0 axioms).
% 2.08/1.34 % [INFO] Problem is first-order (TPTP FOF).
% 2.34/1.34 % [INFO] Type checking passed.
% 2.34/1.34 % [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 ...
% 280.05/56.47 % External prover 'cvc4' found a proof!
% 280.05/56.47 % [INFO] Killing All external provers ...
% 280.05/56.47 % Time passed: 55960ms (effective reasoning time: 55492ms)
% 280.05/56.47 % 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)>
% 280.05/56.48 % Axioms used in derivation (41): rc3_funct_1, cc1_relat_1, rc1_funct_1, t8_funct_1, t4_subset, fc5_relat_1, rc2_xboole_0, antisymmetry_r2_hidden, fc1_zfmisc_1, d4_funct_1, fc1_xboole_0, d5_tarski, fc4_relat_1, d12_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, fc5_funct_1, rc2_funct_1, rc1_subset_1, cc2_funct_1, t3_subset, existence_m1_subset_1, commutativity_k2_tarski, dt_k8_relat_1, rc2_relat_1, rc1_relat_1, reflexivity_r1_tarski, t8_boole, rc1_xboole_0, t2_subset, fc7_relat_1, fc12_relat_1
% 280.05/56.48 % No. of inferences in proof: 729
% 280.05/56.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 55960 ms resp. 55492 ms w/o parsing
% 280.58/56.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 280.58/56.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------