TSTP Solution File: SET023-3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET023-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 11:52:00 EDT 2023
% Result : Unsatisfiable 4.70s 2.10s
% Output : Refutation 5.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 217
% Syntax : Number of formulae : 364 ( 27 unt; 71 typ; 0 def)
% Number of atoms : 749 ( 112 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 2902 ( 430 ~; 456 |; 0 &;2016 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 119 ( 119 >; 0 *; 0 +; 0 <<)
% Number of symbols : 73 ( 71 usr; 8 con; 0-5 aty)
% Number of variables : 664 ( 0 ^; 664 !; 0 ?; 664 :)
% Comments :
%------------------------------------------------------------------------------
thf(little_set_type,type,
little_set: $i > $o ).
thf(second_type,type,
second: $i > $i ).
thf(a_type,type,
a: $i ).
thf(successor_type,type,
successor: $i > $i ).
thf(union_type,type,
union: $i > $i > $i ).
thf(singleton_set_type,type,
singleton_set: $i > $i ).
thf(proper_subset_type,type,
proper_subset: $i > $i > $o ).
thf(homomorphism_type,type,
homomorphism: $i > $i > $i > $i > $i > $o ).
thf(maps_type,type,
maps: $i > $i > $i > $o ).
thf(member_type,type,
member: $i > $i > $o ).
thf(image_type,type,
image: $i > $i > $i ).
thf(first_type,type,
first: $i > $i ).
thf(f22_type,type,
f22: $i > $i > $i > $i ).
thf(one_to_one_function_type,type,
one_to_one_function: $i > $o ).
thf(function_type,type,
function: $i > $o ).
thf(single_valued_set_type,type,
single_valued_set: $i > $o ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(f19_type,type,
f19: $i > $i ).
thf(f21_type,type,
f21: $i > $i ).
thf(relation_type,type,
relation: $i > $o ).
thf(sigma_type,type,
sigma: $i > $i ).
thf(f16_type,type,
f16: $i > $i > $i ).
thf(f1_type,type,
f1: $i > $i > $i ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(f20_type,type,
f20: $i > $i ).
thf(non_ordered_pair_type,type,
non_ordered_pair: $i > $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(f25_type,type,
f25: $i ).
thf(domain_of_type,type,
domain_of: $i > $i ).
thf(range_of_type,type,
range_of: $i > $i ).
thf(ordered_pair_predicate_type,type,
ordered_pair_predicate: $i > $o ).
thf(f27_type,type,
f27: $i > $i > $i ).
thf(closed_type,type,
closed: $i > $i > $o ).
thf(cross_product_type,type,
cross_product: $i > $i > $i ).
thf(f4_type,type,
f4: $i > $i > $i ).
thf(f5_type,type,
f5: $i > $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(infinity_type,type,
infinity: $i ).
thf(disjoint_type,type,
disjoint: $i > $i > $o ).
thf(f17_type,type,
f17: $i > $i > $i ).
thf(converse_type,type,
converse: $i > $i ).
thf(apply_type,type,
apply: $i > $i > $i ).
thf(apply_to_two_arguments_type,type,
apply_to_two_arguments: $i > $i > $i > $i ).
thf(estin_type,type,
estin: $i ).
thf(compose_type,type,
compose: $i > $i > $i ).
thf(f29_type,type,
f29: $i > $i > $i > $i ).
thf(f31_type,type,
f31: $i > $i > $i > $i ).
thf(f28_type,type,
f28: $i > $i > $i > $i ).
thf(identity_relation_type,type,
identity_relation: $i ).
thf(rotate_right_type,type,
rotate_right: $i > $i ).
thf(f10_type,type,
f10: $i > $i > $i ).
thf(f11_type,type,
f11: $i > $i > $i ).
thf(f9_type,type,
f9: $i > $i > $i ).
thf(f30_type,type,
f30: $i > $i > $i > $i ).
thf(f8_type,type,
f8: $i > $i > $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(f24_type,type,
f24: $i > $i ).
thf(f33_type,type,
f33: $i > $i > $i > $i > $i > $i ).
thf(f2_type,type,
f2: $i > $i ).
thf(f3_type,type,
f3: $i > $i ).
thf(f32_type,type,
f32: $i > $i > $i > $i > $i > $i ).
thf(flip_range_of_type,type,
flip_range_of: $i > $i ).
thf(f12_type,type,
f12: $i > $i > $i ).
thf(f14_type,type,
f14: $i > $i > $i ).
thf(f13_type,type,
f13: $i > $i > $i ).
thf(restrict_type,type,
restrict: $i > $i > $i ).
thf(universal_set_type,type,
universal_set: $i ).
thf(f6_type,type,
f6: $i > $i > $i ).
thf(f7_type,type,
f7: $i > $i > $i ).
thf(f26_type,type,
f26: $i > $i ).
thf(45,axiom,
! [A: $i] :
( ~ ( member @ A @ identity_relation )
| ( ordered_pair_predicate @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation1) ).
thf(244,plain,
! [A: $i] :
( ~ ( member @ A @ identity_relation )
| ( ordered_pair_predicate @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(96,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( rotate_right @ B ) )
| ~ ( little_set @ A )
| ~ ( little_set @ C )
| ~ ( little_set @ D )
| ~ ( little_set @ E )
| ( A
!= ( ordered_pair @ C @ ( ordered_pair @ D @ E ) ) )
| ~ ( member @ ( ordered_pair @ D @ ( ordered_pair @ E @ C ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right6) ).
thf(365,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( rotate_right @ B ) )
| ~ ( little_set @ A )
| ~ ( little_set @ C )
| ~ ( little_set @ D )
| ~ ( little_set @ E )
| ( A
!= ( ordered_pair @ C @ ( ordered_pair @ D @ E ) ) )
| ~ ( member @ ( ordered_pair @ D @ ( ordered_pair @ E @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(140,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( single_valued_set @ A )
| ~ ( little_set @ B )
| ~ ( little_set @ C )
| ~ ( little_set @ D )
| ~ ( member @ ( ordered_pair @ B @ C ) @ A )
| ~ ( member @ ( ordered_pair @ B @ D ) @ A )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set1) ).
thf(479,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( single_valued_set @ A )
| ~ ( little_set @ B )
| ~ ( little_set @ C )
| ~ ( little_set @ D )
| ~ ( member @ ( ordered_pair @ B @ C ) @ A )
| ~ ( member @ ( ordered_pair @ B @ D ) @ A )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(40,axiom,
! [A: $i] :
~ ( member @ A @ empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
thf(234,plain,
! [A: $i] :
~ ( member @ A @ empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( disjoint @ A @ B )
| ~ ( member @ C @ A )
| ~ ( member @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint1) ).
thf(217,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( disjoint @ A @ B )
| ~ ( member @ C @ A )
| ~ ( member @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(73,axiom,
! [A: $i] :
( ~ ( function @ A )
| ( relation @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function1) ).
thf(308,plain,
! [A: $i] :
( ~ ( function @ A )
| ( relation @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(101,axiom,
! [A: $i] :
( ( member @ A @ universal_set )
| ~ ( little_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',universal_set) ).
thf(379,plain,
! [A: $i] :
( ( member @ A @ universal_set )
| ~ ( little_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( flip_range_of @ B ) )
| ( little_set @ ( f14 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range3) ).
thf(408,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( flip_range_of @ B ) )
| ( little_set @ ( f14 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
thf(170,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(104,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( compose @ B @ C ) )
| ~ ( little_set @ A )
| ~ ( little_set @ D )
| ~ ( little_set @ E )
| ~ ( little_set @ F )
| ( A
!= ( ordered_pair @ D @ E ) )
| ~ ( member @ ( ordered_pair @ D @ F ) @ B )
| ~ ( member @ ( ordered_pair @ F @ E ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose7) ).
thf(385,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( compose @ B @ C ) )
| ~ ( little_set @ A )
| ~ ( little_set @ D )
| ~ ( little_set @ E )
| ~ ( little_set @ F )
| ( A
!= ( ordered_pair @ D @ E ) )
| ~ ( member @ ( ordered_pair @ D @ F ) @ B )
| ~ ( member @ ( ordered_pair @ F @ E ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( apply @ B @ C ) )
| ~ ( ordered_pair_predicate @ D )
| ~ ( member @ D @ B )
| ( ( first @ D )
!= C )
| ~ ( member @ A @ ( second @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply5) ).
thf(340,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( apply @ B @ C ) )
| ~ ( ordered_pair_predicate @ D )
| ~ ( member @ D @ B )
| ( ( first @ D )
!= C )
| ~ ( member @ A @ ( second @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset1) ).
thf(185,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( powerset @ B ) )
| ( subset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(78,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( homomorphism @ A @ B @ C @ D @ E )
| ~ ( closed @ B @ C )
| ~ ( closed @ D @ E )
| ~ ( maps @ A @ B @ D )
| ( ( apply @ A @ ( apply_to_two_arguments @ C @ ( f32 @ A @ B @ C @ D @ E ) @ ( f33 @ A @ B @ C @ D @ E ) ) )
!= ( apply_to_two_arguments @ E @ ( apply @ A @ ( f32 @ A @ B @ C @ D @ E ) ) @ ( apply @ A @ ( f33 @ A @ B @ C @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism7) ).
thf(320,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( homomorphism @ A @ B @ C @ D @ E )
| ~ ( closed @ B @ C )
| ~ ( closed @ D @ E )
| ~ ( maps @ A @ B @ D )
| ( ( apply @ A @ ( apply_to_two_arguments @ C @ ( f32 @ A @ B @ C @ D @ E ) @ ( f33 @ A @ B @ C @ D @ E ) ) )
!= ( apply_to_two_arguments @ E @ ( apply @ A @ ( f32 @ A @ B @ C @ D @ E ) ) @ ( apply @ A @ ( f33 @ A @ B @ C @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( apply @ B @ C ) )
| ( ( first @ ( f28 @ A @ B @ C ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply3) ).
thf(257,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( apply @ B @ C ) )
| ( ( first @ ( f28 @ A @ B @ C ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( non_ordered_pair @ B @ C ) )
| ( A = B )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair1) ).
thf(174,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( non_ordered_pair @ B @ C ) )
| ( A = B )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( image @ B @ C ) )
| ~ ( little_set @ A )
| ~ ( ordered_pair_predicate @ D )
| ~ ( member @ D @ C )
| ~ ( member @ ( first @ D ) @ B )
| ( ( second @ D )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution5) ).
thf(404,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( image @ B @ C ) )
| ~ ( little_set @ A )
| ~ ( ordered_pair_predicate @ D )
| ~ ( member @ D @ C )
| ~ ( member @ ( first @ D ) @ B )
| ( ( second @ D )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(105,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( flip_range_of @ B ) )
| ~ ( little_set @ A )
| ~ ( little_set @ C )
| ~ ( little_set @ D )
| ~ ( little_set @ E )
| ( A
!= ( ordered_pair @ C @ ( ordered_pair @ D @ E ) ) )
| ~ ( member @ ( ordered_pair @ C @ ( ordered_pair @ E @ D ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range6) ).
thf(389,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( flip_range_of @ B ) )
| ~ ( little_set @ A )
| ~ ( little_set @ C )
| ~ ( little_set @ D )
| ~ ( little_set @ E )
| ( A
!= ( ordered_pair @ C @ ( ordered_pair @ D @ E ) ) )
| ~ ( member @ ( ordered_pair @ C @ ( ordered_pair @ E @ D ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(87,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( first @ B ) )
| ( little_set @ ( f5 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first2) ).
thf(344,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( first @ B ) )
| ( little_set @ ( f5 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( image @ B @ C ) )
| ( member @ ( first @ ( f22 @ A @ B @ C ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution3) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( image @ B @ C ) )
| ( member @ ( first @ ( f22 @ A @ B @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( domain_of @ B ) )
| ( member @ ( f8 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
thf(284,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( domain_of @ B ) )
| ( member @ ( f8 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ( restrict @ A @ B )
= ( intersection @ A @ ( cross_product @ B @ universal_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restrict) ).
thf(325,plain,
! [B: $i,A: $i] :
( ( restrict @ A @ B )
= ( intersection @ A @ ( cross_product @ B @ universal_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( converse @ B ) )
| ( ordered_pair_predicate @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse1) ).
thf(228,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( converse @ B ) )
| ( ordered_pair_predicate @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( sigma @ B ) )
| ( member @ A @ ( f16 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sigma2) ).
thf(289,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( sigma @ B ) )
| ( member @ A @ ( f16 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(127,axiom,
! [A: $i] :
( ( single_valued_set @ A )
| ( little_set @ ( f20 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set3) ).
thf(448,plain,
! [A: $i] :
( ( single_valued_set @ A )
| ( little_set @ ( f20 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( apply @ B @ C ) )
| ( ordered_pair_predicate @ ( f28 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply1) ).
thf(316,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( apply @ B @ C ) )
| ( ordered_pair_predicate @ ( f28 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( second @ B ) )
| ( little_set @ ( f6 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second1) ).
thf(492,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( second @ B ) )
| ( little_set @ ( f6 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( proper_subset @ A @ B )
| ~ ( subset @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',proper_subset3) ).
thf(179,plain,
! [B: $i,A: $i] :
( ( proper_subset @ A @ B )
| ~ ( subset @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( image @ B @ C ) )
| ( ( second @ ( f22 @ A @ B @ C ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution4) ).
thf(376,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( image @ B @ C ) )
| ( ( second @ ( f22 @ A @ B @ C ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',proper_subset1) ).
thf(253,plain,
! [B: $i,A: $i] :
( ~ ( proper_subset @ A @ B )
| ( subset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(143,axiom,
! [A: $i] :
( ( single_valued_set @ A )
| ( little_set @ ( f21 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set4) ).
thf(485,plain,
! [A: $i] :
( ( single_valued_set @ A )
| ( little_set @ ( f21 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( compose @ B @ C ) )
| ( member @ ( ordered_pair @ ( f29 @ A @ B @ C ) @ ( f31 @ A @ B @ C ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose5) ).
thf(238,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( compose @ B @ C ) )
| ( member @ ( ordered_pair @ ( f29 @ A @ B @ C ) @ ( f31 @ A @ B @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( little_set @ A )
| ~ ( little_set @ B )
| ( ( non_ordered_pair @ C @ A )
!= ( non_ordered_pair @ C @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_cancellation) ).
thf(353,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( little_set @ A )
| ~ ( little_set @ B )
| ( ( non_ordered_pair @ C @ A )
!= ( non_ordered_pair @ C @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(1,negated_conjecture,
~ ( little_set @ ( second @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_second_component_is_small) ).
thf(147,plain,
~ ( little_set @ ( second @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ( member @ A @ ( powerset @ B ) )
| ~ ( little_set @ A )
| ~ ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset2) ).
thf(397,plain,
! [B: $i,A: $i] :
( ( member @ A @ ( powerset @ B ) )
| ~ ( little_set @ A )
| ~ ( subset @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(34,axiom,
! [A: $i] :
( ~ ( one_to_one_function @ A )
| ( function @ ( converse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one_function2) ).
thf(221,plain,
! [A: $i] :
( ~ ( one_to_one_function @ A )
| ( function @ ( converse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(66,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( homomorphism @ A @ B @ C @ D @ E )
| ~ ( closed @ B @ C )
| ~ ( closed @ D @ E )
| ~ ( maps @ A @ B @ D )
| ( member @ ( f33 @ A @ B @ C @ D @ E ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism6) ).
thf(293,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( homomorphism @ A @ B @ C @ D @ E )
| ~ ( closed @ B @ C )
| ~ ( closed @ D @ E )
| ~ ( maps @ A @ B @ D )
| ( member @ ( f33 @ A @ B @ C @ D @ E ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( range_of @ B ) )
| ~ ( little_set @ A )
| ~ ( ordered_pair_predicate @ C )
| ~ ( member @ C @ B )
| ( A
!= ( second @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of4) ).
thf(428,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( range_of @ B ) )
| ~ ( little_set @ A )
| ~ ( ordered_pair_predicate @ C )
| ~ ( member @ C @ B )
| ( A
!= ( second @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(54,axiom,
! [A: $i] :
( ~ ( member @ A @ infinity )
| ( member @ ( successor @ A ) @ infinity ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity3) ).
thf(265,plain,
! [A: $i] :
( ~ ( member @ A @ infinity )
| ( member @ ( successor @ A ) @ infinity ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( intersection @ B @ C ) )
| ~ ( member @ A @ B )
| ~ ( member @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
thf(206,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( intersection @ B @ C ) )
| ~ ( member @ A @ B )
| ~ ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(129,axiom,
! [A: $i] :
( ~ ( little_set @ A )
| ( A = empty_set )
| ( member @ ( ordered_pair @ A @ ( f26 @ A ) ) @ f25 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice3) ).
thf(452,plain,
! [A: $i] :
( ~ ( little_set @ A )
| ( A = empty_set )
| ( member @ ( ordered_pair @ A @ ( f26 @ A ) ) @ f25 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( cross_product @ B @ C ) )
| ( member @ ( first @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product2) ).
thf(248,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( cross_product @ B @ C ) )
| ( member @ ( first @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(56,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C @ D @ E )
| ( closed @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism1) ).
thf(270,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C @ D @ E )
| ( closed @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(24,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( first @ B ) )
| ( member @ A @ ( f4 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first4) ).
thf(201,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( first @ B ) )
| ( member @ A @ ( f4 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( rotate_right @ B ) )
| ( little_set @ ( f10 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right2) ).
thf(381,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( rotate_right @ B ) )
| ( little_set @ ( f10 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( compose @ B @ C ) )
| ( little_set @ ( f30 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose2) ).
thf(334,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( compose @ B @ C ) )
| ( little_set @ ( f30 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(70,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C @ D @ E )
| ( closed @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism2) ).
thf(302,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C @ D @ E )
| ( closed @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(68,axiom,
! [A: $i] :
( ~ ( ordered_pair_predicate @ A )
| ( A
= ( ordered_pair @ ( f2 @ A ) @ ( f3 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_predicate3) ).
thf(297,plain,
! [A: $i] :
( ~ ( ordered_pair_predicate @ A )
| ( A
= ( ordered_pair @ ( f2 @ A ) @ ( f3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(117,axiom,
! [B: $i,A: $i] :
( ( member @ A @ ( converse @ B ) )
| ~ ( little_set @ A )
| ~ ( ordered_pair_predicate @ A )
| ~ ( member @ ( ordered_pair @ ( second @ A ) @ ( first @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse3) ).
thf(424,plain,
! [B: $i,A: $i] :
( ( member @ A @ ( converse @ B ) )
| ~ ( little_set @ A )
| ~ ( ordered_pair_predicate @ A )
| ~ ( member @ ( ordered_pair @ ( second @ A ) @ ( first @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( subset @ ( range_of @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps3) ).
thf(275,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( subset @ ( range_of @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( sigma @ B ) )
| ( member @ ( f16 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sigma1) ).
thf(165,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( sigma @ B ) )
| ( member @ ( f16 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',two_sets_equal) ).
thf(260,plain,
! [B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(89,axiom,
! [A: $i] :
( ~ ( little_set @ A )
| ( little_set @ ( sigma @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sigma4) ).
thf(349,plain,
! [A: $i] :
( ~ ( little_set @ A )
| ( little_set @ ( sigma @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(142,axiom,
little_set @ infinity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity1) ).
thf(484,plain,
little_set @ infinity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(94,axiom,
! [A: $i] :
( ( member @ A @ estin )
| ~ ( little_set @ A )
| ~ ( ordered_pair_predicate @ A )
| ~ ( member @ ( first @ A ) @ ( second @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation3) ).
thf(361,plain,
! [A: $i] :
( ( member @ A @ estin )
| ~ ( little_set @ A )
| ~ ( ordered_pair_predicate @ A )
| ~ ( member @ ( first @ A ) @ ( second @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(133,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( flip_range_of @ B ) )
| ( little_set @ ( f12 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range1) ).
thf(461,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( flip_range_of @ B ) )
| ( little_set @ ( f12 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( ( domain_of @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps2) ).
thf(188,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( ( domain_of @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( little_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(356,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( little_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(137,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( second @ B ) )
| ( member @ A @ ( f7 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second4) ).
thf(471,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( second @ B ) )
| ( member @ A @ ( f7 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ~ ( closed @ A @ B )
| ( maps @ B @ ( cross_product @ A @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed3) ).
thf(193,plain,
! [B: $i,A: $i] :
( ~ ( closed @ A @ B )
| ( maps @ B @ ( cross_product @ A @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(29,axiom,
member @ empty_set @ infinity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity2) ).
thf(212,plain,
member @ empty_set @ infinity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ( ordered_pair_predicate @ A )
| ~ ( little_set @ B )
| ~ ( little_set @ C )
| ( A
!= ( ordered_pair @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_predicate4) ).
thf(393,plain,
! [C: $i,B: $i,A: $i] :
( ( ordered_pair_predicate @ A )
| ~ ( little_set @ B )
| ~ ( little_set @ C )
| ( A
!= ( ordered_pair @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(131,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( first @ B ) )
| ( little_set @ ( f4 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first1) ).
thf(457,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( first @ B ) )
| ( little_set @ ( f4 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(98,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( rotate_right @ B ) )
| ( little_set @ ( f9 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right1) ).
thf(371,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( rotate_right @ B ) )
| ( little_set @ ( f9 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(7,axiom,
! [A: $i] :
( ( single_valued_set @ A )
| ( member @ ( ordered_pair @ ( f19 @ A ) @ ( f21 @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set6) ).
thf(161,plain,
! [A: $i] :
( ( single_valued_set @ A )
| ( member @ ( ordered_pair @ ( f19 @ A ) @ ( f21 @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ~ ( member @ ( f17 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset3) ).
thf(279,plain,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ~ ( member @ ( f17 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(125,axiom,
! [B: $i,A: $i] :
( ~ ( little_set @ A )
| ~ ( function @ B )
| ( little_set @ ( image @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution6) ).
thf(444,plain,
! [B: $i,A: $i] :
( ~ ( little_set @ A )
| ~ ( function @ B )
| ( little_set @ ( image @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(2,axiom,
! [A: $i] :
( ( successor @ A )
= ( union @ A @ ( singleton_set @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor) ).
thf(149,plain,
! [A: $i] :
( ( successor @ A )
= ( union @ A @ ( singleton_set @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(63,axiom,
! [A: $i] :
( ( A = empty_set )
| ( member @ ( f24 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
thf(286,plain,
! [A: $i] :
( ( A = empty_set )
| ( member @ ( f24 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset1) ).
thf(291,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(61,axiom,
! [A: $i] :
( ( A = empty_set )
| ( disjoint @ ( f24 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
thf(281,plain,
! [A: $i] :
( ( A = empty_set )
| ( disjoint @ ( f24 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( rotate_right @ B ) )
| ( little_set @ ( f11 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right3) ).
thf(413,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( rotate_right @ B ) )
| ( little_set @ ( f11 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( range_of @ B ) )
| ( ordered_pair_predicate @ ( f27 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of1) ).
thf(191,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( range_of @ B ) )
| ( ordered_pair_predicate @ ( f27 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ( closed @ A @ B )
| ~ ( little_set @ A )
| ~ ( little_set @ B )
| ~ ( maps @ B @ ( cross_product @ A @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed4) ).
thf(402,plain,
! [B: $i,A: $i] :
( ( closed @ A @ B )
| ~ ( little_set @ A )
| ~ ( little_set @ B )
| ~ ( maps @ B @ ( cross_product @ A @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(75,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( flip_range_of @ B ) )
| ( A
= ( ordered_pair @ ( f12 @ A @ B ) @ ( ordered_pair @ ( f13 @ A @ B ) @ ( f14 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range4) ).
thf(313,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( flip_range_of @ B ) )
| ( A
= ( ordered_pair @ ( f12 @ A @ B ) @ ( ordered_pair @ ( f13 @ A @ B ) @ ( f14 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( non_ordered_pair @ B @ C ) )
| ~ ( little_set @ A )
| ( A != C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair3) ).
thf(466,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( non_ordered_pair @ B @ C ) )
| ~ ( little_set @ A )
| ( A != C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( image @ B @ C ) )
| ( member @ ( f22 @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution2) ).
thf(236,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( image @ B @ C ) )
| ( member @ ( f22 @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( one_to_one_function @ A )
| ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one_function1) ).
thf(159,plain,
! [A: $i] :
( ~ ( one_to_one_function @ A )
| ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,axiom,
function @ f25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).
thf(187,plain,
function @ f25,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(12,axiom,
! [A: $i] :
( ( single_valued_set @ A )
| ( member @ ( ordered_pair @ ( f19 @ A ) @ ( f20 @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set5) ).
thf(172,plain,
! [A: $i] :
( ( single_valued_set @ A )
| ( member @ ( ordered_pair @ ( f19 @ A ) @ ( f20 @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ( member @ ( f17 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2) ).
thf(219,plain,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ( member @ ( f17 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(115,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( little_set @ A )
| ~ ( little_set @ B )
| ( ( ordered_pair @ A @ C )
!= ( ordered_pair @ B @ D ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_components_are_equal) ).
thf(419,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( little_set @ A )
| ~ ( little_set @ B )
| ( ( ordered_pair @ A @ C )
!= ( ordered_pair @ B @ D ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(38,axiom,
! [A: $i] :
( ~ ( member @ A @ estin )
| ( ordered_pair_predicate @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation1) ).
thf(230,plain,
! [A: $i] :
( ~ ( member @ A @ estin )
| ( ordered_pair_predicate @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( sigma @ B ) )
| ~ ( member @ C @ B )
| ~ ( member @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sigma3) ).
thf(318,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( sigma @ B ) )
| ~ ( member @ C @ B )
| ~ ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(121,axiom,
! [A: $i] :
( ~ ( member @ A @ identity_relation )
| ( ( first @ A )
= ( second @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation2) ).
thf(434,plain,
! [A: $i] :
( ~ ( member @ A @ identity_relation )
| ( ( first @ A )
= ( second @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( range_of @ B ) )
| ( member @ ( f27 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of2) ).
thf(208,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( range_of @ B ) )
| ( member @ ( f27 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(139,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( flip_range_of @ B ) )
| ( little_set @ ( f13 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range2) ).
thf(477,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( flip_range_of @ B ) )
| ( little_set @ ( f13 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(79,axiom,
! [A: $i] :
( ( one_to_one_function @ A )
| ~ ( function @ A )
| ~ ( function @ ( converse @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one_function3) ).
thf(323,plain,
! [A: $i] :
( ( one_to_one_function @ A )
| ~ ( function @ A )
| ~ ( function @ ( converse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(30,axiom,
! [A: $i] :
( ~ ( function @ A )
| ( single_valued_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function2) ).
thf(213,plain,
! [A: $i] :
( ~ ( function @ A )
| ( single_valued_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( apply @ B @ C ) )
| ( member @ ( f28 @ A @ B @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply2) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( apply @ B @ C ) )
| ( member @ ( f28 @ A @ B @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(4,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C @ D @ E )
| ( maps @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism3) ).
thf(155,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C @ D @ E )
| ( maps @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(82,axiom,
! [A: $i] :
( ~ ( little_set @ A )
| ( little_set @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset3) ).
thf(330,plain,
! [A: $i] :
( ~ ( little_set @ A )
| ( little_set @ ( powerset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ~ ( little_set @ A )
| ~ ( little_set @ B )
| ( ( first @ ( ordered_pair @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_first) ).
thf(399,plain,
! [B: $i,A: $i] :
( ~ ( little_set @ A )
| ~ ( little_set @ B )
| ( ( first @ ( ordered_pair @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( compose @ B @ C ) )
| ( little_set @ ( f29 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose1) ).
thf(455,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( compose @ B @ C ) )
| ( little_set @ ( f29 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(35,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C @ D @ E )
| ~ ( member @ F @ B )
| ~ ( member @ G @ B )
| ( ( apply @ A @ ( apply_to_two_arguments @ C @ F @ G ) )
= ( apply_to_two_arguments @ E @ ( apply @ A @ F ) @ ( apply @ A @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism4) ).
thf(223,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( homomorphism @ A @ B @ C @ D @ E )
| ~ ( member @ F @ B )
| ~ ( member @ G @ B )
| ( ( apply @ A @ ( apply_to_two_arguments @ C @ F @ G ) )
= ( apply_to_two_arguments @ E @ ( apply @ A @ F ) @ ( apply @ A @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( flip_range_of @ B ) )
| ( member @ ( ordered_pair @ ( f12 @ A @ B ) @ ( ordered_pair @ ( f14 @ A @ B ) @ ( f13 @ A @ B ) ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range5) ).
thf(306,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( flip_range_of @ B ) )
| ( member @ ( ordered_pair @ ( f12 @ A @ B ) @ ( ordered_pair @ ( f14 @ A @ B ) @ ( f13 @ A @ B ) ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( image @ B @ C ) )
| ( ordered_pair_predicate @ ( f22 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution1) ).
thf(226,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( image @ B @ C ) )
| ( ordered_pair_predicate @ ( f22 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( domain_of @ B ) )
| ( A
= ( first @ ( f8 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
thf(267,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( domain_of @ B ) )
| ( A
= ( first @ ( f8 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( f1 @ A @ B ) @ A )
| ~ ( member @ ( f1 @ A @ B ) @ B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality3) ).
thf(167,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( f1 @ A @ B ) @ A )
| ~ ( member @ ( f1 @ A @ B ) @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( domain_of @ B ) )
| ~ ( little_set @ A )
| ~ ( ordered_pair_predicate @ C )
| ~ ( member @ C @ B )
| ( A
!= ( first @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
thf(473,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( domain_of @ B ) )
| ~ ( little_set @ A )
| ~ ( ordered_pair_predicate @ C )
| ~ ( member @ C @ B )
| ( A
!= ( first @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( apply @ B @ C ) )
| ( member @ A @ ( second @ ( f28 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply4) ).
thf(490,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( apply @ B @ C ) )
| ( member @ A @ ( second @ ( f28 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( cross_product @ B @ C ) )
| ~ ( little_set @ A )
| ~ ( ordered_pair_predicate @ A )
| ~ ( member @ ( first @ A ) @ B )
| ~ ( member @ ( second @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product4) ).
thf(426,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( cross_product @ B @ C ) )
| ~ ( little_set @ A )
| ~ ( ordered_pair_predicate @ A )
| ~ ( member @ ( first @ A ) @ B )
| ~ ( member @ ( second @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(50,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( domain_of @ B ) )
| ( ordered_pair_predicate @ ( f8 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
thf(255,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( domain_of @ B ) )
| ( ordered_pair_predicate @ ( f8 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(144,axiom,
! [B: $i,A: $i] :
( ( little_set @ ( f1 @ A @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).
thf(487,plain,
! [B: $i,A: $i] :
( ( little_set @ ( f1 @ A @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( compose @ B @ C ) )
| ( member @ ( ordered_pair @ ( f31 @ A @ B @ C ) @ ( f30 @ A @ B @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose6) ).
thf(295,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( compose @ B @ C ) )
| ( member @ ( ordered_pair @ ( f31 @ A @ B @ C ) @ ( f30 @ A @ B @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( little_set @ A )
| ~ ( little_set @ B )
| ~ ( little_set @ C )
| ~ ( little_set @ D )
| ( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second_components_are_equal) ).
thf(327,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( little_set @ A )
| ~ ( little_set @ B )
| ~ ( little_set @ C )
| ~ ( little_set @ D )
| ( ( ordered_pair @ A @ B )
!= ( ordered_pair @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ( apply_to_two_arguments @ A @ B @ C )
= ( apply @ A @ ( ordered_pair @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply_to_two_arguments) ).
thf(263,plain,
! [C: $i,B: $i,A: $i] :
( ( apply_to_two_arguments @ A @ B @ C )
= ( apply @ A @ ( ordered_pair @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( rotate_right @ B ) )
| ( A
= ( ordered_pair @ ( f9 @ A @ B ) @ ( ordered_pair @ ( f10 @ A @ B ) @ ( f11 @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right4) ).
thf(310,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( rotate_right @ B ) )
| ( A
= ( ordered_pair @ ( f9 @ A @ B ) @ ( ordered_pair @ ( f10 @ A @ B ) @ ( f11 @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
thf(199,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(123,axiom,
ordered_pair_predicate @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_ordered_pair_predicate) ).
thf(441,plain,
ordered_pair_predicate @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(134,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( range_of @ B ) )
| ( A
= ( second @ ( f27 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of3) ).
thf(463,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( range_of @ B ) )
| ( A
= ( second @ ( f27 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(136,axiom,
! [B: $i,A: $i] : ( little_set @ ( non_ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair4) ).
thf(470,plain,
! [B: $i,A: $i] : ( little_set @ ( non_ordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( function @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps1) ).
thf(177,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( maps @ A @ B @ C )
| ( function @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
! [A: $i] :
( ( single_valued_set @ A )
| ( ( f20 @ A )
!= ( f21 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set7) ).
thf(182,plain,
! [A: $i] :
( ( single_valued_set @ A )
| ( ( f20 @ A )
!= ( f21 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(85,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( second @ B ) )
| ~ ( little_set @ C )
| ~ ( little_set @ D )
| ( B
!= ( ordered_pair @ C @ D ) )
| ~ ( member @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second5) ).
thf(336,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( second @ B ) )
| ~ ( little_set @ C )
| ~ ( little_set @ D )
| ( B
!= ( ordered_pair @ C @ D ) )
| ~ ( member @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(126,axiom,
! [A: $i] :
( ~ ( ordered_pair_predicate @ A )
| ( little_set @ ( first @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_component_is_small) ).
thf(446,plain,
! [A: $i] :
( ~ ( ordered_pair_predicate @ A )
| ( little_set @ ( first @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( compose @ B @ C ) )
| ( A
= ( ordered_pair @ ( f29 @ A @ B @ C ) @ ( f30 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose4) ).
thf(250,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( compose @ B @ C ) )
| ( A
= ( ordered_pair @ ( f29 @ A @ B @ C ) @ ( f30 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(128,axiom,
! [A: $i] :
( ~ ( member @ A @ estin )
| ( member @ ( first @ A ) @ ( second @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation2) ).
thf(450,plain,
! [A: $i] :
( ~ ( member @ A @ estin )
| ( member @ ( first @ A ) @ ( second @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(95,axiom,
! [A: $i] :
( ~ ( ordered_pair_predicate @ A )
| ( little_set @ ( f3 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_predicate2) ).
thf(363,plain,
! [A: $i] :
( ~ ( ordered_pair_predicate @ A )
| ( little_set @ ( f3 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(141,axiom,
! [B: $i,A: $i] :
( ~ ( closed @ A @ B )
| ( little_set @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed2) ).
thf(482,plain,
! [B: $i,A: $i] :
( ~ ( closed @ A @ B )
| ( little_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( first @ B ) )
| ( B
= ( ordered_pair @ ( f4 @ A @ B ) @ ( f5 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first3) ).
thf(203,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( first @ B ) )
| ( B
= ( ordered_pair @ ( f4 @ A @ B ) @ ( f5 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ( union @ A @ B )
= ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
thf(304,plain,
! [B: $i,A: $i] :
( ( union @ A @ B )
= ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( compose @ B @ C ) )
| ( little_set @ ( f31 @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose3) ).
thf(351,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( compose @ B @ C ) )
| ( little_set @ ( f31 @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( rotate_right @ B ) )
| ( member @ ( ordered_pair @ ( f10 @ A @ B ) @ ( ordered_pair @ ( f11 @ A @ B ) @ ( f9 @ A @ B ) ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right5) ).
thf(246,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( rotate_right @ B ) )
| ( member @ ( ordered_pair @ ( f10 @ A @ B ) @ ( ordered_pair @ ( f11 @ A @ B ) @ ( f9 @ A @ B ) ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ( member @ ( f1 @ A @ B ) @ A )
| ( member @ ( f1 @ A @ B ) @ B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
thf(272,plain,
! [B: $i,A: $i] :
( ( member @ ( f1 @ A @ B ) @ A )
| ( member @ ( f1 @ A @ B ) @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ( member @ A @ ( complement @ B ) )
| ~ ( little_set @ A )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
thf(383,plain,
! [B: $i,A: $i] :
( ( member @ A @ ( complement @ B ) )
| ~ ( little_set @ A )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(88,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( second @ B ) )
| ( B
= ( ordered_pair @ ( f6 @ A @ B ) @ ( f7 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second3) ).
thf(346,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( second @ B ) )
| ( B
= ( ordered_pair @ ( f6 @ A @ B ) @ ( f7 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',proper_subset2) ).
thf(151,plain,
! [B: $i,A: $i] :
( ~ ( proper_subset @ A @ B )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(69,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( homomorphism @ A @ B @ C @ D @ E )
| ~ ( closed @ B @ C )
| ~ ( closed @ D @ E )
| ~ ( maps @ A @ B @ D )
| ( member @ ( f32 @ A @ B @ C @ D @ E ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism5) ).
thf(300,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( homomorphism @ A @ B @ C @ D @ E )
| ~ ( closed @ B @ C )
| ~ ( closed @ D @ E )
| ~ ( maps @ A @ B @ D )
| ( member @ ( f32 @ A @ B @ C @ D @ E ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(120,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( second @ B ) )
| ( little_set @ ( f7 @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second2) ).
thf(432,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( second @ B ) )
| ( little_set @ ( f7 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ~ ( little_set @ A )
| ~ ( little_set @ B )
| ( ( second @ ( ordered_pair @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_second) ).
thf(410,plain,
! [B: $i,A: $i] :
( ~ ( little_set @ A )
| ~ ( little_set @ B )
| ( ( second @ ( ordered_pair @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(116,axiom,
! [A: $i] :
( ~ ( ordered_pair_predicate @ A )
| ( little_set @ ( f2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_predicate1) ).
thf(422,plain,
! [A: $i] :
( ~ ( ordered_pair_predicate @ A )
| ( little_set @ ( f2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(99,axiom,
! [A: $i] :
( ( member @ A @ identity_relation )
| ~ ( little_set @ A )
| ~ ( ordered_pair_predicate @ A )
| ( ( first @ A )
!= ( second @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation3) ).
thf(373,plain,
! [A: $i] :
( ( member @ A @ identity_relation )
| ~ ( little_set @ A )
| ~ ( ordered_pair_predicate @ A )
| ( ( first @ A )
!= ( second @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( member @ B @ A )
| ( ordered_pair_predicate @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',relation1) ).
thf(210,plain,
! [B: $i,A: $i] :
( ~ ( relation @ A )
| ~ ( member @ B @ A )
| ( ordered_pair_predicate @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
= ( non_ordered_pair @ ( singleton_set @ A ) @ ( non_ordered_pair @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
thf(242,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
= ( non_ordered_pair @ ( singleton_set @ A ) @ ( non_ordered_pair @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(93,axiom,
! [A: $i] :
( ~ ( little_set @ A )
| ( A = empty_set )
| ( member @ ( f26 @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice2) ).
thf(358,plain,
! [A: $i] :
( ~ ( little_set @ A )
| ( A = empty_set )
| ( member @ ( f26 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( maps @ A @ B @ C )
| ~ ( function @ A )
| ( ( domain_of @ A )
!= B )
| ~ ( subset @ ( range_of @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps4) ).
thf(195,plain,
! [C: $i,B: $i,A: $i] :
( ( maps @ A @ B @ C )
| ~ ( function @ A )
| ( ( domain_of @ A )
!= B )
| ~ ( subset @ ( range_of @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( first @ B ) )
| ~ ( little_set @ C )
| ~ ( little_set @ D )
| ( B
!= ( ordered_pair @ C @ D ) )
| ~ ( member @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first5) ).
thf(437,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( member @ A @ ( first @ B ) )
| ~ ( little_set @ C )
| ~ ( little_set @ D )
| ( B
!= ( ordered_pair @ C @ D ) )
| ~ ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( non_ordered_pair @ B @ C ) )
| ~ ( little_set @ A )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair2) ).
thf(415,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( non_ordered_pair @ B @ C ) )
| ~ ( little_set @ A )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ~ ( closed @ A @ B )
| ( little_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed1) ).
thf(332,plain,
! [B: $i,A: $i] :
( ~ ( closed @ A @ B )
| ( little_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(132,axiom,
! [A: $i] :
( ( single_valued_set @ A )
| ( little_set @ ( f19 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_set2) ).
thf(459,plain,
! [A: $i] :
( ( single_valued_set @ A )
| ( little_set @ ( f19 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(8,axiom,
! [A: $i] :
( ( function @ A )
| ~ ( relation @ A )
| ~ ( single_valued_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function3) ).
thf(163,plain,
! [A: $i] :
( ( function @ A )
| ~ ( relation @ A )
| ~ ( single_valued_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( complement @ B ) )
| ~ ( member @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
thf(277,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( complement @ B ) )
| ~ ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( converse @ B ) )
| ( member @ ( ordered_pair @ ( second @ A ) @ ( first @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse2) ).
thf(442,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( converse @ B ) )
| ( member @ ( ordered_pair @ ( second @ A ) @ ( first @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( cross_product @ B @ C ) )
| ( member @ ( second @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product3) ).
thf(369,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( cross_product @ B @ C ) )
| ( member @ ( second @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(31,axiom,
! [A: $i] :
( ( singleton_set @ A )
= ( non_ordered_pair @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
thf(215,plain,
! [A: $i] :
( ( singleton_set @ A )
= ( non_ordered_pair @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( cross_product @ B @ C ) )
| ( ordered_pair_predicate @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product1) ).
thf(232,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( cross_product @ B @ C ) )
| ( ordered_pair_predicate @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(499,plain,
$false,
inference(cvc4,[status(thm)],[244,365,479,234,217,308,379,408,170,385,340,185,320,257,174,404,389,344,157,284,325,228,289,448,316,492,179,376,253,485,238,353,147,397,221,293,428,265,206,452,248,270,201,381,334,302,297,424,275,165,260,349,484,361,461,188,356,471,193,212,393,457,371,161,279,444,149,286,291,281,413,191,402,313,466,236,159,187,172,219,419,230,318,434,208,477,323,213,240,155,330,399,455,223,306,226,267,167,473,490,426,255,487,295,327,263,310,199,441,463,470,177,182,336,446,250,450,363,482,203,304,351,246,272,383,346,151,300,432,410,422,373,210,242,358,195,437,415,332,459,163,277,442,369,215,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET023-3 : TPTP v8.1.2. Released v1.0.0.
% 0.09/0.10 % Command : run_Leo-III %s %d
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Thu May 18 19:16:50 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.62/0.67 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/0.84 % [INFO] Parsing done (163ms).
% 1.19/0.85 % [INFO] Running in sequential loop mode.
% 1.43/1.03 % [INFO] eprover registered as external prover.
% 1.43/1.03 % [INFO] cvc4 registered as external prover.
% 1.43/1.04 % [INFO] Scanning for conjecture ...
% 1.66/1.11 % [INFO] Found a conjecture and 149 axioms. Running axiom selection ...
% 1.82/1.17 % [INFO] Axiom selection finished. Selected 145 axioms (removed 4 axioms).
% 2.16/1.25 % [INFO] Problem is propositional (TPTP CNF).
% 2.16/1.26 % [INFO] Type checking passed.
% 2.16/1.26 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 4.70/2.09 % External prover 'cvc4' found a proof!
% 4.70/2.09 % [INFO] Killing All external provers ...
% 4.70/2.09 % Time passed: 1701ms (effective reasoning time: 1243ms)
% 4.70/2.09 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 4.70/2.10 % Axioms used in derivation (145): first_component_is_small, image_and_substitution1, cross_product4, complement1, single_valued_set4, image_and_substitution2, second2, maps4, first2, first1, function3, apply5, homomorphism4, flip_range5, closed3, infinity3, range_of3, apply1, regularity1, sigma2, proper_subset3, domain4, singleton_set, compose4, sigma1, relation1, ordered_pair_predicate2, single_valued_set7, one_to_one_function3, element_relation2, powerset1, union, rotate_right1, identity_relation2, apply_to_two_arguments, compose2, homomorphism3, image_and_substitution5, second5, rotate_right3, successor, non_ordered_pair2, empty_set, homomorphism7, choice3, ordered_pair, image_and_substitution3, closed4, homomorphism1, flip_range4, rotate_right6, infinity2, property_of_first, subset3, compose3, apply4, image_and_substitution6, choice1, second3, single_valued_set3, range_of4, left_cancellation, converse3, domain3, regularity2, first3, cross_product3, rotate_right2, element_relation3, homomorphism6, extensionality2, intersection1, flip_range1, property_of_second, subset2, compose7, non_ordered_pair1, ordered_pair_predicate1, sigma4, proper_subset1, one_to_one_function2, maps1, first4, compose6, function1, maps3, domain2, intersection3, second4, rotate_right5, identity_relation3, closed1, converse2, disjoint1, second1, element_relation1, infinity1, image_and_substitution4, cross_product2, one_to_one_function1, extensionality1, non_ordered_pair4, sigma3, ordered_pair_predicate4, second_components_are_equal, single_valued_set2, powerset3, two_sets_equal, homomorphism5, apply3, flip_range2, maps2, rotate_right4, complement2, flip_range6, cross_product1, function2, compose5, apply2, range_of2, universal_set, domain1, closed2, identity_relation1, subset1, proper_subset2, converse1, single_valued_set5, first_components_are_equal, intersection2, powerset2, first5, non_ordered_pair3, single_valued_set1, ordered_pair_predicate3, choice2, restrict, homomorphism2, a2, an_ordered_pair_predicate, single_valued_set6, extensionality3, flip_range3, compose1, range_of1
% 4.70/2.10 % No. of inferences in proof: 293
% 4.70/2.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1701 ms resp. 1243 ms w/o parsing
% 5.06/2.16 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.06/2.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------