%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM011-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:08:05 AM UTC 2026
% Result : Unsatisfiable 40.06s 8.68s
% Output : Refutation 35.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 150
% Syntax : Number of formulae : 373 ( 51 unt; 0 typ; 0 def)
% Number of atoms : 1113 ( 185 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 4296 ( 622 ~; 688 |; 0 &;2986 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 83 ( 80 usr; 15 con; 0-3 aty)
% Number of variables : 679 ( 0 ^; 679 !; 0 ?; 679 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_set_decl,type,
empty_set: $i ).
thf(successor_decl,type,
successor: $i > $i ).
thf(f75_decl,type,
f75: $i ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(estin_decl,type,
estin: $i ).
thf(ordered_pair_predicate_decl,type,
ordered_pair_predicate: $i > $o ).
thf(cross_product_decl,type,
cross_product: $i > $i > $i ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(first_decl,type,
first: $i > $i ).
thf(f4_decl,type,
f4: $i > $i > $i ).
thf(second_decl,type,
second: $i > $i ).
thf(converse_decl,type,
converse: $i > $i ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(f28_decl,type,
f28: $i > $i > $i > $i ).
thf(identity_relation_decl,type,
identity_relation: $i ).
thf(little_set_decl,type,
little_set: $i > $o ).
thf(f7_decl,type,
f7: $i > $i > $i ).
thf(function_decl,type,
function: $i > $o ).
thf(image_decl,type,
image: $i > $i > $i ).
thf(rotate_right_decl,type,
rotate_right: $i > $i ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(f9_decl,type,
f9: $i > $i > $i ).
thf(f10_decl,type,
f10: $i > $i > $i ).
thf(f11_decl,type,
f11: $i > $i > $i ).
thf(flip_range_of_decl,type,
flip_range_of: $i > $i ).
thf(f12_decl,type,
f12: $i > $i > $i ).
thf(f13_decl,type,
f13: $i > $i > $i ).
thf(f14_decl,type,
f14: $i > $i > $i ).
thf(f5_decl,type,
f5: $i > $i > $i ).
thf(intersection_decl,type,
intersection: $i > $i > $i ).
thf(identity_decl,type,
identity: $i > $i > $i > $o ).
thf(compose_decl,type,
compose: $i > $i > $i ).
thf(f29_decl,type,
f29: $i > $i > $i > $i ).
thf(f31_decl,type,
f31: $i > $i > $i > $i ).
thf(f30_decl,type,
f30: $i > $i > $i > $i ).
thf(range_of_decl,type,
range_of: $i > $i ).
thf(domain_of_decl,type,
domain_of: $i > $i ).
thf(f6_decl,type,
f6: $i > $i > $i ).
thf(single_valued_set_decl,type,
single_valued_set: $i > $o ).
thf(f37_decl,type,
f37: $i > $i > $i > $i ).
thf(even_numbers_decl,type,
even_numbers: $i ).
thf(apply_to_two_arguments_decl,type,
apply_to_two_arguments: $i > $i > $i > $i ).
thf(plus_decl,type,
plus: $i ).
thf(f59_decl,type,
f59: $i > $i ).
thf(natural_numbers_decl,type,
natural_numbers: $i ).
thf(f49_decl,type,
f49: $i > $i ).
thf(f1_decl,type,
f1: $i > $i > $i ).
thf(non_ordered_pair_decl,type,
non_ordered_pair: $i > $i > $i ).
thf(disjoint_decl,type,
disjoint: $i > $i > $o ).
thf(f23_decl,type,
f23: $i > $i > $i ).
thf(sigma_decl,type,
sigma: $i > $i ).
thf(times_decl,type,
times: $i ).
thf(f50_decl,type,
f50: $i > $i > $i ).
thf(f53_decl,type,
f53: $i > $i > $i ).
thf(f25_decl,type,
f25: $i ).
thf(prime_numbers_decl,type,
prime_numbers: $i ).
thf(commutes_decl,type,
commutes: $i > $i > $o ).
thf(infinity_decl,type,
infinity: $i ).
thf(f51_decl,type,
f51: $i > $i > $i ).
thf(f52_decl,type,
f52: $i > $i > $i ).
thf(twin_prime_numbers_decl,type,
twin_prime_numbers: $i ).
thf(singleton_set_decl,type,
singleton_set: $i > $i ).
thf(universal_set_decl,type,
universal_set: $i ).
thf(f54_decl,type,
f54: $i > $i ).
thf(f44_decl,type,
f44: $i > $i ).
thf(complement_decl,type,
complement: $i > $i ).
thf(associative_decl,type,
associative: $i > $i > $o ).
thf(f45_decl,type,
f45: $i > $i > $i ).
thf(f46_decl,type,
f46: $i > $i > $i ).
thf(f47_decl,type,
f47: $i > $i > $i ).
thf(f48_decl,type,
f48: $i > $i > $i ).
thf(finite_decl,type,
finite: $i > $o ).
thf(f57_decl,type,
f57: $i > $i ).
thf(union_decl,type,
union: $i > $i > $i ).
thf(f55_decl,type,
f55: $i > $i ).
thf(f56_decl,type,
f56: $i > $i ).
thf(f43_decl,type,
f43: $i > $i > $i ).
thf(f24_decl,type,
f24: $i > $i ).
thf(f26_decl,type,
f26: $i > $i ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ~ ( A @ little_set )
| ( C @ ( B @ non_ordered_pair ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',non_ordered_pair2) ).
thf(365,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ~ ( A @ little_set )
| ( C @ ( B @ non_ordered_pair ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(138,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ f54 @ ( C @ ( D @ ( plus @ apply_to_two_arguments ) ) @ ( C @ ( B @ successor @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( A @ f54 @ ( D @ ( C @ ( B @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( natural_numbers @ ( D @ member ) )
| ~ ( natural_numbers @ ( C @ member ) )
| ~ ( natural_numbers @ ( B @ member ) )
| ~ ( A @ little_set )
| ( times @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times13) ).
thf(479,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ f54 @ ( C @ ( D @ ( plus @ apply_to_two_arguments ) ) @ ( C @ ( B @ successor @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( A @ f54 @ ( D @ ( C @ ( B @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( natural_numbers @ ( D @ member ) )
| ~ ( natural_numbers @ ( C @ member ) )
| ~ ( natural_numbers @ ( B @ member ) )
| ~ ( A @ little_set )
| ( times @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(134,axiom,
! [A: $i] :
( ( A @ ( A @ f24 @ member ) )
| ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).
thf(468,plain,
! [A: $i] :
( ( A @ ( A @ f24 @ member ) )
| ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(139,axiom,
! [B: $i,A: $i] :
( ( A @ f49 @ ( B @ ( B @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( natural_numbers @ ( B @ member ) )
| ~ ( A @ little_set )
| ( plus @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus12) ).
thf(481,plain,
! [B: $i,A: $i] :
( ( A @ f49 @ ( B @ ( B @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( natural_numbers @ ( B @ member ) )
| ~ ( A @ little_set )
| ( plus @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ( A @ little_set )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(408,plain,
! [B: $i,A: $i] :
( ( A @ little_set )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ apply_to_two_arguments ) ) )
= ( C @ ( D @ ( B @ apply_to_two_arguments ) ) ) )
| ~ ( A @ ( D @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ commutes ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutes1) ).
thf(308,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ apply_to_two_arguments ) ) )
= ( C @ ( D @ ( B @ apply_to_two_arguments ) ) ) )
| ~ ( A @ ( D @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ commutes ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(123,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f51 ) @ member ) )
| ~ ( B @ ( empty_set @ ( B @ ( A @ f50 ) @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ little_set )
| ~ ( times @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times6) ).
thf(440,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f51 ) @ member ) )
| ~ ( B @ ( empty_set @ ( B @ ( A @ f50 ) @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ little_set )
| ~ ( times @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ second )
!= A )
| ~ ( B @ ( D @ first @ member ) )
| ~ ( C @ ( D @ member ) )
| ~ ( D @ ordered_pair_predicate )
| ~ ( A @ little_set )
| ( C @ ( B @ image ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image_and_substitution5) ).
thf(202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ second )
!= A )
| ~ ( B @ ( D @ first @ member ) )
| ~ ( C @ ( D @ member ) )
| ~ ( D @ ordered_pair_predicate )
| ~ ( A @ little_set )
| ( C @ ( B @ image ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(29,axiom,
! [A: $i] :
( ( ( A @ first )
= ( A @ second ) )
| ~ ( identity_relation @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_relation2) ).
thf(217,plain,
! [A: $i] :
( ( ( A @ first )
= ( A @ second ) )
| ~ ( identity_relation @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( plus @ apply_to_two_arguments ) ) )
!= A )
| ~ ( natural_numbers @ ( B @ member ) )
| ~ ( natural_numbers @ ( A @ member ) )
| ( even_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',even_numbers4) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( plus @ apply_to_two_arguments ) ) )
!= A )
| ~ ( natural_numbers @ ( B @ member ) )
| ~ ( natural_numbers @ ( A @ member ) )
| ( even_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(98,axiom,
! [A: $i] :
( ( natural_numbers @ ( A @ f57 @ member ) )
| ~ ( A @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite1) ).
thf(385,plain,
! [A: $i] :
( ( natural_numbers @ ( A @ f57 @ member ) )
| ~ ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(122,axiom,
! [A: $i] :
( ( A @ successor )
= ( A @ singleton_set @ ( A @ union ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor) ).
thf(438,plain,
! [A: $i] :
( ( A @ successor )
= ( A @ singleton_set @ ( A @ union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(439,plain,
! [A: $i] :
( ( A @ singleton_set @ ( A @ union ) )
= ( A @ successor ) ),
inference(lifteq,[status(thm)],[438]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ union ) )
= ( B @ complement @ ( A @ complement @ intersection ) @ complement ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
thf(400,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ union ) )
= ( B @ complement @ ( A @ complement @ intersection ) @ complement ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(401,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ union ) )
= ( B @ complement @ ( A @ complement @ intersection ) @ complement ) ),
inference(lifteq,[status(thm)],[400]) ).
thf(550,plain,
! [A: $i] :
( ( A @ singleton_set @ complement @ ( A @ complement @ intersection ) @ complement )
= ( A @ successor ) ),
inference(rewrite,[status(thm)],[439,401]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ ordered_pair_predicate )
| ~ ( estin @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation1) ).
thf(153,plain,
! [A: $i] :
( ( A @ ordered_pair_predicate )
| ~ ( estin @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ~ ( A @ little_set )
| ( C @ ( B @ non_ordered_pair ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',non_ordered_pair3) ).
thf(404,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ~ ( A @ little_set )
| ( C @ ( B @ non_ordered_pair ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(113,axiom,
! [A: $i] :
( ( ( A @ f56 @ ( A @ f55 @ ( times @ apply_to_two_arguments ) ) )
= A )
| ( A
= ( empty_set @ successor ) )
| ( A = empty_set )
| ~ ( natural_numbers @ ( A @ member ) )
| ( prime_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prime_numbers7) ).
thf(417,plain,
! [A: $i] :
( ( ( A @ f56 @ ( A @ f55 @ ( times @ apply_to_two_arguments ) ) )
= A )
| ( A
= ( empty_set @ successor ) )
| ( A = empty_set )
| ~ ( natural_numbers @ ( A @ member ) )
| ( prime_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(64,axiom,
f25 @ function,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice1) ).
thf(301,plain,
f25 @ function,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ singleton_set )
= ( A @ ( A @ non_ordered_pair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
thf(320,plain,
! [A: $i] :
( ( A @ singleton_set )
= ( A @ ( A @ non_ordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( B @ ( B @ ( A @ f43 ) @ member ) )
| ~ ( B @ ( empty_set @ member ) )
| ~ ( B @ little_set )
| ~ ( natural_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',natural_numbers1) ).
thf(436,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( B @ ( B @ ( A @ f43 ) @ member ) )
| ~ ( B @ ( empty_set @ member ) )
| ~ ( B @ little_set )
| ~ ( natural_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(46,axiom,
! [A: $i] :
( ( ( A @ f59 @ ( A @ f59 @ ( plus @ apply_to_two_arguments ) ) )
= A )
| ~ ( even_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',even_numbers3) ).
thf(257,plain,
! [A: $i] :
( ( ( A @ f59 @ ( A @ f59 @ ( plus @ apply_to_two_arguments ) ) )
= A )
| ~ ( even_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ second @ ( A @ member ) )
| ( ( D @ first )
!= C )
| ~ ( B @ ( D @ member ) )
| ~ ( D @ ordered_pair_predicate )
| ( C @ ( B @ apply ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply5) ).
thf(184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ second @ ( A @ member ) )
| ( ( D @ first )
!= C )
| ~ ( B @ ( D @ member ) )
| ~ ( D @ ordered_pair_predicate )
| ( C @ ( B @ apply ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ ordered_pair ) ) )
| ~ ( C @ little_set )
| ~ ( B @ little_set )
| ( A @ ordered_pair_predicate ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_predicate4) ).
thf(357,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ ( B @ ordered_pair ) ) )
| ~ ( C @ little_set )
| ~ ( B @ little_set )
| ( A @ ordered_pair_predicate ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ member ) )
| ~ ( B @ ( A @ member ) )
| ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).
thf(196,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ member ) )
| ~ ( B @ ( A @ member ) )
| ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(131,axiom,
! [A: $i] :
( ( natural_numbers @ ( A @ f55 @ member ) )
| ( A
= ( empty_set @ successor ) )
| ( A = empty_set )
| ~ ( natural_numbers @ ( A @ member ) )
| ( prime_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prime_numbers5) ).
thf(460,plain,
! [A: $i] :
( ( natural_numbers @ ( A @ f55 @ member ) )
| ( A
= ( empty_set @ successor ) )
| ( A = empty_set )
| ~ ( natural_numbers @ ( A @ member ) )
| ( prime_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ powerset @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset1) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ powerset @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(112,axiom,
! [B: $i,A: $i] : ( B @ ( A @ non_ordered_pair ) @ little_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',non_ordered_pair4) ).
thf(416,plain,
! [B: $i,A: $i] : ( B @ ( A @ non_ordered_pair ) @ little_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(1,negated_conjecture,
( empty_set
= ( f75 @ successor ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_zero_is_first) ).
thf(151,plain,
( empty_set
= ( f75 @ successor ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(152,plain,
( ( f75 @ successor )
= empty_set ),
inference(lifteq,[status(thm)],[151]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ f23 ) @ member ) )
| ( B @ ( A @ disjoint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint3) ).
thf(289,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ f23 ) @ member ) )
| ( B @ ( A @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(127,axiom,
! [A: $i] :
( ( A
!= ( empty_set @ successor ) )
| ~ ( prime_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prime_numbers3) ).
thf(448,plain,
! [A: $i] :
( ( A
!= ( empty_set @ successor ) )
| ~ ( prime_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f52 ) @ member ) )
| ( natural_numbers @ ( B @ ( A @ f50 ) @ member ) )
| ~ ( B @ little_set )
| ~ ( times @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times2) ).
thf(316,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f52 ) @ member ) )
| ( natural_numbers @ ( B @ ( A @ f50 ) @ member ) )
| ~ ( B @ little_set )
| ~ ( times @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f7 ) @ ( A @ member ) )
| ~ ( B @ second @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',second4) ).
thf(179,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f7 ) @ ( A @ member ) )
| ~ ( B @ second @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(321,plain,
! [A: $i] :
( ( A @ ( A @ non_ordered_pair ) )
= ( A @ singleton_set ) ),
inference(lifteq,[status(thm)],[320]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ f37 ) ) @ ( B @ apply_to_two_arguments ) ) )
!= ( C @ ( B @ ( A @ f37 ) ) ) )
| ( ( C @ ( B @ ( A @ f37 ) ) @ ( C @ ( B @ apply_to_two_arguments ) ) )
!= ( C @ ( B @ ( A @ f37 ) ) ) )
| ~ ( A @ ( C @ member ) )
| ( C @ ( B @ ( A @ identity ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity5) ).
thf(348,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ ( B @ ( A @ f37 ) ) @ ( B @ apply_to_two_arguments ) ) )
!= ( C @ ( B @ ( A @ f37 ) ) ) )
| ( ( C @ ( B @ ( A @ f37 ) ) @ ( C @ ( B @ apply_to_two_arguments ) ) )
!= ( C @ ( B @ ( A @ f37 ) ) ) )
| ~ ( A @ ( C @ member ) )
| ( C @ ( B @ ( A @ identity ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(87,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( E @ ordered_pair ) @ ( C @ ordered_pair ) @ member ) )
| ( A
!= ( E @ ( D @ ordered_pair ) @ ( C @ ordered_pair ) ) )
| ~ ( E @ little_set )
| ~ ( D @ little_set )
| ~ ( C @ little_set )
| ~ ( A @ little_set )
| ( B @ flip_range_of @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip_range6) ).
thf(353,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( E @ ordered_pair ) @ ( C @ ordered_pair ) @ member ) )
| ( A
!= ( E @ ( D @ ordered_pair ) @ ( C @ ordered_pair ) ) )
| ~ ( E @ little_set )
| ~ ( D @ little_set )
| ~ ( C @ little_set )
| ~ ( A @ little_set )
| ( B @ flip_range_of @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ second @ member ) )
| ~ ( B @ ( A @ first @ member ) )
| ~ ( A @ ordered_pair_predicate )
| ~ ( A @ little_set )
| ( C @ ( B @ cross_product ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product4) ).
thf(211,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ second @ member ) )
| ~ ( B @ ( A @ first @ member ) )
| ~ ( A @ ordered_pair_predicate )
| ~ ( A @ little_set )
| ( C @ ( B @ cross_product ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ first @ ( A @ second @ ordered_pair ) @ member ) )
| ~ ( B @ converse @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse2) ).
thf(253,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ first @ ( A @ second @ ordered_pair ) @ member ) )
| ~ ( B @ converse @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( A = B )
| ~ ( C @ ( B @ non_ordered_pair ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',non_ordered_pair1) ).
thf(280,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( A = B )
| ~ ( C @ ( B @ non_ordered_pair ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(133,axiom,
! [A: $i] :
( ( A @ ( A @ f24 @ disjoint ) )
| ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).
thf(465,plain,
! [A: $i] :
( ( A @ ( A @ f24 @ disjoint ) )
| ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(466,plain,
! [A: $i] :
( ( A @ ( A @ f24 @ disjoint ) )
| ( A = empty_set ) ),
inference(cnf,[status(esa)],[465]) ).
thf(467,plain,
! [A: $i] :
( ( A @ ( A @ f24 @ disjoint ) )
| ( A = empty_set ) ),
inference(lifteq,[status(thm)],[466]) ).
thf(140,axiom,
natural_numbers @ ( f75 @ member ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_natural_number) ).
thf(483,plain,
natural_numbers @ ( f75 @ member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(118,axiom,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
thf(428,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(429,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(polarity_switch,[status(thm)],[428]) ).
thf(531,plain,
! [A: $i] :
( ( ( natural_numbers @ ( f75 @ member ) )
!= ( empty_set @ ( A @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[483,429]) ).
thf(532,plain,
! [A: $i] :
( ( natural_numbers @ ( f75 @ member ) )
!= ( empty_set @ ( A @ member ) ) ),
inference(simp,[status(thm)],[531]) ).
thf(534,plain,
! [A: $i] :
( ( natural_numbers != empty_set )
| ( f75 != A ) ),
inference(simp,[status(thm)],[532]) ).
thf(536,plain,
natural_numbers != empty_set,
inference(simp,[status(thm)],[534]) ).
thf(632,plain,
! [A: $i] :
( ( A != natural_numbers )
| ( empty_set != empty_set )
| ( A @ ( A @ f24 @ disjoint ) ) ),
inference(paramod_ordered,[status(thm)],[467,536]) ).
thf(633,plain,
! [A: $i] :
( ( A != natural_numbers )
| ( A @ ( A @ f24 @ disjoint ) ) ),
inference(simp,[status(thm)],[632]) ).
thf(634,plain,
natural_numbers @ ( natural_numbers @ f24 @ disjoint ),
inference(pattern_uni,[status(thm)],[633:[bind(A,$thf( natural_numbers ))]]) ).
thf(146,axiom,
infinity @ ( empty_set @ member ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infinity2) ).
thf(496,plain,
infinity @ ( empty_set @ member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ member ) )
| ~ ( B @ complement @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
thf(414,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ member ) )
| ~ ( B @ complement @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(415,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ member ) )
| ~ ( B @ complement @ ( A @ member ) ) ),
inference(cnf,[status(esa)],[414]) ).
thf(560,plain,
! [B: $i,A: $i] :
( ( ( infinity @ ( empty_set @ member ) )
!= ( B @ ( A @ member ) ) )
| ~ $true
| ~ ( B @ complement @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[496,415]) ).
thf(561,plain,
! [B: $i,A: $i] :
( ( ( infinity @ ( empty_set @ member ) )
!= ( B @ ( A @ member ) ) )
| ~ ( B @ complement @ ( A @ member ) ) ),
inference(simp,[status(thm)],[560]) ).
thf(562,plain,
~ ( infinity @ complement @ ( empty_set @ member ) ),
inference(pattern_uni,[status(thm)],[561:[bind(A,$thf( empty_set )),bind(B,$thf( infinity ))]]) ).
thf(719,plain,
( ( ( infinity @ complement @ ( empty_set @ member ) )
!= ( infinity @ ( empty_set @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[496,562]) ).
thf(720,plain,
( ( infinity @ complement @ ( empty_set @ member ) )
!= ( infinity @ ( empty_set @ member ) ) ),
inference(simp,[status(thm)],[719]) ).
thf(733,plain,
( ( ( infinity @ complement )
!= infinity )
| ( empty_set != empty_set ) ),
inference(simp,[status(thm)],[720]) ).
thf(734,plain,
( ( infinity @ complement )
!= infinity ),
inference(simp,[status(thm)],[733]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f5 ) @ little_set )
| ~ ( B @ first @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first2) ).
thf(293,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f5 ) @ little_set )
| ~ ( B @ first @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(103,axiom,
! [A: $i] :
( ( A @ f44 @ little_set )
| ~ ( A @ little_set )
| ( natural_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',natural_numbers3) ).
thf(396,plain,
! [A: $i] :
( ( A @ f44 @ little_set )
| ~ ( A @ little_set )
| ( natural_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(154,plain,
! [A: $i] :
( ( A @ ordered_pair_predicate )
| ~ ( estin @ ( A @ member ) ) ),
inference(cnf,[status(esa)],[153]) ).
thf(521,plain,
! [A: $i] :
( ( ( infinity @ ( empty_set @ member ) )
!= ( estin @ ( A @ member ) ) )
| ( A @ ordered_pair_predicate )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[496,154]) ).
thf(522,plain,
! [A: $i] :
( ( ( infinity @ ( empty_set @ member ) )
!= ( estin @ ( A @ member ) ) )
| ( A @ ordered_pair_predicate ) ),
inference(simp,[status(thm)],[521]) ).
thf(525,plain,
! [A: $i] :
( ( infinity != estin )
| ( empty_set != A )
| ( A @ ordered_pair_predicate ) ),
inference(simp,[status(thm)],[522]) ).
thf(527,plain,
( ( infinity != estin )
| ( empty_set @ ordered_pair_predicate ) ),
inference(simp,[status(thm)],[525]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ first @ ( A @ second @ ordered_pair ) @ member ) )
| ~ ( A @ ordered_pair_predicate )
| ~ ( A @ little_set )
| ( B @ converse @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse3) ).
thf(206,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ first @ ( A @ second @ ordered_pair ) @ member ) )
| ~ ( A @ ordered_pair_predicate )
| ~ ( A @ little_set )
| ( B @ converse @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( empty_set @ successor @ non_ordered_pair ) @ ( B @ member ) )
| ( ( C @ ( B @ ( times @ apply_to_two_arguments ) ) )
!= A )
| ~ ( natural_numbers @ ( C @ member ) )
| ~ ( natural_numbers @ ( B @ member ) )
| ~ ( prime_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prime_numbers4) ).
thf(452,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( empty_set @ successor @ non_ordered_pair ) @ ( B @ member ) )
| ( ( C @ ( B @ ( times @ apply_to_two_arguments ) ) )
!= A )
| ~ ( natural_numbers @ ( C @ member ) )
| ~ ( natural_numbers @ ( B @ member ) )
| ~ ( prime_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f28 ) ) @ second @ ( A @ member ) )
| ~ ( C @ ( B @ apply ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply4) ).
thf(248,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f28 ) ) @ second @ ( A @ member ) )
| ~ ( C @ ( B @ apply ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(120,axiom,
! [A: $i] :
( ( A != empty_set )
| ~ ( prime_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prime_numbers2) ).
thf(432,plain,
! [A: $i] :
( ( A != empty_set )
| ~ ( prime_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(433,plain,
! [A: $i] :
( ( A != empty_set )
| ~ ( prime_numbers @ ( A @ member ) ) ),
inference(cnf,[status(esa)],[432]) ).
thf(434,plain,
! [A: $i] :
( ~ ( prime_numbers @ ( A @ member ) )
| ( A != empty_set ) ),
inference(lifteq,[status(thm)],[433]) ).
thf(435,plain,
~ ( prime_numbers @ ( empty_set @ member ) ),
inference(simp,[status(thm)],[434]) ).
thf(508,plain,
( ( ( natural_numbers @ ( f75 @ member ) )
!= ( prime_numbers @ ( empty_set @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[483,435]) ).
thf(509,plain,
( ( natural_numbers @ ( f75 @ member ) )
!= ( prime_numbers @ ( empty_set @ member ) ) ),
inference(simp,[status(thm)],[508]) ).
thf(512,plain,
( ( prime_numbers != natural_numbers )
| ( f75 != empty_set ) ),
inference(simp,[status(thm)],[509]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( A @ ( D @ ( B @ ordered_pair ) @ member ) )
| ~ ( A @ ( C @ ( B @ ordered_pair ) @ member ) )
| ~ ( D @ little_set )
| ~ ( C @ little_set )
| ~ ( B @ little_set )
| ~ ( A @ single_valued_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_set1) ).
thf(270,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( A @ ( D @ ( B @ ordered_pair ) @ member ) )
| ~ ( A @ ( C @ ( B @ ordered_pair ) @ member ) )
| ~ ( D @ little_set )
| ~ ( C @ little_set )
| ~ ( B @ little_set )
| ~ ( A @ single_valued_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ member ) )
| ( B
!= ( D @ ( C @ ordered_pair ) ) )
| ~ ( D @ little_set )
| ~ ( C @ little_set )
| ( B @ first @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first5) ).
thf(381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ member ) )
| ( B
!= ( D @ ( C @ ordered_pair ) ) )
| ~ ( D @ little_set )
| ~ ( C @ little_set )
| ( B @ first @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ second @ ( A @ first @ member ) )
| ~ ( estin @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation2) ).
thf(220,plain,
! [A: $i] :
( ( A @ second @ ( A @ first @ member ) )
| ~ ( estin @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(80,axiom,
! [A: $i] :
( ~ ( A @ f44 @ ( A @ member ) )
| ( natural_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',natural_numbers6) ).
thf(334,plain,
! [A: $i] :
( ~ ( A @ f44 @ ( A @ member ) )
| ( natural_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(65,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( E @ ordered_pair ) @ ( D @ ordered_pair ) @ member ) )
| ( A
!= ( E @ ( D @ ordered_pair ) @ ( C @ ordered_pair ) ) )
| ~ ( E @ little_set )
| ~ ( D @ little_set )
| ~ ( C @ little_set )
| ~ ( A @ little_set )
| ( B @ rotate_right @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate_right6) ).
thf(302,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( E @ ordered_pair ) @ ( D @ ordered_pair ) @ member ) )
| ( A
!= ( E @ ( D @ ordered_pair ) @ ( C @ ordered_pair ) ) )
| ~ ( E @ little_set )
| ~ ( D @ little_set )
| ~ ( C @ little_set )
| ~ ( A @ little_set )
| ( B @ rotate_right @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f13 ) @ little_set )
| ~ ( B @ flip_range_of @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip_range2) ).
thf(260,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f13 ) @ little_set )
| ~ ( B @ flip_range_of @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f4 ) @ ( A @ member ) )
| ~ ( B @ first @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first4) ).
thf(159,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f4 ) @ ( A @ member ) )
| ~ ( B @ first @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f4 ) @ ( A @ member ) )
| ~ ( B @ first @ ( A @ member ) ) ),
inference(cnf,[status(esa)],[159]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f29 ) ) @ little_set )
| ~ ( C @ ( B @ compose ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose1) ).
thf(392,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f29 ) ) @ little_set )
| ~ ( C @ ( B @ compose ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f53 ) @ member ) )
| ( natural_numbers @ ( B @ ( A @ f50 ) @ member ) )
| ~ ( B @ little_set )
| ~ ( times @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times3) ).
thf(297,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f53 ) @ member ) )
| ( natural_numbers @ ( B @ ( A @ f50 ) @ member ) )
| ~ ( B @ little_set )
| ~ ( times @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(116,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f46 ) @ member ) )
| ~ ( B @ ( B @ ( A @ f45 ) @ ( B @ ( A @ f45 ) @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ little_set )
| ~ ( plus @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus6) ).
thf(424,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f46 ) @ member ) )
| ~ ( B @ ( B @ ( A @ f45 ) @ ( B @ ( A @ f45 ) @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ little_set )
| ~ ( plus @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ f28 ) ) @ member ) )
| ~ ( C @ ( B @ apply ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply2) ).
thf(165,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ f28 ) ) @ member ) )
| ~ ( C @ ( B @ apply ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(141,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f53 ) @ member ) )
| ~ ( B @ ( empty_set @ ( B @ ( A @ f50 ) @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ little_set )
| ~ ( times @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times8) ).
thf(484,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f53 ) @ member ) )
| ~ ( B @ ( empty_set @ ( B @ ( A @ f50 ) @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ little_set )
| ~ ( times @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(89,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f11 ) @ little_set )
| ~ ( B @ rotate_right @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate_right3) ).
thf(361,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f11 ) @ little_set )
| ~ ( B @ rotate_right @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(129,axiom,
! [A: $i] :
( ( infinity @ ( A @ successor @ member ) )
| ~ ( infinity @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infinity3) ).
thf(456,plain,
! [A: $i] :
( ( infinity @ ( A @ successor @ member ) )
| ~ ( infinity @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ disjoint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint1) ).
thf(324,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ member ) )
| ( B
!= ( D @ ( C @ ordered_pair ) ) )
| ~ ( D @ little_set )
| ~ ( C @ little_set )
| ( B @ second @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',second5) ).
thf(285,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ member ) )
| ( B
!= ( D @ ( C @ ordered_pair ) ) )
| ~ ( D @ little_set )
| ~ ( C @ little_set )
| ( B @ second @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ f13 ) @ ( B @ ( A @ f14 ) @ ordered_pair ) @ ( B @ ( A @ f12 ) @ ordered_pair ) @ member ) )
| ~ ( B @ flip_range_of @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip_range5) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ f13 ) @ ( B @ ( A @ f14 ) @ ordered_pair ) @ ( B @ ( A @ f12 ) @ ordered_pair ) @ member ) )
| ~ ( B @ flip_range_of @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ordered_pair_predicate )
| ~ ( C @ ( B @ cross_product ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product1) ).
thf(155,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ordered_pair_predicate )
| ~ ( C @ ( B @ cross_product ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ordered_pair_predicate )
| ~ ( C @ ( B @ cross_product ) @ ( A @ member ) ) ),
inference(cnf,[status(esa)],[155]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ ( A @ f14 ) @ ( B @ ( A @ f13 ) @ ordered_pair ) @ ( B @ ( A @ f12 ) @ ordered_pair ) ) )
| ~ ( B @ flip_range_of @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip_range4) ).
thf(188,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ ( A @ f14 ) @ ( B @ ( A @ f13 ) @ ordered_pair ) @ ( B @ ( A @ f12 ) @ ordered_pair ) ) )
| ~ ( B @ flip_range_of @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ first @ member ) )
| ~ ( C @ ( B @ cross_product ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product2) ).
thf(169,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ first @ member ) )
| ~ ( C @ ( B @ cross_product ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ f49 @ ( D @ successor @ ( C @ ( B @ successor @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( A @ f49 @ ( D @ ( C @ ( B @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( natural_numbers @ ( D @ member ) )
| ~ ( natural_numbers @ ( C @ member ) )
| ~ ( natural_numbers @ ( B @ member ) )
| ~ ( A @ little_set )
| ( plus @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus13) ).
thf(420,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ f49 @ ( D @ successor @ ( C @ ( B @ successor @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( A @ f49 @ ( D @ ( C @ ( B @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( natural_numbers @ ( D @ member ) )
| ~ ( natural_numbers @ ( C @ member ) )
| ~ ( natural_numbers @ ( B @ member ) )
| ~ ( A @ little_set )
| ( plus @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(148,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f47 ) @ member ) )
| ~ ( B @ ( B @ ( A @ f45 ) @ ( B @ ( A @ f45 ) @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ little_set )
| ~ ( plus @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus7) ).
thf(499,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f47 ) @ member ) )
| ~ ( B @ ( B @ ( A @ f45 ) @ ( B @ ( A @ f45 ) @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ little_set )
| ~ ( plus @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ f5 ) @ ( B @ ( A @ f4 ) @ ordered_pair ) ) )
| ~ ( B @ first @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first3) ).
thf(193,plain,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ f5 ) @ ( B @ ( A @ f4 ) @ ordered_pair ) ) )
| ~ ( B @ first @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(143,axiom,
! [A: $i] :
( ~ ( prime_numbers @ ( A @ successor @ successor @ member ) )
| ~ ( prime_numbers @ ( A @ member ) )
| ( twin_prime_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',twin_primes3) ).
thf(489,plain,
! [A: $i] :
( ~ ( prime_numbers @ ( A @ successor @ successor @ member ) )
| ~ ( prime_numbers @ ( A @ member ) )
| ( twin_prime_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(77,axiom,
! [A: $i] :
( ~ ( A @ f54 @ ( A @ member ) )
| ( times @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times14) ).
thf(328,plain,
! [A: $i] :
( ~ ( A @ f54 @ ( A @ member ) )
| ( times @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(135,axiom,
! [A: $i] :
( ( natural_numbers @ ( A @ f56 @ member ) )
| ( A
= ( empty_set @ successor ) )
| ( A = empty_set )
| ~ ( natural_numbers @ ( A @ member ) )
| ( prime_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prime_numbers6) ).
thf(471,plain,
! [A: $i] :
( ( natural_numbers @ ( A @ f56 @ member ) )
| ( A
= ( empty_set @ successor ) )
| ( A = empty_set )
| ~ ( natural_numbers @ ( A @ member ) )
| ( prime_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ image ) @ little_set )
| ~ ( B @ function )
| ~ ( A @ little_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image_and_substitution6) ).
thf(173,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ image ) @ little_set )
| ~ ( B @ function )
| ~ ( A @ little_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ apply_to_two_arguments ) ) )
= ( C @ ( B @ ordered_pair ) @ ( A @ apply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_to_two_arguments) ).
thf(371,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ apply_to_two_arguments ) ) )
= ( C @ ( B @ ordered_pair ) @ ( A @ apply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(150,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( B @ ( B @ ( A @ f48 ) @ ( B @ ( A @ f47 ) @ ( B @ ( A @ f46 ) @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ ( B @ ( A @ f45 ) @ ( B @ ( A @ f45 ) @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ little_set )
| ~ ( plus @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus9) ).
thf(503,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( B @ ( B @ ( A @ f48 ) @ ( B @ ( A @ f47 ) @ ( B @ ( A @ f46 ) @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ ( B @ ( A @ f45 ) @ ( B @ ( A @ f45 ) @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ little_set )
| ~ ( plus @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ single_valued_set )
| ~ ( A @ function ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function2) ).
thf(237,plain,
! [A: $i] :
( ( A @ single_valued_set )
| ~ ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ subset ) )
| ~ ( A @ little_set )
| ( B @ powerset @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset2) ).
thf(244,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ subset ) )
| ~ ( A @ little_set )
| ( B @ powerset @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ powerset @ little_set )
| ~ ( A @ little_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset3) ).
thf(266,plain,
! [A: $i] :
( ( A @ powerset @ little_set )
| ~ ( A @ little_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(68,axiom,
! [A: $i] :
( ( natural_numbers @ ( A @ member ) )
| ~ ( even_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',even_numbers1) ).
thf(311,plain,
! [A: $i] :
( ( natural_numbers @ ( A @ member ) )
| ~ ( even_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(540,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ non_ordered_pair ) )
!= ( C @ ( B @ non_ordered_pair ) ) )
| ( A @ singleton_set @ little_set ) ),
inference(paramod_ordered,[status(thm)],[321,416]) ).
thf(541,plain,
! [A: $i] : ( A @ singleton_set @ little_set ),
inference(pattern_uni,[status(thm)],[540:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f12 ) @ little_set )
| ~ ( B @ flip_range_of @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip_range1) ).
thf(398,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f12 ) @ little_set )
| ~ ( B @ flip_range_of @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f14 ) @ little_set )
| ~ ( B @ flip_range_of @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip_range3) ).
thf(412,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f14 ) @ little_set )
| ~ ( B @ flip_range_of @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ f49 @ little_set )
| ~ ( A @ little_set )
| ( plus @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus11) ).
thf(264,plain,
! [A: $i] :
( ( A @ f49 @ little_set )
| ~ ( A @ little_set )
| ( plus @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ second @ member ) )
| ~ ( C @ ( B @ cross_product ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product3) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ second @ member ) )
| ~ ( C @ ( B @ cross_product ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(125,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( B @ ( B @ ( A @ f52 ) @ ( B @ ( A @ f53 ) @ ( plus @ apply_to_two_arguments ) ) @ ( B @ ( A @ f52 ) @ ( B @ ( A @ f51 ) @ successor @ ordered_pair ) @ ordered_pair ) @ member ) )
| ( natural_numbers @ ( B @ ( A @ f50 ) @ member ) )
| ~ ( B @ little_set )
| ~ ( times @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times5) ).
thf(444,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( B @ ( B @ ( A @ f52 ) @ ( B @ ( A @ f53 ) @ ( plus @ apply_to_two_arguments ) ) @ ( B @ ( A @ f52 ) @ ( B @ ( A @ f51 ) @ successor @ ordered_pair ) @ ordered_pair ) @ member ) )
| ( natural_numbers @ ( B @ ( A @ f50 ) @ member ) )
| ~ ( B @ little_set )
| ~ ( times @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( B @ apply_to_two_arguments ) ) )
= D )
| ~ ( A @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ identity ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity3) ).
thf(375,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( B @ apply_to_two_arguments ) ) )
= D )
| ~ ( A @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ identity ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(449,plain,
! [A: $i] :
( ( A
!= ( empty_set @ successor ) )
| ~ ( prime_numbers @ ( A @ member ) ) ),
inference(cnf,[status(esa)],[448]) ).
thf(450,plain,
! [A: $i] :
( ~ ( prime_numbers @ ( A @ member ) )
| ( A
!= ( empty_set @ successor ) ) ),
inference(lifteq,[status(thm)],[449]) ).
thf(451,plain,
~ ( prime_numbers @ ( empty_set @ successor @ member ) ),
inference(simp,[status(thm)],[450]) ).
thf(510,plain,
( ( ( prime_numbers @ ( empty_set @ successor @ member ) )
!= ( natural_numbers @ ( f75 @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[483,451]) ).
thf(511,plain,
( ( prime_numbers @ ( empty_set @ successor @ member ) )
!= ( natural_numbers @ ( f75 @ member ) ) ),
inference(simp,[status(thm)],[510]) ).
thf(513,plain,
( ( prime_numbers != natural_numbers )
| ( ( empty_set @ successor )
!= f75 ) ),
inference(simp,[status(thm)],[511]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( B @ ( B @ ( A @ f43 ) @ successor @ member ) )
| ~ ( B @ ( empty_set @ member ) )
| ~ ( B @ little_set )
| ~ ( natural_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',natural_numbers2) ).
thf(430,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( B @ ( B @ ( A @ f43 ) @ successor @ member ) )
| ~ ( B @ ( empty_set @ member ) )
| ~ ( B @ little_set )
| ~ ( natural_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(59,axiom,
! [A: $i] :
( ~ ( A @ f49 @ ( A @ member ) )
| ( plus @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus14) ).
thf(291,plain,
! [A: $i] :
( ~ ( A @ f49 @ ( A @ member ) )
| ( plus @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(19,axiom,
! [A: $i] :
( ~ ( A @ second @ ( A @ first @ member ) )
| ~ ( A @ ordered_pair_predicate )
| ~ ( A @ little_set )
| ( estin @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation3) ).
thf(191,plain,
! [A: $i] :
( ~ ( A @ second @ ( A @ first @ member ) )
| ~ ( A @ ordered_pair_predicate )
| ~ ( A @ little_set )
| ( estin @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(106,axiom,
! [A: $i] :
( ( A @ f54 @ little_set )
| ~ ( A @ little_set )
| ( times @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times11) ).
thf(402,plain,
! [A: $i] :
( ( A @ f54 @ little_set )
| ~ ( A @ little_set )
| ( times @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(69,axiom,
infinity @ little_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infinity1) ).
thf(313,plain,
infinity @ little_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ ( A @ f11 ) @ ( B @ ( A @ f10 ) @ ordered_pair ) @ ( B @ ( A @ f9 ) @ ordered_pair ) ) )
| ~ ( B @ rotate_right @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate_right4) ).
thf(181,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ ( A @ f11 ) @ ( B @ ( A @ f10 ) @ ordered_pair ) @ ( B @ ( A @ f9 ) @ ordered_pair ) ) )
| ~ ( B @ rotate_right @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
thf(230,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(72,axiom,
! [A: $i] :
( ( prime_numbers @ ( A @ member ) )
| ~ ( twin_prime_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',twin_primes1) ).
thf(318,plain,
! [A: $i] :
( ( prime_numbers @ ( A @ member ) )
| ~ ( twin_prime_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ f30 ) ) @ ( C @ ( B @ ( A @ f29 ) ) @ ordered_pair ) ) )
| ~ ( C @ ( B @ compose ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose4) ).
thf(208,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ f30 ) ) @ ( C @ ( B @ ( A @ f29 ) ) @ ordered_pair ) ) )
| ~ ( C @ ( B @ compose ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(565,plain,
! [B: $i,A: $i] :
( ( ( natural_numbers @ ( f75 @ member ) )
!= ( B @ ( A @ member ) ) )
| ~ $true
| ~ ( B @ complement @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[483,415]) ).
thf(566,plain,
! [B: $i,A: $i] :
( ( ( natural_numbers @ ( f75 @ member ) )
!= ( B @ ( A @ member ) ) )
| ~ ( B @ complement @ ( A @ member ) ) ),
inference(simp,[status(thm)],[565]) ).
thf(567,plain,
~ ( natural_numbers @ complement @ ( f75 @ member ) ),
inference(pattern_uni,[status(thm)],[566:[bind(A,$thf( f75 )),bind(B,$thf( natural_numbers ))]]) ).
thf(137,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( B @ ( B @ ( A @ f53 ) @ ( B @ ( A @ f52 ) @ ( B @ ( A @ f51 ) @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ ( empty_set @ ( B @ ( A @ f50 ) @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ little_set )
| ~ ( times @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times9) ).
thf(477,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( B @ ( B @ ( A @ f53 ) @ ( B @ ( A @ f52 ) @ ( B @ ( A @ f51 ) @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ ( empty_set @ ( B @ ( A @ f50 ) @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ little_set )
| ~ ( times @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ apply_to_two_arguments ) ) )
= D )
| ~ ( A @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ identity ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity2) ).
thf(387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ apply_to_two_arguments ) ) )
= D )
| ~ ( A @ ( D @ member ) )
| ~ ( C @ ( B @ ( A @ identity ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(145,axiom,
! [A: $i] :
( ( prime_numbers @ ( A @ successor @ successor @ member ) )
| ~ ( twin_prime_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',twin_primes2) ).
thf(494,plain,
! [A: $i] :
( ( prime_numbers @ ( A @ successor @ successor @ member ) )
| ~ ( twin_prime_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ f1 ) @ little_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality1) ).
thf(345,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ f1 ) @ little_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(529,plain,
! [A: $i] :
( ( ( infinity @ ( empty_set @ member ) )
!= ( empty_set @ ( A @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[496,429]) ).
thf(530,plain,
! [A: $i] :
( ( infinity @ ( empty_set @ member ) )
!= ( empty_set @ ( A @ member ) ) ),
inference(simp,[status(thm)],[529]) ).
thf(533,plain,
! [A: $i] :
( ( infinity != empty_set )
| ( empty_set != A ) ),
inference(simp,[status(thm)],[530]) ).
thf(535,plain,
infinity != empty_set,
inference(simp,[status(thm)],[533]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ second ) )
| ~ ( B @ ( C @ member ) )
| ~ ( C @ ordered_pair_predicate )
| ~ ( A @ little_set )
| ( B @ range_of @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of4) ).
thf(213,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ second ) )
| ~ ( B @ ( C @ member ) )
| ~ ( C @ ordered_pair_predicate )
| ~ ( A @ little_set )
| ( B @ range_of @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(514,plain,
( ( ( infinity @ ( empty_set @ member ) )
!= ( prime_numbers @ ( empty_set @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[496,435]) ).
thf(515,plain,
( ( infinity @ ( empty_set @ member ) )
!= ( prime_numbers @ ( empty_set @ member ) ) ),
inference(simp,[status(thm)],[514]) ).
thf(518,plain,
( ( infinity != prime_numbers )
| ( empty_set != empty_set ) ),
inference(simp,[status(thm)],[515]) ).
thf(520,plain,
infinity != prime_numbers,
inference(simp,[status(thm)],[518]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ member ) )
| ~ ( C @ ( B @ ( A @ identity ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity1) ).
thf(198,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ member ) )
| ~ ( C @ ( B @ ( A @ identity ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ member ) )
| ~ ( B @ ( C @ member ) )
| ( B @ sigma @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sigma3) ).
thf(330,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ member ) )
| ~ ( B @ ( C @ member ) )
| ( B @ sigma @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f31 ) ) @ little_set )
| ~ ( C @ ( B @ compose ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose3) ).
thf(299,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f31 ) ) @ little_set )
| ~ ( C @ ( B @ compose ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ first ) )
| ~ ( B @ ( C @ member ) )
| ~ ( C @ ordered_pair_predicate )
| ~ ( A @ little_set )
| ( B @ domain_of @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
thf(226,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ first ) )
| ~ ( B @ ( C @ member ) )
| ~ ( C @ ordered_pair_predicate )
| ~ ( A @ little_set )
| ( B @ domain_of @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ ordered_pair_predicate )
| ~ ( identity_relation @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_relation1) ).
thf(167,plain,
! [A: $i] :
( ( A @ ordered_pair_predicate )
| ~ ( identity_relation @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f46 ) @ member ) )
| ( natural_numbers @ ( B @ ( A @ f45 ) @ member ) )
| ~ ( B @ little_set )
| ~ ( plus @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus1) ).
thf(394,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f46 ) @ member ) )
| ( natural_numbers @ ( B @ ( A @ f45 ) @ member ) )
| ~ ( B @ little_set )
| ~ ( plus @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(66,axiom,
! [A: $i] :
( ( natural_numbers @ ( A @ member ) )
| ~ ( prime_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prime_numbers1) ).
thf(306,plain,
! [A: $i] :
( ( natural_numbers @ ( A @ member ) )
| ~ ( prime_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(39,axiom,
! [A: $i] :
( ( ( A @ first )
!= ( A @ second ) )
| ~ ( A @ ordered_pair_predicate )
| ~ ( A @ little_set )
| ( identity_relation @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_relation3) ).
thf(241,plain,
! [A: $i] :
( ( ( A @ first )
!= ( A @ second ) )
| ~ ( A @ ordered_pair_predicate )
| ~ ( A @ little_set )
| ( identity_relation @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(652,plain,
! [A: $i] :
( ( A != f75 )
| ( ( empty_set @ successor )
= empty_set )
| ( A @ ( A @ f24 @ disjoint ) ) ),
inference(paramod_ordered,[status(thm)],[467,152]) ).
thf(653,plain,
( ( ( empty_set @ successor )
= empty_set )
| ( f75 @ ( f75 @ f24 @ disjoint ) ) ),
inference(pattern_uni,[status(thm)],[652:[bind(A,$thf( f75 ))]]) ).
thf(117,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( B @ ( B @ ( A @ f52 ) @ ( B @ ( A @ f53 ) @ ( plus @ apply_to_two_arguments ) ) @ ( B @ ( A @ f52 ) @ ( B @ ( A @ f51 ) @ successor @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ ( empty_set @ ( B @ ( A @ f50 ) @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ little_set )
| ~ ( times @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times10) ).
thf(426,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( B @ ( B @ ( A @ f52 ) @ ( B @ ( A @ f53 ) @ ( plus @ apply_to_two_arguments ) ) @ ( B @ ( A @ f52 ) @ ( B @ ( A @ f51 ) @ successor @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ ( empty_set @ ( B @ ( A @ f50 ) @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ little_set )
| ~ ( times @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ f37 ) ) @ member ) )
| ~ ( A @ ( C @ member ) )
| ( C @ ( B @ ( A @ identity ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity4) ).
thf(255,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ f37 ) ) @ member ) )
| ~ ( A @ ( C @ member ) )
| ( C @ ( B @ ( A @ identity ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(83,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( C @ ( B @ apply_to_two_arguments ) ) @ ( B @ apply_to_two_arguments ) ) )
= ( E @ ( D @ ( B @ apply_to_two_arguments ) ) @ ( C @ ( B @ apply_to_two_arguments ) ) ) )
| ~ ( A @ ( E @ member ) )
| ~ ( A @ ( D @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ associative ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_system1) ).
thf(342,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( C @ ( B @ apply_to_two_arguments ) ) @ ( B @ apply_to_two_arguments ) ) )
= ( E @ ( D @ ( B @ apply_to_two_arguments ) ) @ ( C @ ( B @ apply_to_two_arguments ) ) ) )
| ~ ( A @ ( E @ member ) )
| ~ ( A @ ( D @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ associative ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(742,plain,
( ( ( natural_numbers @ complement @ ( f75 @ member ) )
!= ( infinity @ ( empty_set @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[496,567]) ).
thf(743,plain,
( ( natural_numbers @ complement @ ( f75 @ member ) )
!= ( infinity @ ( empty_set @ member ) ) ),
inference(simp,[status(thm)],[742]) ).
thf(754,plain,
( ( ( natural_numbers @ complement )
!= infinity )
| ( f75 != empty_set ) ),
inference(simp,[status(thm)],[743]) ).
thf(130,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f52 ) @ member ) )
| ~ ( B @ ( empty_set @ ( B @ ( A @ f50 ) @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ little_set )
| ~ ( times @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times7) ).
thf(458,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f52 ) @ member ) )
| ~ ( B @ ( empty_set @ ( B @ ( A @ f50 ) @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ little_set )
| ~ ( times @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ sigma @ little_set )
| ~ ( A @ little_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sigma4) ).
thf(295,plain,
! [A: $i] :
( ( A @ sigma @ little_set )
| ~ ( A @ little_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f4 ) @ little_set )
| ~ ( B @ first @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first1) ).
thf(177,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f4 ) @ little_set )
| ~ ( B @ first @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(132,axiom,
! [A: $i] :
( ( A @ f44 @ ( empty_set @ member ) )
| ~ ( A @ little_set )
| ( natural_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',natural_numbers4) ).
thf(463,plain,
! [A: $i] :
( ( A @ f44 @ ( empty_set @ member ) )
| ~ ( A @ little_set )
| ( natural_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(82,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( F @ ordered_pair ) @ member ) )
| ~ ( B @ ( F @ ( D @ ordered_pair ) @ member ) )
| ( A
!= ( E @ ( D @ ordered_pair ) ) )
| ~ ( F @ little_set )
| ~ ( E @ little_set )
| ~ ( D @ little_set )
| ~ ( A @ little_set )
| ( C @ ( B @ compose ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose7) ).
thf(338,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( F @ ordered_pair ) @ member ) )
| ~ ( B @ ( F @ ( D @ ordered_pair ) @ member ) )
| ( A
!= ( E @ ( D @ ordered_pair ) ) )
| ~ ( F @ little_set )
| ~ ( E @ little_set )
| ~ ( D @ little_set )
| ~ ( A @ little_set )
| ( C @ ( B @ compose ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( A @ little_set )
| ( B @ complement @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
thf(336,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( A @ little_set )
| ( B @ complement @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset1) ).
thf(175,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( B @ ( B @ ( A @ f53 ) @ ( B @ ( A @ f52 ) @ ( B @ ( A @ f51 ) @ ordered_pair ) @ ordered_pair ) @ member ) )
| ( natural_numbers @ ( B @ ( A @ f50 ) @ member ) )
| ~ ( B @ little_set )
| ~ ( times @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times4) ).
thf(314,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( B @ ( B @ ( A @ f53 ) @ ( B @ ( A @ f52 ) @ ( B @ ( A @ f51 ) @ ordered_pair ) @ ordered_pair ) @ member ) )
| ( natural_numbers @ ( B @ ( A @ f50 ) @ member ) )
| ~ ( B @ little_set )
| ~ ( times @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( B @ ( B @ ( A @ f48 ) @ successor @ ( B @ ( A @ f47 ) @ ( B @ ( A @ f46 ) @ successor @ ordered_pair ) @ ordered_pair ) @ member ) )
| ( natural_numbers @ ( B @ ( A @ f45 ) @ member ) )
| ~ ( B @ little_set )
| ~ ( plus @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus5) ).
thf(446,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( B @ ( B @ ( A @ f48 ) @ successor @ ( B @ ( A @ f47 ) @ ( B @ ( A @ f46 ) @ successor @ ordered_pair ) @ ordered_pair ) @ member ) )
| ( natural_numbers @ ( B @ ( A @ f45 ) @ member ) )
| ~ ( B @ little_set )
| ~ ( plus @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ( A @ f54 @ ( empty_set @ ( B @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( natural_numbers @ ( B @ member ) )
| ~ ( A @ little_set )
| ( times @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times12) ).
thf(497,plain,
! [B: $i,A: $i] :
( ( A @ f54 @ ( empty_set @ ( B @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( natural_numbers @ ( B @ member ) )
| ~ ( A @ little_set )
| ( times @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(90,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( B @ ( A @ non_ordered_pair ) @ ( A @ singleton_set @ non_ordered_pair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
thf(363,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( B @ ( A @ non_ordered_pair ) @ ( A @ singleton_set @ non_ordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ f28 ) ) @ first )
= C )
| ~ ( C @ ( B @ apply ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply3) ).
thf(250,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ f28 ) ) @ first )
= C )
| ~ ( C @ ( B @ apply ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(100,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f47 ) @ member ) )
| ( natural_numbers @ ( B @ ( A @ f45 ) @ member ) )
| ~ ( B @ little_set )
| ~ ( plus @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus2) ).
thf(390,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f47 ) @ member ) )
| ( natural_numbers @ ( B @ ( A @ f45 ) @ member ) )
| ~ ( B @ little_set )
| ~ ( plus @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f7 ) @ little_set )
| ~ ( B @ second @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',second2) ).
thf(171,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f7 ) @ little_set )
| ~ ( B @ second @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(729,plain,
( ( ( natural_numbers @ ( f75 @ member ) )
!= ( infinity @ complement @ ( empty_set @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[483,562]) ).
thf(730,plain,
( ( natural_numbers @ ( f75 @ member ) )
!= ( infinity @ complement @ ( empty_set @ member ) ) ),
inference(simp,[status(thm)],[729]) ).
thf(731,plain,
( ( ( infinity @ complement )
!= natural_numbers )
| ( f75 != empty_set ) ),
inference(simp,[status(thm)],[730]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ powerset @ ( A @ member ) ) ),
inference(cnf,[status(esa)],[157]) ).
thf(86,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( B @ ( B @ ( A @ f48 ) @ ( B @ ( A @ f47 ) @ ( B @ ( A @ f46 ) @ ordered_pair ) @ ordered_pair ) @ member ) )
| ( natural_numbers @ ( B @ ( A @ f45 ) @ member ) )
| ~ ( B @ little_set )
| ~ ( plus @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus4) ).
thf(351,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( B @ ( B @ ( A @ f48 ) @ ( B @ ( A @ f47 ) @ ( B @ ( A @ f46 ) @ ordered_pair ) @ ordered_pair ) @ member ) )
| ( natural_numbers @ ( B @ ( A @ f45 ) @ member ) )
| ~ ( B @ little_set )
| ~ ( plus @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( B @ ( A @ f1 ) @ member ) )
| ( A @ ( B @ ( A @ f1 ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality2) ).
thf(378,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( B @ ( A @ f1 ) @ member ) )
| ( A @ ( B @ ( A @ f1 ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
thf(235,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ f9 ) @ ( B @ ( A @ f11 ) @ ordered_pair ) @ ( B @ ( A @ f10 ) @ ordered_pair ) @ member ) )
| ~ ( B @ rotate_right @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate_right5) ).
thf(246,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ f9 ) @ ( B @ ( A @ f11 ) @ ordered_pair ) @ ( B @ ( A @ f10 ) @ ordered_pair ) @ member ) )
| ~ ( B @ rotate_right @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f51 ) @ member ) )
| ( natural_numbers @ ( B @ ( A @ f50 ) @ member ) )
| ~ ( B @ little_set )
| ~ ( times @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times1) ).
thf(410,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f51 ) @ member ) )
| ( natural_numbers @ ( B @ ( A @ f50 ) @ member ) )
| ~ ( B @ little_set )
| ~ ( times @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(48,axiom,
! [A: $i] :
( ( natural_numbers @ ( A @ f59 @ member ) )
| ~ ( even_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',even_numbers2) ).
thf(262,plain,
! [A: $i] :
( ( natural_numbers @ ( A @ f59 @ member ) )
| ~ ( even_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ( A @ f44 @ ( B @ successor @ member ) )
| ~ ( A @ f44 @ ( B @ member ) )
| ~ ( A @ little_set )
| ( natural_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',natural_numbers5) ).
thf(422,plain,
! [B: $i,A: $i] :
( ( A @ f44 @ ( B @ successor @ member ) )
| ~ ( A @ f44 @ ( B @ member ) )
| ~ ( A @ little_set )
| ( natural_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ ( B @ ( A @ f1 ) @ member ) )
| ~ ( A @ ( B @ ( A @ f1 ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality3) ).
thf(273,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ ( B @ ( A @ f1 ) @ member ) )
| ~ ( A @ ( B @ ( A @ f1 ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(94,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f6 ) @ little_set )
| ~ ( B @ second @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',second1) ).
thf(373,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f6 ) @ little_set )
| ~ ( B @ second @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(76,axiom,
! [A: $i] :
( ~ ( A @ little_set )
| ( universal_set @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',universal_set) ).
thf(326,plain,
! [A: $i] :
( ~ ( A @ little_set )
| ( universal_set @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f28 ) ) @ ordered_pair_predicate )
| ~ ( C @ ( B @ apply ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply1) ).
thf(239,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f28 ) ) @ ordered_pair_predicate )
| ~ ( C @ ( B @ apply ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f30 ) ) @ little_set )
| ~ ( C @ ( B @ compose ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose2) ).
thf(268,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f30 ) ) @ little_set )
| ~ ( C @ ( B @ compose ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(136,axiom,
! [A: $i] :
( ( f25 @ ( A @ f26 @ ( A @ ordered_pair ) @ member ) )
| ( A = empty_set )
| ~ ( A @ little_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice3) ).
thf(474,plain,
! [A: $i] :
( ( f25 @ ( A @ f26 @ ( A @ ordered_pair ) @ member ) )
| ( A = empty_set )
| ~ ( A @ little_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(56,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ f23 ) @ member ) )
| ( B @ ( A @ disjoint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint2) ).
thf(283,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ f23 ) @ member ) )
| ( B @ ( A @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(79,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f10 ) @ little_set )
| ~ ( B @ rotate_right @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate_right2) ).
thf(332,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f10 ) @ little_set )
| ~ ( B @ rotate_right @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(523,plain,
! [A: $i] :
( ( ( natural_numbers @ ( f75 @ member ) )
!= ( estin @ ( A @ member ) ) )
| ( A @ ordered_pair_predicate )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[483,154]) ).
thf(524,plain,
! [A: $i] :
( ( ( natural_numbers @ ( f75 @ member ) )
!= ( estin @ ( A @ member ) ) )
| ( A @ ordered_pair_predicate ) ),
inference(simp,[status(thm)],[523]) ).
thf(526,plain,
! [A: $i] :
( ( natural_numbers != estin )
| ( f75 != A )
| ( A @ ordered_pair_predicate ) ),
inference(simp,[status(thm)],[524]) ).
thf(528,plain,
( ( natural_numbers != estin )
| ( f75 @ ordered_pair_predicate ) ),
inference(simp,[status(thm)],[526]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f48 ) @ member ) )
| ~ ( B @ ( B @ ( A @ f45 ) @ ( B @ ( A @ f45 ) @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ little_set )
| ~ ( plus @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus8) ).
thf(442,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f48 ) @ member ) )
| ~ ( B @ ( B @ ( A @ f45 ) @ ( B @ ( A @ f45 ) @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ little_set )
| ~ ( plus @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( B @ ( B @ ( A @ f48 ) @ successor @ ( B @ ( A @ f47 ) @ ( B @ ( A @ f46 ) @ successor @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ ( B @ ( A @ f45 ) @ ( B @ ( A @ f45 ) @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ little_set )
| ~ ( plus @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus10) ).
thf(501,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( B @ ( B @ ( A @ f48 ) @ successor @ ( B @ ( A @ f47 ) @ ( B @ ( A @ f46 ) @ successor @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ ( B @ ( A @ f45 ) @ ( B @ ( A @ f45 ) @ ( empty_set @ ordered_pair ) @ ordered_pair ) @ member ) )
| ~ ( B @ little_set )
| ~ ( plus @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f48 ) @ member ) )
| ( natural_numbers @ ( B @ ( A @ f45 ) @ member ) )
| ~ ( B @ little_set )
| ~ ( plus @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus3) ).
thf(369,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ( natural_numbers @ ( B @ ( A @ f48 ) @ member ) )
| ( natural_numbers @ ( B @ ( A @ f45 ) @ member ) )
| ~ ( B @ little_set )
| ~ ( plus @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( A @ ordered_pair_predicate )
| ~ ( B @ converse @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',converse1) ).
thf(163,plain,
! [B: $i,A: $i] :
( ( A @ ordered_pair_predicate )
| ~ ( B @ converse @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ f31 ) ) @ ( C @ ( B @ ( A @ f29 ) ) @ ordered_pair ) @ member ) )
| ~ ( C @ ( B @ compose ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose5) ).
thf(200,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ f31 ) ) @ ( C @ ( B @ ( A @ f29 ) ) @ ordered_pair ) @ member ) )
| ~ ( C @ ( B @ compose ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f9 ) @ little_set )
| ~ ( B @ rotate_right @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate_right1) ).
thf(322,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f9 ) @ little_set )
| ~ ( B @ rotate_right @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(142,axiom,
! [A: $i] :
( ~ ( A @ ( empty_set @ successor @ non_ordered_pair ) @ ( A @ f55 @ member ) )
| ( A
= ( empty_set @ successor ) )
| ( A = empty_set )
| ~ ( natural_numbers @ ( A @ member ) )
| ( prime_numbers @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prime_numbers8) ).
thf(486,plain,
! [A: $i] :
( ~ ( A @ ( empty_set @ successor @ non_ordered_pair ) @ ( A @ f55 @ member ) )
| ( A
= ( empty_set @ successor ) )
| ( A = empty_set )
| ~ ( natural_numbers @ ( A @ member ) )
| ( prime_numbers @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(750,plain,
( ( ( natural_numbers @ complement @ ( f75 @ member ) )
!= ( natural_numbers @ ( f75 @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[483,567]) ).
thf(751,plain,
( ( natural_numbers @ complement @ ( f75 @ member ) )
!= ( natural_numbers @ ( f75 @ member ) ) ),
inference(simp,[status(thm)],[750]) ).
thf(753,plain,
( ( ( natural_numbers @ complement )
!= natural_numbers )
| ( f75 != f75 ) ),
inference(simp,[status(thm)],[751]) ).
thf(755,plain,
( ( natural_numbers @ complement )
!= natural_numbers ),
inference(simp,[status(thm)],[753]) ).
thf(144,axiom,
! [A: $i] :
( ( A @ ( A @ f26 @ member ) )
| ( A = empty_set )
| ~ ( A @ little_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice2) ).
thf(491,plain,
! [A: $i] :
( ( A @ ( A @ f26 @ member ) )
| ( A = empty_set )
| ~ ( A @ little_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ f30 ) ) @ ( C @ ( B @ ( A @ f31 ) ) @ ordered_pair ) @ member ) )
| ~ ( C @ ( B @ compose ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose6) ).
thf(222,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ f30 ) ) @ ( C @ ( B @ ( A @ f31 ) ) @ ordered_pair ) @ member ) )
| ~ ( C @ ( B @ compose ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ f7 ) @ ( B @ ( A @ f6 ) @ ordered_pair ) ) )
| ~ ( B @ second @ ( A @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',second3) ).
thf(232,plain,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ f7 ) @ ( B @ ( A @ f6 ) @ ordered_pair ) ) )
| ~ ( B @ second @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(6589,plain,
$false,
inference(e,[status(thm)],[365,479,468,481,408,308,440,202,217,276,385,550,153,404,417,301,320,436,257,184,357,196,460,157,416,152,289,448,316,179,321,348,353,211,253,280,634,734,293,396,428,527,206,452,248,512,270,381,220,334,302,260,160,392,297,424,429,165,467,484,361,435,456,324,285,224,156,188,169,420,499,193,489,328,471,173,371,503,237,244,266,311,541,398,412,264,161,444,375,513,430,562,291,191,402,313,181,159,230,318,208,451,567,477,387,494,345,535,213,483,520,155,198,330,299,226,438,167,394,306,241,653,426,255,342,754,458,295,414,177,463,338,336,154,175,314,446,497,363,250,465,390,401,171,731,158,351,378,536,235,246,151,432,410,262,422,273,373,326,239,268,474,400,283,415,332,528,442,501,369,163,200,322,486,755,491,222,496,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM011-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.62 % Computer : n019.cluster.edu
% 0.15/0.62 % Model : x86_64 x86_64
% 0.15/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.62 % Memory : 8046.5625MB
% 0.15/0.62 % OS : Linux 6.8.0-71-generic
% 0.15/0.62 % CPULimit : 300
% 0.15/0.62 % WCLimit : 300
% 0.15/0.62 % DateTime : Sat Sep 26 01:53:04 UTC 2026
% 0.15/0.63 % CPUTime :
% 0.15/0.63 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.99/1.21 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.35/1.48 % [INFO] Parsing done (263ms).
% 1.35/1.49 % [INFO] Running in sequential loop mode.
% 2.49/1.87 % [INFO] eprover registered as external prover.
% 2.49/1.88 % [INFO] Scanning for conjecture ...
% 2.68/2.01 % [INFO] Found a conjecture (or negated_conjecture) and 220 axioms. Running axiom selection ...
% 3.31/2.16 % [INFO] Axiom selection finished. Selected 149 axioms (removed 71 axioms).
% 3.98/2.30 % [INFO] Problem is propositional (TPTP CNF).
% 3.98/2.32 % [INFO] Type checking passed.
% 3.98/2.33 % [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 ...
% 40.06/8.67 % External prover 'e' found a proof!
% 40.06/8.67 % [INFO] Killing All external provers ...
% 40.06/8.67 % Time passed: 7901ms (effective reasoning time: 7174ms)
% 40.06/8.68 % Axioms used in derivation (149): non_ordered_pair1, associative_system1, twin_primes3, cross_product4, second2, complement1, plus10, apply5, first2, plus12, first1, flip_range5, infinity3, times12, apply1, regularity1, prime_numbers5, domain4, singleton_set, compose4, natural_numbers3, powerset1, union, rotate_right1, plus8, element_relation2, identity_relation2, apply_to_two_arguments, times3, compose2, image_and_substitution5, finite1, second5, rotate_right3, prime_numbers8, successor, non_ordered_pair2, empty_set, even_numbers4, choice3, ordered_pair, identity3, flip_range4, prime_numbers2, identity2, rotate_right6, disjoint2, times2, infinity2, times11, second3, prime_numbers6, compose3, apply4, plus4, image_and_substitution6, range_of4, choice1, converse3, natural_numbers5, regularity2, first3, cross_product3, rotate_right2, element_relation3, plus7, compose7, extensionality2, intersection1, flip_range1, even_numbers3, times7, natural_numbers2, sigma4, times6, times1, prime_numbers1, first4, prime_numbers3, compose6, commutes1, intersection3, natural_numbers1, identity4, second4, rotate_right5, identity_relation3, plus3, converse2, disjoint1, disjoint3, second1, element_relation1, twin_primes1, infinity1, times10, cross_product2, plus1, plus6, extensionality1, non_ordered_pair4, sigma3, ordered_pair_predicate4, plus14, powerset3, plus2, times8, times5, flip_range2, even_numbers2, apply3, rotate_right4, complement2, flip_range6, twin_primes2, cross_product1, plus5, plus13, function2, compose5, apply2, prime_numbers4, natural_numbers6, universal_set, converse1, identity_relation1, subset1, times13, identity5, intersection2, powerset2, identity1, times4, first5, natural_numbers4, non_ordered_pair3, single_valued_set1, times14, even_numbers1, choice2, a2, plus11, times9, plus9, prime_numbers7, extensionality3, flip_range3, a_natural_number, compose1
% 40.06/8.68 % No. of inferences in proof: 373
% 40.06/8.68 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7901 ms resp. 7174 ms w/o parsing
% 35.69/8.82 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 35.69/8.82 % [INFO] Killing All external provers ...
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