%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET027-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n010.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 08:28:58 AM UTC 2026
% Result : Unsatisfiable 20.16s 11.56s
% Output : Refutation 18.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 131
% Syntax : Number of formulae : 330 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 868 ( 180 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 3165 ( 522 ~; 500 |; 0 &;2143 @)
% ( 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 : 68 ( 65 usr; 11 con; 0-5 aty)
% Number of variables : 700 ( 0 ^; 700 !; 0 ?; 700 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(c_decl,type,
c: $i ).
thf(homomorphism_decl,type,
homomorphism: $i > $i > $i > $i > $i > $o ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(apply_decl,type,
apply: $i > $i > $i ).
thf(apply_to_two_arguments_decl,type,
apply_to_two_arguments: $i > $i > $i > $i ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(little_set_decl,type,
little_set: $i > $o ).
thf(compose_decl,type,
compose: $i > $i > $i ).
thf(flip_range_of_decl,type,
flip_range_of: $i > $i ).
thf(ordered_pair_predicate_decl,type,
ordered_pair_predicate: $i > $o ).
thf(image_decl,type,
image: $i > $i > $i ).
thf(f22_decl,type,
f22: $i > $i > $i > $i ).
thf(second_decl,type,
second: $i > $i ).
thf(non_ordered_pair_decl,type,
non_ordered_pair: $i > $i > $i ).
thf(singleton_set_decl,type,
singleton_set: $i > $i ).
thf(identity_relation_decl,type,
identity_relation: $i ).
thf(successor_decl,type,
successor: $i > $i ).
thf(union_decl,type,
union: $i > $i > $i ).
thf(single_valued_set_decl,type,
single_valued_set: $i > $o ).
thf(rotate_right_decl,type,
rotate_right: $i > $i ).
thf(closed_decl,type,
closed: $i > $i > $o ).
thf(maps_decl,type,
maps: $i > $i > $i > $o ).
thf(f32_decl,type,
f32: $i > $i > $i > $i > $i > $i ).
thf(f33_decl,type,
f33: $i > $i > $i > $i > $i > $i ).
thf(estin_decl,type,
estin: $i ).
thf(first_decl,type,
first: $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(f24_decl,type,
f24: $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(f12_decl,type,
f12: $i > $i > $i ).
thf(f13_decl,type,
f13: $i > $i > $i ).
thf(f14_decl,type,
f14: $i > $i > $i ).
thf(cross_product_decl,type,
cross_product: $i > $i > $i ).
thf(f4_decl,type,
f4: $i > $i > $i ).
thf(f5_decl,type,
f5: $i > $i > $i ).
thf(relation_decl,type,
relation: $i > $o ).
thf(infinity_decl,type,
infinity: $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(disjoint_decl,type,
disjoint: $i > $i > $o ).
thf(f26_decl,type,
f26: $i > $i ).
thf(f25_decl,type,
f25: $i ).
thf(complement_decl,type,
complement: $i > $i ).
thf(intersection_decl,type,
intersection: $i > $i > $i ).
thf(f7_decl,type,
f7: $i > $i > $i ).
thf(function_decl,type,
function: $i > $o ).
thf(f6_decl,type,
f6: $i > $i > $i ).
thf(restrict_decl,type,
restrict: $i > $i > $i ).
thf(universal_set_decl,type,
universal_set: $i ).
thf(one_to_one_function_decl,type,
one_to_one_function: $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(f1_decl,type,
f1: $i > $i > $i ).
thf(sigma_decl,type,
sigma: $i > $i ).
thf(domain_of_decl,type,
domain_of: $i > $i ).
thf(range_of_decl,type,
range_of: $i > $i ).
thf(f27_decl,type,
f27: $i > $i > $i ).
thf(proper_subset_decl,type,
proper_subset: $i > $i > $o ).
thf(f8_decl,type,
f8: $i > $i > $i ).
thf(b_decl,type,
b: $i ).
thf(f17_decl,type,
f17: $i > $i > $i ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ apply_to_two_arguments ) ) )
= ( C @ ( B @ ordered_pair ) @ ( A @ apply ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply_to_two_arguments) ).
thf(137,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)],[3]) ).
thf(138,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ apply_to_two_arguments ) ) )
= ( C @ ( B @ ordered_pair ) @ ( A @ apply ) ) ),
inference(lifteq,[status(thm)],[137]) ).
thf(91,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f10 ) @ little_set )
| ~ ( B @ rotate_right @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right2) ).
thf(347,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f10 ) @ little_set )
| ~ ( B @ rotate_right @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ member ) )
| ~ ( B @ ( A @ member ) )
| ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
thf(333,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)],[84]) ).
thf(93,axiom,
! [A: $i] :
( ( A @ singleton_set @ ( A @ member ) )
| ~ ( A @ little_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_singleton_sets) ).
thf(352,plain,
! [A: $i] :
( ( A @ singleton_set @ ( A @ member ) )
| ~ ( A @ little_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ cross_product ) @ ( B @ maps ) ) )
| ~ ( B @ little_set )
| ~ ( A @ little_set )
| ( B @ ( A @ closed ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed4) ).
thf(408,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ cross_product ) @ ( B @ maps ) ) )
| ~ ( B @ little_set )
| ~ ( A @ little_set )
| ( B @ ( A @ closed ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ second @ member ) )
| ~ ( C @ ( B @ cross_product ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product3) ).
thf(217,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)],[32]) ).
thf(130,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ f17 ) @ member ) )
| ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset3) ).
thf(440,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ f17 ) @ member ) )
| ( B @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(54,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ closed ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ homomorphism ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism2) ).
thf(269,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ closed ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ homomorphism ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(25,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/sandbox/benchmark/theBenchmark.p',flip_range4) ).
thf(202,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)],[25]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f4 ) @ little_set )
| ~ ( B @ first @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first1) ).
thf(384,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f4 ) @ little_set )
| ~ ( B @ first @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ ( A @ f24 @ member ) )
| ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
thf(192,plain,
! [A: $i] :
( ( A @ ( A @ f24 @ member ) )
| ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(193,plain,
! [A: $i] :
( ( A @ ( A @ f24 @ member ) )
| ( A = empty_set ) ),
inference(cnf,[status(esa)],[192]) ).
thf(194,plain,
! [A: $i] :
( ( A @ ( A @ f24 @ member ) )
| ( A = empty_set ) ),
inference(lifteq,[status(thm)],[193]) ).
thf(120,axiom,
c @ ( b @ subset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_subset_c) ).
thf(418,plain,
c @ ( b @ subset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(1,negated_conjecture,
~ ( c @ ( a @ subset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_subset_c) ).
thf(132,plain,
~ ( c @ ( a @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(133,plain,
~ ( c @ ( a @ subset ) ),
inference(polarity_switch,[status(thm)],[132]) ).
thf(448,plain,
( ( ( c @ ( b @ subset ) )
!= ( c @ ( a @ subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[418,133]) ).
thf(449,plain,
( ( c @ ( b @ subset ) )
!= ( c @ ( a @ subset ) ) ),
inference(simp,[status(thm)],[448]) ).
thf(450,plain,
( ( c != c )
| ( b != a ) ),
inference(simp,[status(thm)],[449]) ).
thf(451,plain,
b != a,
inference(simp,[status(thm)],[450]) ).
thf(569,plain,
! [A: $i] :
( ( A != b )
| ( empty_set != a )
| ( A @ ( A @ f24 @ member ) ) ),
inference(paramod_ordered,[status(thm)],[194,451]) ).
thf(570,plain,
( ( empty_set != a )
| ( b @ ( b @ f24 @ member ) ) ),
inference(pattern_uni,[status(thm)],[569:[bind(A,$thf( b ))]]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ member ) )
| ~ ( B @ complement @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
thf(380,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ member ) )
| ~ ( B @ complement @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(381,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ member ) )
| ~ ( B @ complement @ ( A @ member ) ) ),
inference(cnf,[status(esa)],[380]) ).
thf(481,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ complement @ ( A @ member ) )
!= ( B @ ( A @ member ) ) )
| ~ ( B @ ( A @ member ) ) ),
inference(eqfactor_ordered,[status(thm)],[381]) ).
thf(484,plain,
! [B: $i,A: $i] :
( ( ( B @ complement )
!= B )
| ( A != A )
| ~ ( B @ ( A @ member ) ) ),
inference(simp,[status(thm)],[481]) ).
thf(486,plain,
! [B: $i,A: $i] :
( ( ( B @ complement )
!= B )
| ~ ( B @ ( A @ member ) ) ),
inference(simp,[status(thm)],[484]) ).
thf(696,plain,
! [B: $i,A: $i] :
( ( ( b @ ( b @ f24 @ member ) )
!= ( B @ ( A @ member ) ) )
| ( ( B @ complement )
!= B )
| ~ $true
| ( empty_set != a ) ),
inference(paramod_ordered,[status(thm)],[570,486]) ).
thf(697,plain,
! [B: $i,A: $i] :
( ( ( b @ ( b @ f24 @ member ) )
!= ( B @ ( A @ member ) ) )
| ( ( B @ complement )
!= B )
| ( empty_set != a ) ),
inference(simp,[status(thm)],[696]) ).
thf(698,plain,
( ( ( b @ complement )
!= b )
| ( empty_set != a ) ),
inference(pattern_uni,[status(thm)],[697:[bind(A,$thf( b @ f24 )),bind(B,$thf( b ))]]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
thf(404,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( C @ ( A @ ordered_pair ) )
!= ( D @ ( B @ ordered_pair ) ) )
| ~ ( B @ little_set )
| ~ ( A @ little_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_components_are_equal) ).
thf(185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( C @ ( A @ ordered_pair ) )
!= ( D @ ( B @ ordered_pair ) ) )
| ~ ( B @ little_set )
| ~ ( A @ little_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ restrict ) )
= ( universal_set @ ( B @ cross_product ) @ ( A @ intersection ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restrict) ).
thf(288,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ restrict ) )
= ( universal_set @ ( B @ cross_product ) @ ( A @ intersection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(94,axiom,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
thf(354,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(355,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(polarity_switch,[status(thm)],[354]) ).
thf(708,plain,
! [A: $i] :
( ( ( b @ ( b @ f24 @ member ) )
!= ( empty_set @ ( A @ member ) ) )
| ~ $true
| ( empty_set != a ) ),
inference(paramod_ordered,[status(thm)],[570,355]) ).
thf(709,plain,
! [A: $i] :
( ( ( b @ ( b @ f24 @ member ) )
!= ( empty_set @ ( A @ member ) ) )
| ( empty_set != a ) ),
inference(simp,[status(thm)],[708]) ).
thf(720,plain,
! [A: $i] :
( ( b != empty_set )
| ( ( b @ f24 )
!= A )
| ( empty_set != a ) ),
inference(simp,[status(thm)],[709]) ).
thf(724,plain,
( ( b != empty_set )
| ( empty_set != a ) ),
inference(simp,[status(thm)],[720]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ordered_pair ) )
= ( B @ ( A @ non_ordered_pair ) @ ( A @ singleton_set @ non_ordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
thf(157,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)],[10]) ).
thf(122,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ ( A @ subset ) )
| ( B @ ( A @ proper_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',proper_subset3) ).
thf(421,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ ( A @ subset ) )
| ( B @ ( A @ proper_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f22 ) ) @ ordered_pair_predicate )
| ~ ( C @ ( B @ image ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution1) ).
thf(284,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f22 ) ) @ ordered_pair_predicate )
| ~ ( C @ ( B @ image ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f29 ) ) @ little_set )
| ~ ( C @ ( B @ compose ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose1) ).
thf(416,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)],[119]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f27 ) @ ordered_pair_predicate )
| ~ ( B @ range_of @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of1) ).
thf(325,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f27 ) @ ordered_pair_predicate )
| ~ ( B @ range_of @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ f22 ) ) @ member ) )
| ~ ( C @ ( B @ image ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution2) ).
thf(152,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ f22 ) ) @ member ) )
| ~ ( C @ ( B @ image ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(289,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ restrict ) )
= ( universal_set @ ( B @ cross_product ) @ ( A @ intersection ) ) ),
inference(lifteq,[status(thm)],[288]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f31 ) ) @ little_set )
| ~ ( C @ ( B @ compose ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose3) ).
thf(316,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)],[76]) ).
thf(31,axiom,
infinity @ ( empty_set @ member ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity2) ).
thf(216,plain,
infinity @ ( empty_set @ member ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ singleton_set )
= ( A @ ( A @ non_ordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
thf(219,plain,
! [A: $i] :
( ( A @ singleton_set )
= ( A @ ( A @ non_ordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(220,plain,
! [A: $i] :
( ( A @ ( A @ non_ordered_pair ) )
= ( A @ singleton_set ) ),
inference(lifteq,[status(thm)],[219]) ).
thf(109,axiom,
! [B: $i,A: $i] : ( B @ ( A @ non_ordered_pair ) @ little_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair4) ).
thf(395,plain,
! [B: $i,A: $i] : ( B @ ( A @ non_ordered_pair ) @ little_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(491,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)],[220,395]) ).
thf(492,plain,
! [A: $i] : ( A @ singleton_set @ little_set ),
inference(pattern_uni,[status(thm)],[491:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(78,axiom,
f25 @ function,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).
thf(321,plain,
f25 @ function,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(476,plain,
! [B: $i,A: $i] :
( ( ( infinity @ ( empty_set @ member ) )
!= ( B @ complement @ ( A @ member ) ) )
| ~ ( B @ ( A @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[216,381]) ).
thf(477,plain,
! [B: $i,A: $i] :
( ( ( infinity @ ( empty_set @ member ) )
!= ( B @ complement @ ( A @ member ) ) )
| ~ ( B @ ( A @ member ) ) ),
inference(simp,[status(thm)],[476]) ).
thf(482,plain,
! [B: $i,A: $i] :
( ( ( B @ complement )
!= infinity )
| ( empty_set != A )
| ~ ( B @ ( A @ member ) ) ),
inference(simp,[status(thm)],[477]) ).
thf(485,plain,
! [A: $i] :
( ( ( A @ complement )
!= infinity )
| ~ ( A @ ( empty_set @ member ) ) ),
inference(simp,[status(thm)],[482]) ).
thf(478,plain,
! [B: $i,A: $i] :
( ( ( infinity @ ( empty_set @ member ) )
!= ( B @ ( A @ member ) ) )
| ~ $true
| ~ ( B @ complement @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[216,381]) ).
thf(479,plain,
! [B: $i,A: $i] :
( ( ( infinity @ ( empty_set @ member ) )
!= ( B @ ( A @ member ) ) )
| ~ ( B @ complement @ ( A @ member ) ) ),
inference(simp,[status(thm)],[478]) ).
thf(480,plain,
~ ( infinity @ complement @ ( empty_set @ member ) ),
inference(pattern_uni,[status(thm)],[479:[bind(A,$thf( empty_set )),bind(B,$thf( infinity ))]]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ f5 ) @ ( B @ ( A @ f4 ) @ ordered_pair ) ) )
| ~ ( B @ first @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first3) ).
thf(211,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)],[29]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ ( A @ f24 @ disjoint ) )
| ( A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
thf(253,plain,
! [A: $i] :
( ( A @ ( A @ f24 @ disjoint ) )
| ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(34,axiom,
! [A: $i] :
( ( ( A @ first )
!= ( A @ second ) )
| ~ ( A @ ordered_pair_predicate )
| ~ ( A @ little_set )
| ( identity_relation @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation3) ).
thf(221,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)],[34]) ).
thf(444,plain,
! [A: $i] :
( ( ( infinity @ ( empty_set @ member ) )
!= ( empty_set @ ( A @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[216,355]) ).
thf(445,plain,
! [A: $i] :
( ( infinity @ ( empty_set @ member ) )
!= ( empty_set @ ( A @ member ) ) ),
inference(simp,[status(thm)],[444]) ).
thf(446,plain,
! [A: $i] :
( ( infinity != empty_set )
| ( empty_set != A ) ),
inference(simp,[status(thm)],[445]) ).
thf(447,plain,
infinity != empty_set,
inference(simp,[status(thm)],[446]) ).
thf(573,plain,
! [A: $i] :
( ( A != infinity )
| ( empty_set != empty_set )
| ( A @ ( A @ f24 @ member ) ) ),
inference(paramod_ordered,[status(thm)],[194,447]) ).
thf(574,plain,
! [A: $i] :
( ( A != infinity )
| ( A @ ( A @ f24 @ member ) ) ),
inference(simp,[status(thm)],[573]) ).
thf(575,plain,
infinity @ ( infinity @ f24 @ member ),
inference(pattern_uni,[status(thm)],[574:[bind(A,$thf( infinity ))]]) ).
thf(864,plain,
! [B: $i,A: $i] :
( ( ( infinity @ ( infinity @ f24 @ member ) )
!= ( B @ ( A @ member ) ) )
| ~ $true
| ~ ( B @ complement @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[575,381]) ).
thf(865,plain,
! [B: $i,A: $i] :
( ( ( infinity @ ( infinity @ f24 @ member ) )
!= ( B @ ( A @ member ) ) )
| ~ ( B @ complement @ ( A @ member ) ) ),
inference(simp,[status(thm)],[864]) ).
thf(866,plain,
~ ( infinity @ complement @ ( infinity @ f24 @ member ) ),
inference(pattern_uni,[status(thm)],[865:[bind(A,$thf( infinity @ f24 )),bind(B,$thf( infinity ))]]) ).
thf(110,axiom,
! [A: $i] :
( ( A @ relation )
| ~ ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function1) ).
thf(396,plain,
! [A: $i] :
( ( A @ relation )
| ~ ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(52,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/sandbox/benchmark/theBenchmark.p',compose6) ).
thf(265,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)],[52]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ function )
| ~ ( C @ ( B @ ( A @ maps ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps1) ).
thf(312,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ function )
| ~ ( C @ ( B @ ( A @ maps ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( B @ little_set )
| ~ ( B @ ( A @ closed ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed2) ).
thf(307,plain,
! [B: $i,A: $i] :
( ( B @ little_set )
| ~ ( B @ ( A @ closed ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f13 ) @ little_set )
| ~ ( B @ flip_range_of @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range2) ).
thf(292,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f13 ) @ little_set )
| ~ ( B @ flip_range_of @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',image_and_substitution5) ).
thf(233,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)],[39]) ).
thf(45,axiom,
! [A: $i] :
( ( ( A @ first )
= ( A @ second ) )
| ~ ( identity_relation @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation2) ).
thf(248,plain,
! [A: $i] :
( ( ( A @ first )
= ( A @ second ) )
| ~ ( identity_relation @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( B @ ( B @ ( A @ f1 ) @ member ) )
| ~ ( A @ ( B @ ( A @ f1 ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality3) ).
thf(302,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)],[70]) ).
thf(123,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ powerset @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset1) ).
thf(424,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ powerset @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(50,axiom,
! [A: $i] :
( ( f25 @ ( A @ f26 @ ( A @ ordered_pair ) @ member ) )
| ( A = empty_set )
| ~ ( A @ little_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice3) ).
thf(260,plain,
! [A: $i] :
( ( f25 @ ( A @ f26 @ ( A @ ordered_pair ) @ member ) )
| ( A = empty_set )
| ~ ( A @ little_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ f1 ) @ little_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).
thf(349,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ f1 ) @ little_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(57,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f7 ) @ ( A @ member ) )
| ~ ( B @ second @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second4) ).
thf(275,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f7 ) @ ( A @ member ) )
| ~ ( B @ second @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ second @ little_set )
| ~ ( A @ ordered_pair_predicate ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second_component_is_small) ).
thf(229,plain,
! [A: $i] :
( ( A @ second @ little_set )
| ~ ( A @ ordered_pair_predicate ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(128,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',two_sets_equal) ).
thf(435,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(82,axiom,
! [A: $i] :
( ( A @ ( A @ f26 @ member ) )
| ( A = empty_set )
| ~ ( A @ little_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice2) ).
thf(329,plain,
! [A: $i] :
( ( A @ ( A @ f26 @ member ) )
| ( A = empty_set )
| ~ ( A @ little_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ f22 ) ) @ second )
= A )
| ~ ( C @ ( B @ image ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution4) ).
thf(224,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ f22 ) ) @ second )
= A )
| ~ ( C @ ( B @ image ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',first5) ).
thf(188,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)],[21]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ ( A @ f27 ) @ second ) )
| ~ ( B @ range_of @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of3) ).
thf(388,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ ( A @ f27 ) @ second ) )
| ~ ( B @ range_of @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f14 ) @ little_set )
| ~ ( B @ flip_range_of @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range3) ).
thf(356,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f14 ) @ little_set )
| ~ ( B @ flip_range_of @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(15,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/sandbox/benchmark/theBenchmark.p',second5) ).
thf(169,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)],[15]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ first @ little_set )
| ~ ( A @ ordered_pair_predicate ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_component_is_small) ).
thf(256,plain,
! [A: $i] :
( ( A @ first @ little_set )
| ~ ( A @ ordered_pair_predicate ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(87,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f9 ) @ little_set )
| ~ ( B @ rotate_right @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right1) ).
thf(339,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f9 ) @ little_set )
| ~ ( B @ rotate_right @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(589,plain,
! [A: $i] :
( ( A != f25 )
| ( empty_set @ function )
| ( A @ ( A @ f24 @ member ) ) ),
inference(paramod_ordered,[status(thm)],[194,321]) ).
thf(590,plain,
( ( empty_set @ function )
| ( f25 @ ( f25 @ f24 @ member ) ) ),
inference(pattern_uni,[status(thm)],[589:[bind(A,$thf( f25 ))]]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',rotate_right6) ).
thf(173,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)],[16]) ).
thf(100,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ proper_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',proper_subset2) ).
thf(371,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ proper_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(2,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( F @ ( C @ apply_to_two_arguments ) ) @ ( A @ apply ) )
= ( G @ ( A @ apply ) @ ( F @ ( A @ apply ) @ ( E @ apply_to_two_arguments ) ) ) )
| ~ ( B @ ( G @ member ) )
| ~ ( B @ ( F @ member ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ homomorphism ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism4) ).
thf(134,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( F @ ( C @ apply_to_two_arguments ) ) @ ( A @ apply ) )
= ( G @ ( A @ apply ) @ ( F @ ( A @ apply ) @ ( E @ apply_to_two_arguments ) ) ) )
| ~ ( B @ ( G @ member ) )
| ~ ( B @ ( F @ member ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ homomorphism ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',cross_product4) ).
thf(244,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)],[43]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ~ ( A @ little_set )
| ( C @ ( B @ non_ordered_pair ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair2) ).
thf(360,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)],[97]) ).
thf(26,axiom,
! [A: $i] :
( ~ ( A @ second @ ( A @ first @ member ) )
| ~ ( A @ ordered_pair_predicate )
| ~ ( A @ little_set )
| ( estin @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation3) ).
thf(205,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)],[26]) ).
thf(111,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/sandbox/benchmark/theBenchmark.p',domain4) ).
thf(398,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)],[111]) ).
thf(89,axiom,
! [A: $i] :
( ~ ( A @ little_set )
| ( universal_set @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',universal_set) ).
thf(343,plain,
! [A: $i] :
( ~ ( A @ little_set )
| ( universal_set @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ first @ member ) )
| ~ ( C @ ( B @ cross_product ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product2) ).
thf(237,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)],[40]) ).
thf(68,axiom,
! [B: $i,A: $i] :
( ( A @ little_set )
| ~ ( B @ ( A @ closed ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed1) ).
thf(298,plain,
! [B: $i,A: $i] :
( ( A @ little_set )
| ~ ( B @ ( A @ closed ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(117,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f6 ) @ little_set )
| ~ ( B @ second @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second1) ).
thf(412,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f6 ) @ little_set )
| ~ ( B @ second @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(125,axiom,
b @ ( a @ subset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_subset_b) ).
thf(430,plain,
b @ ( a @ subset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',single_valued_set1) ).
thf(166,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)],[14]) ).
thf(7,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/sandbox/benchmark/theBenchmark.p',ordered_pair_predicate4) ).
thf(148,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)],[7]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ successor )
= ( A @ singleton_set @ ( A @ union ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor) ).
thf(161,plain,
! [A: $i] :
( ( A @ successor )
= ( A @ singleton_set @ ( A @ union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(59,axiom,
! [A: $i] :
( ~ ( A @ single_valued_set )
| ~ ( A @ relation )
| ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function3) ).
thf(279,plain,
! [A: $i] :
( ~ ( A @ single_valued_set )
| ~ ( A @ relation )
| ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f7 ) @ little_set )
| ~ ( B @ second @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second2) ).
thf(375,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f7 ) @ little_set )
| ~ ( B @ second @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ ordered_pair_predicate )
| ~ ( estin @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation1) ).
thf(180,plain,
! [A: $i] :
( ( A @ ordered_pair_predicate )
| ~ ( estin @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(67,axiom,
! [A: $i] :
( ( A @ powerset @ little_set )
| ~ ( A @ little_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset3) ).
thf(296,plain,
! [A: $i] :
( ( A @ powerset @ little_set )
| ~ ( A @ little_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f5 ) @ little_set )
| ~ ( B @ first @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first2) ).
thf(402,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f5 ) @ little_set )
| ~ ( B @ first @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(62,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/sandbox/benchmark/theBenchmark.p',rotate_right5) ).
thf(286,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)],[62]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ f7 ) @ ( B @ ( A @ f6 ) @ ordered_pair ) ) )
| ~ ( B @ second @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second3) ).
thf(281,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)],[60]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ~ ( A @ little_set )
| ( C @ ( B @ non_ordered_pair ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair3) ).
thf(391,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)],[108]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ image ) @ little_set )
| ~ ( B @ function )
| ~ ( A @ little_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution6) ).
thf(382,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ image ) @ little_set )
| ~ ( B @ function )
| ~ ( A @ little_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(6,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/sandbox/benchmark/theBenchmark.p',flip_range6) ).
thf(144,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)],[6]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ f27 ) @ member ) )
| ~ ( B @ range_of @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of2) ).
thf(335,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ f27 ) @ member ) )
| ~ ( B @ range_of @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ ordered_pair_predicate )
| ~ ( identity_relation @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation1) ).
thf(159,plain,
! [A: $i] :
( ( A @ ordered_pair_predicate )
| ~ ( identity_relation @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( A @ little_set )
| ( B @ complement @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
thf(406,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( A @ little_set )
| ( B @ complement @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ f17 ) @ member ) )
| ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2) ).
thf(419,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ f17 ) @ member ) )
| ( B @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ( A
= ( B @ ( A @ f8 ) @ first ) )
| ~ ( B @ domain_of @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
thf(377,plain,
! [B: $i,A: $i] :
( ( A
= ( B @ ( A @ f8 ) @ first ) )
| ~ ( B @ domain_of @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ union ) )
= ( B @ complement @ ( A @ complement @ intersection ) @ complement ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
thf(271,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ union ) )
= ( B @ complement @ ( A @ complement @ intersection ) @ complement ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(5,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/sandbox/benchmark/theBenchmark.p',compose7) ).
thf(140,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)],[5]) ).
thf(141,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(cnf,[status(esa)],[140]) ).
thf(142,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 ) )
| ~ ( F @ little_set )
| ~ ( E @ little_set )
| ~ ( D @ little_set )
| ~ ( A @ little_set )
| ( C @ ( B @ compose ) @ ( A @ member ) )
| ( A
!= ( E @ ( D @ ordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[141]) ).
thf(143,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( E @ ordered_pair ) @ member ) )
| ~ ( A @ ( E @ ( C @ ordered_pair ) @ member ) )
| ~ ( E @ little_set )
| ~ ( D @ little_set )
| ~ ( C @ little_set )
| ~ ( D @ ( C @ ordered_pair ) @ little_set )
| ( B @ ( A @ compose ) @ ( D @ ( C @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[142]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( B @ ( A @ ordered_pair ) @ little_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pairs_are_small1) ).
thf(139,plain,
! [B: $i,A: $i] : ( B @ ( A @ ordered_pair ) @ little_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(736,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( E @ ordered_pair ) @ member ) )
| ~ ( A @ ( E @ ( C @ ordered_pair ) @ member ) )
| ~ ( E @ little_set )
| ~ ( D @ little_set )
| ~ ( C @ little_set )
| ~ $true
| ( B @ ( A @ compose ) @ ( D @ ( C @ ordered_pair ) @ member ) ) ),
inference(rewrite,[status(thm)],[143,139]) ).
thf(737,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( E @ ordered_pair ) @ member ) )
| ~ ( A @ ( E @ ( C @ ordered_pair ) @ member ) )
| ~ ( E @ little_set )
| ~ ( D @ little_set )
| ~ ( C @ little_set )
| ( B @ ( A @ compose ) @ ( D @ ( C @ ordered_pair ) @ member ) ) ),
inference(simp,[status(thm)],[736]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( C @ non_ordered_pair ) )
!= ( B @ ( C @ non_ordered_pair ) ) )
| ~ ( B @ little_set )
| ~ ( A @ little_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_cancellation) ).
thf(318,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( A @ ( C @ non_ordered_pair ) )
!= ( B @ ( C @ non_ordered_pair ) ) )
| ~ ( B @ little_set )
| ~ ( A @ little_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ member ) )
| ~ ( B @ ( C @ member ) )
| ( B @ sigma @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sigma3) ).
thf(345,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)],[90]) ).
thf(46,axiom,
! [A: $i] :
( ( infinity @ ( A @ successor @ member ) )
| ~ ( infinity @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity3) ).
thf(251,plain,
! [A: $i] :
( ( infinity @ ( A @ successor @ member ) )
| ~ ( infinity @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(24,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/sandbox/benchmark/theBenchmark.p',apply5) ).
thf(198,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)],[24]) ).
thf(452,plain,
( ( ( b @ ( a @ subset ) )
!= ( c @ ( a @ subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[430,133]) ).
thf(453,plain,
( ( b @ ( a @ subset ) )
!= ( c @ ( a @ subset ) ) ),
inference(simp,[status(thm)],[452]) ).
thf(454,plain,
( ( b != c )
| ( a != a ) ),
inference(simp,[status(thm)],[453]) ).
thf(455,plain,
b != c,
inference(simp,[status(thm)],[454]) ).
thf(53,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ f32 ) ) ) ) @ member ) )
| ~ ( D @ ( B @ ( A @ maps ) ) )
| ~ ( E @ ( D @ closed ) )
| ~ ( C @ ( B @ closed ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ homomorphism ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism5) ).
thf(267,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ f32 ) ) ) ) @ member ) )
| ~ ( D @ ( B @ ( A @ maps ) ) )
| ~ ( E @ ( D @ closed ) )
| ~ ( C @ ( B @ closed ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ homomorphism ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ range_of @ subset ) )
| ~ ( C @ ( B @ ( A @ maps ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps3) ).
thf(438,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ range_of @ subset ) )
| ~ ( C @ ( B @ ( A @ maps ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ subset ) )
| ~ ( A @ little_set )
| ( B @ powerset @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset2) ).
thf(431,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ subset ) )
| ~ ( A @ little_set )
| ( B @ powerset @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(487,plain,
( ( ( infinity @ complement @ ( empty_set @ member ) )
!= ( infinity @ ( empty_set @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[216,480]) ).
thf(488,plain,
( ( infinity @ complement @ ( empty_set @ member ) )
!= ( infinity @ ( empty_set @ member ) ) ),
inference(simp,[status(thm)],[487]) ).
thf(489,plain,
( ( ( infinity @ complement )
!= infinity )
| ( empty_set != empty_set ) ),
inference(simp,[status(thm)],[488]) ).
thf(490,plain,
( ( infinity @ complement )
!= infinity ),
inference(simp,[status(thm)],[489]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ range_of @ subset ) )
| ( ( A @ domain_of )
!= B )
| ~ ( A @ function )
| ( C @ ( B @ ( A @ maps ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps4) ).
thf(426,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ range_of @ subset ) )
| ( ( A @ domain_of )
!= B )
| ~ ( A @ function )
| ( C @ ( B @ ( A @ maps ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(162,plain,
! [A: $i] :
( ( A @ singleton_set @ ( A @ union ) )
= ( A @ successor ) ),
inference(lifteq,[status(thm)],[161]) ).
thf(372,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ proper_subset ) ) ),
inference(cnf,[status(esa)],[371]) ).
thf(373,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ proper_subset ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[372]) ).
thf(374,plain,
! [A: $i] :
~ ( A @ ( A @ proper_subset ) ),
inference(simp,[status(thm)],[373]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f4 ) @ ( A @ member ) )
| ~ ( B @ first @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first4) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f4 ) @ ( A @ member ) )
| ~ ( B @ first @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(118,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ f8 ) @ member ) )
| ~ ( B @ domain_of @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
thf(414,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ f8 ) @ member ) )
| ~ ( B @ domain_of @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( A @ little_set )
| ~ ( B @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(327,plain,
! [B: $i,A: $i] :
( ( A @ little_set )
| ~ ( B @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(51,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ f33 ) ) ) ) @ member ) )
| ~ ( D @ ( B @ ( A @ maps ) ) )
| ~ ( E @ ( D @ closed ) )
| ~ ( C @ ( B @ closed ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ homomorphism ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism6) ).
thf(263,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ f33 ) ) ) ) @ member ) )
| ~ ( D @ ( B @ ( A @ maps ) ) )
| ~ ( E @ ( D @ closed ) )
| ~ ( C @ ( B @ closed ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ homomorphism ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(17,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ f33 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ f32 ) ) ) ) @ ( C @ apply_to_two_arguments ) ) @ ( A @ apply ) )
!= ( E @ ( D @ ( C @ ( B @ ( A @ f33 ) ) ) ) @ ( A @ apply ) @ ( E @ ( D @ ( C @ ( B @ ( A @ f32 ) ) ) ) @ ( A @ apply ) @ ( E @ apply_to_two_arguments ) ) ) )
| ~ ( D @ ( B @ ( A @ maps ) ) )
| ~ ( E @ ( D @ closed ) )
| ~ ( C @ ( B @ closed ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ homomorphism ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism7) ).
thf(177,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ f33 ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ f32 ) ) ) ) @ ( C @ apply_to_two_arguments ) ) @ ( A @ apply ) )
!= ( E @ ( D @ ( C @ ( B @ ( A @ f33 ) ) ) ) @ ( A @ apply ) @ ( E @ ( D @ ( C @ ( B @ ( A @ f32 ) ) ) ) @ ( A @ apply ) @ ( E @ apply_to_two_arguments ) ) ) )
| ~ ( D @ ( B @ ( A @ maps ) ) )
| ~ ( E @ ( D @ closed ) )
| ~ ( C @ ( B @ closed ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ homomorphism ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ordered_pair ) @ first )
= A )
| ~ ( B @ little_set )
| ~ ( A @ little_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_first) ).
thf(182,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ordered_pair ) @ first )
= A )
| ~ ( B @ little_set )
| ~ ( A @ little_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ordered_pair ) @ second )
= B )
| ~ ( B @ little_set )
| ~ ( A @ little_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_second) ).
thf(154,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ordered_pair ) @ second )
= B )
| ~ ( B @ little_set )
| ~ ( A @ little_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(106,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f12 ) @ little_set )
| ~ ( B @ flip_range_of @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_range1) ).
thf(386,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f12 ) @ little_set )
| ~ ( B @ flip_range_of @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ sigma @ little_set )
| ~ ( A @ little_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sigma4) ).
thf(314,plain,
! [A: $i] :
( ( A @ sigma @ little_set )
| ~ ( A @ little_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',compose5) ).
thf(231,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)],[38]) ).
thf(99,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( B @ ( A @ f1 ) @ member ) )
| ( A @ ( B @ ( A @ f1 ) @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
thf(368,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)],[99]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ second @ ( A @ first @ member ) )
| ~ ( estin @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation2) ).
thf(258,plain,
! [A: $i] :
( ( A @ second @ ( A @ first @ member ) )
| ~ ( estin @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ non_ordered_pair ) @ ( A @ singleton_set @ non_ordered_pair ) )
= ( B @ ( A @ ordered_pair ) ) ),
inference(lifteq,[status(thm)],[157]) ).
thf(64,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ maps ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ homomorphism ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism3) ).
thf(290,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ maps ) ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ homomorphism ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(44,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ closed ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ homomorphism ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism1) ).
thf(246,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ closed ) )
| ~ ( E @ ( D @ ( C @ ( B @ ( A @ homomorphism ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ cross_product ) @ ( B @ maps ) ) )
| ~ ( B @ ( A @ closed ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed3) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( A @ cross_product ) @ ( B @ maps ) ) )
| ~ ( B @ ( A @ closed ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(272,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ union ) )
= ( B @ complement @ ( A @ complement @ intersection ) @ complement ) ),
inference(lifteq,[status(thm)],[271]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( B @ ordered_pair_predicate )
| ~ ( A @ ( B @ member ) )
| ~ ( A @ relation ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',relation1) ).
thf(214,plain,
! [B: $i,A: $i] :
( ( B @ ordered_pair_predicate )
| ~ ( A @ ( B @ member ) )
| ~ ( A @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ proper_subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',proper_subset1) ).
thf(433,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ proper_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(502,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ union ) )
!= ( C @ singleton_set @ ( C @ union ) ) )
| ( ( B @ complement @ ( A @ complement @ intersection ) @ complement )
= ( C @ successor ) ) ),
inference(paramod_ordered,[status(thm)],[272,162]) ).
thf(503,plain,
! [A: $i] :
( ( A @ singleton_set @ complement @ ( A @ complement @ intersection ) @ complement )
= ( A @ successor ) ),
inference(pattern_uni,[status(thm)],[502:[bind(A,$thf( D )),bind(B,$thf( D @ singleton_set )),bind(C,$thf( D ))]]) ).
thf(510,plain,
! [A: $i] :
( ( A @ singleton_set @ complement @ ( A @ complement @ intersection ) @ complement )
= ( A @ successor ) ),
inference(simp,[status(thm)],[503]) ).
thf(69,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f30 ) ) @ little_set )
| ~ ( C @ ( B @ compose ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose2) ).
thf(300,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)],[69]) ).
thf(116,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f8 ) @ ordered_pair_predicate )
| ~ ( B @ domain_of @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
thf(410,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f8 ) @ ordered_pair_predicate )
| ~ ( B @ domain_of @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(56,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/sandbox/benchmark/theBenchmark.p',flip_range5) ).
thf(273,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)],[56]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
thf(305,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ function )
| ~ ( A @ one_to_one_function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one_function1) ).
thf(294,plain,
! [A: $i] :
( ( A @ function )
| ~ ( A @ one_to_one_function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ disjoint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint1) ).
thf(341,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ f11 ) @ little_set )
| ~ ( B @ rotate_right @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_right3) ).
thf(358,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ f11 ) @ little_set )
| ~ ( B @ rotate_right @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(23,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/sandbox/benchmark/theBenchmark.p',rotate_right4) ).
thf(195,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)],[23]) ).
thf(41,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/sandbox/benchmark/theBenchmark.p',compose4) ).
thf(239,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)],[41]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ little_set )
| ~ ( A @ ordered_pair_predicate ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pairs_are_small2) ).
thf(242,plain,
! [A: $i] :
( ( A @ little_set )
| ~ ( A @ ordered_pair_predicate ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(83,axiom,
infinity @ little_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity1) ).
thf(332,plain,
infinity @ little_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ ordered_pair ) )
!= ( D @ ( C @ ordered_pair ) ) )
| ~ ( D @ little_set )
| ~ ( C @ little_set )
| ~ ( B @ little_set )
| ~ ( A @ little_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',second_components_are_equal) ).
thf(163,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ ordered_pair ) )
!= ( D @ ( C @ ordered_pair ) ) )
| ~ ( D @ little_set )
| ~ ( C @ little_set )
| ~ ( B @ little_set )
| ~ ( A @ little_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ f22 ) ) @ first @ member ) )
| ~ ( C @ ( B @ image ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_and_substitution3) ).
thf(277,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ f22 ) ) @ first @ member ) )
| ~ ( C @ ( B @ image ) @ ( A @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset1) ).
thf(442,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ordered_pair_predicate )
| ~ ( C @ ( B @ cross_product ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product1) ).
thf(227,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)],[36]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ domain_of )
= B )
| ~ ( C @ ( B @ ( A @ maps ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps2) ).
thf(322,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ domain_of )
= B )
| ~ ( C @ ( B @ ( A @ maps ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(86,axiom,
! [A: $i] :
( ( A @ single_valued_set )
| ~ ( A @ function ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function2) ).
thf(337,plain,
! [A: $i] :
( ( A @ single_valued_set )
| ~ ( A @ function ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( A = B )
| ~ ( C @ ( B @ non_ordered_pair ) @ ( A @ member ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair1) ).
thf(309,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)],[73]) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',range_of4) ).
thf(364,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)],[98]) ).
thf(1303,plain,
$false,
inference(e,[status(thm)],[138,347,333,352,408,217,440,269,202,384,698,404,185,288,724,570,157,421,284,416,325,152,289,316,216,492,321,485,480,211,253,221,866,132,396,133,265,312,307,292,233,248,380,381,220,302,424,192,260,349,275,137,229,435,329,224,188,388,356,169,256,339,590,173,371,134,244,360,205,398,343,237,298,412,430,166,148,161,279,375,180,296,402,286,281,391,382,144,335,159,406,219,419,377,451,271,737,318,345,140,251,198,455,267,438,431,490,426,162,374,209,355,194,414,327,263,177,182,154,386,314,231,368,258,158,139,418,290,246,207,272,214,433,510,300,447,410,273,305,294,341,358,195,239,242,395,332,575,163,277,442,227,322,486,337,354,309,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET027-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.24/5.51 % Computer : n010.cluster.edu
% 0.24/5.51 % Model : x86_64 x86_64
% 0.24/5.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/5.51 % Memory : 8046.5625MB
% 0.24/5.51 % OS : Linux 6.8.0-71-generic
% 0.24/5.51 % CPULimit : 300
% 0.24/5.51 % WCLimit : 300
% 0.24/5.51 % DateTime : Sat Sep 26 06:55:20 UTC 2026
% 0.24/5.51 % CPUTime :
% 0.24/5.51 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.42/6.35 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.34/6.78 % [INFO] Parsing done (426ms).
% 2.81/6.80 % [INFO] Running in sequential loop mode.
% 3.55/7.38 % [INFO] eprover registered as external prover.
% 3.55/7.39 % [INFO] Scanning for conjecture ...
% 3.96/7.57 % [INFO] Found a conjecture (or negated_conjecture) and 154 axioms. Running axiom selection ...
% 4.36/7.78 % [INFO] Axiom selection finished. Selected 130 axioms (removed 24 axioms).
% 5.12/7.96 % [INFO] Problem is propositional (TPTP CNF).
% 5.12/7.99 % [INFO] Type checking passed.
% 5.12/7.99 % [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 ...
% 20.16/11.55 % External prover 'e' found a proof!
% 20.16/11.55 % [INFO] Killing All external provers ...
% 20.16/11.55 % Time passed: 5832ms (effective reasoning time: 4740ms)
% 20.16/11.56 % Axioms used in derivation (130): first_component_is_small, non_ordered_pair1, image_and_substitution1, cross_product4, complement1, image_and_substitution2, second2, maps4, first2, first1, function3, apply5, homomorphism4, flip_range5, closed3, infinity3, range_of3, regularity1, proper_subset3, domain4, singleton_set, compose4, relation1, 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, second3, subset3, compose3, image_and_substitution6, choice1, range_of4, left_cancellation, domain3, regularity2, first3, cross_product3, rotate_right2, element_relation3, homomorphism6, extensionality2, intersection1, flip_range1, property_of_second, subset2, compose7, sigma4, proper_subset1, maps1, property_of_singleton_sets, first4, compose6, function1, maps3, domain2, intersection3, second4, rotate_right5, identity_relation3, closed1, a_subset_b, disjoint1, b_subset_c, 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, powerset3, two_sets_equal, homomorphism5, flip_range2, maps2, ordered_pairs_are_small1, rotate_right4, second_component_is_small, complement2, flip_range6, cross_product1, function2, compose5, range_of2, universal_set, proper_subset2, domain1, closed2, identity_relation1, subset1, first_components_are_equal, intersection2, powerset2, first5, non_ordered_pair3, single_valued_set1, choice2, restrict, homomorphism2, a2, ordered_pairs_are_small2, extensionality3, flip_range3, compose1, range_of1
% 20.16/11.56 % No. of inferences in proof: 330
% 20.16/11.56 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 5832 ms resp. 4740 ms w/o parsing
% 18.87/11.68 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.87/11.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------