TSTP Solution File: SEU217+2 by Etableau---0.67
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Etableau---0.67
% Problem : SEU217+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 09:24:52 EDT 2022
% Result : Theorem 0.20s 0.45s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.13 % Problem : SEU217+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jun 18 23:58:44 EDT 2022
% 0.20/0.35 % CPUTime :
% 0.20/0.44 # No SInE strategy applied
% 0.20/0.44 # Auto-Mode selected heuristic G_E___207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y
% 0.20/0.44 # and selection function SelectMaxLComplexAvoidPosPred.
% 0.20/0.44 #
% 0.20/0.44 # Presaturation interreduction done
% 0.20/0.44 # Number of axioms: 382 Number of unprocessed: 338
% 0.20/0.44 # Tableaux proof search.
% 0.20/0.44 # APR header successfully linked.
% 0.20/0.44 # Hello from C++
% 0.20/0.45 # The folding up rule is enabled...
% 0.20/0.45 # Local unification is enabled...
% 0.20/0.45 # Any saturation attempts will use folding labels...
% 0.20/0.45 # 338 beginning clauses after preprocessing and clausification
% 0.20/0.45 # Creating start rules for all 2 conjectures.
% 0.20/0.45 # There are 2 start rule candidates:
% 0.20/0.45 # Found 51 unit axioms.
% 0.20/0.45 # Unsuccessfully attempted saturation on 1 start tableaux, moving on.
% 0.20/0.45 # 2 start rule tableaux created.
% 0.20/0.45 # 287 extension rule candidate clauses
% 0.20/0.45 # 51 unit axiom clauses
% 0.20/0.45
% 0.20/0.45 # Requested 8, 32 cores available to the main process.
% 0.20/0.45 # There are not enough tableaux to fork, creating more from the initial 2
% 0.20/0.45 # Closed tableau found in foldup close cycle with 0 folds and 1 closures done.
% 0.20/0.45 # There were 0 total branch saturation attempts.
% 0.20/0.45 # There were 0 of these attempts blocked.
% 0.20/0.45 # There were 0 deferred branch saturation attempts.
% 0.20/0.45 # There were 0 free duplicated saturations.
% 0.20/0.45 # There were 0 total successful branch saturations.
% 0.20/0.45 # There were 0 successful branch saturations in interreduction.
% 0.20/0.45 # There were 0 successful branch saturations on the branch.
% 0.20/0.45 # There were 0 successful branch saturations after the branch.
% 0.20/0.45 # SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 # SZS output start for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.45 # Begin clausification derivation
% 0.20/0.45
% 0.20/0.45 # End clausification derivation
% 0.20/0.45 # Begin listing active clauses obtained from FOF to CNF conversion
% 0.20/0.45 cnf(i_0_321, negated_conjecture, (in(esk68_0,esk67_0))).
% 0.20/0.45 cnf(i_0_365, lemma, (relation_dom(empty_set)=empty_set)).
% 0.20/0.45 cnf(i_0_184, plain, (empty(empty_set))).
% 0.20/0.45 cnf(i_0_237, plain, (empty(esk55_0))).
% 0.20/0.45 cnf(i_0_240, plain, (empty(esk57_0))).
% 0.20/0.45 cnf(i_0_234, plain, (function(esk54_0))).
% 0.20/0.45 cnf(i_0_183, plain, (relation(empty_set))).
% 0.20/0.45 cnf(i_0_235, plain, (relation(esk54_0))).
% 0.20/0.45 cnf(i_0_364, lemma, (relation_rng(empty_set)=empty_set)).
% 0.20/0.45 cnf(i_0_236, plain, (relation(esk55_0))).
% 0.20/0.45 cnf(i_0_241, plain, (relation(esk58_0))).
% 0.20/0.45 cnf(i_0_247, plain, (relation(esk61_0))).
% 0.20/0.45 cnf(i_0_182, plain, (relation_empty_yielding(empty_set))).
% 0.20/0.45 cnf(i_0_246, plain, (relation_empty_yielding(esk61_0))).
% 0.20/0.45 cnf(i_0_191, plain, (function(identity_relation(X1)))).
% 0.20/0.45 cnf(i_0_171, plain, (relation(identity_relation(X1)))).
% 0.20/0.45 cnf(i_0_378, lemma, (relation_dom(identity_relation(X1))=X1)).
% 0.20/0.45 cnf(i_0_377, lemma, (relation_rng(identity_relation(X1))=X1)).
% 0.20/0.45 cnf(i_0_243, plain, (empty(esk59_1(X1)))).
% 0.20/0.45 cnf(i_0_310, lemma, (subset(empty_set,X1))).
% 0.20/0.45 cnf(i_0_251, plain, (subset(X1,X1))).
% 0.20/0.45 cnf(i_0_400, lemma, (union(powerset(X1))=X1)).
% 0.20/0.45 cnf(i_0_271, lemma, (in(X1,esk62_1(X1)))).
% 0.20/0.45 cnf(i_0_405, plain, (in(X1,esk73_1(X1)))).
% 0.20/0.45 cnf(i_0_356, plain, (set_difference(empty_set,X1)=empty_set)).
% 0.20/0.45 cnf(i_0_290, plain, (set_union2(X1,empty_set)=X1)).
% 0.20/0.45 cnf(i_0_336, plain, (set_difference(X1,empty_set)=X1)).
% 0.20/0.45 cnf(i_0_209, plain, (set_union2(X1,X1)=X1)).
% 0.20/0.45 cnf(i_0_293, lemma, (unordered_pair(empty_set,empty_set)=powerset(empty_set))).
% 0.20/0.45 cnf(i_0_158, plain, (element(X1,powerset(X1)))).
% 0.20/0.45 cnf(i_0_179, plain, (element(esk52_1(X1),X1))).
% 0.20/0.45 cnf(i_0_244, plain, (element(esk59_1(X1),powerset(X1)))).
% 0.20/0.45 cnf(i_0_383, lemma, (subset(X1,set_union2(X1,X2)))).
% 0.20/0.45 cnf(i_0_322, lemma, (subset(set_difference(X1,X2),X1))).
% 0.20/0.45 cnf(i_0_306, plain, (set_difference(X1,X1)=empty_set)).
% 0.20/0.45 cnf(i_0_332, lemma, (set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2))).
% 0.20/0.45 cnf(i_0_343, lemma, (set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2))).
% 0.20/0.45 cnf(i_0_44, plain, (set_meet(empty_set)=empty_set)).
% 0.20/0.45 cnf(i_0_73, plain, (in(X1,unordered_pair(X2,X1)))).
% 0.20/0.45 cnf(i_0_74, plain, (in(X1,unordered_pair(X1,X2)))).
% 0.20/0.45 cnf(i_0_5, plain, (unordered_pair(X1,X2)=unordered_pair(X2,X1))).
% 0.20/0.45 cnf(i_0_6, plain, (set_union2(X1,X2)=set_union2(X2,X1))).
% 0.20/0.45 cnf(i_0_7, plain, (set_difference(X1,set_difference(X1,X2))=set_difference(X2,set_difference(X2,X1)))).
% 0.20/0.45 cnf(i_0_320, negated_conjecture, (apply(identity_relation(esk67_0),esk68_0)!=esk68_0)).
% 0.20/0.45 cnf(i_0_242, plain, (~empty(esk58_0))).
% 0.20/0.45 cnf(i_0_245, plain, (~empty(esk60_0))).
% 0.20/0.45 cnf(i_0_188, plain, (~empty(powerset(X1)))).
% 0.20/0.45 cnf(i_0_214, plain, (~proper_subset(X1,X1))).
% 0.20/0.45 cnf(i_0_215, lemma, (unordered_pair(X1,X1)!=empty_set)).
% 0.20/0.45 cnf(i_0_196, plain, (~empty(unordered_pair(X1,X2)))).
% 0.20/0.45 cnf(i_0_57, plain, (~in(X1,empty_set))).
% 0.20/0.45 cnf(i_0_375, plain, (X1=empty_set|~empty(X1))).
% 0.20/0.45 cnf(i_0_4, plain, (relation(X1)|~empty(X1))).
% 0.20/0.45 cnf(i_0_382, plain, (~empty(X1)|~in(X2,X1))).
% 0.20/0.45 cnf(i_0_1, plain, (~in(X1,X2)|~in(X2,X1))).
% 0.20/0.45 cnf(i_0_3, plain, (function(X1)|~empty(X1))).
% 0.20/0.45 cnf(i_0_366, lemma, (~subset(X1,X2)|~proper_subset(X2,X1))).
% 0.20/0.45 cnf(i_0_238, plain, (empty(X1)|~empty(esk56_1(X1)))).
% 0.20/0.45 cnf(i_0_2, plain, (~proper_subset(X1,X2)|~proper_subset(X2,X1))).
% 0.20/0.45 cnf(i_0_342, lemma, (X1=empty_set|~subset(X1,empty_set))).
% 0.20/0.45 cnf(i_0_197, plain, (empty(X1)|~empty(set_union2(X2,X1)))).
% 0.20/0.45 cnf(i_0_195, plain, (empty(X1)|~empty(set_union2(X1,X2)))).
% 0.20/0.45 cnf(i_0_201, plain, (empty(X1)|~relation(X1)|~empty(relation_dom(X1)))).
% 0.20/0.45 cnf(i_0_202, plain, (empty(X1)|~relation(X1)|~empty(relation_rng(X1)))).
% 0.20/0.45 cnf(i_0_204, plain, (empty(relation_dom(X1))|~empty(X1))).
% 0.20/0.45 cnf(i_0_149, plain, (subset(X1,X2)|~proper_subset(X1,X2))).
% 0.20/0.45 cnf(i_0_217, lemma, (~disjoint(unordered_pair(X1,X1),X2)|~in(X1,X2))).
% 0.20/0.45 cnf(i_0_206, plain, (empty(relation_rng(X1))|~empty(X1))).
% 0.20/0.45 cnf(i_0_203, plain, (relation(relation_dom(X1))|~empty(X1))).
% 0.20/0.45 cnf(i_0_205, plain, (relation(relation_rng(X1))|~empty(X1))).
% 0.20/0.45 cnf(i_0_166, plain, (relation(relation_inverse(X1))|~relation(X1))).
% 0.20/0.45 cnf(i_0_369, lemma, (X1=empty_set|relation_dom(X1)!=empty_set|~relation(X1))).
% 0.20/0.45 cnf(i_0_368, lemma, (X1=empty_set|relation_rng(X1)!=empty_set|~relation(X1))).
% 0.20/0.45 cnf(i_0_390, plain, (X1=X2|~empty(X2)|~empty(X1))).
% 0.20/0.45 cnf(i_0_56, plain, (X1=empty_set|in(esk20_1(X1),X1))).
% 0.20/0.45 cnf(i_0_222, lemma, (subset(X1,X2)|set_difference(X1,X2)!=empty_set)).
% 0.20/0.45 cnf(i_0_291, plain, (element(X1,X2)|~in(X1,X2))).
% 0.20/0.45 cnf(i_0_338, plain, (subset(X1,X2)|~element(X1,powerset(X2)))).
% 0.20/0.45 cnf(i_0_212, plain, (relation_inverse(relation_inverse(X1))=X1|~relation(X1))).
% 0.20/0.45 cnf(i_0_370, lemma, (relation_dom(X1)=empty_set|relation_rng(X1)!=empty_set|~relation(X1))).
% 0.20/0.45 cnf(i_0_385, lemma, (set_difference(X1,X2)=X1|~disjoint(X1,X2))).
% 0.20/0.45 cnf(i_0_42, plain, (relation(X1)|in(esk15_1(X1),X1))).
% 0.20/0.45 cnf(i_0_384, lemma, (disjoint(X1,X2)|set_difference(X1,X2)!=X1)).
% 0.20/0.45 cnf(i_0_371, lemma, (relation_rng(X1)=empty_set|relation_dom(X1)!=empty_set|~relation(X1))).
% 0.20/0.45 cnf(i_0_373, lemma, (set_difference(X1,unordered_pair(X2,X2))!=X1|~in(X2,X1))).
% 0.20/0.45 cnf(i_0_363, plain, (~element(X1,powerset(X2))|~empty(X2)|~in(X3,X1))).
% 0.20/0.45 cnf(i_0_67, plain, (empty(X1)|~element(X1,X2)|~empty(X2))).
% 0.20/0.45 cnf(i_0_330, lemma, (in(X1,X2)|~subset(unordered_pair(X3,X1),X2))).
% 0.20/0.45 cnf(i_0_331, lemma, (in(X1,X2)|~subset(unordered_pair(X1,X3),X2))).
% 0.20/0.45 cnf(i_0_323, lemma, (relation_rng(relation_inverse(X1))=relation_dom(X1)|~relation(X1))).
% 0.20/0.45 cnf(i_0_252, plain, (disjoint(X1,X2)|~disjoint(X2,X1))).
% 0.20/0.45 cnf(i_0_339, lemma, (~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1))).
% 0.20/0.45 cnf(i_0_93, plain, (subset(X1,X2)|~in(esk33_2(X1,X2),X2))).
% 0.20/0.45 cnf(i_0_358, lemma, (~disjoint(X1,X2)|~in(X3,set_difference(X1,set_difference(X1,X2))))).
% 0.20/0.45 cnf(i_0_174, plain, (relation(relation_dom_restriction(X1,X2))|~relation(X1))).
% 0.20/0.45 cnf(i_0_176, plain, (relation(relation_rng_restriction(X1,X2))|~relation(X2))).
% 0.20/0.45 cnf(i_0_221, lemma, (set_difference(X1,X2)=empty_set|~subset(X1,X2))).
% 0.20/0.45 cnf(i_0_324, lemma, (relation_dom(relation_inverse(X1))=relation_rng(X1)|~relation(X1))).
% 0.20/0.45 cnf(i_0_14, plain, (X1=X2|~subset(X2,X1)|~subset(X1,X2))).
% 0.20/0.45 cnf(i_0_200, plain, (empty(X1)|empty(X2)|~empty(cartesian_product2(X1,X2)))).
% 0.20/0.45 cnf(i_0_361, lemma, (~element(X1,powerset(X2))|~in(X3,subset_complement(X2,X1))|~in(X3,X1))).
% 0.20/0.45 cnf(i_0_406, lemma, (X1=X2|unordered_pair(X3,X3)!=unordered_pair(X1,X2))).
% 0.20/0.45 cnf(i_0_267, lemma, (set_union2(X1,X2)=X2|~subset(X1,X2))).
% 0.20/0.45 cnf(i_0_228, lemma, (subset(X1,union(X2))|~in(X1,X2))).
% 0.20/0.45 cnf(i_0_395, lemma, (X1=X2|unordered_pair(X1,X1)!=unordered_pair(X2,X3))).
% 0.20/0.45 cnf(i_0_337, plain, (element(X1,powerset(X2))|~subset(X1,X2))).
% 0.20/0.45 cnf(i_0_66, plain, (element(X1,X2)|~empty(X2)|~empty(X1))).
% 0.20/0.45 cnf(i_0_134, plain, (disjoint(X1,X2)|set_difference(X1,set_difference(X1,X2))!=empty_set)).
% 0.20/0.45 cnf(i_0_232, lemma, (element(X1,powerset(X2))|~in(esk53_2(X1,X2),X2))).
% 0.20/0.45 cnf(i_0_376, lemma, (X1=X2|~subset(unordered_pair(X1,X1),unordered_pair(X2,X2)))).
% 0.20/0.45 cnf(i_0_69, plain, (empty(X1)|in(X2,X1)|~element(X2,X1))).
% 0.20/0.45 cnf(i_0_269, lemma, (in(powerset(X1),esk62_1(X2))|~in(X1,esk62_1(X2)))).
% 0.20/0.45 cnf(i_0_239, plain, (element(esk56_1(X1),powerset(X1))|empty(X1))).
% 0.20/0.45 cnf(i_0_181, plain, (empty(relation_composition(X1,X2))|~relation(X1)|~empty(X2))).
% 0.20/0.45 cnf(i_0_208, plain, (empty(relation_composition(X1,X2))|~relation(X2)|~empty(X1))).
% 0.20/0.45 cnf(i_0_193, plain, (relation(set_union2(X1,X2))|~relation(X2)|~relation(X1))).
% 0.20/0.45 cnf(i_0_180, plain, (relation(relation_composition(X1,X2))|~relation(X1)|~empty(X2))).
% 0.20/0.45 cnf(i_0_95, plain, (in(X1,X2)|~subset(X3,X2)|~in(X1,X3))).
% 0.20/0.45 cnf(i_0_147, plain, (X1=X2|proper_subset(X1,X2)|~subset(X1,X2))).
% 0.20/0.45 cnf(i_0_388, lemma, (in(X1,X2)|~relation(X3)|~in(X1,relation_dom(relation_dom_restriction(X3,X2))))).
% 0.20/0.45 cnf(i_0_259, lemma, (in(X1,X2)|~relation(X3)|~in(X1,relation_rng(relation_rng_restriction(X2,X3))))).
% 0.20/0.45 cnf(i_0_279, lemma, (relation_image(X1,relation_dom(X1))=relation_rng(X1)|~relation(X1))).
% 0.20/0.45 cnf(i_0_389, lemma, (subset(relation_dom_restriction(X1,X2),X1)|~relation(X1))).
% 0.20/0.45 cnf(i_0_207, plain, (relation(relation_composition(X1,X2))|~relation(X2)|~empty(X1))).
% 0.20/0.45 cnf(i_0_169, plain, (relation(relation_composition(X1,X2))|~relation(X2)|~relation(X1))).
% 0.20/0.45 cnf(i_0_350, lemma, (X1=empty_set|complements_of_subsets(X2,X1)!=empty_set|~element(X1,powerset(powerset(X2))))).
% 0.20/0.45 cnf(i_0_261, lemma, (subset(relation_rng_restriction(X1,X2),X2)|~relation(X2))).
% 0.20/0.45 cnf(i_0_398, lemma, (relation_composition(identity_relation(X1),X2)=relation_dom_restriction(X2,X1)|~relation(X2))).
% 0.20/0.45 cnf(i_0_219, lemma, (subset(unordered_pair(X1,X1),X2)|~in(X1,X2))).
% 0.20/0.45 cnf(i_0_129, plain, (set_union2(relation_dom(X1),relation_rng(X1))=relation_field(X1)|~relation(X1))).
% 0.20/0.45 cnf(i_0_286, lemma, (X1=empty_set|relation_inverse_image(X2,X1)!=empty_set|~subset(X1,relation_rng(X2))|~relation(X2))).
% 0.20/0.45 cnf(i_0_292, lemma, (subset(X1,X2)|~subset(X3,X2)|~subset(X1,X3))).
% 0.20/0.45 cnf(i_0_367, lemma, (disjoint(X1,X2)|~disjoint(X3,X2)|~subset(X1,X3))).
% 0.20/0.45 cnf(i_0_41, plain, (relation(X1)|esk15_1(X1)!=unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)))).
% 0.20/0.45 cnf(i_0_94, plain, (subset(X1,X2)|in(esk33_2(X1,X2),X1))).
% 0.20/0.45 cnf(i_0_340, lemma, (disjoint(X1,X2)|in(esk69_2(X1,X2),X2))).
% 0.20/0.45 cnf(i_0_248, plain, (union_of_subsets(X1,X2)=union(X2)|~element(X2,powerset(powerset(X1))))).
% 0.20/0.45 cnf(i_0_249, plain, (meet_of_subsets(X1,X2)=set_meet(X2)|~element(X2,powerset(powerset(X1))))).
% 0.20/0.45 cnf(i_0_127, plain, (subset_complement(X1,X2)=set_difference(X1,X2)|~element(X2,powerset(X1)))).
% 0.20/0.45 cnf(i_0_341, lemma, (disjoint(X1,X2)|in(esk69_2(X1,X2),X1))).
% 0.20/0.45 cnf(i_0_223, lemma, (in(X1,X2)|~element(X3,powerset(X2))|~in(X1,X3))).
% 0.20/0.45 cnf(i_0_256, lemma, (X1=X2|X1=X3|unordered_pair(X1,X4)!=unordered_pair(X2,X3))).
% 0.20/0.45 cnf(i_0_218, lemma, (disjoint(unordered_pair(X1,X1),X2)|in(X1,X2))).
% 0.20/0.45 cnf(i_0_387, lemma, (in(X1,relation_dom(X2))|~relation(X2)|~in(X1,relation_dom(relation_dom_restriction(X2,X3))))).
% 0.20/0.45 cnf(i_0_258, lemma, (in(X1,relation_rng(X2))|~relation(X2)|~in(X1,relation_rng(relation_rng_restriction(X3,X2))))).
% 0.20/0.45 cnf(i_0_403, plain, (in(esk74_2(X1,X2),esk73_1(X1))|~in(X2,esk73_1(X1)))).
% 0.20/0.45 cnf(i_0_216, lemma, (set_union2(unordered_pair(X1,X1),X2)=X2|~in(X1,X2))).
% 0.20/0.45 cnf(i_0_233, lemma, (element(X1,powerset(X2))|in(esk53_2(X1,X2),X1))).
% 0.20/0.45 cnf(i_0_372, lemma, (set_difference(X1,unordered_pair(X2,X2))=X1|in(X2,X1))).
% 0.20/0.45 cnf(i_0_357, plain, (element(X1,X2)|~element(X3,powerset(X2))|~in(X1,X3))).
% 0.20/0.45 cnf(i_0_277, lemma, (subset(relation_image(X1,X2),relation_rng(X1))|~relation(X1))).
% 0.20/0.45 cnf(i_0_285, lemma, (subset(relation_inverse_image(X1,X2),relation_dom(X1))|~relation(X1))).
% 0.20/0.45 cnf(i_0_185, plain, (function(relation_composition(X1,X2))|~relation(X2)|~relation(X1)|~function(X2)|~function(X1))).
% 0.20/0.45 cnf(i_0_135, plain, (set_difference(X1,set_difference(X1,X2))=empty_set|~disjoint(X1,X2))).
% 0.20/0.45 cnf(i_0_309, plain, (X1=X2|~in(esk65_2(X1,X2),X2)|~in(esk65_2(X1,X2),X1))).
% 0.20/0.45 cnf(i_0_402, plain, (in(X1,esk74_2(X2,X3))|~subset(X1,X3)|~in(X3,esk73_1(X2)))).
% 0.20/0.45 cnf(i_0_260, lemma, (subset(relation_rng(relation_rng_restriction(X1,X2)),X1)|~relation(X2))).
% 0.20/0.45 cnf(i_0_329, lemma, (subset(unordered_pair(X1,X2),X3)|~in(X2,X3)|~in(X1,X3))).
% 0.20/0.45 cnf(i_0_305, lemma, (set_difference(X1,set_difference(X1,X2))=X1|~subset(X1,X2))).
% 0.20/0.45 cnf(i_0_394, lemma, (subset(set_union2(X1,X2),X3)|~subset(X2,X3)|~subset(X1,X3))).
% 0.20/0.45 cnf(i_0_227, lemma, (X1=unordered_pair(X2,X2)|X1=empty_set|~subset(X1,unordered_pair(X2,X2)))).
% 0.20/0.45 cnf(i_0_211, plain, (subset_complement(X1,subset_complement(X1,X2))=X2|~element(X2,powerset(X1)))).
% 0.20/0.45 cnf(i_0_270, lemma, (in(X1,esk62_1(X2))|~subset(X1,X3)|~in(X3,esk62_1(X2)))).
% 0.20/0.45 cnf(i_0_404, plain, (in(X1,esk73_1(X2))|~subset(X1,X3)|~in(X3,esk73_1(X2)))).
% 0.20/0.45 cnf(i_0_299, lemma, (subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))|~relation(X1))).
% 0.20/0.45 cnf(i_0_344, lemma, (disjoint(X1,X2)|~element(X2,powerset(X3))|~element(X1,powerset(X3))|~subset(X1,subset_complement(X3,X2)))).
% 0.20/0.45 cnf(i_0_303, lemma, (subset(relation_dom(X1),relation_dom(X2))|~subset(X1,X2)|~relation(X2)|~relation(X1))).
% 0.20/0.45 cnf(i_0_302, lemma, (subset(relation_rng(X1),relation_rng(X2))|~subset(X1,X2)|~relation(X2)|~relation(X1))).
% 0.20/0.45 cnf(i_0_399, lemma, (subset(relation_rng(relation_dom_restriction(X1,X2)),relation_rng(X1))|~relation(X1))).
% 0.20/0.45 cnf(i_0_280, lemma, (relation_image(X1,relation_rng(X2))=relation_rng(relation_composition(X2,X1))|~relation(X1)|~relation(X2))).
% 0.20/0.45 cnf(i_0_262, lemma, (subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2))|~relation(X2))).
% 0.20/0.45 cnf(i_0_163, plain, (element(subset_complement(X1,X2),powerset(X1))|~element(X2,powerset(X1)))).
% 0.20/0.45 cnf(i_0_187, plain, (relation(set_difference(X1,set_difference(X1,X2)))|~relation(X2)|~relation(X1))).
% 0.20/0.45 cnf(i_0_59, plain, (X1=powerset(X2)|~subset(esk21_2(X2,X1),X2)|~in(esk21_2(X2,X1),X1))).
% 0.20/0.45 cnf(i_0_349, lemma, (relation_dom(relation_composition(X1,X2))=relation_dom(X1)|~subset(relation_rng(X1),relation_dom(X2))|~relation(X2)|~relation(X1))).
% 0.20/0.45 cnf(i_0_213, plain, (complements_of_subsets(X1,complements_of_subsets(X1,X2))=X2|~element(X2,powerset(powerset(X1))))).
% 0.20/0.45 cnf(i_0_274, lemma, (in(esk63_3(X1,X2,X3),X2)|~relation(X3)|~in(X1,relation_image(X3,X2)))).
% 0.20/0.45 cnf(i_0_282, lemma, (in(esk64_3(X1,X2,X3),X2)|~relation(X3)|~in(X1,relation_inverse_image(X3,X2)))).
% 0.20/0.45 cnf(i_0_268, lemma, (are_equipotent(X1,esk62_1(X2))|in(X1,esk62_1(X2))|~subset(X1,esk62_1(X2)))).
% 0.20/0.45 cnf(i_0_264, lemma, (subset(cartesian_product2(X1,X2),cartesian_product2(X3,X2))|~subset(X1,X3))).
% 0.20/0.45 cnf(i_0_230, lemma, (in(X1,X2)|~in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),cartesian_product2(X4,X2)))).
% 0.20/0.45 cnf(i_0_231, lemma, (in(X1,X2)|~in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),cartesian_product2(X2,X4)))).
% 0.20/0.45 cnf(i_0_263, lemma, (subset(cartesian_product2(X1,X2),cartesian_product2(X1,X3))|~subset(X2,X3))).
% 0.20/0.45 cnf(i_0_401, plain, (are_equipotent(X1,esk73_1(X2))|in(X1,esk73_1(X2))|~subset(X1,esk73_1(X2)))).
% 0.20/0.45 cnf(i_0_71, plain, (X1=unordered_pair(X2,X3)|esk24_3(X2,X3,X1)!=X3|~in(esk24_3(X2,X3,X1),X1))).
% 0.20/0.45 cnf(i_0_72, plain, (X1=unordered_pair(X2,X3)|esk24_3(X2,X3,X1)!=X2|~in(esk24_3(X2,X3,X1),X1))).
% 0.20/0.45 cnf(i_0_170, plain, (element(union_of_subsets(X1,X2),powerset(X1))|~element(X2,powerset(powerset(X1))))).
% 0.20/0.45 cnf(i_0_313, lemma, (subset(set_difference(X1,X2),set_difference(X3,X2))|~subset(X1,X3))).
% 0.20/0.45 cnf(i_0_172, plain, (element(meet_of_subsets(X1,X2),powerset(X1))|~element(X2,powerset(powerset(X1))))).
% 0.20/0.45 cnf(i_0_295, lemma, (in(X1,relation_dom(X2))|~relation(X2)|~in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2))).
% 0.20/0.45 cnf(i_0_294, lemma, (in(X1,relation_rng(X2))|~relation(X2)|~in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2))).
% 0.20/0.45 cnf(i_0_311, lemma, (in(X1,relation_field(X2))|~relation(X2)|~in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2))).
% 0.20/0.45 cnf(i_0_272, lemma, (relation_rng_restriction(X1,relation_dom_restriction(X2,X3))=relation_dom_restriction(relation_rng_restriction(X1,X2),X3)|~relation(X2))).
% 0.20/0.45 cnf(i_0_53, plain, (X1=unordered_pair(X2,X2)|esk19_2(X2,X1)!=X2|~in(esk19_2(X2,X1),X1))).
% 0.20/0.45 cnf(i_0_386, lemma, (in(X1,relation_dom(relation_dom_restriction(X2,X3)))|~relation(X2)|~in(X1,relation_dom(X2))|~in(X1,X3))).
% 0.20/0.45 cnf(i_0_52, plain, (esk19_2(X1,X2)=X1|X2=unordered_pair(X1,X1)|in(esk19_2(X1,X2),X2))).
% 0.20/0.45 cnf(i_0_312, lemma, (in(X1,relation_field(X2))|~relation(X2)|~in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2))).
% 0.20/0.45 cnf(i_0_346, lemma, (subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1))|~relation(X2)|~relation(X1))).
% 0.20/0.45 cnf(i_0_347, lemma, (subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2))|~relation(X2)|~relation(X1))).
% 0.20/0.45 cnf(i_0_175, plain, (element(complements_of_subsets(X1,X2),powerset(powerset(X1)))|~element(X2,powerset(powerset(X1))))).
% 0.20/0.45 cnf(i_0_257, lemma, (in(X1,relation_rng(relation_rng_restriction(X2,X3)))|~relation(X3)|~in(X1,relation_rng(X3))|~in(X1,X2))).
% 0.20/0.45 cnf(i_0_113, plain, (X1=union(X2)|~in(esk39_2(X2,X1),X3)|~in(esk39_2(X2,X1),X1)|~in(X3,X2))).
% 0.20/0.45 cnf(i_0_308, plain, (X1=X2|in(esk65_2(X1,X2),X1)|in(esk65_2(X1,X2),X2))).
% 0.20/0.45 cnf(i_0_359, lemma, (disjoint(X1,X2)|in(esk70_2(X1,X2),set_difference(X1,set_difference(X1,X2))))).
% 0.20/0.45 cnf(i_0_298, lemma, (in(X1,relation_dom(X2))|~relation(X3)|~relation(X2)|~function(X3)|~function(X2)|~in(X1,relation_dom(relation_composition(X2,X3))))).
% 0.20/0.45 cnf(i_0_352, lemma, (relation_rng(relation_composition(X1,X2))=relation_rng(X2)|~subset(relation_dom(X2),relation_rng(X1))|~relation(X1)|~relation(X2))).
% 0.20/0.45 cnf(i_0_276, lemma, (in(esk63_3(X1,X2,X3),relation_dom(X3))|~relation(X3)|~in(X1,relation_image(X3,X2)))).
% 0.20/0.45 cnf(i_0_284, lemma, (in(esk64_3(X1,X2,X3),relation_rng(X3))|~relation(X3)|~in(X1,relation_inverse_image(X3,X2)))).
% 0.20/0.45 cnf(i_0_381, lemma, (in(X1,X2)|~relation(X3)|~in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),relation_composition(identity_relation(X2),X3)))).
% 0.20/0.45 cnf(i_0_58, plain, (X1=powerset(X2)|subset(esk21_2(X2,X1),X2)|in(esk21_2(X2,X1),X1))).
% 0.20/0.45 cnf(i_0_287, lemma, (subset(relation_inverse_image(X1,X2),relation_inverse_image(X1,X3))|~subset(X2,X3)|~relation(X1))).
% 0.20/0.45 cnf(i_0_345, lemma, (subset(X1,subset_complement(X2,X3))|~disjoint(X1,X3)|~element(X3,powerset(X2))|~element(X1,powerset(X2)))).
% 0.20/0.45 cnf(i_0_250, plain, (subset_difference(X1,X2,X3)=set_difference(X2,X3)|~element(X3,powerset(X1))|~element(X2,powerset(X1)))).
% 0.20/0.45 cnf(i_0_392, lemma, (X1=apply(X2,X3)|~relation(X2)|~function(X2)|~in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2))).
% 0.20/0.45 cnf(i_0_314, lemma, (X1=X2|unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3))!=unordered_pair(unordered_pair(X4,X2),unordered_pair(X4,X4)))).
% 0.20/0.45 cnf(i_0_396, lemma, (set_difference(relation_dom(X1),set_difference(relation_dom(X1),X2))=relation_dom(relation_dom_restriction(X1,X2))|~relation(X1))).
% 0.20/0.45 cnf(i_0_47, plain, (X1=set_meet(X2)|X2=empty_set|~in(esk17_2(X2,X1),esk18_2(X2,X1))|~in(esk17_2(X2,X1),X1))).
% 0.20/0.45 cnf(i_0_77, plain, (X1=set_union2(X2,X3)|~in(esk25_3(X2,X3,X1),X1)|~in(esk25_3(X2,X3,X1),X3))).
% 0.20/0.45 cnf(i_0_78, plain, (X1=set_union2(X2,X3)|~in(esk25_3(X2,X3,X1),X1)|~in(esk25_3(X2,X3,X1),X2))).
% 0.20/0.45 cnf(i_0_266, lemma, (subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))|~subset(X2,X4)|~subset(X1,X3))).
% 0.20/0.45 cnf(i_0_111, plain, (X1=union(X2)|in(esk40_2(X2,X1),X2)|in(esk39_2(X2,X1),X1))).
% 0.20/0.45 cnf(i_0_265, lemma, (set_difference(relation_rng(X1),set_difference(relation_rng(X1),X2))=relation_rng(relation_rng_restriction(X2,X1))|~relation(X1))).
% 0.20/0.45 cnf(i_0_315, lemma, (X1=X2|unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1))!=unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)))).
% 0.20/0.45 cnf(i_0_289, lemma, (subset(X1,set_difference(X2,set_difference(X2,X3)))|~subset(X1,X3)|~subset(X1,X2))).
% 0.20/0.45 cnf(i_0_173, plain, (element(subset_difference(X1,X2,X3),powerset(X1))|~element(X3,powerset(X1))|~element(X2,powerset(X1)))).
% 0.20/0.45 cnf(i_0_224, lemma, (subset(X1,set_difference(X2,unordered_pair(X3,X3)))|in(X3,X1)|~subset(X1,X2))).
% 0.20/0.45 cnf(i_0_360, lemma, (X1=empty_set|in(X2,subset_complement(X1,X3))|in(X2,X3)|~element(X3,powerset(X1))|~element(X2,X1))).
% 0.20/0.45 cnf(i_0_46, plain, (X1=set_meet(X2)|X2=empty_set|in(esk17_2(X2,X1),X1)|in(esk17_2(X2,X1),X3)|~in(X3,X2))).
% 0.20/0.45 cnf(i_0_112, plain, (X1=union(X2)|in(esk39_2(X2,X1),esk40_2(X2,X1))|in(esk39_2(X2,X1),X1))).
% 0.20/0.45 cnf(i_0_297, lemma, (in(apply(X1,X2),relation_dom(X3))|~relation(X3)|~relation(X1)|~function(X3)|~function(X1)|~in(X2,relation_dom(relation_composition(X1,X3))))).
% 0.20/0.45 cnf(i_0_296, lemma, (in(X1,relation_dom(relation_composition(X2,X3)))|~relation(X3)|~relation(X2)|~function(X3)|~function(X2)|~in(apply(X2,X1),relation_dom(X3))|~in(X1,relation_dom(X2)))).
% 0.20/0.45 cnf(i_0_278, lemma, (relation_image(X1,set_difference(relation_dom(X1),set_difference(relation_dom(X1),X2)))=relation_image(X1,X2)|~relation(X1))).
% 0.20/0.45 cnf(i_0_48, plain, (X1=set_meet(X2)|X2=empty_set|in(esk18_2(X2,X1),X2)|~in(esk17_2(X2,X1),X1))).
% 0.20/0.45 cnf(i_0_301, lemma, (apply(X1,apply(X2,X3))=apply(relation_composition(X2,X1),X3)|~relation(X1)|~relation(X2)|~function(X1)|~function(X2)|~in(X3,relation_dom(X2)))).
% 0.20/0.45 cnf(i_0_117, plain, (X1=set_difference(X2,X3)|in(esk41_3(X2,X3,X1),X1)|~in(esk41_3(X2,X3,X1),X3))).
% 0.20/0.45 cnf(i_0_300, lemma, (apply(X1,apply(X2,X3))=apply(relation_composition(X2,X1),X3)|~relation(X2)|~relation(X1)|~function(X2)|~function(X1)|~in(X3,relation_dom(relation_composition(X2,X1))))).
% 0.20/0.45 cnf(i_0_354, lemma, (subset_difference(X1,X1,meet_of_subsets(X1,X2))=union_of_subsets(X1,complements_of_subsets(X1,X2))|X2=empty_set|~element(X2,powerset(powerset(X1))))).
% 0.20/0.45 cnf(i_0_304, lemma, (subset(set_difference(X1,set_difference(X1,X2)),set_difference(X3,set_difference(X3,X2)))|~subset(X1,X3))).
% 0.20/0.45 cnf(i_0_124, plain, (X1=relation_rng(X2)|~relation(X2)|~in(unordered_pair(unordered_pair(X3,esk43_2(X2,X1)),unordered_pair(X3,X3)),X2)|~in(esk43_2(X2,X1),X1))).
% 0.20/0.45 cnf(i_0_90, plain, (subset(X1,X2)|~relation(X2)|~relation(X1)|~in(unordered_pair(unordered_pair(esk31_2(X1,X2),esk31_2(X1,X2)),unordered_pair(esk31_2(X1,X2),esk32_2(X1,X2))),X2))).
% 0.20/0.45 cnf(i_0_353, lemma, (subset_difference(X1,X1,union_of_subsets(X1,X2))=meet_of_subsets(X1,complements_of_subsets(X1,X2))|X2=empty_set|~element(X2,powerset(powerset(X1))))).
% 0.20/0.45 cnf(i_0_229, lemma, (in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),cartesian_product2(X3,X4))|~in(X2,X4)|~in(X1,X3))).
% 0.20/0.45 cnf(i_0_84, plain, (X1=cartesian_product2(X2,X3)|in(esk29_3(X2,X3,X1),X2)|in(esk28_3(X2,X3,X1),X1))).
% 0.20/0.45 cnf(i_0_107, plain, (X1=relation_dom(X2)|~relation(X2)|~in(unordered_pair(unordered_pair(esk36_2(X2,X1),X3),unordered_pair(esk36_2(X2,X1),esk36_2(X2,X1))),X2)|~in(esk36_2(X2,X1),X1))).
% 0.20/0.45 cnf(i_0_380, lemma, (in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)|~relation(X3)|~in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),relation_composition(identity_relation(X4),X3)))).
% 0.20/0.45 cnf(i_0_273, lemma, (in(X1,relation_image(X2,X3))|~relation(X2)|~in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X2)|~in(X4,X3))).
% 0.20/0.45 cnf(i_0_83, plain, (X1=cartesian_product2(X2,X3)|in(esk30_3(X2,X3,X1),X3)|in(esk28_3(X2,X3,X1),X1))).
% 0.20/0.45 cnf(i_0_118, plain, (X1=set_difference(X2,X3)|in(esk41_3(X2,X3,X1),X2)|in(esk41_3(X2,X3,X1),X1))).
% 0.20/0.45 cnf(i_0_281, lemma, (in(X1,relation_inverse_image(X2,X3))|~relation(X2)|~in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),X2)|~in(X4,X3))).
% 0.20/0.45 cnf(i_0_70, plain, (esk24_3(X1,X2,X3)=X1|esk24_3(X1,X2,X3)=X2|X3=unordered_pair(X1,X2)|in(esk24_3(X1,X2,X3),X3))).
% 0.20/0.45 cnf(i_0_144, plain, (X1=complements_of_subsets(X2,X3)|element(esk51_3(X2,X3,X1),powerset(X2))|~element(X1,powerset(powerset(X2)))|~element(X3,powerset(powerset(X2))))).
% 0.20/0.45 cnf(i_0_98, plain, (X1=set_difference(X2,set_difference(X2,X3))|~in(esk34_3(X2,X3,X1),X1)|~in(esk34_3(X2,X3,X1),X3)|~in(esk34_3(X2,X3,X1),X2))).
% 0.20/0.45 cnf(i_0_143, plain, (X1=complements_of_subsets(X2,X3)|~element(X1,powerset(powerset(X2)))|~element(X3,powerset(powerset(X2)))|~in(subset_complement(X2,esk51_3(X2,X3,X1)),X3)|~in(esk51_3(X2,X3,X1),X1))).
% 0.20/0.45 cnf(i_0_97, plain, (X1=set_difference(X2,set_difference(X2,X3))|in(esk34_3(X2,X3,X1),X2)|in(esk34_3(X2,X3,X1),X1))).
% 0.20/0.45 cnf(i_0_29, plain, (X1=relation_image(X2,X3)|in(esk9_3(X2,X3,X1),X3)|in(esk8_3(X2,X3,X1),X1)|~relation(X2))).
% 0.20/0.45 cnf(i_0_35, plain, (X1=relation_inverse_image(X2,X3)|in(esk12_3(X2,X3,X1),X3)|in(esk11_3(X2,X3,X1),X1)|~relation(X2))).
% 0.20/0.45 cnf(i_0_283, lemma, (in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,esk64_3(X1,X2,X3))),X3)|~relation(X3)|~in(X1,relation_inverse_image(X3,X2)))).
% 0.20/0.45 cnf(i_0_362, lemma, (X1=empty_set|in(unordered_pair(unordered_pair(esk71_1(X1),esk71_1(X1)),unordered_pair(esk71_1(X1),esk72_1(X1))),X1)|~relation(X1))).
% 0.20/0.45 cnf(i_0_96, plain, (X1=set_difference(X2,set_difference(X2,X3))|in(esk34_3(X2,X3,X1),X3)|in(esk34_3(X2,X3,X1),X1))).
% 0.20/0.45 cnf(i_0_31, plain, (X1=relation_image(X2,X3)|~relation(X2)|~in(unordered_pair(unordered_pair(X4,esk8_3(X2,X3,X1)),unordered_pair(X4,X4)),X2)|~in(esk8_3(X2,X3,X1),X1)|~in(X4,X3))).
% 0.20/0.45 cnf(i_0_85, plain, (X1=cartesian_product2(X2,X3)|esk28_3(X2,X3,X1)!=unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))|~in(esk28_3(X2,X3,X1),X1)|~in(X5,X3)|~in(X4,X2))).
% 0.20/0.45 cnf(i_0_10, plain, (X1=identity_relation(X2)|esk2_2(X2,X1)!=esk1_2(X2,X1)|~relation(X1)|~in(unordered_pair(unordered_pair(esk1_2(X2,X1),esk1_2(X2,X1)),unordered_pair(esk1_2(X2,X1),esk2_2(X2,X1))),X1)|~in(esk1_2(X2,X1),X2))).
% 0.20/0.45 cnf(i_0_119, plain, (X1=set_difference(X2,X3)|in(esk41_3(X2,X3,X1),X3)|~in(esk41_3(X2,X3,X1),X1)|~in(esk41_3(X2,X3,X1),X2))).
% 0.20/0.45 cnf(i_0_379, lemma, (in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),relation_composition(identity_relation(X3),X4))|~relation(X4)|~in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X4)|~in(X1,X3))).
% 0.20/0.45 cnf(i_0_43, plain, (unordered_pair(unordered_pair(esk13_2(X1,X2),esk13_2(X1,X2)),unordered_pair(esk13_2(X1,X2),esk14_2(X1,X2)))=X2|~relation(X1)|~in(X2,X1))).
% 0.20/0.45 cnf(i_0_76, plain, (X1=set_union2(X2,X3)|in(esk25_3(X2,X3,X1),X2)|in(esk25_3(X2,X3,X1),X3)|in(esk25_3(X2,X3,X1),X1))).
% 0.20/0.45 cnf(i_0_37, plain, (X1=relation_inverse_image(X2,X3)|~relation(X2)|~in(unordered_pair(unordered_pair(esk11_3(X2,X3,X1),X4),unordered_pair(esk11_3(X2,X3,X1),esk11_3(X2,X3,X1))),X2)|~in(esk11_3(X2,X3,X1),X1)|~in(X4,X3))).
% 0.20/0.45 cnf(i_0_91, plain, (subset(X1,X2)|in(unordered_pair(unordered_pair(esk31_2(X1,X2),esk31_2(X1,X2)),unordered_pair(esk31_2(X1,X2),esk32_2(X1,X2))),X1)|~relation(X2)|~relation(X1))).
% 0.20/0.45 cnf(i_0_142, plain, (X1=complements_of_subsets(X2,X3)|in(subset_complement(X2,esk51_3(X2,X3,X1)),X3)|in(esk51_3(X2,X3,X1),X1)|~element(X1,powerset(powerset(X2)))|~element(X3,powerset(powerset(X2))))).
% 0.20/0.45 cnf(i_0_275, lemma, (in(unordered_pair(unordered_pair(X1,esk63_3(X1,X2,X3)),unordered_pair(esk63_3(X1,X2,X3),esk63_3(X1,X2,X3))),X3)|~relation(X3)|~in(X1,relation_image(X3,X2)))).
% 0.20/0.45 cnf(i_0_8, plain, (esk2_2(X1,X2)=esk1_2(X1,X2)|X2=identity_relation(X1)|in(unordered_pair(unordered_pair(esk1_2(X1,X2),esk1_2(X1,X2)),unordered_pair(esk1_2(X1,X2),esk2_2(X1,X2))),X2)|~relation(X2))).
% 0.20/0.45 cnf(i_0_9, plain, (X1=identity_relation(X2)|in(unordered_pair(unordered_pair(esk1_2(X2,X1),esk1_2(X2,X1)),unordered_pair(esk1_2(X2,X1),esk2_2(X2,X1))),X1)|in(esk1_2(X2,X1),X2)|~relation(X1))).
% 0.20/0.45 cnf(i_0_63, plain, (X1=X2|~relation(X2)|~relation(X1)|~in(unordered_pair(unordered_pair(esk22_2(X1,X2),esk22_2(X1,X2)),unordered_pair(esk22_2(X1,X2),esk23_2(X1,X2))),X2)|~in(unordered_pair(unordered_pair(esk22_2(X1,X2),esk22_2(X1,X2)),unordered_pair(esk22_2(X1,X2),esk23_2(X1,X2))),X1))).
% 0.20/0.45 cnf(i_0_131, plain, (X1=relation_inverse(X2)|~relation(X1)|~relation(X2)|~in(unordered_pair(unordered_pair(esk45_2(X2,X1),esk45_2(X2,X1)),unordered_pair(esk45_2(X2,X1),esk46_2(X2,X1))),X1)|~in(unordered_pair(unordered_pair(esk45_2(X2,X1),esk46_2(X2,X1)),unordered_pair(esk46_2(X2,X1),esk46_2(X2,X1))),X2))).
% 0.20/0.45 cnf(i_0_106, plain, (X1=relation_dom(X2)|in(unordered_pair(unordered_pair(esk36_2(X2,X1),esk36_2(X2,X1)),unordered_pair(esk36_2(X2,X1),esk37_2(X2,X1))),X2)|in(esk36_2(X2,X1),X1)|~relation(X2))).
% 0.20/0.45 cnf(i_0_123, plain, (X1=relation_rng(X2)|in(unordered_pair(unordered_pair(esk43_2(X2,X1),esk44_2(X2,X1)),unordered_pair(esk44_2(X2,X1),esk44_2(X2,X1))),X2)|in(esk43_2(X2,X1),X1)|~relation(X2))).
% 0.20/0.45 cnf(i_0_30, plain, (X1=relation_image(X2,X3)|in(unordered_pair(unordered_pair(esk8_3(X2,X3,X1),esk9_3(X2,X3,X1)),unordered_pair(esk9_3(X2,X3,X1),esk9_3(X2,X3,X1))),X2)|in(esk8_3(X2,X3,X1),X1)|~relation(X2))).
% 0.20/0.45 cnf(i_0_82, plain, (unordered_pair(unordered_pair(esk29_3(X1,X2,X3),esk29_3(X1,X2,X3)),unordered_pair(esk29_3(X1,X2,X3),esk30_3(X1,X2,X3)))=esk28_3(X1,X2,X3)|X3=cartesian_product2(X1,X2)|in(esk28_3(X1,X2,X3),X3))).
% 0.20/0.45 cnf(i_0_36, plain, (X1=relation_inverse_image(X2,X3)|in(unordered_pair(unordered_pair(esk11_3(X2,X3,X1),esk11_3(X2,X3,X1)),unordered_pair(esk11_3(X2,X3,X1),esk12_3(X2,X3,X1))),X2)|in(esk11_3(X2,X3,X1),X1)|~relation(X2))).
% 0.20/0.45 cnf(i_0_19, plain, (X1=relation_dom_restriction(X2,X3)|~relation(X1)|~relation(X2)|~in(unordered_pair(unordered_pair(esk3_3(X2,X3,X1),esk3_3(X2,X3,X1)),unordered_pair(esk3_3(X2,X3,X1),esk4_3(X2,X3,X1))),X1)|~in(unordered_pair(unordered_pair(esk3_3(X2,X3,X1),esk3_3(X2,X3,X1)),unordered_pair(esk3_3(X2,X3,X1),esk4_3(X2,X3,X1))),X2)|~in(esk3_3(X2,X3,X1),X3))).
% 0.20/0.45 cnf(i_0_25, plain, (X1=relation_rng_restriction(X2,X3)|~relation(X1)|~relation(X3)|~in(unordered_pair(unordered_pair(esk6_3(X2,X3,X1),esk5_3(X2,X3,X1)),unordered_pair(esk5_3(X2,X3,X1),esk5_3(X2,X3,X1))),X1)|~in(unordered_pair(unordered_pair(esk6_3(X2,X3,X1),esk5_3(X2,X3,X1)),unordered_pair(esk5_3(X2,X3,X1),esk5_3(X2,X3,X1))),X3)|~in(esk6_3(X2,X3,X1),X2))).
% 0.20/0.45 cnf(i_0_18, plain, (X1=relation_dom_restriction(X2,X3)|in(unordered_pair(unordered_pair(esk3_3(X2,X3,X1),esk3_3(X2,X3,X1)),unordered_pair(esk3_3(X2,X3,X1),esk4_3(X2,X3,X1))),X1)|in(esk3_3(X2,X3,X1),X3)|~relation(X1)|~relation(X2))).
% 0.20/0.45 cnf(i_0_24, plain, (X1=relation_rng_restriction(X2,X3)|in(unordered_pair(unordered_pair(esk6_3(X2,X3,X1),esk5_3(X2,X3,X1)),unordered_pair(esk5_3(X2,X3,X1),esk5_3(X2,X3,X1))),X1)|in(esk6_3(X2,X3,X1),X2)|~relation(X1)|~relation(X3))).
% 0.20/0.45 cnf(i_0_62, plain, (X1=X2|in(unordered_pair(unordered_pair(esk22_2(X1,X2),esk22_2(X1,X2)),unordered_pair(esk22_2(X1,X2),esk23_2(X1,X2))),X1)|in(unordered_pair(unordered_pair(esk22_2(X1,X2),esk22_2(X1,X2)),unordered_pair(esk22_2(X1,X2),esk23_2(X1,X2))),X2)|~relation(X2)|~relation(X1))).
% 0.20/0.45 cnf(i_0_130, plain, (X1=relation_inverse(X2)|in(unordered_pair(unordered_pair(esk45_2(X2,X1),esk46_2(X2,X1)),unordered_pair(esk46_2(X2,X1),esk46_2(X2,X1))),X2)|in(unordered_pair(unordered_pair(esk45_2(X2,X1),esk45_2(X2,X1)),unordered_pair(esk45_2(X2,X1),esk46_2(X2,X1))),X1)|~relation(X1)|~relation(X2))).
% 0.20/0.45 cnf(i_0_138, plain, (X1=relation_composition(X2,X3)|~relation(X1)|~relation(X3)|~relation(X2)|~in(unordered_pair(unordered_pair(esk48_3(X2,X3,X1),esk48_3(X2,X3,X1)),unordered_pair(esk48_3(X2,X3,X1),esk49_3(X2,X3,X1))),X1)|~in(unordered_pair(unordered_pair(esk48_3(X2,X3,X1),X4),unordered_pair(esk48_3(X2,X3,X1),esk48_3(X2,X3,X1))),X2)|~in(unordered_pair(unordered_pair(X4,esk49_3(X2,X3,X1)),unordered_pair(X4,X4)),X3))).
% 0.20/0.45 cnf(i_0_17, plain, (X1=relation_dom_restriction(X2,X3)|in(unordered_pair(unordered_pair(esk3_3(X2,X3,X1),esk3_3(X2,X3,X1)),unordered_pair(esk3_3(X2,X3,X1),esk4_3(X2,X3,X1))),X2)|in(unordered_pair(unordered_pair(esk3_3(X2,X3,X1),esk3_3(X2,X3,X1)),unordered_pair(esk3_3(X2,X3,X1),esk4_3(X2,X3,X1))),X1)|~relation(X1)|~relation(X2))).
% 0.20/0.45 cnf(i_0_23, plain, (X1=relation_rng_restriction(X2,X3)|in(unordered_pair(unordered_pair(esk6_3(X2,X3,X1),esk5_3(X2,X3,X1)),unordered_pair(esk5_3(X2,X3,X1),esk5_3(X2,X3,X1))),X3)|in(unordered_pair(unordered_pair(esk6_3(X2,X3,X1),esk5_3(X2,X3,X1)),unordered_pair(esk5_3(X2,X3,X1),esk5_3(X2,X3,X1))),X1)|~relation(X1)|~relation(X3))).
% 0.20/0.45 cnf(i_0_137, plain, (X1=relation_composition(X2,X3)|in(unordered_pair(unordered_pair(esk48_3(X2,X3,X1),esk48_3(X2,X3,X1)),unordered_pair(esk48_3(X2,X3,X1),esk50_3(X2,X3,X1))),X2)|in(unordered_pair(unordered_pair(esk48_3(X2,X3,X1),esk48_3(X2,X3,X1)),unordered_pair(esk48_3(X2,X3,X1),esk49_3(X2,X3,X1))),X1)|~relation(X1)|~relation(X3)|~relation(X2))).
% 0.20/0.45 cnf(i_0_136, plain, (X1=relation_composition(X2,X3)|in(unordered_pair(unordered_pair(esk49_3(X2,X3,X1),esk50_3(X2,X3,X1)),unordered_pair(esk50_3(X2,X3,X1),esk50_3(X2,X3,X1))),X3)|in(unordered_pair(unordered_pair(esk48_3(X2,X3,X1),esk48_3(X2,X3,X1)),unordered_pair(esk48_3(X2,X3,X1),esk49_3(X2,X3,X1))),X1)|~relation(X1)|~relation(X3)|~relation(X2))).
% 0.20/0.45 cnf(i_0_121, plain, (~in(X1,set_difference(X2,X3))|~in(X1,X3))).
% 0.20/0.45 cnf(i_0_318, lemma, (apply(identity_relation(X1),X2)=X2|~in(X2,X1))).
% 0.20/0.45 cnf(i_0_55, plain, (X1=X2|~in(X1,unordered_pair(X2,X2)))).
% 0.20/0.45 cnf(i_0_61, plain, (subset(X1,X2)|~in(X1,powerset(X2)))).
% 0.20/0.45 cnf(i_0_122, plain, (in(X1,X2)|~in(X1,set_difference(X2,X3)))).
% 0.20/0.45 cnf(i_0_60, plain, (in(X1,powerset(X2))|~subset(X1,X2))).
% 0.20/0.45 cnf(i_0_100, plain, (in(X1,X2)|~in(X1,set_difference(X3,set_difference(X3,X2))))).
% 0.20/0.45 cnf(i_0_79, plain, (in(X1,set_union2(X2,X3))|~in(X1,X3))).
% 0.20/0.45 cnf(i_0_80, plain, (in(X1,set_union2(X2,X3))|~in(X1,X2))).
% 0.20/0.45 cnf(i_0_75, plain, (X1=X2|X1=X3|~in(X1,unordered_pair(X3,X2)))).
% 0.20/0.45 cnf(i_0_81, plain, (in(X1,X2)|in(X1,X3)|~in(X1,set_union2(X3,X2)))).
% 0.20/0.45 cnf(i_0_102, plain, (apply(X1,X2)=empty_set|in(X2,relation_dom(X1))|~relation(X1)|~function(X1))).
% 0.20/0.45 cnf(i_0_120, plain, (in(X1,set_difference(X2,X3))|in(X1,X3)|~in(X1,X2))).
% 0.20/0.45 cnf(i_0_114, plain, (in(X1,union(X2))|~in(X3,X2)|~in(X1,X3))).
% 0.20/0.45 cnf(i_0_49, plain, (X1=empty_set|in(X2,set_meet(X1))|~in(X2,esk16_3(X1,set_meet(X1),X2)))).
% 0.20/0.45 cnf(i_0_12, plain, (X1=X2|~in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),identity_relation(X3)))).
% 0.20/0.45 cnf(i_0_13, plain, (in(X1,X2)|~in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),identity_relation(X2)))).
% 0.20/0.45 cnf(i_0_51, plain, (X1=empty_set|in(X2,X3)|~in(X2,set_meet(X1))|~in(X3,X1))).
% 0.20/0.45 cnf(i_0_116, plain, (in(X1,esk38_3(X2,union(X2),X1))|~in(X1,union(X2)))).
% 0.20/0.45 cnf(i_0_115, plain, (in(esk38_3(X1,union(X1),X2),X1)|~in(X2,union(X1)))).
% 0.20/0.45 cnf(i_0_99, plain, (in(X1,set_difference(X2,set_difference(X2,X3)))|~in(X1,X3)|~in(X1,X2))).
% 0.20/0.45 cnf(i_0_316, lemma, (identity_relation(relation_dom(X1))=X1|apply(X1,esk66_2(relation_dom(X1),X1))!=esk66_2(relation_dom(X1),X1)|~relation(X1)|~function(X1))).
% 0.20/0.45 cnf(i_0_22, plain, (in(X1,X2)|~relation(X3)|~in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),relation_dom_restriction(X3,X2)))).
% 0.20/0.45 cnf(i_0_28, plain, (in(X1,X2)|~relation(X3)|~in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),relation_rng_restriction(X2,X3)))).
% 0.20/0.45 cnf(i_0_89, plain, (in(esk26_4(X1,X2,cartesian_product2(X1,X2),X3),X1)|~in(X3,cartesian_product2(X1,X2)))).
% 0.20/0.45 cnf(i_0_50, plain, (X1=empty_set|in(esk16_3(X1,set_meet(X1),X2),X1)|in(X2,set_meet(X1)))).
% 0.20/0.45 cnf(i_0_11, plain, (in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X1)),identity_relation(X2))|~in(X1,X2))).
% 0.20/0.45 cnf(i_0_317, lemma, (identity_relation(relation_dom(X1))=X1|in(esk66_2(relation_dom(X1),X1),relation_dom(X1))|~relation(X1)|~function(X1))).
% 0.20/0.45 cnf(i_0_88, plain, (in(esk27_4(X1,X2,cartesian_product2(X1,X2),X3),X2)|~in(X3,cartesian_product2(X1,X2)))).
% 0.20/0.45 cnf(i_0_33, plain, (in(esk7_4(X1,X2,relation_image(X1,X2),X3),X2)|~relation(X1)|~in(X3,relation_image(X1,X2)))).
% 0.20/0.45 cnf(i_0_39, plain, (in(esk10_4(X1,X2,relation_inverse_image(X1,X2),X3),X2)|~relation(X1)|~in(X3,relation_inverse_image(X1,X2)))).
% 0.20/0.45 cnf(i_0_145, plain, (in(X1,complements_of_subsets(X2,X3))|~element(X3,powerset(powerset(X2)))|~element(X1,powerset(X2))|~in(subset_complement(X2,X1),X3))).
% 0.20/0.45 cnf(i_0_21, plain, (in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)|~relation(X3)|~in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),relation_dom_restriction(X3,X4)))).
% 0.20/0.45 cnf(i_0_105, plain, (in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,apply(X2,X1))),X2)|~relation(X2)|~function(X2)|~in(X1,relation_dom(X2)))).
% 0.20/0.45 cnf(i_0_146, plain, (in(subset_complement(X1,X2),X3)|~element(X3,powerset(powerset(X1)))|~in(X2,complements_of_subsets(X1,X3)))).
% 0.20/0.45 cnf(i_0_109, plain, (in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,esk35_3(X2,relation_dom(X2),X1))),X2)|~relation(X2)|~in(X1,relation_dom(X2)))).
% 0.20/0.45 cnf(i_0_27, plain, (in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)|~relation(X3)|~in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),relation_rng_restriction(X4,X3)))).
% 0.20/0.45 cnf(i_0_40, plain, (in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,esk10_4(X2,X3,relation_inverse_image(X2,X3),X1))),X2)|~relation(X2)|~in(X1,relation_inverse_image(X2,X3)))).
% 0.20/0.45 cnf(i_0_132, plain, (in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),relation_inverse(X3))|~relation(X3)|~in(unordered_pair(unordered_pair(X2,X1),unordered_pair(X2,X2)),X3))).
% 0.20/0.45 cnf(i_0_133, plain, (in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)|~relation(X3)|~in(unordered_pair(unordered_pair(X2,X1),unordered_pair(X2,X2)),relation_inverse(X3)))).
% 0.20/0.45 cnf(i_0_26, plain, (in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),relation_rng_restriction(X3,X4))|~relation(X4)|~in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X4)|~in(X2,X3))).
% 0.20/0.45 cnf(i_0_20, plain, (in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),relation_dom_restriction(X3,X4))|~relation(X3)|~in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3)|~in(X1,X4))).
% 0.20/0.45 cnf(i_0_139, plain, (in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),relation_composition(X3,X4))|~relation(X4)|~relation(X3)|~in(unordered_pair(unordered_pair(X5,X2),unordered_pair(X5,X5)),X4)|~in(unordered_pair(unordered_pair(X1,X5),unordered_pair(X1,X1)),X3))).
% 0.20/0.45 cnf(i_0_126, plain, (in(unordered_pair(unordered_pair(X1,esk42_3(X2,relation_rng(X2),X1)),unordered_pair(esk42_3(X2,relation_rng(X2),X1),esk42_3(X2,relation_rng(X2),X1))),X2)|~relation(X2)|~in(X1,relation_rng(X2)))).
% 0.20/0.45 cnf(i_0_141, plain, (in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,esk47_5(X2,X3,relation_composition(X2,X3),X1,X4))),X2)|~relation(X3)|~relation(X2)|~in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),relation_composition(X2,X3)))).
% 0.20/0.45 cnf(i_0_34, plain, (in(unordered_pair(unordered_pair(X1,esk7_4(X2,X3,relation_image(X2,X3),X1)),unordered_pair(esk7_4(X2,X3,relation_image(X2,X3),X1),esk7_4(X2,X3,relation_image(X2,X3),X1))),X2)|~relation(X2)|~in(X1,relation_image(X2,X3)))).
% 0.20/0.45 cnf(i_0_87, plain, (unordered_pair(unordered_pair(esk26_4(X1,X2,cartesian_product2(X1,X2),X3),esk26_4(X1,X2,cartesian_product2(X1,X2),X3)),unordered_pair(esk26_4(X1,X2,cartesian_product2(X1,X2),X3),esk27_4(X1,X2,cartesian_product2(X1,X2),X3)))=X3|~in(X3,cartesian_product2(X1,X2)))).
% 0.20/0.45 cnf(i_0_140, plain, (in(unordered_pair(unordered_pair(X1,esk47_5(X2,X3,relation_composition(X2,X3),X4,X1)),unordered_pair(esk47_5(X2,X3,relation_composition(X2,X3),X4,X1),esk47_5(X2,X3,relation_composition(X2,X3),X4,X1))),X3)|~relation(X3)|~relation(X2)|~in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),relation_composition(X2,X3)))).
% 0.20/0.45 # End listing active clauses. There is an equivalent clause to each of these in the clausification!
% 0.20/0.45 # Begin printing tableau
% 0.20/0.45 # Found 3 steps
% 0.20/0.45 cnf(i_0_320, negated_conjecture, (apply(identity_relation(esk67_0),esk68_0)!=esk68_0), inference(start_rule)).
% 0.20/0.45 cnf(i_0_484, plain, (apply(identity_relation(esk67_0),esk68_0)!=esk68_0), inference(extension_rule, [i_0_318])).
% 0.20/0.45 cnf(i_0_1213, plain, (~in(esk68_0,esk67_0)), inference(closure_rule, [i_0_321])).
% 0.20/0.45 # End printing tableau
% 0.20/0.45 # SZS output end
% 0.20/0.45 # Branches closed with saturation will be marked with an "s"
% 0.20/0.45 # Returning from population with 17 new_tableaux and 0 remaining starting tableaux.
% 0.20/0.45 # We now have 17 tableaux to operate on
% 0.20/0.45 # Found closed tableau during pool population.
% 0.20/0.45 # Proof search is over...
% 0.20/0.45 # Freeing feature tree
%------------------------------------------------------------------------------