TSTP Solution File: SEU230+2 by Etableau---0.67
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Etableau---0.67
% Problem : SEU230+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 : n024.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 09:25:01 EDT 2022
% Result : Theorem 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU230+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 11:57:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.46 # No SInE strategy applied
% 0.19/0.46 # Auto-Mode selected heuristic G_E___207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S0Y
% 0.19/0.46 # and selection function SelectMaxLComplexAvoidPosPred.
% 0.19/0.46 #
% 0.19/0.46 # Presaturation interreduction done
% 0.19/0.46 # Number of axioms: 471 Number of unprocessed: 415
% 0.19/0.46 # Tableaux proof search.
% 0.19/0.46 # APR header successfully linked.
% 0.19/0.46 # Hello from C++
% 0.19/0.46 # The folding up rule is enabled...
% 0.19/0.46 # Local unification is enabled...
% 0.19/0.46 # Any saturation attempts will use folding labels...
% 0.19/0.46 # 415 beginning clauses after preprocessing and clausification
% 0.19/0.46 # Creating start rules for all 1 conjectures.
% 0.19/0.46 # There are 1 start rule candidates:
% 0.19/0.46 # Found 63 unit axioms.
% 0.19/0.46 # 1 start rule tableaux created.
% 0.19/0.46 # 352 extension rule candidate clauses
% 0.19/0.46 # 63 unit axiom clauses
% 0.19/0.46
% 0.19/0.46 # Requested 8, 32 cores available to the main process.
% 0.19/0.46 # There are not enough tableaux to fork, creating more from the initial 1
% 0.19/0.46 # Closed tableau found in foldup close cycle with 0 folds and 1 closures done.
% 0.19/0.46 # There were 0 total branch saturation attempts.
% 0.19/0.46 # There were 0 of these attempts blocked.
% 0.19/0.46 # There were 0 deferred branch saturation attempts.
% 0.19/0.46 # There were 0 free duplicated saturations.
% 0.19/0.46 # There were 0 total successful branch saturations.
% 0.19/0.46 # There were 0 successful branch saturations in interreduction.
% 0.19/0.46 # There were 0 successful branch saturations on the branch.
% 0.19/0.46 # There were 0 successful branch saturations after the branch.
% 0.19/0.46 # SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 # SZS output start for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 # Begin clausification derivation
% 0.19/0.46
% 0.19/0.46 # End clausification derivation
% 0.19/0.46 # Begin listing active clauses obtained from FOF to CNF conversion
% 0.19/0.46 cnf(i_0_228, plain, (empty(empty_set))).
% 0.19/0.46 cnf(i_0_450, lemma, (relation_dom(empty_set)=empty_set)).
% 0.19/0.46 cnf(i_0_291, plain, (empty(esk65_0))).
% 0.19/0.46 cnf(i_0_294, plain, (empty(esk67_0))).
% 0.19/0.46 cnf(i_0_296, plain, (empty(esk68_0))).
% 0.19/0.46 cnf(i_0_288, plain, (function(esk64_0))).
% 0.19/0.46 cnf(i_0_295, plain, (function(esk68_0))).
% 0.19/0.46 cnf(i_0_304, plain, (function(esk72_0))).
% 0.19/0.46 cnf(i_0_449, lemma, (relation_rng(empty_set)=empty_set)).
% 0.19/0.46 cnf(i_0_308, plain, (function(esk74_0))).
% 0.19/0.46 cnf(i_0_227, plain, (relation(empty_set))).
% 0.19/0.46 cnf(i_0_289, plain, (relation(esk64_0))).
% 0.19/0.46 cnf(i_0_290, plain, (relation(esk65_0))).
% 0.19/0.46 cnf(i_0_297, plain, (relation(esk68_0))).
% 0.19/0.46 cnf(i_0_298, plain, (relation(esk69_0))).
% 0.19/0.46 cnf(i_0_305, plain, (relation(esk72_0))).
% 0.19/0.46 cnf(i_0_307, plain, (relation(esk73_0))).
% 0.19/0.46 cnf(i_0_310, plain, (relation(esk74_0))).
% 0.19/0.46 cnf(i_0_303, plain, (one_to_one(esk72_0))).
% 0.19/0.46 cnf(i_0_226, plain, (relation_empty_yielding(empty_set))).
% 0.19/0.46 cnf(i_0_306, plain, (relation_empty_yielding(esk73_0))).
% 0.19/0.46 cnf(i_0_309, plain, (relation_empty_yielding(esk74_0))).
% 0.19/0.46 cnf(i_0_357, plain, (set_union2(X1,empty_set)=X1)).
% 0.19/0.46 cnf(i_0_260, plain, (set_union2(X1,X1)=X1)).
% 0.19/0.46 cnf(i_0_300, plain, (empty(esk70_1(X1)))).
% 0.19/0.46 cnf(i_0_238, plain, (function(identity_relation(X1)))).
% 0.19/0.46 cnf(i_0_213, plain, (relation(identity_relation(X1)))).
% 0.19/0.46 cnf(i_0_377, lemma, (subset(empty_set,X1))).
% 0.19/0.46 cnf(i_0_314, plain, (subset(X1,X1))).
% 0.19/0.46 cnf(i_0_469, lemma, (relation_dom(identity_relation(X1))=X1)).
% 0.19/0.46 cnf(i_0_335, lemma, (in(X1,esk76_1(X1)))).
% 0.19/0.46 cnf(i_0_499, plain, (in(X1,esk91_1(X1)))).
% 0.19/0.46 cnf(i_0_360, lemma, (unordered_pair(empty_set,empty_set)=powerset(empty_set))).
% 0.19/0.46 cnf(i_0_494, lemma, (union(powerset(X1))=X1)).
% 0.19/0.46 cnf(i_0_468, lemma, (relation_rng(identity_relation(X1))=X1)).
% 0.19/0.46 cnf(i_0_423, plain, (set_difference(empty_set,X1)=empty_set)).
% 0.19/0.46 cnf(i_0_402, plain, (set_difference(X1,empty_set)=X1)).
% 0.19/0.46 cnf(i_0_200, plain, (element(X1,powerset(X1)))).
% 0.19/0.46 cnf(i_0_221, plain, (element(esk62_1(X1),X1))).
% 0.19/0.46 cnf(i_0_477, lemma, (subset(X1,set_union2(X1,X2)))).
% 0.19/0.46 cnf(i_0_301, plain, (element(esk70_1(X1),powerset(X1)))).
% 0.19/0.46 cnf(i_0_388, lemma, (subset(set_difference(X1,X2),X1))).
% 0.19/0.46 cnf(i_0_373, plain, (set_difference(X1,X1)=empty_set)).
% 0.19/0.46 cnf(i_0_398, lemma, (set_union2(X1,set_difference(X2,X1))=set_union2(X1,X2))).
% 0.19/0.46 cnf(i_0_410, lemma, (set_difference(set_union2(X1,X2),X2)=set_difference(X1,X2))).
% 0.19/0.46 cnf(i_0_70, plain, (set_meet(empty_set)=empty_set)).
% 0.19/0.46 cnf(i_0_99, plain, (in(X1,unordered_pair(X2,X1)))).
% 0.19/0.46 cnf(i_0_100, plain, (in(X1,unordered_pair(X1,X2)))).
% 0.19/0.46 cnf(i_0_62, plain, (in(X1,unordered_triple(X2,X3,X1)))).
% 0.19/0.46 cnf(i_0_63, plain, (in(X1,unordered_triple(X2,X1,X3)))).
% 0.19/0.46 cnf(i_0_64, plain, (in(X1,unordered_triple(X1,X2,X3)))).
% 0.19/0.46 cnf(i_0_8, plain, (unordered_pair(X1,X2)=unordered_pair(X2,X1))).
% 0.19/0.46 cnf(i_0_9, plain, (set_union2(X1,X2)=set_union2(X2,X1))).
% 0.19/0.46 cnf(i_0_10, plain, (set_difference(X1,set_difference(X1,X2))=set_difference(X2,set_difference(X2,X1)))).
% 0.19/0.46 cnf(i_0_319, negated_conjecture, (~in(esk75_0,set_union2(esk75_0,unordered_pair(esk75_0,esk75_0))))).
% 0.19/0.46 cnf(i_0_299, plain, (~empty(esk69_0))).
% 0.19/0.46 cnf(i_0_302, plain, (~empty(esk71_0))).
% 0.19/0.46 cnf(i_0_266, lemma, (unordered_pair(X1,X1)!=empty_set)).
% 0.19/0.46 cnf(i_0_235, plain, (~empty(powerset(X1)))).
% 0.19/0.46 cnf(i_0_265, plain, (~proper_subset(X1,X1))).
% 0.19/0.46 cnf(i_0_245, plain, (~empty(unordered_pair(X1,X2)))).
% 0.19/0.46 cnf(i_0_233, plain, (~empty(set_union2(X1,unordered_pair(X1,X1))))).
% 0.19/0.46 cnf(i_0_83, plain, (~in(X1,empty_set))).
% 0.19/0.46 cnf(i_0_465, plain, (X1=empty_set|~empty(X1))).
% 0.19/0.46 cnf(i_0_3, plain, (function(X1)|~empty(X1))).
% 0.19/0.46 cnf(i_0_4, plain, (relation(X1)|~empty(X1))).
% 0.19/0.46 cnf(i_0_474, plain, (~empty(X1)|~in(X2,X1))).
% 0.19/0.46 cnf(i_0_451, lemma, (~subset(X1,X2)|~proper_subset(X2,X1))).
% 0.19/0.46 cnf(i_0_292, plain, (empty(X1)|~empty(esk66_1(X1)))).
% 0.19/0.46 cnf(i_0_1, plain, (~in(X1,X2)|~in(X2,X1))).
% 0.19/0.46 cnf(i_0_254, plain, (relation(relation_dom(X1))|~empty(X1))).
% 0.19/0.46 cnf(i_0_256, plain, (relation(relation_rng(X1))|~empty(X1))).
% 0.19/0.46 cnf(i_0_2, plain, (~proper_subset(X1,X2)|~proper_subset(X2,X1))).
% 0.19/0.46 cnf(i_0_409, lemma, (X1=empty_set|~subset(X1,empty_set))).
% 0.19/0.46 cnf(i_0_246, plain, (empty(X1)|~empty(set_union2(X2,X1)))).
% 0.19/0.46 cnf(i_0_242, plain, (empty(X1)|~empty(set_union2(X1,X2)))).
% 0.19/0.46 cnf(i_0_252, plain, (empty(X1)|~relation(X1)|~empty(relation_dom(X1)))).
% 0.19/0.46 cnf(i_0_253, plain, (empty(X1)|~relation(X1)|~empty(relation_rng(X1)))).
% 0.19/0.46 cnf(i_0_268, lemma, (~disjoint(unordered_pair(X1,X1),X2)|~in(X1,X2))).
% 0.19/0.46 cnf(i_0_186, plain, (subset(X1,X2)|~proper_subset(X1,X2))).
% 0.19/0.46 cnf(i_0_255, plain, (empty(relation_dom(X1))|~empty(X1))).
% 0.19/0.46 cnf(i_0_257, plain, (empty(relation_rng(X1))|~empty(X1))).
% 0.19/0.46 cnf(i_0_225, plain, (empty(relation_inverse(X1))|~empty(X1))).
% 0.19/0.46 cnf(i_0_224, plain, (relation(relation_inverse(X1))|~empty(X1))).
% 0.19/0.46 cnf(i_0_208, plain, (relation(relation_inverse(X1))|~relation(X1))).
% 0.19/0.46 cnf(i_0_455, lemma, (X1=empty_set|relation_dom(X1)!=empty_set|~relation(X1))).
% 0.19/0.46 cnf(i_0_454, lemma, (X1=empty_set|relation_rng(X1)!=empty_set|~relation(X1))).
% 0.19/0.46 cnf(i_0_5, plain, (one_to_one(X1)|~empty(X1))).
% 0.19/0.46 cnf(i_0_273, lemma, (subset(X1,X2)|set_difference(X1,X2)!=empty_set)).
% 0.19/0.46 cnf(i_0_358, plain, (element(X1,X2)|~in(X1,X2))).
% 0.19/0.46 cnf(i_0_331, lemma, (set_union2(X1,X2)=X2|~subset(X1,X2))).
% 0.19/0.46 cnf(i_0_500, lemma, (X1=X2|unordered_pair(X3,X3)!=unordered_pair(X1,X2))).
% 0.19/0.46 cnf(i_0_489, lemma, (X1=X2|unordered_pair(X1,X1)!=unordered_pair(X2,X3))).
% 0.19/0.46 cnf(i_0_459, lemma, (set_difference(X1,unordered_pair(X2,X2))!=X1|~in(X2,X1))).
% 0.19/0.46 cnf(i_0_484, plain, (X1=X2|~empty(X2)|~empty(X1))).
% 0.19/0.46 cnf(i_0_405, plain, (subset(X1,X2)|~element(X1,powerset(X2)))).
% 0.19/0.46 cnf(i_0_456, lemma, (relation_dom(X1)=empty_set|relation_rng(X1)!=empty_set|~relation(X1))).
% 0.19/0.46 cnf(i_0_479, lemma, (set_difference(X1,X2)=X1|~disjoint(X1,X2))).
% 0.19/0.46 cnf(i_0_448, plain, (~element(X1,powerset(X2))|~empty(X2)|~in(X3,X1))).
% 0.19/0.46 cnf(i_0_82, plain, (X1=empty_set|in(esk25_1(X1),X1))).
% 0.19/0.46 cnf(i_0_396, lemma, (in(X1,X2)|~subset(unordered_pair(X3,X1),X2))).
% 0.19/0.46 cnf(i_0_397, lemma, (in(X1,X2)|~subset(unordered_pair(X1,X3),X2))).
% 0.19/0.46 cnf(i_0_263, plain, (relation_inverse(relation_inverse(X1))=X1|~relation(X1))).
% 0.19/0.46 cnf(i_0_197, plain, (function(function_inverse(X1))|~relation(X1)|~function(X1))).
% 0.19/0.46 cnf(i_0_198, plain, (relation(function_inverse(X1))|~relation(X1)|~function(X1))).
% 0.19/0.46 cnf(i_0_478, lemma, (disjoint(X1,X2)|set_difference(X1,X2)!=X1)).
% 0.19/0.46 cnf(i_0_168, plain, (one_to_one(X1)|esk56_1(X1)!=esk55_1(X1)|~relation(X1)|~function(X1))).
% 0.19/0.46 cnf(i_0_403, lemma, (~in(X1,X2)|~in(X3,X1)|~in(X2,X3))).
% 0.19/0.46 cnf(i_0_68, plain, (relation(X1)|in(esk20_1(X1),X1))).
% 0.19/0.46 cnf(i_0_475, plain, (~in(X1,esk90_2(X2,X3))|~in(X2,X3)|~in(X1,X3))).
% 0.19/0.46 cnf(i_0_457, lemma, (relation_rng(X1)=empty_set|relation_dom(X1)!=empty_set|~relation(X1))).
% 0.19/0.46 cnf(i_0_389, lemma, (relation_rng(relation_inverse(X1))=relation_dom(X1)|~relation(X1))).
% 0.19/0.46 cnf(i_0_93, plain, (empty(X1)|~element(X1,X2)|~empty(X2))).
% 0.19/0.46 cnf(i_0_315, plain, (disjoint(X1,X2)|~disjoint(X2,X1))).
% 0.19/0.46 cnf(i_0_406, lemma, (~disjoint(X1,X2)|~in(X3,X2)|~in(X3,X1))).
% 0.19/0.46 cnf(i_0_119, plain, (subset(X1,X2)|~in(esk38_2(X1,X2),X2))).
% 0.19/0.46 cnf(i_0_267, lemma, (set_union2(unordered_pair(X1,X1),X2)=X2|~in(X1,X2))).
% 0.19/0.46 cnf(i_0_466, lemma, (X1=X2|~subset(unordered_pair(X1,X1),unordered_pair(X2,X2)))).
% 0.19/0.46 cnf(i_0_216, plain, (relation(relation_dom_restriction(X1,X2))|~relation(X1))).
% 0.19/0.46 cnf(i_0_390, lemma, (relation_dom(relation_inverse(X1))=relation_rng(X1)|~relation(X1))).
% 0.19/0.46 cnf(i_0_272, lemma, (set_difference(X1,X2)=empty_set|~subset(X1,X2))).
% 0.19/0.46 cnf(i_0_425, lemma, (~disjoint(X1,X2)|~in(X3,set_difference(X1,set_difference(X1,X2))))).
% 0.19/0.46 cnf(i_0_218, plain, (relation(relation_rng_restriction(X1,X2))|~relation(X2))).
% 0.19/0.46 cnf(i_0_17, plain, (X1=X2|~subset(X2,X1)|~subset(X1,X2))).
% 0.19/0.46 cnf(i_0_251, plain, (empty(X1)|empty(X2)|~empty(cartesian_product2(X1,X2)))).
% 0.19/0.46 cnf(i_0_240, plain, (relation(set_union2(X1,X2))|~relation(X2)|~relation(X1))).
% 0.19/0.46 cnf(i_0_279, lemma, (subset(X1,union(X2))|~in(X1,X2))).
% 0.19/0.46 cnf(i_0_442, lemma, (~element(X1,powerset(X2))|~in(X3,subset_complement(X2,X1))|~in(X3,X1))).
% 0.19/0.46 cnf(i_0_92, plain, (element(X1,X2)|~empty(X2)|~empty(X1))).
% 0.19/0.46 cnf(i_0_243, plain, (function(relation_inverse(X1))|~one_to_one(X1)|~relation(X1)|~function(X1))).
% 0.19/0.46 cnf(i_0_476, plain, (in(esk90_2(X1,X2),X2)|~in(X1,X2))).
% 0.19/0.46 cnf(i_0_270, lemma, (subset(unordered_pair(X1,X1),X2)|~in(X1,X2))).
% 0.19/0.46 cnf(i_0_404, plain, (element(X1,powerset(X2))|~subset(X1,X2))).
% 0.19/0.46 cnf(i_0_187, plain, (relation_inverse(X1)=function_inverse(X1)|~one_to_one(X1)|~relation(X1)|~function(X1))).
% 0.19/0.46 cnf(i_0_452, lemma, (one_to_one(function_inverse(X1))|~one_to_one(X1)|~relation(X1)|~function(X1))).
% 0.19/0.46 cnf(i_0_166, plain, (disjoint(X1,X2)|set_difference(X1,set_difference(X1,X2))!=empty_set)).
% 0.19/0.46 cnf(i_0_283, lemma, (element(X1,powerset(X2))|~in(esk63_2(X1,X2),X2))).
% 0.19/0.46 cnf(i_0_387, lemma, (apply(identity_relation(X1),X2)=X2|~in(X2,X1))).
% 0.19/0.46 cnf(i_0_320, lemma, (X1=X2|X1=X3|unordered_pair(X1,X4)!=unordered_pair(X2,X3))).
% 0.19/0.46 cnf(i_0_293, plain, (element(esk66_1(X1),powerset(X1))|empty(X1))).
% 0.19/0.46 cnf(i_0_269, lemma, (disjoint(unordered_pair(X1,X1),X2)|in(X1,X2))).
% 0.19/0.46 cnf(i_0_223, plain, (empty(relation_composition(X1,X2))|~relation(X1)|~empty(X2))).
% 0.19/0.46 cnf(i_0_259, plain, (empty(relation_composition(X1,X2))|~relation(X2)|~empty(X1))).
% 0.19/0.46 cnf(i_0_247, plain, (function(relation_dom_restriction(X1,X2))|~relation(X1)|~function(X1))).
% 0.19/0.46 cnf(i_0_345, lemma, (relation_image(X1,relation_dom(X1))=relation_rng(X1)|~relation(X1))).
% 0.19/0.46 cnf(i_0_95, plain, (empty(X1)|in(X2,X1)|~element(X2,X1))).
% 0.19/0.46 cnf(i_0_443, lemma, (relation_rng(function_inverse(X1))=relation_dom(X1)|~one_to_one(X1)|~relation(X1)|~function(X1))).
% 0.19/0.46 cnf(i_0_184, plain, (X1=X2|proper_subset(X1,X2)|~subset(X1,X2))).
% 0.19/0.46 cnf(i_0_222, plain, (relation(relation_composition(X1,X2))|~relation(X1)|~empty(X2))).
% 0.19/0.46 cnf(i_0_258, plain, (relation(relation_composition(X1,X2))|~relation(X2)|~empty(X1))).
% 0.19/0.46 cnf(i_0_211, plain, (relation(relation_composition(X1,X2))|~relation(X2)|~relation(X1))).
% 0.19/0.46 cnf(i_0_229, plain, (relation_empty_yielding(relation_dom_restriction(X1,X2))|~relation_empty_yielding(X1)|~relation(X1))).
% 0.19/0.46 cnf(i_0_483, lemma, (subset(relation_dom_restriction(X1,X2),X1)|~relation(X1))).
% 0.19/0.46 cnf(i_0_333, lemma, (in(powerset(X1),esk76_1(X2))|~in(X1,esk76_1(X2)))).
% 0.19/0.46 cnf(i_0_67, plain, (relation(X1)|esk20_1(X1)!=unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)))).
% 0.19/0.46 cnf(i_0_121, plain, (in(X1,X2)|~subset(X3,X2)|~in(X1,X3))).
% 0.19/0.46 cnf(i_0_444, lemma, (relation_dom(function_inverse(X1))=relation_rng(X1)|~one_to_one(X1)|~relation(X1)|~function(X1))).
% 0.19/0.46 cnf(i_0_325, lemma, (subset(relation_rng_restriction(X1,X2),X2)|~relation(X2))).
% 0.19/0.46 cnf(i_0_417, lemma, (X1=empty_set|complements_of_subsets(X2,X1)!=empty_set|~element(X1,powerset(powerset(X2))))).
% 0.19/0.46 cnf(i_0_353, lemma, (X1=empty_set|relation_inverse_image(X2,X1)!=empty_set|~subset(X1,relation_rng(X2))|~relation(X2))).
% 0.19/0.46 cnf(i_0_482, lemma, (in(X1,X2)|~relation(X3)|~in(X1,relation_dom(relation_dom_restriction(X3,X2))))).
% 0.19/0.46 cnf(i_0_120, plain, (subset(X1,X2)|in(esk38_2(X1,X2),X1))).
% 0.19/0.46 cnf(i_0_323, lemma, (in(X1,X2)|~relation(X3)|~in(X1,relation_rng(relation_rng_restriction(X2,X3))))).
% 0.19/0.46 cnf(i_0_395, lemma, (subset(unordered_pair(X1,X2),X3)|~in(X2,X3)|~in(X1,X3))).
% 0.19/0.46 cnf(i_0_161, plain, (relation_field(X1)=set_union2(relation_dom(X1),relation_rng(X1))|~relation(X1))).
% 0.19/0.46 cnf(i_0_407, lemma, (disjoint(X1,X2)|in(esk81_2(X1,X2),X2))).
% 0.19/0.46 cnf(i_0_359, lemma, (subset(X1,X2)|~subset(X3,X2)|~subset(X1,X3))).
% 0.19/0.46 cnf(i_0_453, lemma, (disjoint(X1,X2)|~disjoint(X3,X2)|~subset(X1,X3))).
% 0.19/0.46 cnf(i_0_311, plain, (union_of_subsets(X1,X2)=union(X2)|~element(X2,powerset(powerset(X1))))).
% 0.19/0.46 cnf(i_0_408, lemma, (disjoint(X1,X2)|in(esk81_2(X1,X2),X1))).
% 0.19/0.46 cnf(i_0_278, lemma, (X1=unordered_pair(X2,X2)|X1=empty_set|~subset(X1,unordered_pair(X2,X2)))).
% 0.19/0.46 cnf(i_0_492, lemma, (relation_composition(identity_relation(X1),X2)=relation_dom_restriction(X2,X1)|~relation(X2))).
% 0.19/0.46 cnf(i_0_458, lemma, (set_difference(X1,unordered_pair(X2,X2))=X1|in(X2,X1))).
% 0.19/0.46 cnf(i_0_312, plain, (meet_of_subsets(X1,X2)=set_meet(X2)|~element(X2,powerset(powerset(X1))))).
% 0.19/0.46 cnf(i_0_159, plain, (subset_complement(X1,X2)=set_difference(X1,X2)|~element(X2,powerset(X1)))).
% 0.19/0.46 cnf(i_0_481, lemma, (in(X1,relation_dom(X2))|~relation(X2)|~in(X1,relation_dom(relation_dom_restriction(X2,X3))))).
% 0.19/0.46 cnf(i_0_274, lemma, (in(X1,X2)|~element(X3,powerset(X2))|~in(X1,X3))).
% 0.19/0.46 cnf(i_0_281, lemma, (in(X1,X2)|~in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),cartesian_product2(X4,X2)))).
% 0.19/0.46 cnf(i_0_171, plain, (one_to_one(X1)|in(esk55_1(X1),relation_dom(X1))|~relation(X1)|~function(X1))).
% 0.19/0.46 cnf(i_0_284, lemma, (element(X1,powerset(X2))|in(esk63_2(X1,X2),X1))).
% 0.19/0.46 cnf(i_0_322, lemma, (in(X1,relation_rng(X2))|~relation(X2)|~in(X1,relation_rng(relation_rng_restriction(X3,X2))))).
% 0.19/0.46 cnf(i_0_424, plain, (element(X1,X2)|~element(X3,powerset(X2))|~in(X1,X3))).
% 0.19/0.46 cnf(i_0_341, lemma, (subset(relation_image(X1,X2),relation_rng(X1))|~relation(X1))).
% 0.19/0.46 cnf(i_0_352, lemma, (subset(relation_inverse_image(X1,X2),relation_dom(X1))|~relation(X1))).
% 0.19/0.46 cnf(i_0_282, lemma, (in(X1,X2)|~in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),cartesian_product2(X2,X4)))).
% 0.19/0.46 cnf(i_0_497, plain, (in(esk92_2(X1,X2),esk91_1(X1))|~in(X2,esk91_1(X1)))).
% 0.19/0.46 cnf(i_0_362, lemma, (in(X1,relation_dom(X2))|~relation(X2)|~in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2))).
% 0.19/0.46 cnf(i_0_170, plain, (one_to_one(X1)|in(esk56_1(X1),relation_dom(X1))|~relation(X1)|~function(X1))).
% 0.19/0.46 cnf(i_0_167, plain, (set_difference(X1,set_difference(X1,X2))=empty_set|~disjoint(X1,X2))).
% 0.19/0.46 cnf(i_0_231, plain, (function(relation_composition(X1,X2))|~relation(X2)|~relation(X1)|~function(X2)|~function(X1))).
% 0.19/0.46 cnf(i_0_324, lemma, (subset(relation_rng(relation_rng_restriction(X1,X2)),X1)|~relation(X2))).
% 0.19/0.46 cnf(i_0_376, plain, (X1=X2|~in(esk79_2(X1,X2),X2)|~in(esk79_2(X1,X2),X1))).
% 0.19/0.46 cnf(i_0_372, lemma, (set_difference(X1,set_difference(X1,X2))=X1|~subset(X1,X2))).
% 0.19/0.46 cnf(i_0_361, lemma, (in(X1,relation_rng(X2))|~relation(X2)|~in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2))).
% 0.19/0.46 cnf(i_0_378, lemma, (in(X1,relation_field(X2))|~relation(X2)|~in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2))).
% 0.19/0.46 cnf(i_0_379, lemma, (in(X1,relation_field(X2))|~relation(X2)|~in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),X2))).
% 0.19/0.46 cnf(i_0_262, plain, (subset_complement(X1,subset_complement(X1,X2))=X2|~element(X2,powerset(X1)))).
% 0.19/0.46 cnf(i_0_488, lemma, (subset(set_union2(X1,X2),X3)|~subset(X2,X3)|~subset(X1,X3))).
% 0.19/0.46 cnf(i_0_366, lemma, (subset(X1,cartesian_product2(relation_dom(X1),relation_rng(X1)))|~relation(X1))).
% 0.19/0.46 cnf(i_0_496, plain, (in(X1,esk92_2(X2,X3))|~subset(X1,X3)|~in(X3,esk91_1(X2)))).
% 0.19/0.46 cnf(i_0_381, lemma, (X1=X2|unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3))!=unordered_pair(unordered_pair(X4,X2),unordered_pair(X4,X4)))).
% 0.19/0.46 cnf(i_0_382, lemma, (X1=X2|unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1))!=unordered_pair(unordered_pair(X2,X4),unordered_pair(X2,X2)))).
% 0.19/0.46 cnf(i_0_493, lemma, (subset(relation_rng(relation_dom_restriction(X1,X2)),relation_rng(X1))|~relation(X1))).
% 0.19/0.46 cnf(i_0_411, lemma, (disjoint(X1,X2)|~element(X2,powerset(X3))|~element(X1,powerset(X3))|~subset(X1,subset_complement(X3,X2)))).
% 0.19/0.46 cnf(i_0_370, lemma, (subset(relation_dom(X1),relation_dom(X2))|~subset(X1,X2)|~relation(X2)|~relation(X1))).
% 0.19/0.46 cnf(i_0_369, lemma, (subset(relation_rng(X1),relation_rng(X2))|~subset(X1,X2)|~relation(X2)|~relation(X1))).
% 0.19/0.46 cnf(i_0_205, plain, (element(subset_complement(X1,X2),powerset(X1))|~element(X2,powerset(X1)))).
% 0.19/0.46 cnf(i_0_326, lemma, (subset(relation_rng(relation_rng_restriction(X1,X2)),relation_rng(X2))|~relation(X2))).
% 0.19/0.46 cnf(i_0_334, lemma, (in(X1,esk76_1(X2))|~subset(X1,X3)|~in(X3,esk76_1(X2)))).
% 0.19/0.46 cnf(i_0_498, plain, (in(X1,esk91_1(X2))|~subset(X1,X3)|~in(X3,esk91_1(X2)))).
% 0.19/0.46 cnf(i_0_264, plain, (complements_of_subsets(X1,complements_of_subsets(X1,X2))=X2|~element(X2,powerset(powerset(X1))))).
% 0.19/0.46 cnf(i_0_234, plain, (relation(set_difference(X1,set_difference(X1,X2)))|~relation(X2)|~relation(X1))).
% 0.19/0.46 cnf(i_0_85, plain, (X1=powerset(X2)|~subset(esk26_2(X2,X1),X2)|~in(esk26_2(X2,X1),X1))).
% 0.19/0.46 cnf(i_0_212, plain, (element(union_of_subsets(X1,X2),powerset(X1))|~element(X2,powerset(powerset(X1))))).
% 0.19/0.46 cnf(i_0_214, plain, (element(meet_of_subsets(X1,X2),powerset(X1))|~element(X2,powerset(powerset(X1))))).
% 0.19/0.46 cnf(i_0_328, lemma, (subset(cartesian_product2(X1,X2),cartesian_product2(X3,X2))|~subset(X1,X3))).
% 0.19/0.46 cnf(i_0_79, plain, (X1=unordered_pair(X2,X2)|esk24_2(X2,X1)!=X2|~in(esk24_2(X2,X1),X1))).
% 0.19/0.46 cnf(i_0_97, plain, (X1=unordered_pair(X2,X3)|esk29_3(X2,X3,X1)!=X3|~in(esk29_3(X2,X3,X1),X1))).
% 0.19/0.46 cnf(i_0_98, plain, (X1=unordered_pair(X2,X3)|esk29_3(X2,X3,X1)!=X2|~in(esk29_3(X2,X3,X1),X1))).
% 0.19/0.46 cnf(i_0_169, plain, (apply(X1,esk56_1(X1))=apply(X1,esk55_1(X1))|one_to_one(X1)|~relation(X1)|~function(X1))).
% 0.19/0.46 cnf(i_0_327, lemma, (subset(cartesian_product2(X1,X2),cartesian_product2(X1,X3))|~subset(X2,X3))).
% 0.19/0.46 cnf(i_0_347, lemma, (relation_image(X1,relation_rng(X2))=relation_rng(relation_composition(X2,X1))|~relation(X1)|~relation(X2))).
% 0.19/0.46 cnf(i_0_380, lemma, (subset(set_difference(X1,X2),set_difference(X3,X2))|~subset(X1,X3))).
% 0.19/0.46 cnf(i_0_338, lemma, (in(esk77_3(X1,X2,X3),X2)|~relation(X3)|~in(X1,relation_image(X3,X2)))).
% 0.19/0.46 cnf(i_0_332, lemma, (are_equipotent(X1,esk76_1(X2))|in(X1,esk76_1(X2))|~subset(X1,esk76_1(X2)))).
% 0.19/0.46 cnf(i_0_495, plain, (are_equipotent(X1,esk91_1(X2))|in(X1,esk91_1(X2))|~subset(X1,esk91_1(X2)))).
% 0.19/0.46 cnf(i_0_413, lemma, (subset(relation_dom(relation_composition(X1,X2)),relation_dom(X1))|~relation(X2)|~relation(X1))).
% 0.19/0.46 cnf(i_0_414, lemma, (subset(relation_rng(relation_composition(X1,X2)),relation_rng(X2))|~relation(X2)|~relation(X1))).
% 0.19/0.46 cnf(i_0_342, lemma, (subset(relation_image(X1,relation_inverse_image(X1,X2)),X2)|~relation(X1)|~function(X1))).
% 0.19/0.46 cnf(i_0_336, lemma, (relation_rng_restriction(X1,relation_dom_restriction(X2,X3))=relation_dom_restriction(relation_rng_restriction(X1,X2),X3)|~relation(X2))).
% 0.19/0.46 cnf(i_0_349, lemma, (in(esk78_3(X1,X2,X3),X2)|~relation(X3)|~in(X1,relation_inverse_image(X3,X2)))).
% 0.19/0.46 cnf(i_0_473, lemma, (in(X1,X2)|~relation(X3)|~in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),relation_composition(identity_relation(X2),X3)))).
% 0.19/0.46 cnf(i_0_486, lemma, (X1=apply(X2,X3)|~relation(X2)|~function(X2)|~in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2))).
% 0.19/0.46 cnf(i_0_139, plain, (X1=union(X2)|~in(esk44_2(X2,X1),X3)|~in(esk44_2(X2,X1),X1)|~in(X3,X2))).
% 0.19/0.46 cnf(i_0_365, lemma, (in(X1,relation_dom(X2))|~relation(X3)|~relation(X2)|~function(X3)|~function(X2)|~in(X1,relation_dom(relation_composition(X2,X3))))).
% 0.19/0.46 cnf(i_0_416, lemma, (relation_dom(relation_composition(X1,X2))=relation_dom(X1)|~subset(relation_rng(X1),relation_dom(X2))|~relation(X2)|~relation(X1))).
% 0.19/0.46 cnf(i_0_78, plain, (esk24_2(X1,X2)=X1|X2=unordered_pair(X1,X1)|in(esk24_2(X1,X2),X2))).
% 0.19/0.46 cnf(i_0_480, lemma, (in(X1,relation_dom(relation_dom_restriction(X2,X3)))|~relation(X2)|~in(X1,relation_dom(X2))|~in(X1,X3))).
% 0.19/0.46 cnf(i_0_321, lemma, (in(X1,relation_rng(relation_rng_restriction(X2,X3)))|~relation(X3)|~in(X1,relation_rng(X3))|~in(X1,X2))).
% 0.19/0.46 cnf(i_0_217, plain, (element(complements_of_subsets(X1,X2),powerset(powerset(X1)))|~element(X2,powerset(powerset(X1))))).
% 0.19/0.46 cnf(i_0_419, lemma, (relation_rng(relation_composition(X1,X2))=relation_rng(X2)|~subset(relation_dom(X2),relation_rng(X1))|~relation(X1)|~relation(X2))).
% 0.19/0.46 cnf(i_0_346, lemma, (relation_image(X1,relation_inverse_image(X1,X2))=X2|~subset(X2,relation_rng(X1))|~relation(X1)|~function(X1))).
% 0.19/0.46 cnf(i_0_354, lemma, (subset(relation_inverse_image(X1,X2),relation_inverse_image(X1,X3))|~subset(X2,X3)|~relation(X1))).
% 0.19/0.46 cnf(i_0_412, lemma, (subset(X1,subset_complement(X2,X3))|~disjoint(X1,X3)|~element(X3,powerset(X2))|~element(X1,powerset(X2)))).
% 0.19/0.46 cnf(i_0_275, lemma, (subset(X1,set_difference(X2,unordered_pair(X3,X3)))|in(X3,X1)|~subset(X1,X2))).
% 0.19/0.46 cnf(i_0_375, plain, (X1=X2|in(esk79_2(X1,X2),X1)|in(esk79_2(X1,X2),X2))).
% 0.19/0.46 cnf(i_0_426, lemma, (disjoint(X1,X2)|in(esk82_2(X1,X2),set_difference(X1,set_difference(X1,X2))))).
% 0.19/0.46 cnf(i_0_313, plain, (subset_difference(X1,X2,X3)=set_difference(X2,X3)|~element(X3,powerset(X1))|~element(X2,powerset(X1)))).
% 0.19/0.46 cnf(i_0_330, lemma, (subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))|~subset(X2,X4)|~subset(X1,X3))).
% 0.19/0.46 cnf(i_0_344, lemma, (subset(X1,relation_inverse_image(X2,relation_image(X2,X1)))|~subset(X1,relation_dom(X2))|~relation(X2))).
% 0.19/0.46 cnf(i_0_356, lemma, (subset(X1,set_difference(X2,set_difference(X2,X3)))|~subset(X1,X3)|~subset(X1,X2))).
% 0.19/0.46 cnf(i_0_340, lemma, (in(esk77_3(X1,X2,X3),relation_dom(X3))|~relation(X3)|~in(X1,relation_image(X3,X2)))).
% 0.19/0.46 cnf(i_0_351, lemma, (in(esk78_3(X1,X2,X3),relation_rng(X3))|~relation(X3)|~in(X1,relation_inverse_image(X3,X2)))).
% 0.19/0.46 cnf(i_0_103, plain, (X1=set_union2(X2,X3)|~in(esk30_3(X2,X3,X1),X1)|~in(esk30_3(X2,X3,X1),X3))).
% 0.19/0.46 cnf(i_0_104, plain, (X1=set_union2(X2,X3)|~in(esk30_3(X2,X3,X1),X1)|~in(esk30_3(X2,X3,X1),X2))).
% 0.19/0.46 cnf(i_0_84, plain, (X1=powerset(X2)|subset(esk26_2(X2,X1),X2)|in(esk26_2(X2,X1),X1))).
% 0.19/0.46 cnf(i_0_490, lemma, (set_difference(relation_dom(X1),set_difference(relation_dom(X1),X2))=relation_dom(relation_dom_restriction(X1,X2))|~relation(X1))).
% 0.19/0.46 cnf(i_0_73, plain, (X1=set_meet(X2)|X2=empty_set|~in(esk22_2(X2,X1),esk23_2(X2,X1))|~in(esk22_2(X2,X1),X1))).
% 0.19/0.46 cnf(i_0_59, plain, (X1=unordered_triple(X2,X3,X4)|esk17_4(X2,X3,X4,X1)!=X4|~in(esk17_4(X2,X3,X4,X1),X1))).
% 0.19/0.46 cnf(i_0_60, plain, (X1=unordered_triple(X2,X3,X4)|esk17_4(X2,X3,X4,X1)!=X3|~in(esk17_4(X2,X3,X4,X1),X1))).
% 0.19/0.46 cnf(i_0_61, plain, (X1=unordered_triple(X2,X3,X4)|esk17_4(X2,X3,X4,X1)!=X2|~in(esk17_4(X2,X3,X4,X1),X1))).
% 0.19/0.46 cnf(i_0_329, lemma, (set_difference(relation_rng(X1),set_difference(relation_rng(X1),X2))=relation_rng(relation_rng_restriction(X2,X1))|~relation(X1))).
% 0.19/0.46 cnf(i_0_280, lemma, (in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),cartesian_product2(X3,X4))|~in(X2,X4)|~in(X1,X3))).
% 0.19/0.46 cnf(i_0_137, plain, (X1=union(X2)|in(esk45_2(X2,X1),X2)|in(esk44_2(X2,X1),X1))).
% 0.19/0.46 cnf(i_0_470, lemma, (apply(relation_dom_restriction(X1,X2),X3)=apply(X1,X3)|~relation(X1)|~function(X1)|~in(X3,X2))).
% 0.19/0.46 cnf(i_0_364, lemma, (in(apply(X1,X2),relation_dom(X3))|~relation(X3)|~relation(X1)|~function(X3)|~function(X1)|~in(X2,relation_dom(relation_composition(X1,X3))))).
% 0.19/0.46 cnf(i_0_215, plain, (element(subset_difference(X1,X2,X3),powerset(X1))|~element(X3,powerset(X1))|~element(X2,powerset(X1)))).
% 0.19/0.46 cnf(i_0_172, plain, (X1=X2|apply(X3,X1)!=apply(X3,X2)|~one_to_one(X3)|~relation(X3)|~function(X3)|~in(X2,relation_dom(X3))|~in(X1,relation_dom(X3)))).
% 0.19/0.46 cnf(i_0_138, plain, (X1=union(X2)|in(esk44_2(X2,X1),esk45_2(X2,X1))|in(esk44_2(X2,X1),X1))).
% 0.19/0.46 cnf(i_0_150, plain, (X1=relation_rng(X2)|in(esk49_2(X2,X1),relation_dom(X2))|in(esk48_2(X2,X1),X1)|~relation(X2)|~function(X2))).
% 0.19/0.46 cnf(i_0_343, lemma, (relation_image(X1,set_difference(relation_dom(X1),set_difference(relation_dom(X1),X2)))=relation_image(X1,X2)|~relation(X1))).
% 0.19/0.46 cnf(i_0_447, lemma, (apply(X1,apply(function_inverse(X1),X2))=X2|~one_to_one(X1)|~relation(X1)|~function(X1)|~in(X2,relation_rng(X1)))).
% 0.19/0.46 cnf(i_0_446, lemma, (apply(relation_composition(function_inverse(X1),X1),X2)=X2|~one_to_one(X1)|~relation(X1)|~function(X1)|~in(X2,relation_rng(X1)))).
% 0.19/0.46 cnf(i_0_467, lemma, (apply(relation_dom_restriction(X1,X2),X3)=apply(X1,X3)|~relation(X1)|~function(X1)|~in(X3,relation_dom(relation_dom_restriction(X1,X2))))).
% 0.19/0.46 cnf(i_0_74, plain, (X1=set_meet(X2)|X2=empty_set|in(esk23_2(X2,X1),X2)|~in(esk22_2(X2,X1),X1))).
% 0.19/0.46 cnf(i_0_427, lemma, (X1=empty_set|in(X2,subset_complement(X1,X3))|in(X2,X3)|~element(X3,powerset(X1))|~element(X2,X1))).
% 0.19/0.46 cnf(i_0_472, 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)))).
% 0.19/0.46 cnf(i_0_72, plain, (X1=set_meet(X2)|X2=empty_set|in(esk22_2(X2,X1),X1)|in(esk22_2(X2,X1),X3)|~in(X3,X2))).
% 0.19/0.46 cnf(i_0_371, lemma, (subset(set_difference(X1,set_difference(X1,X2)),set_difference(X3,set_difference(X3,X2)))|~subset(X1,X3))).
% 0.19/0.46 cnf(i_0_151, plain, (X1=relation_rng(X2)|esk48_2(X2,X1)!=apply(X2,X3)|~relation(X2)|~function(X2)|~in(esk48_2(X2,X1),X1)|~in(X3,relation_dom(X2)))).
% 0.19/0.46 cnf(i_0_156, plain, (X1=relation_rng(X2)|~relation(X2)|~in(unordered_pair(unordered_pair(X3,esk51_2(X2,X1)),unordered_pair(X3,X3)),X2)|~in(esk51_2(X2,X1),X1))).
% 0.19/0.46 cnf(i_0_421, 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))))).
% 0.19/0.46 cnf(i_0_116, plain, (subset(X1,X2)|~relation(X2)|~relation(X1)|~in(unordered_pair(unordered_pair(esk36_2(X1,X2),esk36_2(X1,X2)),unordered_pair(esk36_2(X1,X2),esk37_2(X1,X2))),X2))).
% 0.19/0.46 cnf(i_0_420, 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))))).
% 0.19/0.46 cnf(i_0_350, lemma, (in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,esk78_3(X1,X2,X3))),X3)|~relation(X3)|~in(X1,relation_inverse_image(X3,X2)))).
% 0.19/0.46 cnf(i_0_149, plain, (apply(X1,esk49_2(X1,X2))=esk48_2(X1,X2)|X2=relation_rng(X1)|in(esk48_2(X1,X2),X2)|~relation(X1)|~function(X1))).
% 0.19/0.46 cnf(i_0_445, lemma, (X1=empty_set|in(unordered_pair(unordered_pair(esk87_1(X1),esk87_1(X1)),unordered_pair(esk87_1(X1),esk88_1(X1))),X1)|~relation(X1))).
% 0.19/0.46 cnf(i_0_368, lemma, (apply(relation_composition(X1,X2),X3)=apply(X2,apply(X1,X3))|~relation(X2)|~relation(X1)|~function(X2)|~function(X1)|~in(X3,relation_dom(X1)))).
% 0.19/0.46 cnf(i_0_363, 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)))).
% 0.19/0.46 cnf(i_0_143, plain, (X1=set_difference(X2,X3)|in(esk46_3(X2,X3,X1),X1)|~in(esk46_3(X2,X3,X1),X3))).
% 0.19/0.46 cnf(i_0_133, plain, (X1=relation_dom(X2)|~relation(X2)|~in(unordered_pair(unordered_pair(esk41_2(X2,X1),X3),unordered_pair(esk41_2(X2,X1),esk41_2(X2,X1))),X2)|~in(esk41_2(X2,X1),X1))).
% 0.19/0.46 cnf(i_0_110, plain, (X1=cartesian_product2(X2,X3)|in(esk34_3(X2,X3,X1),X2)|in(esk33_3(X2,X3,X1),X1))).
% 0.19/0.46 cnf(i_0_337, lemma, (in(X1,relation_image(X2,X3))|~relation(X2)|~in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),X2)|~in(X4,X3))).
% 0.19/0.46 cnf(i_0_348, 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))).
% 0.19/0.46 cnf(i_0_471, 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))).
% 0.19/0.46 cnf(i_0_109, plain, (X1=cartesian_product2(X2,X3)|in(esk35_3(X2,X3,X1),X3)|in(esk33_3(X2,X3,X1),X1))).
% 0.19/0.46 cnf(i_0_367, lemma, (apply(relation_composition(X1,X2),X3)=apply(X2,apply(X1,X3))|~relation(X1)|~relation(X2)|~function(X1)|~function(X2)|~in(X3,relation_dom(relation_composition(X1,X2))))).
% 0.19/0.46 cnf(i_0_144, plain, (X1=set_difference(X2,X3)|in(esk46_3(X2,X3,X1),X2)|in(esk46_3(X2,X3,X1),X1))).
% 0.19/0.46 cnf(i_0_96, plain, (esk29_3(X1,X2,X3)=X1|esk29_3(X1,X2,X3)=X2|X3=unordered_pair(X1,X2)|in(esk29_3(X1,X2,X3),X3))).
% 0.19/0.46 cnf(i_0_181, plain, (X1=complements_of_subsets(X2,X3)|element(esk61_3(X2,X3,X1),powerset(X2))|~element(X1,powerset(powerset(X2)))|~element(X3,powerset(powerset(X2))))).
% 0.19/0.46 cnf(i_0_124, plain, (X1=set_difference(X2,set_difference(X2,X3))|~in(esk39_3(X2,X3,X1),X1)|~in(esk39_3(X2,X3,X1),X3)|~in(esk39_3(X2,X3,X1),X2))).
% 0.19/0.46 cnf(i_0_180, plain, (X1=complements_of_subsets(X2,X3)|~element(X1,powerset(powerset(X2)))|~element(X3,powerset(powerset(X2)))|~in(subset_complement(X2,esk61_3(X2,X3,X1)),X3)|~in(esk61_3(X2,X3,X1),X1))).
% 0.19/0.46 cnf(i_0_123, plain, (X1=set_difference(X2,set_difference(X2,X3))|in(esk39_3(X2,X3,X1),X2)|in(esk39_3(X2,X3,X1),X1))).
% 0.19/0.46 cnf(i_0_48, plain, (X1=relation_image(X2,X3)|~relation(X2)|~in(unordered_pair(unordered_pair(X4,esk12_3(X2,X3,X1)),unordered_pair(X4,X4)),X2)|~in(esk12_3(X2,X3,X1),X1)|~in(X4,X3))).
% 0.19/0.46 cnf(i_0_46, plain, (X1=relation_image(X2,X3)|in(esk13_3(X2,X3,X1),X3)|in(esk12_3(X2,X3,X1),X1)|~relation(X2))).
% 0.19/0.46 cnf(i_0_436, lemma, (X1=function_inverse(X2)|in(esk86_2(X2,X1),relation_dom(X2))|in(esk83_2(X2,X1),relation_rng(X2))|relation_rng(X2)!=relation_dom(X1)|~one_to_one(X2)|~relation(X1)|~relation(X2)|~function(X1)|~function(X2))).
% 0.19/0.46 cnf(i_0_52, plain, (X1=relation_inverse_image(X2,X3)|in(esk16_3(X2,X3,X1),X3)|in(esk15_3(X2,X3,X1),X1)|~relation(X2))).
% 0.19/0.46 cnf(i_0_42, plain, (X1=relation_inverse_image(X2,X3)|~relation(X2)|~function(X2)|~in(apply(X2,esk10_3(X2,X3,X1)),X3)|~in(esk10_3(X2,X3,X1),relation_dom(X2))|~in(esk10_3(X2,X3,X1),X1))).
% 0.19/0.46 cnf(i_0_29, plain, (X1=relation_image(X2,X3)|esk6_3(X2,X3,X1)!=apply(X2,X4)|~relation(X2)|~function(X2)|~in(esk6_3(X2,X3,X1),X1)|~in(X4,relation_dom(X2))|~in(X4,X3))).
% 0.19/0.46 cnf(i_0_111, plain, (X1=cartesian_product2(X2,X3)|esk33_3(X2,X3,X1)!=unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))|~in(esk33_3(X2,X3,X1),X1)|~in(X5,X3)|~in(X4,X2))).
% 0.19/0.46 cnf(i_0_27, plain, (X1=relation_image(X2,X3)|in(esk7_3(X2,X3,X1),X3)|in(esk6_3(X2,X3,X1),X1)|~relation(X2)|~function(X2))).
% 0.19/0.46 cnf(i_0_145, plain, (X1=set_difference(X2,X3)|in(esk46_3(X2,X3,X1),X3)|~in(esk46_3(X2,X3,X1),X1)|~in(esk46_3(X2,X3,X1),X2))).
% 0.19/0.46 cnf(i_0_69, plain, (unordered_pair(unordered_pair(esk18_2(X1,X2),esk18_2(X1,X2)),unordered_pair(esk18_2(X1,X2),esk19_2(X1,X2)))=X2|~relation(X1)|~in(X2,X1))).
% 0.19/0.46 cnf(i_0_433, lemma, (apply(X1,esk83_2(X2,X1))=esk84_2(X2,X1)|X1=function_inverse(X2)|in(esk86_2(X2,X1),relation_dom(X2))|relation_rng(X2)!=relation_dom(X1)|~one_to_one(X2)|~relation(X1)|~relation(X2)|~function(X1)|~function(X2))).
% 0.19/0.46 cnf(i_0_122, plain, (X1=set_difference(X2,set_difference(X2,X3))|in(esk39_3(X2,X3,X1),X3)|in(esk39_3(X2,X3,X1),X1))).
% 0.19/0.46 cnf(i_0_13, 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))).
% 0.19/0.46 cnf(i_0_460, lemma, (X1=relation_dom_restriction(X2,X3)|apply(X1,esk89_3(X3,X1,X2))!=apply(X2,esk89_3(X3,X1,X2))|relation_dom(X1)!=set_difference(relation_dom(X2),set_difference(relation_dom(X2),X3))|~relation(X2)|~relation(X1)|~function(X2)|~function(X1))).
% 0.19/0.46 cnf(i_0_54, plain, (X1=relation_inverse_image(X2,X3)|~relation(X2)|~in(unordered_pair(unordered_pair(esk15_3(X2,X3,X1),X4),unordered_pair(esk15_3(X2,X3,X1),esk15_3(X2,X3,X1))),X2)|~in(esk15_3(X2,X3,X1),X1)|~in(X4,X3))).
% 0.19/0.46 cnf(i_0_430, lemma, (X1=function_inverse(X2)|in(esk86_2(X2,X1),relation_dom(X2))|apply(X2,esk84_2(X2,X1))!=esk83_2(X2,X1)|relation_rng(X2)!=relation_dom(X1)|~one_to_one(X2)|~relation(X1)|~relation(X2)|~function(X1)|~function(X2)|~in(esk84_2(X2,X1),relation_dom(X2)))).
% 0.19/0.46 cnf(i_0_28, plain, (X1=relation_image(X2,X3)|in(esk7_3(X2,X3,X1),relation_dom(X2))|in(esk6_3(X2,X3,X1),X1)|~relation(X2)|~function(X2))).
% 0.19/0.46 cnf(i_0_41, plain, (X1=relation_inverse_image(X2,X3)|in(esk10_3(X2,X3,X1),relation_dom(X2))|in(esk10_3(X2,X3,X1),X1)|~relation(X2)|~function(X2))).
% 0.19/0.46 cnf(i_0_40, plain, (X1=relation_inverse_image(X2,X3)|in(apply(X2,esk10_3(X2,X3,X1)),X3)|in(esk10_3(X2,X3,X1),X1)|~relation(X2)|~function(X2))).
% 0.19/0.46 cnf(i_0_339, lemma, (in(unordered_pair(unordered_pair(X1,esk77_3(X1,X2,X3)),unordered_pair(esk77_3(X1,X2,X3),esk77_3(X1,X2,X3))),X3)|~relation(X3)|~in(X1,relation_image(X3,X2)))).
% 0.19/0.46 cnf(i_0_117, plain, (subset(X1,X2)|in(unordered_pair(unordered_pair(esk36_2(X1,X2),esk36_2(X1,X2)),unordered_pair(esk36_2(X1,X2),esk37_2(X1,X2))),X1)|~relation(X2)|~relation(X1))).
% 0.19/0.46 cnf(i_0_435, lemma, (apply(X1,esk86_2(X1,X2))=esk85_2(X1,X2)|X2=function_inverse(X1)|in(esk83_2(X1,X2),relation_rng(X1))|relation_rng(X1)!=relation_dom(X2)|~one_to_one(X1)|~relation(X2)|~relation(X1)|~function(X2)|~function(X1))).
% 0.19/0.46 cnf(i_0_102, plain, (X1=set_union2(X2,X3)|in(esk30_3(X2,X3,X1),X2)|in(esk30_3(X2,X3,X1),X3)|in(esk30_3(X2,X3,X1),X1))).
% 0.19/0.46 cnf(i_0_461, lemma, (X1=relation_dom_restriction(X2,X3)|in(esk89_3(X3,X1,X2),relation_dom(X1))|relation_dom(X1)!=set_difference(relation_dom(X2),set_difference(relation_dom(X2),X3))|~relation(X2)|~relation(X1)|~function(X2)|~function(X1))).
% 0.19/0.46 cnf(i_0_434, lemma, (X1=function_inverse(X2)|in(esk83_2(X2,X1),relation_rng(X2))|apply(X1,esk85_2(X2,X1))!=esk86_2(X2,X1)|relation_rng(X2)!=relation_dom(X1)|~one_to_one(X2)|~relation(X1)|~relation(X2)|~function(X1)|~function(X2)|~in(esk85_2(X2,X1),relation_rng(X2)))).
% 0.19/0.46 cnf(i_0_428, lemma, (X1=function_inverse(X2)|apply(X2,esk84_2(X2,X1))!=esk83_2(X2,X1)|apply(X1,esk85_2(X2,X1))!=esk86_2(X2,X1)|relation_rng(X2)!=relation_dom(X1)|~one_to_one(X2)|~relation(X1)|~relation(X2)|~function(X1)|~function(X2)|~in(esk84_2(X2,X1),relation_dom(X2))|~in(esk85_2(X2,X1),relation_rng(X2)))).
% 0.19/0.46 cnf(i_0_431, lemma, (apply(X1,esk83_2(X2,X1))=esk84_2(X2,X1)|X1=function_inverse(X2)|apply(X1,esk85_2(X2,X1))!=esk86_2(X2,X1)|relation_rng(X2)!=relation_dom(X1)|~one_to_one(X2)|~relation(X1)|~relation(X2)|~function(X1)|~function(X2)|~in(esk85_2(X2,X1),relation_rng(X2)))).
% 0.19/0.46 cnf(i_0_26, plain, (apply(X1,esk7_3(X1,X2,X3))=esk6_3(X1,X2,X3)|X3=relation_image(X1,X2)|in(esk6_3(X1,X2,X3),X3)|~relation(X1)|~function(X1))).
% 0.19/0.46 cnf(i_0_12, 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))).
% 0.19/0.46 cnf(i_0_432, lemma, (apply(X1,esk86_2(X1,X2))=esk85_2(X1,X2)|apply(X2,esk83_2(X1,X2))=esk84_2(X1,X2)|X2=function_inverse(X1)|relation_rng(X1)!=relation_dom(X2)|~one_to_one(X1)|~relation(X2)|~relation(X1)|~function(X2)|~function(X1))).
% 0.19/0.46 cnf(i_0_58, plain, (esk17_4(X1,X2,X3,X4)=X1|esk17_4(X1,X2,X3,X4)=X2|esk17_4(X1,X2,X3,X4)=X3|X4=unordered_triple(X1,X2,X3)|in(esk17_4(X1,X2,X3,X4),X4))).
% 0.19/0.46 cnf(i_0_429, lemma, (apply(X1,esk86_2(X1,X2))=esk85_2(X1,X2)|X2=function_inverse(X1)|apply(X1,esk84_2(X1,X2))!=esk83_2(X1,X2)|relation_rng(X1)!=relation_dom(X2)|~one_to_one(X1)|~relation(X2)|~relation(X1)|~function(X2)|~function(X1)|~in(esk84_2(X1,X2),relation_dom(X1)))).
% 0.19/0.46 cnf(i_0_89, plain, (X1=X2|~relation(X2)|~relation(X1)|~in(unordered_pair(unordered_pair(esk27_2(X1,X2),esk27_2(X1,X2)),unordered_pair(esk27_2(X1,X2),esk28_2(X1,X2))),X2)|~in(unordered_pair(unordered_pair(esk27_2(X1,X2),esk27_2(X1,X2)),unordered_pair(esk27_2(X1,X2),esk28_2(X1,X2))),X1))).
% 0.19/0.46 cnf(i_0_179, plain, (X1=complements_of_subsets(X2,X3)|in(subset_complement(X2,esk61_3(X2,X3,X1)),X3)|in(esk61_3(X2,X3,X1),X1)|~element(X1,powerset(powerset(X2)))|~element(X3,powerset(powerset(X2))))).
% 0.19/0.46 cnf(i_0_163, plain, (X1=relation_inverse(X2)|~relation(X1)|~relation(X2)|~in(unordered_pair(unordered_pair(esk53_2(X2,X1),esk53_2(X2,X1)),unordered_pair(esk53_2(X2,X1),esk54_2(X2,X1))),X1)|~in(unordered_pair(unordered_pair(esk53_2(X2,X1),esk54_2(X2,X1)),unordered_pair(esk54_2(X2,X1),esk54_2(X2,X1))),X2))).
% 0.19/0.46 cnf(i_0_132, plain, (X1=relation_dom(X2)|in(unordered_pair(unordered_pair(esk41_2(X2,X1),esk41_2(X2,X1)),unordered_pair(esk41_2(X2,X1),esk42_2(X2,X1))),X2)|in(esk41_2(X2,X1),X1)|~relation(X2))).
% 0.19/0.46 cnf(i_0_155, plain, (X1=relation_rng(X2)|in(unordered_pair(unordered_pair(esk51_2(X2,X1),esk52_2(X2,X1)),unordered_pair(esk52_2(X2,X1),esk52_2(X2,X1))),X2)|in(esk51_2(X2,X1),X1)|~relation(X2))).
% 0.19/0.46 cnf(i_0_11, 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))).
% 0.19/0.46 cnf(i_0_108, plain, (unordered_pair(unordered_pair(esk34_3(X1,X2,X3),esk34_3(X1,X2,X3)),unordered_pair(esk34_3(X1,X2,X3),esk35_3(X1,X2,X3)))=esk33_3(X1,X2,X3)|X3=cartesian_product2(X1,X2)|in(esk33_3(X1,X2,X3),X3))).
% 0.19/0.46 cnf(i_0_47, plain, (X1=relation_image(X2,X3)|in(unordered_pair(unordered_pair(esk12_3(X2,X3,X1),esk13_3(X2,X3,X1)),unordered_pair(esk13_3(X2,X3,X1),esk13_3(X2,X3,X1))),X2)|in(esk12_3(X2,X3,X1),X1)|~relation(X2))).
% 0.19/0.46 cnf(i_0_22, 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))).
% 0.19/0.46 cnf(i_0_36, plain, (X1=relation_rng_restriction(X2,X3)|~relation(X1)|~relation(X3)|~in(unordered_pair(unordered_pair(esk9_3(X2,X3,X1),esk8_3(X2,X3,X1)),unordered_pair(esk8_3(X2,X3,X1),esk8_3(X2,X3,X1))),X1)|~in(unordered_pair(unordered_pair(esk9_3(X2,X3,X1),esk8_3(X2,X3,X1)),unordered_pair(esk8_3(X2,X3,X1),esk8_3(X2,X3,X1))),X3)|~in(esk9_3(X2,X3,X1),X2))).
% 0.19/0.46 cnf(i_0_53, plain, (X1=relation_inverse_image(X2,X3)|in(unordered_pair(unordered_pair(esk15_3(X2,X3,X1),esk15_3(X2,X3,X1)),unordered_pair(esk15_3(X2,X3,X1),esk16_3(X2,X3,X1))),X2)|in(esk15_3(X2,X3,X1),X1)|~relation(X2))).
% 0.19/0.46 cnf(i_0_21, 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))).
% 0.19/0.46 cnf(i_0_35, plain, (X1=relation_rng_restriction(X2,X3)|in(unordered_pair(unordered_pair(esk9_3(X2,X3,X1),esk8_3(X2,X3,X1)),unordered_pair(esk8_3(X2,X3,X1),esk8_3(X2,X3,X1))),X1)|in(esk9_3(X2,X3,X1),X2)|~relation(X1)|~relation(X3))).
% 0.19/0.46 cnf(i_0_88, plain, (X1=X2|in(unordered_pair(unordered_pair(esk27_2(X1,X2),esk27_2(X1,X2)),unordered_pair(esk27_2(X1,X2),esk28_2(X1,X2))),X1)|in(unordered_pair(unordered_pair(esk27_2(X1,X2),esk27_2(X1,X2)),unordered_pair(esk27_2(X1,X2),esk28_2(X1,X2))),X2)|~relation(X2)|~relation(X1))).
% 0.19/0.46 cnf(i_0_162, plain, (X1=relation_inverse(X2)|in(unordered_pair(unordered_pair(esk53_2(X2,X1),esk54_2(X2,X1)),unordered_pair(esk54_2(X2,X1),esk54_2(X2,X1))),X2)|in(unordered_pair(unordered_pair(esk53_2(X2,X1),esk53_2(X2,X1)),unordered_pair(esk53_2(X2,X1),esk54_2(X2,X1))),X1)|~relation(X1)|~relation(X2))).
% 0.19/0.46 cnf(i_0_175, plain, (X1=relation_composition(X2,X3)|~relation(X1)|~relation(X3)|~relation(X2)|~in(unordered_pair(unordered_pair(esk58_3(X2,X3,X1),esk58_3(X2,X3,X1)),unordered_pair(esk58_3(X2,X3,X1),esk59_3(X2,X3,X1))),X1)|~in(unordered_pair(unordered_pair(esk58_3(X2,X3,X1),X4),unordered_pair(esk58_3(X2,X3,X1),esk58_3(X2,X3,X1))),X2)|~in(unordered_pair(unordered_pair(X4,esk59_3(X2,X3,X1)),unordered_pair(X4,X4)),X3))).
% 0.19/0.46 cnf(i_0_20, 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))).
% 0.19/0.46 cnf(i_0_34, plain, (X1=relation_rng_restriction(X2,X3)|in(unordered_pair(unordered_pair(esk9_3(X2,X3,X1),esk8_3(X2,X3,X1)),unordered_pair(esk8_3(X2,X3,X1),esk8_3(X2,X3,X1))),X3)|in(unordered_pair(unordered_pair(esk9_3(X2,X3,X1),esk8_3(X2,X3,X1)),unordered_pair(esk8_3(X2,X3,X1),esk8_3(X2,X3,X1))),X1)|~relation(X1)|~relation(X3))).
% 0.19/0.46 cnf(i_0_174, plain, (X1=relation_composition(X2,X3)|in(unordered_pair(unordered_pair(esk58_3(X2,X3,X1),esk58_3(X2,X3,X1)),unordered_pair(esk58_3(X2,X3,X1),esk60_3(X2,X3,X1))),X2)|in(unordered_pair(unordered_pair(esk58_3(X2,X3,X1),esk58_3(X2,X3,X1)),unordered_pair(esk58_3(X2,X3,X1),esk59_3(X2,X3,X1))),X1)|~relation(X1)|~relation(X3)|~relation(X2))).
% 0.19/0.46 cnf(i_0_173, plain, (X1=relation_composition(X2,X3)|in(unordered_pair(unordered_pair(esk59_3(X2,X3,X1),esk60_3(X2,X3,X1)),unordered_pair(esk60_3(X2,X3,X1),esk60_3(X2,X3,X1))),X3)|in(unordered_pair(unordered_pair(esk58_3(X2,X3,X1),esk58_3(X2,X3,X1)),unordered_pair(esk58_3(X2,X3,X1),esk59_3(X2,X3,X1))),X1)|~relation(X1)|~relation(X3)|~relation(X2))).
% 0.19/0.46 cnf(i_0_147, plain, (~in(X1,set_difference(X2,X3))|~in(X1,X3))).
% 0.19/0.46 cnf(i_0_81, plain, (X1=X2|~in(X1,unordered_pair(X2,X2)))).
% 0.19/0.46 cnf(i_0_87, plain, (subset(X1,X2)|~in(X1,powerset(X2)))).
% 0.19/0.46 cnf(i_0_148, plain, (in(X1,X2)|~in(X1,set_difference(X2,X3)))).
% 0.19/0.46 cnf(i_0_86, plain, (in(X1,powerset(X2))|~subset(X1,X2))).
% 0.19/0.46 cnf(i_0_126, plain, (in(X1,X2)|~in(X1,set_difference(X3,set_difference(X3,X2))))).
% 0.19/0.46 cnf(i_0_105, plain, (in(X1,set_union2(X2,X3))|~in(X1,X3))).
% 0.19/0.46 cnf(i_0_106, plain, (in(X1,set_union2(X2,X3))|~in(X1,X2))).
% 0.19/0.46 cnf(i_0_101, plain, (X1=X2|X1=X3|~in(X1,unordered_pair(X3,X2)))).
% 0.19/0.46 cnf(i_0_107, plain, (in(X1,X2)|in(X1,X3)|~in(X1,set_union2(X3,X2)))).
% 0.19/0.46 cnf(i_0_45, plain, (in(X1,relation_dom(X2))|~relation(X2)|~function(X2)|~in(X1,relation_inverse_image(X2,X3)))).
% 0.19/0.46 cnf(i_0_140, plain, (in(X1,union(X2))|~in(X3,X2)|~in(X1,X3))).
% 0.19/0.46 cnf(i_0_44, plain, (in(apply(X1,X2),X3)|~relation(X1)|~function(X1)|~in(X2,relation_inverse_image(X1,X3)))).
% 0.19/0.46 cnf(i_0_146, plain, (in(X1,set_difference(X2,X3))|in(X1,X3)|~in(X1,X2))).
% 0.19/0.46 cnf(i_0_15, plain, (X1=X2|~in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),identity_relation(X3)))).
% 0.19/0.46 cnf(i_0_16, plain, (in(X1,X2)|~in(unordered_pair(unordered_pair(X1,X3),unordered_pair(X1,X1)),identity_relation(X2)))).
% 0.19/0.46 cnf(i_0_128, plain, (apply(X1,X2)=empty_set|in(X2,relation_dom(X1))|~relation(X1)|~function(X1))).
% 0.19/0.46 cnf(i_0_75, plain, (X1=empty_set|in(X2,set_meet(X1))|~in(X2,esk21_3(X1,set_meet(X1),X2)))).
% 0.19/0.46 cnf(i_0_65, plain, (X1=X2|X1=X3|X1=X4|~in(X1,unordered_triple(X4,X3,X2)))).
% 0.19/0.46 cnf(i_0_77, plain, (X1=empty_set|in(X2,X3)|~in(X2,set_meet(X1))|~in(X3,X1))).
% 0.19/0.46 cnf(i_0_142, plain, (in(X1,esk43_3(X2,union(X2),X1))|~in(X1,union(X2)))).
% 0.19/0.46 cnf(i_0_14, plain, (in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X1)),identity_relation(X2))|~in(X1,X2))).
% 0.19/0.46 cnf(i_0_141, plain, (in(esk43_3(X1,union(X1),X2),X1)|~in(X2,union(X1)))).
% 0.19/0.46 cnf(i_0_125, plain, (in(X1,set_difference(X2,set_difference(X2,X3)))|~in(X1,X3)|~in(X1,X2))).
% 0.19/0.46 cnf(i_0_152, plain, (in(apply(X1,X2),relation_rng(X1))|~relation(X1)|~function(X1)|~in(X2,relation_dom(X1)))).
% 0.19/0.46 cnf(i_0_76, plain, (X1=empty_set|in(esk21_3(X1,set_meet(X1),X2),X1)|in(X2,set_meet(X1)))).
% 0.19/0.46 cnf(i_0_383, lemma, (identity_relation(relation_dom(X1))=X1|apply(X1,esk80_2(relation_dom(X1),X1))!=esk80_2(relation_dom(X1),X1)|~relation(X1)|~function(X1))).
% 0.19/0.46 cnf(i_0_43, plain, (in(X1,relation_inverse_image(X2,X3))|~relation(X2)|~function(X2)|~in(apply(X2,X1),X3)|~in(X1,relation_dom(X2)))).
% 0.19/0.46 cnf(i_0_25, plain, (in(X1,X2)|~relation(X3)|~in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),relation_dom_restriction(X3,X2)))).
% 0.19/0.46 cnf(i_0_39, plain, (in(X1,X2)|~relation(X3)|~in(unordered_pair(unordered_pair(X4,X1),unordered_pair(X4,X4)),relation_rng_restriction(X2,X3)))).
% 0.19/0.46 cnf(i_0_115, plain, (in(esk31_4(X1,X2,cartesian_product2(X1,X2),X3),X1)|~in(X3,cartesian_product2(X1,X2)))).
% 0.19/0.46 cnf(i_0_114, plain, (in(esk32_4(X1,X2,cartesian_product2(X1,X2),X3),X2)|~in(X3,cartesian_product2(X1,X2)))).
% 0.19/0.46 cnf(i_0_384, lemma, (identity_relation(relation_dom(X1))=X1|in(esk80_2(relation_dom(X1),X1),relation_dom(X1))|~relation(X1)|~function(X1))).
% 0.19/0.46 cnf(i_0_153, plain, (apply(X1,esk47_3(X1,relation_rng(X1),X2))=X2|~relation(X1)|~function(X1)|~in(X2,relation_rng(X1)))).
% 0.19/0.46 cnf(i_0_154, plain, (in(esk47_3(X1,relation_rng(X1),X2),relation_dom(X1))|~relation(X1)|~function(X1)|~in(X2,relation_rng(X1)))).
% 0.19/0.46 cnf(i_0_30, plain, (in(apply(X1,X2),relation_image(X1,X3))|~relation(X1)|~function(X1)|~in(X2,relation_dom(X1))|~in(X2,X3))).
% 0.19/0.46 cnf(i_0_50, plain, (in(esk11_4(X1,X2,relation_image(X1,X2),X3),X2)|~relation(X1)|~in(X3,relation_image(X1,X2)))).
% 0.19/0.46 cnf(i_0_56, plain, (in(esk14_4(X1,X2,relation_inverse_image(X1,X2),X3),X2)|~relation(X1)|~in(X3,relation_inverse_image(X1,X2)))).
% 0.19/0.46 cnf(i_0_131, plain, (in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,apply(X2,X1))),X2)|~relation(X2)|~function(X2)|~in(X1,relation_dom(X2)))).
% 0.19/0.46 cnf(i_0_24, 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)))).
% 0.19/0.46 cnf(i_0_38, 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)))).
% 0.19/0.46 cnf(i_0_135, plain, (in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,esk40_3(X2,relation_dom(X2),X1))),X2)|~relation(X2)|~in(X1,relation_dom(X2)))).
% 0.19/0.46 cnf(i_0_32, plain, (in(esk5_4(X1,X2,relation_image(X1,X2),X3),X2)|~relation(X1)|~function(X1)|~in(X3,relation_image(X1,X2)))).
% 0.19/0.46 cnf(i_0_31, plain, (apply(X1,esk5_4(X1,X2,relation_image(X1,X2),X3))=X3|~relation(X1)|~function(X1)|~in(X3,relation_image(X1,X2)))).
% 0.19/0.46 cnf(i_0_437, lemma, (apply(function_inverse(X1),apply(X1,X2))=X2|~one_to_one(X1)|~relation(X1)|~function(X1)|~in(X2,relation_dom(X1)))).
% 0.19/0.46 cnf(i_0_440, lemma, (in(apply(function_inverse(X1),X2),relation_dom(X1))|~one_to_one(X1)|~relation(X1)|~function(X1)|~in(X2,relation_rng(X1)))).
% 0.19/0.46 cnf(i_0_33, plain, (in(esk5_4(X1,X2,relation_image(X1,X2),X3),relation_dom(X1))|~relation(X1)|~function(X1)|~in(X3,relation_image(X1,X2)))).
% 0.19/0.46 cnf(i_0_165, 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)))).
% 0.19/0.46 cnf(i_0_164, 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))).
% 0.19/0.46 cnf(i_0_183, plain, (in(subset_complement(X1,X2),X3)|~element(X3,powerset(powerset(X1)))|~in(X2,complements_of_subsets(X1,X3)))).
% 0.19/0.46 cnf(i_0_37, 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))).
% 0.19/0.46 cnf(i_0_57, plain, (in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,esk14_4(X2,X3,relation_inverse_image(X2,X3),X1))),X2)|~relation(X2)|~in(X1,relation_inverse_image(X2,X3)))).
% 0.19/0.46 cnf(i_0_182, plain, (in(X1,complements_of_subsets(X2,X3))|~element(X3,powerset(powerset(X2)))|~element(X1,powerset(X2))|~in(subset_complement(X2,X1),X3))).
% 0.19/0.46 cnf(i_0_23, 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))).
% 0.19/0.46 cnf(i_0_176, 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))).
% 0.19/0.46 cnf(i_0_158, plain, (in(unordered_pair(unordered_pair(X1,esk50_3(X2,relation_rng(X2),X1)),unordered_pair(esk50_3(X2,relation_rng(X2),X1),esk50_3(X2,relation_rng(X2),X1))),X2)|~relation(X2)|~in(X1,relation_rng(X2)))).
% 0.19/0.46 cnf(i_0_178, plain, (in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,esk57_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)))).
% 0.19/0.46 cnf(i_0_51, plain, (in(unordered_pair(unordered_pair(X1,esk11_4(X2,X3,relation_image(X2,X3),X1)),unordered_pair(esk11_4(X2,X3,relation_image(X2,X3),X1),esk11_4(X2,X3,relation_image(X2,X3),X1))),X2)|~relation(X2)|~in(X1,relation_image(X2,X3)))).
% 0.19/0.46 cnf(i_0_113, plain, (unordered_pair(unordered_pair(esk31_4(X1,X2,cartesian_product2(X1,X2),X3),esk31_4(X1,X2,cartesian_product2(X1,X2),X3)),unordered_pair(esk31_4(X1,X2,cartesian_product2(X1,X2),X3),esk32_4(X1,X2,cartesian_product2(X1,X2),X3)))=X3|~in(X3,cartesian_product2(X1,X2)))).
% 0.19/0.46 cnf(i_0_177, plain, (in(unordered_pair(unordered_pair(X1,esk57_5(X2,X3,relation_composition(X2,X3),X4,X1)),unordered_pair(esk57_5(X2,X3,relation_composition(X2,X3),X4,X1),esk57_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)))).
% 0.19/0.46 # End listing active clauses. There is an equivalent clause to each of these in the clausification!
% 0.19/0.46 # Begin printing tableau
% 0.19/0.46 # Found 3 steps
% 0.19/0.46 cnf(i_0_319, negated_conjecture, (~in(esk75_0,set_union2(esk75_0,unordered_pair(esk75_0,esk75_0)))), inference(start_rule)).
% 0.19/0.46 cnf(i_0_608, plain, (~in(esk75_0,set_union2(esk75_0,unordered_pair(esk75_0,esk75_0)))), inference(extension_rule, [i_0_105])).
% 0.19/0.46 cnf(i_0_1614, plain, (~in(esk75_0,unordered_pair(esk75_0,esk75_0))), inference(closure_rule, [i_0_99])).
% 0.19/0.46 # End printing tableau
% 0.19/0.46 # SZS output end
% 0.19/0.46 # Branches closed with saturation will be marked with an "s"
% 0.19/0.46 # Returning from population with 17 new_tableaux and 0 remaining starting tableaux.
% 0.19/0.46 # We now have 17 tableaux to operate on
% 0.19/0.46 # Found closed tableau during pool population.
% 0.19/0.46 # Proof search is over...
% 0.19/0.46 # Freeing feature tree
%------------------------------------------------------------------------------