TSTP Solution File: SEU013+1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : SEU013+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jul 23 06:17:04 EDT 2022
% Result : Theorem 233.82s 234.06s
% Output : Refutation 233.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU013+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jul 22 18:32:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 233.82/234.06 GeoParameters:
% 233.82/234.06
% 233.82/234.06 tptp_input = 1
% 233.82/234.06 tptp_output = 0
% 233.82/234.06 nonempty = 1
% 233.82/234.06 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 233.82/234.06 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 233.82/234.06
% 233.82/234.06
% 233.82/234.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 233.82/234.06 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 233.82/234.06
% 233.82/234.06 RuleSystem INPUT:
% 233.82/234.06
% 233.82/234.06 Initial Rules:
% 233.82/234.06 #0: input, references = 7, size of lhs = 2:
% 233.82/234.06 in-{F}(V0,V1), in-{F}(V1,V0) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #1: input, references = 3, size of lhs = 1:
% 233.82/234.06 empty-{F}(V0) | function-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2: input, references = 3, size of lhs = 1:
% 233.82/234.06 empty-{F}(V0) | relation-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #3: input, references = 5, size of lhs = 3:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), one_to_one-{F}(V0) | pppp0-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #4: input, references = 4, size of lhs = 3:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), pppp0-{F}(V0) | one_to_one-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #5: input, references = 10, size of lhs = 7:
% 233.82/234.06 P_relation_dom-{F}(V0,V1), pppp0-{F}(V0), P_apply-{F}(V0,V2,V3), in-{F}(V2,V1), P_apply-{F}(V0,V4,V3), in-{F}(V4,V1), V4 == V2 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #6: input, references = 10, size of lhs = 1:
% 233.82/234.06 P_relation_dom-{F}(V0,V1) | pppp0-{T}(V0), pppp15-{T}(V0,V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #7: input, references = 11, size of lhs = 1:
% 233.82/234.06 pppp15-{F}(V0,V1) | EXISTS V2: pppp3-{T}(V0,V2,V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #8: input, references = 12, size of lhs = 2:
% 233.82/234.06 pppp3-{F}(V0,V1,V2), P_apply-{F}(V0,V1,V3) | EXISTS V4: pppp2-{T}(V0,V4,V1,V2,V3)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #9: input, references = 19, size of lhs = 2:
% 233.82/234.06 pppp3-{F}(V0,V1,V2), P_apply-{F}(V0,V1,V3) | in-{T}(V1,V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #10: input, references = 10, size of lhs = 2:
% 233.82/234.06 pppp2-{F}(V0,V2,V2,V3,V4), P_apply-{F}(V0,V2,V5) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #11: input, references = 5, size of lhs = 3:
% 233.82/234.06 pppp2-{F}(V0,V1,V2,V3,V4), P_apply-{F}(V0,V1,V5), V5 == V4 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #12: input, references = 12, size of lhs = 2:
% 233.82/234.06 pppp2-{F}(V0,V1,V2,V3,V4), P_apply-{F}(V0,V1,V5) | in-{T}(V1,V3)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #13: input, references = 9, size of lhs = 3:
% 233.82/234.06 relation-{F}(V0), P_relation_composition-{F}(V1,V0,V2), relation-{F}(V1) | relation-{T}(V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #14: input, references = 10, size of lhs = 1:
% 233.82/234.06 #-{F} V0 | EXISTS V1: pppp4-{T}(V0,V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #15: input, references = 16, size of lhs = 1:
% 233.82/234.06 pppp4-{F}(V0,V1) | element-{T}(V1,V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #16: input, references = 5, size of lhs = 3:
% 233.82/234.06 relation-{F}(V0), P_relation_composition-{F}(V0,V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #17: input, references = 3, size of lhs = 3:
% 233.82/234.06 relation-{F}(V0), P_relation_composition-{F}(V0,V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #18: input, references = 3, size of lhs = 1:
% 233.82/234.06 P_empty_set-{F}(V0) | empty-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #19: input, references = 3, size of lhs = 1:
% 233.82/234.06 P_empty_set-{F}(V0) | relation-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #20: input, references = 3, size of lhs = 1:
% 233.82/234.06 P_empty_set-{F}(V0) | relation_empty_yielding-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #21: input, references = 3, size of lhs = 6:
% 233.82/234.06 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V2,V1,V3), relation-{F}(V2), function-{F}(V2) | relation-{T}(V3)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #22: input, references = 8, size of lhs = 6:
% 233.82/234.06 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V2,V1,V3), relation-{F}(V2), function-{F}(V2) | function-{T}(V3)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #23: input, references = 6, size of lhs = 3:
% 233.82/234.06 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), empty-{F}(V2) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #24: input, references = 3, size of lhs = 1:
% 233.82/234.06 P_empty_set-{F}(V0) | empty-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #25: input, references = 3, size of lhs = 1:
% 233.82/234.06 P_empty_set-{F}(V0) | empty-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #26: input, references = 3, size of lhs = 1:
% 233.82/234.06 P_empty_set-{F}(V0) | relation-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #27: input, references = 14, size of lhs = 4:
% 233.82/234.06 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), relation-{F}(V1), empty-{F}(V2) | empty-{T}(V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #28: input, references = 5, size of lhs = 3:
% 233.82/234.06 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #29: input, references = 3, size of lhs = 3:
% 233.82/234.06 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #30: input, references = 8, size of lhs = 4:
% 233.82/234.06 P_empty_set-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V2,V1,V3), empty-{F}(V2) | empty-{T}(V3)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #31: input, references = 3, size of lhs = 4:
% 233.82/234.06 P_empty_set-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V2,V1,V3), empty-{F}(V2) | relation-{T}(V3)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #32: input, references = 3, size of lhs = 1:
% 233.82/234.06 P_empty_set-{F}(V0) | EXISTS V1: pppp5-{T}(V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #33: input, references = 3, size of lhs = 1:
% 233.82/234.06 pppp5-{F}(V0) | function-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #34: input, references = 3, size of lhs = 1:
% 233.82/234.06 pppp5-{F}(V0) | relation-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #35: input, references = 4, size of lhs = 1:
% 233.82/234.06 P_empty_set-{F}(V0) | EXISTS V1: pppp6-{T}(V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #36: input, references = 3, size of lhs = 1:
% 233.82/234.06 pppp6-{F}(V0) | relation-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #37: input, references = 5, size of lhs = 1:
% 233.82/234.06 pppp6-{F}(V0) | empty-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #38: input, references = 4, size of lhs = 2:
% 233.82/234.06 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2) | empty-{T}(V1), pppp16-{T}(V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #39: input, references = 3, size of lhs = 1:
% 233.82/234.06 pppp16-{F}(V0) | EXISTS V1: pppp7-{T}(V1,V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #40: input, references = 4, size of lhs = 2:
% 233.82/234.06 pppp7-{F}(V0,V1), empty-{F}(V0) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #41: input, references = 3, size of lhs = 1:
% 233.82/234.06 pppp7-{F}(V0,V1) | element-{T}(V0,V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #42: input, references = 4, size of lhs = 1:
% 233.82/234.06 P_empty_set-{F}(V0) | EXISTS V1: pppp8-{T}(V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #43: input, references = 5, size of lhs = 1:
% 233.82/234.06 pppp8-{F}(V0) | empty-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #44: input, references = 3, size of lhs = 1:
% 233.82/234.06 P_empty_set-{F}(V0) | EXISTS V1: pppp9-{T}(V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #45: input, references = 3, size of lhs = 1:
% 233.82/234.06 pppp9-{F}(V0) | relation-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #46: input, references = 3, size of lhs = 2:
% 233.82/234.06 pppp9-{F}(V0), empty-{F}(V0) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #47: input, references = 4, size of lhs = 2:
% 233.82/234.06 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2) | EXISTS V3: pppp10-{T}(V3,V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #48: input, references = 4, size of lhs = 1:
% 233.82/234.06 pppp10-{F}(V0,V1) | empty-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #49: input, references = 3, size of lhs = 1:
% 233.82/234.06 pppp10-{F}(V0,V1) | element-{T}(V0,V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #50: input, references = 3, size of lhs = 1:
% 233.82/234.06 P_empty_set-{F}(V0) | EXISTS V1: pppp11-{T}(V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #51: input, references = 3, size of lhs = 2:
% 233.82/234.06 pppp11-{F}(V0), empty-{F}(V0) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #52: input, references = 3, size of lhs = 1:
% 233.82/234.06 P_empty_set-{F}(V0) | EXISTS V1: pppp12-{T}(V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #53: input, references = 3, size of lhs = 1:
% 233.82/234.06 pppp12-{F}(V0) | relation_empty_yielding-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #54: input, references = 3, size of lhs = 1:
% 233.82/234.06 pppp12-{F}(V0) | relation-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #55: input, references = 3, size of lhs = 2:
% 233.82/234.06 P_empty_set-{F}(V0), #-{F} V1 | subset-{T}(V1,V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #56: input, references = 11, size of lhs = 2:
% 233.82/234.06 P_empty_set-{F}(V0), in-{F}(V1,V2) | element-{T}(V1,V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #57: input, references = 26, size of lhs = 8:
% 233.82/234.06 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V2,V1,V3), P_relation_dom-{F}(V3,V4), relation-{F}(V2), function-{F}(V2), in-{F}(V5,V4) | pppp1-{T}(V5,V1,V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #58: input, references = 10, size of lhs = 8:
% 233.82/234.06 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V2,V1,V3), P_relation_dom-{F}(V3,V4), relation-{F}(V2), function-{F}(V2), pppp1-{F}(V5,V1,V2) | in-{T}(V5,V4)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #59: input, references = 15, size of lhs = 5:
% 233.82/234.06 P_empty_set-{F}(V0), P_relation_dom-{F}(V3,V4), P_apply-{F}(V3,V1,V5), P_relation_dom-{F}(V2,V6), pppp1-{F}(V1,V2,V3) | in-{T}(V1,V4)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #60: input, references = 13, size of lhs = 5:
% 233.82/234.06 P_empty_set-{F}(V0), P_relation_dom-{F}(V3,V4), P_apply-{F}(V3,V1,V5), P_relation_dom-{F}(V2,V6), pppp1-{F}(V1,V2,V3) | in-{T}(V5,V6)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #61: input, references = 7, size of lhs = 6:
% 233.82/234.06 P_empty_set-{F}(V0), P_relation_dom-{F}(V3,V4), P_apply-{F}(V3,V1,V5), P_relation_dom-{F}(V2,V6), in-{F}(V1,V4), in-{F}(V5,V6) | pppp1-{T}(V1,V2,V3)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #62: input, references = 10, size of lhs = 12:
% 233.82/234.06 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V2,V1,V3), P_relation_dom-{F}(V3,V4), relation-{F}(V2), function-{F}(V2), P_apply-{F}(V3,V5,V6), P_apply-{F}(V2,V5,V7), P_apply-{F}(V1,V7,V8), in-{F}(V5,V4), V6 == V8 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #63: input, references = 4, size of lhs = 2:
% 233.82/234.06 P_empty_set-{F}(V0), element-{F}(V2,V1) | empty-{T}(V1), in-{T}(V2,V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #64: input, references = 3, size of lhs = 3:
% 233.82/234.06 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), element-{F}(V1,V3) | subset-{T}(V1,V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #65: input, references = 3, size of lhs = 3:
% 233.82/234.06 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), subset-{F}(V1,V2) | element-{T}(V1,V3)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #66: input, references = 4, size of lhs = 1:
% 233.82/234.06 P_empty_set-{F}(V0) | EXISTS V1: pppp14-{T}(V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #67: input, references = 5, size of lhs = 1:
% 233.82/234.06 pppp14-{F}(V0) | EXISTS V1: pppp13-{T}(V0,V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #68: input, references = 4, size of lhs = 1:
% 233.82/234.06 pppp14-{F}(V0) | one_to_one-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #69: input, references = 4, size of lhs = 1:
% 233.82/234.06 pppp14-{F}(V0) | function-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #70: input, references = 4, size of lhs = 1:
% 233.82/234.06 pppp14-{F}(V0) | relation-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #71: input, references = 5, size of lhs = 3:
% 233.82/234.06 pppp13-{F}(V0,V1), P_relation_composition-{F}(V0,V1,V2), one_to_one-{F}(V2) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #72: input, references = 4, size of lhs = 2:
% 233.82/234.06 pppp13-{F}(V0,V1), P_relation_composition-{F}(V0,V1,V2) | one_to_one-{T}(V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #73: input, references = 7, size of lhs = 2:
% 233.82/234.06 pppp13-{F}(V0,V1), P_relation_composition-{F}(V0,V1,V2) | function-{T}(V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #74: input, references = 13, size of lhs = 2:
% 233.82/234.06 pppp13-{F}(V0,V1), P_relation_composition-{F}(V0,V1,V2) | relation-{T}(V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #75: input, references = 15, size of lhs = 4:
% 233.82/234.06 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), element-{F}(V1,V3), in-{F}(V4,V1) | element-{T}(V4,V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #76: input, references = 10, size of lhs = 5:
% 233.82/234.06 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), empty-{F}(V1), element-{F}(V3,V2), in-{F}(V4,V3) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #77: input, references = 14, size of lhs = 3:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), V1 == V0 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #78: input, references = 7, size of lhs = 3:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), in-{F}(V2,V1) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #79: input, references = 10, size of lhs = 4:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), empty-{F}(V2), V2 == V1 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #80: input, references = 15, size of lhs = 1:
% 233.82/234.06 #-{F} V0 | EXISTS V1: P_relation_dom-{T}(V0,V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #81: input, references = 36, size of lhs = 2:
% 233.82/234.06 #-{F} V0, #-{F} V1 | EXISTS V2: P_apply-{T}(V0,V1,V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #82: input, references = 15, size of lhs = 2:
% 233.82/234.06 #-{F} V0, #-{F} V1 | EXISTS V2: P_relation_composition-{T}(V0,V1,V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #83: input, references = 4, size of lhs = 0:
% 233.82/234.06 FALSE | EXISTS V0: P_empty_set-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #84: input, references = 3, size of lhs = 1:
% 233.82/234.06 #-{F} V0 | EXISTS V1: P_powerset-{T}(V0,V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 number of initial rules = 85
% 233.82/234.06
% 233.82/234.06 Simplifiers:
% 233.82/234.06 #85: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 P_relation_dom-{F}(V0,V1), P_relation_dom-{F}(V0,V3), V1 == V3 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #86: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 P_apply-{F}(V0,V1,V2), P_apply-{F}(V0,V1,V5), V2 == V5 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #87: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 P_relation_composition-{F}(V0,V1,V2), P_relation_composition-{F}(V0,V1,V5), V2 == V5 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #88: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 P_empty_set-{F}(V0), P_empty_set-{F}(V1), V0 == V1 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #89: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 P_powerset-{F}(V0,V1), P_powerset-{F}(V0,V3), V1 == V3 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #90: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 pppp2-{F}(V0,V1,V2,V3,V4), pppp2-{F}(V0,V6,V2,V3,V4), V1 == V6 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #91: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 pppp2-{F}(V0,V1,V2,V3,V4), pppp2-{F}(V0,V6,V7,V3,V9), V2 == V7 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #92: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 pppp2-{F}(V0,V1,V2,V3,V4), pppp2-{F}(V0,V6,V7,V8,V9), V3 == V8 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #93: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 pppp2-{F}(V0,V1,V2,V3,V4), pppp2-{F}(V0,V6,V2,V8,V9), V4 == V9 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #94: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 pppp3-{F}(V0,V1,V2), pppp3-{F}(V0,V4,V2), V1 == V4 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #95: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 pppp3-{F}(V0,V1,V2), pppp3-{F}(V0,V4,V5), V2 == V5 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #96: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 pppp4-{F}(V0,V1), pppp4-{F}(V0,V3), V1 == V3 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #97: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 pppp5-{F}(V0), pppp5-{F}(V1), V0 == V1 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #98: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 pppp6-{F}(V0), pppp6-{F}(V1), V0 == V1 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #99: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 pppp7-{F}(V0,V1), pppp7-{F}(V2,V1), V0 == V2 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #100: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 pppp8-{F}(V0), pppp8-{F}(V1), V0 == V1 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #101: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 pppp9-{F}(V0), pppp9-{F}(V1), V0 == V1 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #102: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 pppp10-{F}(V0,V1), pppp10-{F}(V2,V1), V0 == V2 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #103: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 pppp11-{F}(V0), pppp11-{F}(V1), V0 == V1 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #104: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 pppp12-{F}(V0), pppp12-{F}(V1), V0 == V1 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #105: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 pppp13-{F}(V0,V1), pppp13-{F}(V0,V3), V1 == V3 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #106: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 pppp13-{F}(V0,V1), pppp13-{F}(V2,V3), V0 == V2 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #107: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 pppp14-{F}(V0), pppp14-{F}(V1), V0 == V1 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #108: unsound, references = 3, size of lhs = 3:
% 233.82/234.06 pppp15-{F}(V0,V1), pppp15-{F}(V0,V3), V1 == V3 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 number of simplifiers = 24
% 233.82/234.06
% 233.82/234.06 Learnt:
% 233.82/234.06 #115: mergings( V0 == V2; #112 ), references = 1, size of lhs = 1:
% 233.82/234.06 P_empty_set-{F}(V0) | pppp6-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #117: mergings( V0 == V2; #113 ), references = 1, size of lhs = 2:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1) | pppp6-{T}(V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #124: mergings( V0 == V2; #121 ), references = 1, size of lhs = 1:
% 233.82/234.06 P_empty_set-{F}(V0) | pppp8-{T}(V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #126: mergings( V0 == V2; #122 ), references = 1, size of lhs = 2:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1) | pppp8-{T}(V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #147: mergings( V2 == V3; #144 ), references = 1, size of lhs = 2:
% 233.82/234.06 empty-{F}(V0), P_empty_set-{F}(V1) | P_relation_dom-{T}(V0,V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #149: mergings( V2 == V3; #145 ), references = 1, size of lhs = 3:
% 233.82/234.06 empty-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2) | P_relation_dom-{T}(V0,V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #160: mergings( V0 == V3; #156 ), references = 17, size of lhs = 3:
% 233.82/234.06 P_empty_set-{F}(V0), element-{F}(V1,V2), V2 == V0 | in-{T}(V1,V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #163: mergings( V0 == V3, V2 == V3; #157 ), references = 1, size of lhs = 4:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), V0 == V1, element-{F}(V2,V0) | in-{T}(V2,V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #165: mergings( V2 == V0; #158 ), references = 1, size of lhs = 3:
% 233.82/234.06 P_empty_set-{F}(V0), pppp11-{F}(V0), element-{F}(V1,V0) | in-{T}(V1,V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #183: exists( #82, #179 ), references = 1, size of lhs = 3:
% 233.82/234.06 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2) | P_relation_composition-{T}(V0,V1,V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #184: exists( #82, #180 ), references = 1, size of lhs = 4:
% 233.82/234.06 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3) | P_relation_composition-{T}(V0,V1,V3)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #209: mergings( V0 == V4; #207 ), references = 1, size of lhs = 2:
% 233.82/234.06 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2) | pppp10-{T}(V0,V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #227: mergings( V0 == V3; #223 ), references = 1, size of lhs = 3:
% 233.82/234.06 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), V1 == V0 | pppp16-{T}(V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #230: mergings( V0 == V3, V1 == V3; #224 ), references = 1, size of lhs = 4:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), V0 == V1, P_powerset-{F}(V0,V2) | pppp16-{T}(V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #233: mergings( V0 == V3, V1 == V3; #225 ), references = 1, size of lhs = 3:
% 233.82/234.06 P_empty_set-{F}(V0), in-{F}(V1,V0), P_powerset-{F}(V0,V2) | pppp16-{T}(V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #267: exists( #81, #262 ), references = 1, size of lhs = 3:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), pppp3-{F}(V2,V3,V1) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #268: exists( #81, #261 ), references = 2, size of lhs = 2:
% 233.82/234.06 in-{F}(V0,V1), pppp3-{F}(V2,V1,V0) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #269: exists( #81, #263 ), references = 1, size of lhs = 5:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), element-{F}(V3,V2), pppp3-{F}(V4,V5,V3) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #272: exists( #7, #265 ), references = 3, size of lhs = 3:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), pppp15-{F}(V2,V1) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #273: exists( #7, #266 ), references = 2, size of lhs = 5:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), element-{F}(V3,V2), pppp15-{F}(V4,V3) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #275: disj( #6, exists( #7, #265 ) ), references = 1, size of lhs = 3:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_relation_dom-{F}(V2,V1) | pppp0-{T}(V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #309: mergings( V3 == V4; #306 ), references = 1, size of lhs = 3:
% 233.82/234.06 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2) | P_relation_composition-{T}(V1,V0,V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #311: mergings( V3 == V4; #307 ), references = 1, size of lhs = 4:
% 233.82/234.06 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3) | P_relation_composition-{T}(V1,V0,V3)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #374: exists( #81, #62 ), references = 8, size of lhs = 10:
% 233.82/234.06 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V2,V1,V3), P_relation_dom-{F}(V3,V4), in-{F}(V5,V4), P_apply-{F}(V2,V5,V6), P_apply-{F}(V1,V6,V7) | P_apply-{T}(V3,V5,V7)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #392: exists( #81, #388 ), references = 1, size of lhs = 5:
% 233.82/234.06 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), P_relation_dom-{F}(V3,V4), in-{F}(V4,V5), pppp1-{F}(V5,V1,V3) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #398: disj( #6, #4+#71 ), references = 6, size of lhs = 5:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), pppp13-{F}(V2,V3), P_relation_composition-{F}(V2,V3,V0) | pppp15-{T}(V0,V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #428: mergings( V3 == V4; #426 ), references = 1, size of lhs = 11:
% 233.82/234.06 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V2,V1,V3), P_relation_dom-{F}(V3,V4), pppp1-{F}(V5,V6,V3), P_relation_dom-{F}(V6,V7), P_apply-{F}(V2,V5,V8), P_apply-{F}(V1,V8,V9) | P_apply-{T}(V3,V5,V9)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #459: exists( #81, #457 ), references = 1, size of lhs = 10:
% 233.82/234.06 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V2,V1,V3), P_relation_dom-{F}(V3,V4), pppp3-{F}(V3,V5,V4), P_apply-{F}(V2,V5,V6), P_apply-{F}(V1,V6,V7) | P_apply-{T}(V3,V5,V7)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #479: mergings( V3 == V4; #477 ), references = 2, size of lhs = 5:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), in-{F}(V3,V4), pppp3-{F}(V5,V4,V2) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #498: mergings( V2 == V3; #496 ), references = 1, size of lhs = 5:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), pppp3-{F}(V3,V4,V2), V4 == V0 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #501: mergings( V3 == V4; #499 ), references = 2, size of lhs = 4:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), pppp15-{F}(V3,V2) | pppp3-{T}(V3,V0,V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #527: exists( #81, #11 ), references = 10, size of lhs = 1:
% 233.82/234.06 pppp2-{F}(V0,V1,V2,V3,V4) | P_apply-{T}(V0,V1,V4)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #565: mergings( V2 == V3; #563 ), references = 9, size of lhs = 5:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), element-{F}(V3,V2), V3 == V0 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #573: mergings( V5 == V6, V6 == V7, V1 == V7; #569 ), references = 2, size of lhs = 5:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), pppp3-{F}(V3,V0,V2), P_apply-{F}(V3,V0,V4) | pppp2-{T}(V3,V0,V0,V2,V4)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #595: exists( #81, #593 ), references = 1, size of lhs = 4:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), pppp3-{F}(V3,V0,V2) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #598: disj( #6, #501+#594 ), references = 1, size of lhs = 6:
% 233.82/234.06 empty-{F}(V0), P_powerset-{F}(V0,V1), P_relation_dom-{F}(V2,V1), P_empty_set-{F}(V3), empty-{F}(V4), P_powerset-{F}(V4,V1) | pppp0-{T}(V2)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #628: mergings( V2 == V3, V3 == V4; #625 ), references = 1, size of lhs = 6:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), P_powerset-{F}(V2,V3), element-{F}(V4,V3), V4 == V0 | pppp4-{T}(V4,V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #795: mergings( V3 == V4, V4 == V5; #791 ), references = 1, size of lhs = 7:
% 233.82/234.06 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), pppp1-{F}(V3,V1,V4), V3 == V0, P_relation_dom-{F}(V4,V5), P_powerset-{F}(V3,V6), element-{F}(V5,V6) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #866: mergings( V3 == V4, V4 == V5; #863 ), references = 4, size of lhs = 6:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), P_relation_dom-{F}(V3,V2), pppp1-{F}(V4,V3,V5), P_relation_dom-{F}(V5,V6) | P_apply-{T}(V5,V4,V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #889: mergings( V11 == V18, V16 == V17, V2 == V3, V3 == V7, V7 == V8, V8 == V9, V9 == V12, V12 == V13, V13 == V14; #879 ), references = 1, size of lhs = 14:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), P_relation_dom-{F}(V2,V3), empty-{F}(V4), P_powerset-{F}(V4,V5), P_relation_dom-{F}(V0,V5), P_empty_set-{F}(V6), V3 == V6, empty-{F}(V7), P_powerset-{F}(V7,V8), P_relation_dom-{F}(V1,V8) | pppp4-{T}(V3,V6)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #925: mergings( V10 == V17, V15 == V16, V2 == V3, V3 == V6, V6 == V7, V7 == V8, V8 == V11, V11 == V12, V12 == V13, V13 == V18, V18 == V19, V19 == V22, V22 == V23, V23 == V24; #908 ), references = 1, size of lhs = 23:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), empty-{F}(V3), P_powerset-{F}(V3,V4), P_relation_dom-{F}(V0,V4), empty-{F}(V5), P_powerset-{F}(V5,V6), P_relation_dom-{F}(V1,V6), relation-{F}(V7), function-{F}(V7), relation-{F}(V8), function-{F}(V8), P_relation_composition-{F}(V8,V7,V2), P_empty_set-{F}(V9), empty-{F}(V10), P_powerset-{F}(V10,V11), P_relation_dom-{F}(V7,V11), P_relation_dom-{F}(V8,V12), P_apply-{F}(V8,V9,V13), in-{F}(V14,V13) | P_relation_dom-{T}(V2,V9)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #940: mergings( V10 == V17, V15 == V16, V2 == V3, V3 == V6, V6 == V7, V7 == V8, V8 == V11, V11 == V12, V12 == V13, V13 == V18, V18 == V19, V19 == V22, V22 == V23, V23 == V24; #909 ), references = 4, size of lhs = 23:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), empty-{F}(V3), P_powerset-{F}(V3,V4), P_relation_dom-{F}(V0,V4), empty-{F}(V5), P_powerset-{F}(V5,V6), P_relation_dom-{F}(V1,V6), relation-{F}(V7), function-{F}(V7), relation-{F}(V8), function-{F}(V8), P_relation_composition-{F}(V8,V7,V2), P_empty_set-{F}(V9), empty-{F}(V10), P_powerset-{F}(V10,V11), P_relation_dom-{F}(V7,V11), P_relation_dom-{F}(V8,V12), P_apply-{F}(V8,V9,V13), V13 == V9 | P_relation_dom-{T}(V2,V9)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #954: mergings( V10 == V16, V14 == V15, V2 == V3, V3 == V6, V6 == V7, V7 == V8, V8 == V11, V11 == V12, V12 == V17, V17 == V18, V18 == V20, V20 == V25, V25 == V26; #910 ), references = 1, size of lhs = 27:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), empty-{F}(V3), P_powerset-{F}(V3,V4), P_relation_dom-{F}(V0,V4), empty-{F}(V5), P_powerset-{F}(V5,V6), P_relation_dom-{F}(V1,V6), relation-{F}(V7), function-{F}(V7), empty-{F}(V8), P_powerset-{F}(V8,V9), P_relation_dom-{F}(V7,V9), relation-{F}(V10), function-{F}(V10), P_relation_composition-{F}(V10,V7,V2), P_relation_composition-{F}(V10,V10,V2), P_relation_dom-{F}(V10,V11), P_empty_set-{F}(V12), relation-{F}(V13), function-{F}(V13), P_relation_composition-{F}(V10,V13,V2), P_apply-{F}(V13,V12,V14), V12 == V14 | P_relation_dom-{T}(V2,V12)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #977: mergings( V9 == V16, V14 == V15, V0 == V1, V1 == V5, V5 == V6, V6 == V7, V7 == V10, V10 == V11, V11 == V12, V12 == V17, V17 == V18, V18 == V21, V21 == V22, V22 == V23, V23 == V29, V29 == V30; #958 ), references = 1, size of lhs = 26:
% 233.82/234.06 empty-{F}(V0), P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V2,V1,V3), relation-{F}(V3), empty-{F}(V4), P_powerset-{F}(V4,V5), P_relation_dom-{F}(V1,V5), empty-{F}(V6), P_powerset-{F}(V6,V7), P_relation_dom-{F}(V2,V7), relation-{F}(V8), function-{F}(V8), relation-{F}(V9), function-{F}(V9), P_relation_composition-{F}(V9,V8,V3), empty-{F}(V10), P_powerset-{F}(V10,V11), P_relation_dom-{F}(V8,V11), P_relation_dom-{F}(V9,V12), P_apply-{F}(V9,V0,V13), in-{F}(V14,V13), P_powerset-{F}(V15,V3) | P_relation_dom-{T}(V3,V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #994: mergings( V9 == V16, V14 == V15, V0 == V1, V1 == V5, V5 == V6, V6 == V7, V7 == V10, V10 == V11, V11 == V12, V12 == V17, V17 == V18, V18 == V21, V21 == V22, V22 == V23, V23 == V29, V29 == V30; #959 ), references = 1, size of lhs = 26:
% 233.82/234.06 empty-{F}(V0), P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V2,V1,V3), V3 == V0, relation-{F}(V3), empty-{F}(V4), P_powerset-{F}(V4,V5), P_relation_dom-{F}(V1,V5), empty-{F}(V6), P_powerset-{F}(V6,V7), P_relation_dom-{F}(V2,V7), relation-{F}(V8), function-{F}(V8), relation-{F}(V9), function-{F}(V9), P_relation_composition-{F}(V9,V8,V3), empty-{F}(V10), P_powerset-{F}(V10,V11), P_relation_dom-{F}(V8,V11), P_relation_dom-{F}(V9,V12), P_apply-{F}(V9,V0,V13), in-{F}(V14,V13) | P_relation_dom-{T}(V3,V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #1011: mergings( V9 == V16, V14 == V15, V0 == V1, V1 == V5, V5 == V6, V6 == V7, V7 == V10, V10 == V11, V11 == V12, V12 == V17, V17 == V18, V18 == V21, V21 == V22, V22 == V23, V23 == V29, V29 == V30; #960 ), references = 1, size of lhs = 26:
% 233.82/234.06 empty-{F}(V0), P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V2,V1,V3), relation-{F}(V3), empty-{F}(V4), P_powerset-{F}(V4,V5), P_relation_dom-{F}(V1,V5), empty-{F}(V6), P_powerset-{F}(V6,V7), P_relation_dom-{F}(V2,V7), relation-{F}(V8), function-{F}(V8), relation-{F}(V9), function-{F}(V9), P_relation_composition-{F}(V9,V8,V3), empty-{F}(V10), P_powerset-{F}(V10,V11), P_relation_dom-{F}(V8,V11), P_relation_dom-{F}(V9,V12), P_apply-{F}(V9,V0,V13), in-{F}(V14,V13), in-{F}(V15,V3) | P_relation_dom-{T}(V3,V0)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #1240: mergings( V3 == V4; #1236 ), references = 1, size of lhs = 7:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), P_powerset-{F}(V2,V3), element-{F}(V4,V3), in-{F}(V5,V6), pppp3-{F}(V7,V6,V4) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #1242: mergings( V3 == V4; #1237 ), references = 1, size of lhs = 7:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), P_powerset-{F}(V2,V3), element-{F}(V4,V3), pppp3-{F}(V5,V6,V4), V6 == V0 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #1245: mergings( V3 == V4; #1243 ), references = 2, size of lhs = 6:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), P_powerset-{F}(V2,V3), element-{F}(V4,V3), pppp15-{F}(V5,V4) | pppp3-{T}(V5,V0,V4)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #1303: mergings( V5 == V6, V1 == V6; #1300 ), references = 2, size of lhs = 7:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), P_powerset-{F}(V2,V3), element-{F}(V4,V3), pppp3-{F}(V5,V0,V4), P_apply-{F}(V5,V0,V6) | pppp2-{T}(V5,V0,V0,V4,V6)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #1523: exists( #81, #1518 ), references = 1, size of lhs = 1:
% 233.82/234.06 pppp3-{F}(V0,V1,V1) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #1524: exists( #81, #1519 ), references = 1, size of lhs = 2:
% 233.82/234.06 pppp3-{F}(V0,V1,V2), pppp3-{F}(V3,V2,V1) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #1614: mergings( V11 == V16, V13 == V15, V5 == V9, V9 == V12; #1609 ), references = 3, size of lhs = 16:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), pppp0-{F}(V1), P_relation_composition-{F}(V1,V0,V2), P_relation_dom-{F}(V2,V3), empty-{F}(V4), P_powerset-{F}(V4,V5), P_relation_dom-{F}(V0,V5), P_empty_set-{F}(V6), P_apply-{F}(V1,V7,V6), in-{F}(V7,V8), P_relation_dom-{F}(V1,V8), pppp3-{F}(V9,V10,V3), P_apply-{F}(V9,V10,V11) | pppp2-{T}(V9,V7,V10,V3,V11)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #1772: mergings( V3 == V4, V4 == V5; #1767 ), references = 5, size of lhs = 9:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), P_powerset-{F}(V2,V3), element-{F}(V4,V3), P_relation_dom-{F}(V5,V4), pppp1-{F}(V6,V7,V5), V6 == V0, P_relation_dom-{F}(V7,V8) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #1777: mergings( V10 == V14, V3 == V4, V4 == V5, V5 == V6; #1768 ), references = 1, size of lhs = 10:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), P_powerset-{F}(V2,V3), element-{F}(V4,V3), P_relation_dom-{F}(V5,V4), P_relation_dom-{F}(V6,V7), pppp1-{F}(V8,V6,V5), P_relation_dom-{F}(V9,V8), pppp1-{F}(V8,V9,V5) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #1780: mergings( V3 == V4, V4 == V5; #1769 ), references = 1, size of lhs = 9:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), P_powerset-{F}(V2,V3), element-{F}(V4,V3), P_relation_dom-{F}(V5,V4), P_relation_dom-{F}(V6,V7), pppp1-{F}(V8,V6,V5), pppp15-{F}(V9,V8) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #1926: exists( #81, #1923 ), references = 1, size of lhs = 16:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), pppp0-{F}(V1), P_relation_composition-{F}(V1,V0,V2), P_relation_dom-{F}(V2,V3), empty-{F}(V4), P_powerset-{F}(V4,V5), P_relation_dom-{F}(V0,V5), P_empty_set-{F}(V6), P_apply-{F}(V1,V7,V6), in-{F}(V7,V8), P_relation_dom-{F}(V1,V8), pppp3-{F}(V9,V10,V3), P_apply-{F}(V9,V7,V11) | P_apply-{T}(V9,V10,V11)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #1933: mergings( V8 == V11, V11 == V15; #1930 ), references = 1, size of lhs = 28:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), pppp0-{F}(V1), P_relation_composition-{F}(V1,V0,V2), P_relation_dom-{F}(V2,V3), pppp15-{F}(V4,V3), empty-{F}(V5), P_powerset-{F}(V5,V6), P_relation_dom-{F}(V0,V6), P_relation_dom-{F}(V1,V7), in-{F}(V8,V7), P_apply-{F}(V1,V8,V9), P_empty_set-{F}(V9), relation-{F}(V10), function-{F}(V10), relation-{F}(V11), function-{F}(V11), P_relation_composition-{F}(V11,V10,V12), P_relation_dom-{F}(V12,V3), empty-{F}(V13), P_powerset-{F}(V13,V14), P_powerset-{F}(V14,V15), P_relation_dom-{F}(V11,V16), element-{F}(V16,V15), P_relation_dom-{F}(V10,V17), P_apply-{F}(V4,V8,V18) | pppp3-{T}(V4,V9,V3)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #1945: mergings( V2 == V5, V5 == V12, V12 == V14, V14 == V17, V17 == V29; #1939 ), references = 1, size of lhs = 53:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V2,V1,V0), relation-{F}(V3), function-{F}(V3), relation-{F}(V4), function-{F}(V4), P_relation_composition-{F}(V4,V3,V0), relation-{F}(V5), function-{F}(V5), relation-{F}(V6), function-{F}(V6), pppp0-{F}(V6), P_relation_composition-{F}(V6,V5,V0), empty-{F}(V7), P_powerset-{F}(V7,V8), P_relation_dom-{F}(V5,V8), P_relation_dom-{F}(V6,V9), relation-{F}(V10), function-{F}(V10), relation-{F}(V11), function-{F}(V11), P_relation_composition-{F}(V11,V10,V0), empty-{F}(V12), P_powerset-{F}(V12,V13), P_powerset-{F}(V13,V14), P_relation_dom-{F}(V11,V15), element-{F}(V15,V14), P_relation_dom-{F}(V10,V16), relation-{F}(V17), function-{F}(V17), relation-{F}(V18), function-{F}(V18), pppp0-{F}(V18), P_relation_composition-{F}(V18,V17,V0), empty-{F}(V19), P_powerset-{F}(V19,V20), P_relation_dom-{F}(V17,V20), P_empty_set-{F}(V21), pppp1-{F}(V21,V1,V2), P_apply-{F}(V6,V21,V21), in-{F}(V21,V9), P_apply-{F}(V18,V21,V21), P_apply-{F}(V4,V21,V22), P_apply-{F}(V3,V22,V23), in-{F}(V21,V24), P_relation_dom-{F}(V18,V24), pppp13-{F}(V25,V26), P_relation_composition-{F}(V25,V26,V0) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #1960: mergings( V7 == V18, V9 == V17, V17 == V22, V18 == V20, V8 == V12, V12 == V21, V3 == V4, V4 == V5, V5 == V10, V10 == V11, V11 == V21; #1948 ), references = 1, size of lhs = 21:
% 233.82/234.06 empty-{F}(V0), P_powerset-{F}(V0,V1), empty-{F}(V2), P_powerset-{F}(V2,V3), P_powerset-{F}(V3,V4), relation-{F}(V5), function-{F}(V5), P_relation_dom-{F}(V5,V1), relation-{F}(V6), function-{F}(V6), pppp0-{F}(V6), pppp13-{F}(V6,V5), empty-{F}(V7), P_powerset-{F}(V7,V1), P_empty_set-{F}(V8), pppp1-{F}(V8,V5,V6), P_apply-{F}(V6,V8,V8), P_apply-{F}(V5,V8,V9), in-{F}(V8,V10), element-{F}(V10,V4), P_relation_dom-{F}(V6,V10) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2029: mergings( V2 == V3, V3 == V7; #2026 ), references = 4, size of lhs = 14:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), P_relation_dom-{F}(V2,V3), P_empty_set-{F}(V4), V3 == V4, empty-{F}(V5), P_powerset-{F}(V5,V6), P_powerset-{F}(V6,V7), P_relation_dom-{F}(V1,V8), element-{F}(V8,V7), P_relation_dom-{F}(V0,V9) | pppp4-{T}(V3,V4)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2208: mergings( V3 == V8; #2206 ), references = 1, size of lhs = 15:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), P_relation_dom-{F}(V2,V3), P_empty_set-{F}(V4), empty-{F}(V5), P_powerset-{F}(V5,V6), P_powerset-{F}(V6,V7), P_relation_dom-{F}(V1,V8), element-{F}(V8,V7), P_relation_dom-{F}(V0,V9), pppp3-{F}(V10,V11,V3), V11 == V4 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2211: mergings( V3 == V7; #2209 ), references = 1, size of lhs = 14:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), P_relation_dom-{F}(V2,V3), pppp15-{F}(V4,V3), P_empty_set-{F}(V5), empty-{F}(V6), P_powerset-{F}(V6,V7), P_powerset-{F}(V7,V8), P_relation_dom-{F}(V1,V9), element-{F}(V9,V8), P_relation_dom-{F}(V0,V10) | pppp3-{T}(V4,V5,V3)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2262: mergings( V5 == V9; #2260 ), references = 1, size of lhs = 15:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), P_relation_dom-{F}(V2,V3), P_empty_set-{F}(V4), empty-{F}(V5), P_powerset-{F}(V5,V6), P_powerset-{F}(V6,V7), P_relation_dom-{F}(V1,V8), element-{F}(V8,V7), P_relation_dom-{F}(V0,V9), pppp3-{F}(V10,V11,V3), P_apply-{F}(V10,V11,V12) | pppp2-{T}(V10,V4,V11,V3,V12)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2273: mergings( V2 == V5, V5 == V8, V8 == V16, V16 == V19; #2268 ), references = 2, size of lhs = 40:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V2,V1,V0), relation-{F}(V3), function-{F}(V3), relation-{F}(V4), function-{F}(V4), P_relation_composition-{F}(V4,V3,V0), relation-{F}(V5), function-{F}(V5), relation-{F}(V6), function-{F}(V6), P_relation_composition-{F}(V6,V5,V0), empty-{F}(V7), P_powerset-{F}(V7,V8), P_powerset-{F}(V8,V9), P_relation_dom-{F}(V6,V10), element-{F}(V10,V9), P_relation_dom-{F}(V5,V11), relation-{F}(V12), function-{F}(V12), relation-{F}(V13), function-{F}(V13), P_relation_composition-{F}(V13,V12,V0), P_empty_set-{F}(V14), pppp1-{F}(V14,V1,V2), P_apply-{F}(V4,V14,V15), P_apply-{F}(V3,V15,V16), empty-{F}(V17), P_powerset-{F}(V17,V18), P_powerset-{F}(V18,V19), P_relation_dom-{F}(V13,V20), element-{F}(V20,V19), P_relation_dom-{F}(V12,V21), pppp13-{F}(V22,V23), P_relation_composition-{F}(V22,V23,V0) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2284: mergings( V11 == V20, V10 == V19, V3 == V4, V4 == V5, V5 == V6, V6 == V12, V12 == V13; #2276 ), references = 3, size of lhs = 19:
% 233.82/234.06 empty-{F}(V0), P_powerset-{F}(V0,V1), P_powerset-{F}(V1,V2), relation-{F}(V3), function-{F}(V3), relation-{F}(V4), function-{F}(V4), pppp13-{F}(V4,V3), P_empty_set-{F}(V5), pppp1-{F}(V5,V3,V4), P_apply-{F}(V4,V5,V6), P_apply-{F}(V3,V6,V7), empty-{F}(V8), P_powerset-{F}(V8,V9), P_powerset-{F}(V9,V10), P_relation_dom-{F}(V4,V11), element-{F}(V11,V2), element-{F}(V11,V10), P_relation_dom-{F}(V3,V12) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2298: mergings( V13 == V21, V2 == V5, V5 == V6, V6 == V14; #2293 ), references = 1, size of lhs = 30:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), relation-{F}(V2), function-{F}(V2), relation-{F}(V3), function-{F}(V3), relation-{F}(V4), function-{F}(V4), P_relation_composition-{F}(V4,V3,V2), empty-{F}(V5), P_powerset-{F}(V5,V6), P_powerset-{F}(V6,V7), relation-{F}(V8), function-{F}(V8), pppp13-{F}(V8,V2), P_empty_set-{F}(V9), in-{F}(V9,V10), P_relation_dom-{F}(V8,V10), element-{F}(V10,V7), P_apply-{F}(V8,V9,V11), pppp1-{F}(V11,V0,V1), P_apply-{F}(V4,V11,V12), P_apply-{F}(V3,V12,V13), empty-{F}(V14), P_powerset-{F}(V14,V15), P_powerset-{F}(V15,V16), element-{F}(V10,V16) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2311: mergings( V1 == V14, V14 == V15; #2306 ), references = 1, size of lhs = 24:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), relation-{F}(V2), empty-{F}(V3), P_powerset-{F}(V3,V4), P_relation_dom-{F}(V0,V4), empty-{F}(V5), P_powerset-{F}(V5,V6), P_relation_dom-{F}(V1,V6), relation-{F}(V7), function-{F}(V7), relation-{F}(V8), function-{F}(V8), P_relation_composition-{F}(V8,V7,V2), empty-{F}(V9), P_empty_set-{F}(V9), empty-{F}(V10), P_powerset-{F}(V10,V11), P_relation_dom-{F}(V7,V11), P_relation_dom-{F}(V8,V12), P_powerset-{F}(V13,V2) | P_apply-{T}(V8,V9,V9)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2314: mergings( V1 == V14, V14 == V15; #2307 ), references = 2, size of lhs = 24:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), relation-{F}(V2), empty-{F}(V3), P_powerset-{F}(V3,V4), P_relation_dom-{F}(V0,V4), empty-{F}(V5), P_powerset-{F}(V5,V6), P_relation_dom-{F}(V1,V6), relation-{F}(V7), function-{F}(V7), relation-{F}(V8), function-{F}(V8), P_relation_composition-{F}(V8,V7,V2), empty-{F}(V9), V2 == V9, P_empty_set-{F}(V9), empty-{F}(V10), P_powerset-{F}(V10,V11), P_relation_dom-{F}(V7,V11), P_relation_dom-{F}(V8,V12) | P_apply-{T}(V8,V9,V9)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2317: mergings( V1 == V14, V14 == V15; #2308 ), references = 1, size of lhs = 24:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), relation-{F}(V2), empty-{F}(V3), P_powerset-{F}(V3,V4), P_relation_dom-{F}(V0,V4), empty-{F}(V5), P_powerset-{F}(V5,V6), P_relation_dom-{F}(V1,V6), relation-{F}(V7), function-{F}(V7), relation-{F}(V8), function-{F}(V8), P_relation_composition-{F}(V8,V7,V2), empty-{F}(V9), P_empty_set-{F}(V9), empty-{F}(V10), P_powerset-{F}(V10,V11), P_relation_dom-{F}(V7,V11), P_relation_dom-{F}(V8,V12), in-{F}(V13,V2) | P_apply-{T}(V8,V9,V9)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2353: exists( #81, #2284 ), references = 2, size of lhs = 18:
% 233.82/234.06 empty-{F}(V0), P_powerset-{F}(V0,V1), P_powerset-{F}(V1,V2), relation-{F}(V3), function-{F}(V3), relation-{F}(V4), function-{F}(V4), pppp13-{F}(V4,V3), P_empty_set-{F}(V5), pppp1-{F}(V5,V3,V4), P_apply-{F}(V4,V5,V6), empty-{F}(V7), P_powerset-{F}(V7,V8), P_powerset-{F}(V8,V9), P_relation_dom-{F}(V4,V10), element-{F}(V10,V2), element-{F}(V10,V9), P_relation_dom-{F}(V3,V11) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2354: exists( #81, #2273 ), references = 1, size of lhs = 39:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V2,V1,V0), relation-{F}(V3), function-{F}(V3), relation-{F}(V4), function-{F}(V4), P_relation_composition-{F}(V4,V3,V0), relation-{F}(V5), function-{F}(V5), relation-{F}(V6), function-{F}(V6), P_relation_composition-{F}(V6,V5,V0), empty-{F}(V7), P_powerset-{F}(V7,V8), P_powerset-{F}(V8,V9), P_relation_dom-{F}(V6,V10), element-{F}(V10,V9), P_relation_dom-{F}(V5,V11), relation-{F}(V12), function-{F}(V12), relation-{F}(V13), function-{F}(V13), P_relation_composition-{F}(V13,V12,V0), P_empty_set-{F}(V14), pppp1-{F}(V14,V1,V2), P_apply-{F}(V4,V14,V15), empty-{F}(V16), P_powerset-{F}(V16,V17), P_powerset-{F}(V17,V18), P_relation_dom-{F}(V13,V19), element-{F}(V19,V18), P_relation_dom-{F}(V12,V20), pppp13-{F}(V21,V22), P_relation_composition-{F}(V21,V22,V0) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2364: mergings( V6 == V0; #2361 ), references = 2, size of lhs = 16:
% 233.82/234.06 empty-{F}(V0), P_powerset-{F}(V0,V1), P_powerset-{F}(V1,V2), relation-{F}(V3), function-{F}(V3), pppp13-{F}(V3,V4), P_empty_set-{F}(V5), pppp1-{F}(V5,V4,V3), P_apply-{F}(V3,V5,V6), empty-{F}(V7), P_powerset-{F}(V7,V8), P_powerset-{F}(V8,V9), P_relation_dom-{F}(V3,V10), element-{F}(V10,V2), element-{F}(V10,V9), P_relation_dom-{F}(V4,V11) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2368: mergings( V7 == V13, V14 == V15, V3 == V8; #2362 ), references = 2, size of lhs = 16:
% 233.82/234.06 empty-{F}(V0), P_powerset-{F}(V0,V1), P_powerset-{F}(V1,V2), relation-{F}(V3), function-{F}(V3), P_empty_set-{F}(V4), P_apply-{F}(V3,V4,V5), empty-{F}(V6), P_powerset-{F}(V6,V7), P_powerset-{F}(V7,V8), P_relation_dom-{F}(V3,V9), element-{F}(V9,V2), element-{F}(V9,V8), pppp13-{F}(V3,V10), pppp1-{F}(V4,V10,V3), P_relation_dom-{F}(V10,V11) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2404: exists( #82, #2398 ), references = 1, size of lhs = 5:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_relation_dom-{F}(V2,V1), pppp13-{F}(V3,V2), pppp7-{F}(V2,V4) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2406: mergings( V3 == V5; #2402 ), references = 1, size of lhs = 5:
% 233.82/234.06 empty-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V2,V0), V2 == V1, pppp13-{F}(V3,V2) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2409: mergings( V3 == V5, V1 == V5; #2403 ), references = 1, size of lhs = 6:
% 233.82/234.06 empty-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V1,V0), empty-{F}(V2), V1 == V2, pppp13-{F}(V3,V1) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2459: mergings( V3 == V5; #2455 ), references = 1, size of lhs = 5:
% 233.82/234.06 empty-{F}(V0), P_empty_set-{F}(V1), pppp13-{F}(V2,V3), P_relation_composition-{F}(V0,V3,V4), P_powerset-{F}(V5,V4) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2461: mergings( V3 == V5; #2456 ), references = 1, size of lhs = 5:
% 233.82/234.06 empty-{F}(V0), P_empty_set-{F}(V1), pppp13-{F}(V2,V3), P_relation_composition-{F}(V0,V3,V4), V4 == V1 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2464: mergings( V3 == V5, V6 == V5; #2457 ), references = 1, size of lhs = 5:
% 233.82/234.06 empty-{F}(V0), P_empty_set-{F}(V1), in-{F}(V2,V1), P_relation_composition-{F}(V0,V3,V1), pppp13-{F}(V4,V3) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2467: mergings( V3 == V4; #2465 ), references = 1, size of lhs = 3:
% 233.82/234.06 empty-{F}(V0), P_empty_set-{F}(V1), pppp13-{F}(V2,V3) | P_relation_composition-{T}(V0,V3,V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2559: mergings( V0 == V12, V2 == V3, V3 == V5, V5 == V8; #2554 ), references = 1, size of lhs = 17:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), P_relation_dom-{F}(V0,V2), P_empty_set-{F}(V3), relation-{F}(V4), function-{F}(V4), relation-{F}(V5), P_relation_composition-{F}(V5,V4,V5), function-{F}(V5), P_relation_composition-{F}(V5,V0,V6), P_relation_dom-{F}(V6,V7), V7 == V3, P_relation_dom-{F}(V5,V7), P_apply-{F}(V4,V3,V8), V3 == V8 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2587: mergings( V9 == V10, V10 == V16; #2582 ), references = 1, size of lhs = 29:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), empty-{F}(V3), P_powerset-{F}(V3,V4), P_powerset-{F}(V4,V5), P_relation_dom-{F}(V1,V6), element-{F}(V6,V5), P_relation_dom-{F}(V0,V7), relation-{F}(V8), function-{F}(V8), empty-{F}(V9), P_powerset-{F}(V9,V10), P_powerset-{F}(V10,V11), relation-{F}(V12), function-{F}(V12), pppp13-{F}(V12,V8), P_relation_composition-{F}(V12,V8,V2), P_empty_set-{F}(V13), P_apply-{F}(V12,V13,V14), empty-{F}(V15), P_powerset-{F}(V15,V16), P_powerset-{F}(V16,V17), P_relation_dom-{F}(V12,V18), element-{F}(V18,V11), element-{F}(V18,V17), P_relation_dom-{F}(V8,V19) | P_relation_dom-{T}(V2,V13)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2590: mergings( V9 == V10, V10 == V16; #2583 ), references = 1, size of lhs = 29:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), empty-{F}(V3), P_powerset-{F}(V3,V4), P_powerset-{F}(V4,V5), P_relation_dom-{F}(V1,V6), element-{F}(V6,V5), P_relation_dom-{F}(V0,V7), relation-{F}(V8), function-{F}(V8), empty-{F}(V9), P_powerset-{F}(V9,V10), P_powerset-{F}(V10,V11), relation-{F}(V12), function-{F}(V12), pppp13-{F}(V12,V8), P_relation_composition-{F}(V12,V8,V2), P_empty_set-{F}(V13), P_apply-{F}(V12,V13,V14), empty-{F}(V15), P_powerset-{F}(V15,V16), P_powerset-{F}(V16,V17), P_relation_dom-{F}(V12,V18), element-{F}(V18,V11), element-{F}(V18,V17), P_relation_dom-{F}(V8,V19) | P_relation_dom-{T}(V2,V13)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2593: mergings( V9 == V10, V10 == V16; #2584 ), references = 1, size of lhs = 29:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), empty-{F}(V3), P_powerset-{F}(V3,V4), P_powerset-{F}(V4,V5), P_relation_dom-{F}(V1,V6), element-{F}(V6,V5), P_relation_dom-{F}(V0,V7), empty-{F}(V8), P_powerset-{F}(V8,V9), P_powerset-{F}(V9,V10), relation-{F}(V11), function-{F}(V11), relation-{F}(V12), function-{F}(V12), pppp13-{F}(V12,V11), P_relation_composition-{F}(V12,V11,V2), P_empty_set-{F}(V13), P_apply-{F}(V12,V13,V14), empty-{F}(V15), P_powerset-{F}(V15,V16), P_powerset-{F}(V16,V17), P_relation_dom-{F}(V12,V18), element-{F}(V18,V10), element-{F}(V18,V17), P_relation_dom-{F}(V11,V19) | P_relation_dom-{T}(V2,V13)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2604: mergings( V8 == V9, V9 == V15, V15 == V22, V22 == V23; #2597 ), references = 1, size of lhs = 32:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), relation-{F}(V2), empty-{F}(V3), P_powerset-{F}(V3,V4), P_powerset-{F}(V4,V5), P_relation_dom-{F}(V1,V6), element-{F}(V6,V5), P_relation_dom-{F}(V0,V7), empty-{F}(V8), V2 == V8, P_empty_set-{F}(V8), relation-{F}(V9), function-{F}(V9), empty-{F}(V10), P_powerset-{F}(V10,V11), P_powerset-{F}(V11,V12), relation-{F}(V13), function-{F}(V13), pppp13-{F}(V13,V9), P_relation_composition-{F}(V13,V9,V2), P_apply-{F}(V13,V8,V14), empty-{F}(V15), P_powerset-{F}(V15,V16), P_powerset-{F}(V16,V17), P_relation_dom-{F}(V13,V18), element-{F}(V18,V12), element-{F}(V18,V17), P_relation_dom-{F}(V9,V19) | P_relation_dom-{T}(V2,V8)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2610: mergings( V8 == V9, V9 == V15, V15 == V22, V14 == V23, V10 == V24; #2598 ), references = 1, size of lhs = 32:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), relation-{F}(V2), function-{F}(V2), empty-{F}(V3), P_powerset-{F}(V3,V4), P_powerset-{F}(V4,V5), P_relation_dom-{F}(V1,V6), element-{F}(V6,V5), P_relation_dom-{F}(V0,V7), empty-{F}(V8), P_empty_set-{F}(V8), relation-{F}(V9), function-{F}(V9), empty-{F}(V10), P_powerset-{F}(V10,V11), P_powerset-{F}(V11,V12), relation-{F}(V13), function-{F}(V13), pppp13-{F}(V13,V9), P_relation_composition-{F}(V13,V9,V2), P_apply-{F}(V13,V8,V14), empty-{F}(V15), P_powerset-{F}(V15,V16), P_powerset-{F}(V16,V17), P_relation_dom-{F}(V13,V18), element-{F}(V18,V12), element-{F}(V18,V17), P_relation_dom-{F}(V9,V19) | P_relation_dom-{T}(V2,V8)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2615: mergings( V8 == V9, V9 == V15, V15 == V22, V22 == V23; #2599 ), references = 1, size of lhs = 33:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), relation-{F}(V2), empty-{F}(V3), P_powerset-{F}(V3,V4), P_powerset-{F}(V4,V5), P_relation_dom-{F}(V1,V6), element-{F}(V6,V5), P_relation_dom-{F}(V0,V7), empty-{F}(V8), P_empty_set-{F}(V8), relation-{F}(V9), function-{F}(V9), empty-{F}(V10), P_powerset-{F}(V10,V11), P_powerset-{F}(V11,V12), relation-{F}(V13), function-{F}(V13), pppp13-{F}(V13,V9), P_relation_composition-{F}(V13,V9,V2), P_apply-{F}(V13,V8,V14), empty-{F}(V15), P_powerset-{F}(V15,V16), P_powerset-{F}(V16,V17), P_relation_dom-{F}(V13,V18), element-{F}(V18,V12), element-{F}(V18,V17), P_relation_dom-{F}(V9,V19), empty-{F}(V20), V2 == V20 | P_relation_dom-{T}(V2,V8)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2643: mergings( V7 == V19, V13 == V20, V3 == V8, V8 == V9, V9 == V14, V14 == V21, V21 == V22, V22 == V23; #2634 ), references = 1, size of lhs = 20:
% 233.82/234.06 empty-{F}(V0), P_powerset-{F}(V0,V1), P_powerset-{F}(V1,V2), empty-{F}(V3), P_powerset-{F}(V3,V4), P_powerset-{F}(V4,V5), relation-{F}(V6), function-{F}(V6), empty-{F}(V7), P_empty_set-{F}(V7), P_apply-{F}(V6,V7,V8), empty-{F}(V9), P_powerset-{F}(V9,V10), P_powerset-{F}(V10,V11), P_relation_dom-{F}(V6,V12), element-{F}(V12,V2), element-{F}(V12,V5), element-{F}(V12,V11), pppp13-{F}(V6,V13), P_relation_dom-{F}(V13,V14) | P_relation_composition-{T}(V6,V13,V7)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2653: mergings( V12 == V18, V2 == V6, V6 == V7, V7 == V13, V13 == V19, V19 == V20, V20 == V21; #2645 ), references = 1, size of lhs = 20:
% 233.82/234.06 empty-{F}(V0), P_powerset-{F}(V0,V1), P_powerset-{F}(V1,V2), empty-{F}(V3), P_powerset-{F}(V3,V4), P_powerset-{F}(V4,V5), relation-{F}(V6), function-{F}(V6), empty-{F}(V7), one_to_one-{F}(V7), P_empty_set-{F}(V7), P_apply-{F}(V6,V7,V8), empty-{F}(V9), P_powerset-{F}(V9,V10), P_powerset-{F}(V10,V11), P_relation_dom-{F}(V6,V12), element-{F}(V12,V2), element-{F}(V12,V5), element-{F}(V12,V11), pppp13-{F}(V6,V13) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2662: mergings( V11 == V17, V2 == V6, V6 == V7, V7 == V12, V12 == V18, V18 == V19, V19 == V20; #2654 ), references = 3, size of lhs = 20:
% 233.82/234.06 pppp14-{F}(V0), relation-{F}(V0), function-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), P_powerset-{F}(V2,V3), empty-{F}(V4), P_powerset-{F}(V4,V5), P_powerset-{F}(V5,V6), empty-{F}(V7), one_to_one-{F}(V7), P_empty_set-{F}(V7), P_apply-{F}(V0,V7,V8), empty-{F}(V9), P_powerset-{F}(V9,V10), P_powerset-{F}(V10,V11), P_relation_dom-{F}(V0,V12), element-{F}(V12,V3), element-{F}(V12,V6), element-{F}(V12,V11) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2671: mergings( V4 == V8, V6 == V9, V9 == V20; #2667 ), references = 1, size of lhs = 28:
% 233.82/234.06 empty-{F}(V0), P_powerset-{F}(V0,V1), empty-{F}(V2), P_powerset-{F}(V2,V3), relation-{F}(V4), function-{F}(V4), P_relation_dom-{F}(V4,V1), empty-{F}(V5), P_powerset-{F}(V5,V1), pppp14-{F}(V6), relation-{F}(V6), function-{F}(V6), P_relation_dom-{F}(V6,V3), empty-{F}(V7), P_powerset-{F}(V7,V8), P_powerset-{F}(V8,V9), element-{F}(V3,V9), empty-{F}(V10), P_powerset-{F}(V10,V11), P_powerset-{F}(V11,V12), element-{F}(V3,V12), empty-{F}(V13), one_to_one-{F}(V13), P_empty_set-{F}(V13), empty-{F}(V14), P_powerset-{F}(V14,V15), P_powerset-{F}(V15,V16), element-{F}(V3,V16) | P_relation_composition-{T}(V6,V4,V13)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2687: exists( #81, #2662 ), references = 1, size of lhs = 19:
% 233.82/234.06 pppp14-{F}(V0), relation-{F}(V0), function-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), P_powerset-{F}(V2,V3), empty-{F}(V4), P_powerset-{F}(V4,V5), P_powerset-{F}(V5,V6), empty-{F}(V7), one_to_one-{F}(V7), P_empty_set-{F}(V7), empty-{F}(V8), P_powerset-{F}(V8,V9), P_powerset-{F}(V9,V10), P_relation_dom-{F}(V0,V11), element-{F}(V11,V3), element-{F}(V11,V6), element-{F}(V11,V10) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2699: exists( #81, #62 ), references = 4, size of lhs = 10:
% 233.82/234.06 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V2,V1,V3), P_relation_dom-{F}(V3,V4), in-{F}(V5,V4), P_apply-{F}(V3,V5,V6), P_apply-{F}(V2,V5,V7) | P_apply-{T}(V1,V7,V6)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2788: exists( #8, #2786 ), references = 2, size of lhs = 13:
% 233.82/234.06 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V2,V1,V3), pppp0-{F}(V3), P_relation_dom-{F}(V3,V4), pppp3-{F}(V2,V5,V4), P_apply-{F}(V2,V5,V6), in-{F}(V7,V4), P_apply-{F}(V3,V7,V8), P_apply-{F}(V1,V6,V8) | pppp2-{T}(V2,V7,V5,V4,V6)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2799: mergings( V2 == V6, V6 == V11; #2796 ), references = 1, size of lhs = 22:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), pppp1-{F}(V3,V0,V1), relation-{F}(V4), function-{F}(V4), relation-{F}(V5), function-{F}(V5), P_relation_composition-{F}(V5,V4,V2), P_apply-{F}(V5,V3,V6), P_apply-{F}(V4,V6,V7), P_empty_set-{F}(V8), relation-{F}(V9), function-{F}(V9), relation-{F}(V10), P_relation_composition-{F}(V10,V9,V2), function-{F}(V10), P_apply-{F}(V10,V3,V11), P_apply-{F}(V9,V11,V12), V7 == V12 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2898: mergings( V1 == V2; #2896 ), references = 1, size of lhs = 6:
% 233.82/234.06 P_relation_dom-{F}(V0,V1), in-{F}(V2,V1), P_apply-{F}(V0,V2,V3), P_apply-{F}(V0,V4,V3), V4 == V2, in-{F}(V4,V1) | pppp15-{T}(V0,V1)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #2993: mergings( V3 == V8; #2991 ), references = 6, size of lhs = 16:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), pppp0-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), P_relation_dom-{F}(V2,V3), in-{F}(V4,V3), P_apply-{F}(V2,V4,V5), P_empty_set-{F}(V6), P_relation_dom-{F}(V0,V7), P_relation_dom-{F}(V8,V7), pppp1-{F}(V4,V8,V1), in-{F}(V9,V7), P_apply-{F}(V0,V9,V5), P_relation_dom-{F}(V1,V10) | P_apply-{T}(V1,V4,V9)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #3002: mergings( V2 == V13, V5 == V7, V7 == V11; #2998 ), references = 2, size of lhs = 22:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), pppp0-{F}(V1), relation-{F}(V2), function-{F}(V2), pppp0-{F}(V2), P_relation_composition-{F}(V2,V0,V3), P_relation_dom-{F}(V3,V4), P_relation_dom-{F}(V2,V4), P_relation_composition-{F}(V2,V1,V5), P_relation_dom-{F}(V5,V4), pppp3-{F}(V5,V6,V4), P_apply-{F}(V5,V6,V7), P_empty_set-{F}(V8), P_relation_dom-{F}(V1,V9), P_relation_dom-{F}(V0,V9), in-{F}(V10,V4), P_apply-{F}(V2,V10,V11), in-{F}(V11,V9), P_apply-{F}(V1,V11,V7) | pppp2-{T}(V5,V10,V6,V4,V7)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #3026: mergings( V7 == V11, V3 == V12; #3023 ), references = 1, size of lhs = 24:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), pppp0-{F}(V2), P_relation_composition-{F}(V0,V2,V3), relation-{F}(V4), function-{F}(V4), pppp0-{F}(V4), P_relation_composition-{F}(V4,V2,V3), P_relation_composition-{F}(V4,V1,V5), P_relation_dom-{F}(V5,V6), P_relation_dom-{F}(V4,V6), P_relation_dom-{F}(V3,V6), pppp3-{F}(V3,V7,V6), in-{F}(V7,V6), P_apply-{F}(V0,V7,V8), P_apply-{F}(V4,V7,V8), P_empty_set-{F}(V9), P_relation_dom-{F}(V2,V10), P_relation_dom-{F}(V1,V10), in-{F}(V8,V10) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #3033: mergings( V8 == V10, V10 == V14, V3 == V4, V4 == V11; #3028 ), references = 2, size of lhs = 20:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), pppp0-{F}(V1), relation-{F}(V2), function-{F}(V2), pppp0-{F}(V2), P_relation_composition-{F}(V2,V1,V3), P_relation_composition-{F}(V2,V0,V4), P_relation_dom-{F}(V4,V5), P_relation_dom-{F}(V3,V5), P_relation_dom-{F}(V2,V5), pppp3-{F}(V3,V6,V5), in-{F}(V6,V5), P_empty_set-{F}(V7), P_relation_dom-{F}(V1,V8), P_relation_dom-{F}(V0,V8), P_relation_dom-{F}(V9,V8), pppp1-{F}(V6,V9,V2) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #3105: mergings( V3 == V12; #3102 ), references = 1, size of lhs = 23:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), pppp0-{F}(V2), relation-{F}(V3), function-{F}(V3), pppp0-{F}(V3), P_relation_composition-{F}(V3,V0,V4), P_relation_dom-{F}(V4,V5), P_relation_dom-{F}(V3,V5), P_relation_composition-{F}(V3,V2,V6), P_relation_dom-{F}(V6,V5), P_relation_composition-{F}(V3,V1,V7), P_relation_dom-{F}(V7,V5), pppp3-{F}(V6,V8,V5), pppp3-{F}(V9,V8,V5), P_empty_set-{F}(V10), P_relation_dom-{F}(V2,V11), P_relation_dom-{F}(V1,V11), P_relation_dom-{F}(V0,V11) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #3108: mergings( V3 == V10; #3106 ), references = 1, size of lhs = 22:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), pppp0-{F}(V2), relation-{F}(V3), function-{F}(V3), pppp0-{F}(V3), P_relation_composition-{F}(V3,V0,V4), P_relation_dom-{F}(V4,V5), P_relation_dom-{F}(V3,V5), P_relation_composition-{F}(V3,V2,V6), pppp15-{F}(V6,V5), P_relation_dom-{F}(V6,V5), P_relation_composition-{F}(V3,V1,V7), P_relation_dom-{F}(V7,V5), P_empty_set-{F}(V8), P_relation_dom-{F}(V2,V9), P_relation_dom-{F}(V1,V9), P_relation_dom-{F}(V0,V9) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #3181: mergings( V3 == V4, V4 == V5, V5 == V6; #3176 ), references = 2, size of lhs = 9:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), P_powerset-{F}(V2,V3), P_relation_dom-{F}(V4,V3), P_relation_dom-{F}(V5,V6), pppp1-{F}(V7,V5,V4), in-{F}(V8,V7), in-{F}(V9,V8) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #3185: mergings( V3 == V4, V4 == V5, V5 == V6; #3177 ), references = 2, size of lhs = 9:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), P_powerset-{F}(V2,V3), P_relation_dom-{F}(V4,V3), P_relation_dom-{F}(V5,V6), pppp1-{F}(V7,V5,V4), in-{F}(V8,V7), V8 == V0 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #3561: mergings( V3 == V8; #3557 ), references = 1, size of lhs = 15:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), P_relation_dom-{F}(V2,V3), P_empty_set-{F}(V4), empty-{F}(V5), P_powerset-{F}(V5,V6), P_powerset-{F}(V6,V7), P_relation_dom-{F}(V1,V7), P_relation_dom-{F}(V0,V8), in-{F}(V9,V10), in-{F}(V10,V11), pppp3-{F}(V12,V11,V3) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #3563: mergings( V3 == V8; #3558 ), references = 2, size of lhs = 15:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), P_relation_dom-{F}(V2,V3), P_empty_set-{F}(V4), empty-{F}(V5), P_powerset-{F}(V5,V6), P_powerset-{F}(V6,V7), P_relation_dom-{F}(V1,V7), P_relation_dom-{F}(V0,V8), in-{F}(V9,V10), V9 == V4, pppp3-{F}(V11,V10,V3) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #3601: mergings( V11 == V17, V12 == V14, V5 == V10, V10 == V13; #3596 ), references = 2, size of lhs = 22:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), pppp0-{F}(V1), relation-{F}(V2), function-{F}(V2), pppp0-{F}(V2), P_relation_composition-{F}(V2,V0,V3), P_relation_dom-{F}(V3,V4), P_relation_composition-{F}(V2,V1,V5), P_relation_dom-{F}(V5,V4), pppp3-{F}(V5,V6,V4), P_apply-{F}(V5,V6,V7), P_relation_dom-{F}(V1,V8), P_relation_dom-{F}(V0,V8), P_empty_set-{F}(V9), P_relation_dom-{F}(V2,V10), in-{F}(V11,V10), P_apply-{F}(V2,V11,V12), in-{F}(V12,V8), P_apply-{F}(V1,V12,V7) | pppp2-{T}(V5,V11,V6,V4,V7)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #3636: mergings( V2 == V7; #3634 ), references = 1, size of lhs = 14:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), P_relation_dom-{F}(V2,V3), P_empty_set-{F}(V4), empty-{F}(V5), P_powerset-{F}(V5,V6), P_powerset-{F}(V6,V7), P_relation_dom-{F}(V1,V7), P_relation_dom-{F}(V0,V8), pppp3-{F}(V9,V10,V3), V10 == V4 | pppp4-{T}(V10,V4)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #3744: mergings( V2 == V16, V21 == V24, V5 == V7, V7 == V8, V8 == V14, V14 == V17, V17 == V22; #3736 ), references = 1, size of lhs = 40:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), pppp0-{F}(V2), relation-{F}(V3), function-{F}(V3), P_relation_composition-{F}(V3,V1,V4), P_relation_dom-{F}(V4,V5), P_relation_dom-{F}(V3,V5), element-{F}(V5,V6), P_relation_composition-{F}(V3,V2,V7), P_relation_dom-{F}(V7,V5), pppp3-{F}(V7,V8,V5), P_apply-{F}(V7,V8,V9), P_relation_dom-{F}(V2,V10), P_relation_dom-{F}(V1,V10), relation-{F}(V11), function-{F}(V11), pppp0-{F}(V11), relation-{F}(V12), function-{F}(V12), pppp0-{F}(V12), P_relation_composition-{F}(V12,V11,V3), P_relation_composition-{F}(V12,V0,V13), P_relation_dom-{F}(V13,V5), P_empty_set-{F}(V14), P_relation_dom-{F}(V11,V15), P_relation_dom-{F}(V0,V15), P_relation_dom-{F}(V12,V16), V16 == V14, P_powerset-{F}(V16,V6), in-{F}(V17,V16), P_apply-{F}(V12,V17,V18), in-{F}(V18,V15), P_apply-{F}(V11,V18,V19), in-{F}(V19,V10), P_apply-{F}(V2,V19,V9) | pppp2-{T}(V7,V17,V8,V5,V9)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #3899: mergings( V7 == V11, V3 == V13; #3896 ), references = 2, size of lhs = 25:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), pppp0-{F}(V2), P_relation_composition-{F}(V0,V2,V3), relation-{F}(V4), function-{F}(V4), pppp0-{F}(V4), P_relation_composition-{F}(V4,V2,V3), P_relation_composition-{F}(V4,V1,V5), P_relation_dom-{F}(V5,V6), P_relation_dom-{F}(V3,V6), in-{F}(V7,V6), pppp3-{F}(V3,V7,V6), P_apply-{F}(V0,V7,V8), P_apply-{F}(V4,V7,V8), P_relation_dom-{F}(V2,V9), P_relation_dom-{F}(V1,V9), in-{F}(V8,V9), P_empty_set-{F}(V10), P_relation_dom-{F}(V4,V11), in-{F}(V7,V11) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #3906: mergings( V8 == V10, V14 == V15, V3 == V4, V4 == V13; #3901 ), references = 4, size of lhs = 21:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), pppp0-{F}(V1), relation-{F}(V2), function-{F}(V2), pppp0-{F}(V2), P_relation_composition-{F}(V2,V1,V3), P_relation_composition-{F}(V2,V0,V4), P_relation_dom-{F}(V4,V5), P_relation_dom-{F}(V3,V5), in-{F}(V6,V5), pppp3-{F}(V3,V6,V5), P_relation_dom-{F}(V1,V7), P_relation_dom-{F}(V0,V7), P_relation_dom-{F}(V8,V7), pppp1-{F}(V6,V8,V2), P_empty_set-{F}(V9), in-{F}(V6,V10), P_relation_dom-{F}(V2,V10) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #4222: mergings( V3 == V5, V5 == V6, V6 == V17; #4218 ), references = 1, size of lhs = 26:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), pppp0-{F}(V2), relation-{F}(V3), function-{F}(V3), pppp0-{F}(V3), P_relation_composition-{F}(V3,V0,V4), P_relation_dom-{F}(V4,V5), P_relation_composition-{F}(V3,V2,V6), P_relation_dom-{F}(V6,V5), P_relation_composition-{F}(V3,V1,V7), P_relation_dom-{F}(V7,V5), pppp3-{F}(V6,V8,V5), pppp3-{F}(V9,V8,V5), element-{F}(V5,V10), P_relation_dom-{F}(V3,V11), P_powerset-{F}(V11,V10), P_relation_dom-{F}(V2,V12), P_relation_dom-{F}(V1,V12), P_relation_dom-{F}(V0,V12), P_empty_set-{F}(V13), V11 == V13 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #4227: mergings( V3 == V5, V5 == V6, V6 == V15; #4223 ), references = 1, size of lhs = 25:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), pppp0-{F}(V2), relation-{F}(V3), function-{F}(V3), pppp0-{F}(V3), P_relation_composition-{F}(V3,V0,V4), P_relation_dom-{F}(V4,V5), P_relation_composition-{F}(V3,V2,V6), pppp15-{F}(V6,V5), P_relation_dom-{F}(V6,V5), P_relation_composition-{F}(V3,V1,V7), P_relation_dom-{F}(V7,V5), element-{F}(V5,V8), P_relation_dom-{F}(V3,V9), P_powerset-{F}(V9,V8), P_relation_dom-{F}(V2,V10), P_relation_dom-{F}(V1,V10), P_relation_dom-{F}(V0,V10), P_empty_set-{F}(V11), V9 == V11 | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #4557: disj( #6, mergings( V3 == V10; #3106 ) ), references = 1, size of lhs = 21:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), pppp0-{F}(V2), relation-{F}(V3), function-{F}(V3), pppp0-{F}(V3), P_relation_composition-{F}(V3,V0,V4), P_relation_dom-{F}(V4,V5), P_relation_dom-{F}(V3,V5), P_relation_composition-{F}(V3,V2,V6), P_relation_dom-{F}(V6,V5), P_relation_composition-{F}(V3,V1,V7), P_relation_dom-{F}(V7,V5), P_empty_set-{F}(V8), P_relation_dom-{F}(V2,V9), P_relation_dom-{F}(V1,V9), P_relation_dom-{F}(V0,V9) | pppp0-{T}(V6)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #4558: disj( #6, mergings( V3 == V5, V5 == V6, V6 == V15; #4223 ) ), references = 1, size of lhs = 24:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), pppp0-{F}(V2), relation-{F}(V3), function-{F}(V3), pppp0-{F}(V3), P_relation_composition-{F}(V3,V0,V4), P_relation_dom-{F}(V4,V5), P_relation_composition-{F}(V3,V2,V6), P_relation_dom-{F}(V6,V5), P_relation_composition-{F}(V3,V1,V7), P_relation_dom-{F}(V7,V5), element-{F}(V5,V8), P_relation_dom-{F}(V3,V9), P_powerset-{F}(V9,V8), P_relation_dom-{F}(V2,V10), P_relation_dom-{F}(V1,V10), P_relation_dom-{F}(V0,V10), P_empty_set-{F}(V11), V9 == V11 | pppp0-{T}(V6)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #4868: mergings( V3 == V12; #4866 ), references = 3, size of lhs = 23:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), pppp0-{F}(V1), relation-{F}(V2), function-{F}(V2), pppp0-{F}(V2), P_relation_composition-{F}(V2,V1,V3), P_relation_composition-{F}(V2,V0,V4), P_relation_dom-{F}(V4,V5), P_relation_dom-{F}(V3,V5), in-{F}(V6,V5), pppp3-{F}(V3,V6,V5), P_relation_dom-{F}(V1,V7), P_relation_dom-{F}(V0,V7), P_relation_dom-{F}(V8,V7), pppp1-{F}(V6,V8,V2), P_empty_set-{F}(V9), P_relation_dom-{F}(V2,V10), P_relation_dom-{F}(V11,V10), pppp1-{F}(V6,V12,V11), P_relation_dom-{F}(V12,V13) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #5086: mergings( V5 == V8, V8 == V11; #5083 ), references = 1, size of lhs = 27:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), pppp0-{F}(V1), P_relation_dom-{F}(V1,V2), P_relation_dom-{F}(V0,V2), in-{F}(V3,V2), P_apply-{F}(V1,V3,V4), P_empty_set-{F}(V5), relation-{F}(V6), function-{F}(V6), relation-{F}(V7), function-{F}(V7), P_relation_composition-{F}(V7,V0,V8), P_relation_dom-{F}(V8,V9), P_relation_composition-{F}(V7,V1,V10), P_relation_dom-{F}(V10,V9), pppp3-{F}(V10,V11,V9), P_apply-{F}(V10,V11,V4), P_relation_dom-{F}(V7,V12), P_relation_composition-{F}(V7,V6,V13), pppp0-{F}(V13), P_relation_dom-{F}(V13,V9), P_apply-{F}(V6,V3,V14), P_apply-{F}(V13,V15,V14), in-{F}(V15,V9) | pppp2-{T}(V10,V15,V11,V9,V4)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #5420: mergings( V9 == V17, V17 == V18, V3 == V4, V4 == V5, V5 == V16; #5414 ), references = 1, size of lhs = 25:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), P_relation_dom-{F}(V2,V1), relation-{F}(V3), function-{F}(V3), P_relation_dom-{F}(V3,V1), relation-{F}(V4), function-{F}(V4), pppp0-{F}(V4), P_relation_dom-{F}(V4,V1), relation-{F}(V5), function-{F}(V5), pppp0-{F}(V5), pppp1-{F}(V6,V2,V5), P_relation_composition-{F}(V5,V0,V7), P_relation_dom-{F}(V7,V8), P_relation_composition-{F}(V5,V4,V9), P_relation_dom-{F}(V9,V8), pppp3-{F}(V9,V6,V8), P_relation_composition-{F}(V5,V3,V10), P_relation_dom-{F}(V10,V8), P_empty_set-{F}(V11), in-{F}(V6,V12), P_relation_dom-{F}(V5,V12) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #5425: mergings( V9 == V21, V3 == V4, V4 == V5, V5 == V19; #5412 ), references = 1, size of lhs = 31:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), P_relation_dom-{F}(V2,V1), relation-{F}(V3), function-{F}(V3), pppp1-{F}(V4,V2,V3), in-{F}(V4,V5), P_relation_dom-{F}(V3,V5), P_relation_composition-{F}(V3,V0,V6), P_relation_dom-{F}(V6,V7), relation-{F}(V8), function-{F}(V8), relation-{F}(V9), function-{F}(V9), pppp0-{F}(V9), relation-{F}(V10), function-{F}(V10), pppp0-{F}(V10), P_relation_composition-{F}(V10,V9,V11), P_relation_dom-{F}(V11,V7), pppp3-{F}(V11,V4,V7), P_relation_composition-{F}(V10,V8,V12), P_relation_dom-{F}(V12,V7), P_relation_dom-{F}(V9,V13), P_relation_dom-{F}(V8,V13), P_relation_dom-{F}(V14,V13), pppp1-{F}(V4,V14,V10), P_empty_set-{F}(V15), in-{F}(V4,V16), P_relation_dom-{F}(V10,V16) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #5432: mergings( V7 == V21, V9 == V20, V20 == V22, V3 == V4, V4 == V5, V5 == V19; #5413 ), references = 1, size of lhs = 30:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V0,V2), P_relation_dom-{F}(V2,V3), relation-{F}(V4), function-{F}(V4), relation-{F}(V5), function-{F}(V5), pppp0-{F}(V5), relation-{F}(V6), function-{F}(V6), pppp0-{F}(V6), P_relation_composition-{F}(V6,V5,V7), P_relation_dom-{F}(V7,V3), pppp3-{F}(V7,V8,V3), in-{F}(V8,V9), P_relation_dom-{F}(V6,V9), P_relation_dom-{F}(V1,V9), pppp1-{F}(V8,V10,V1), P_relation_dom-{F}(V10,V11), P_relation_dom-{F}(V0,V11), P_relation_composition-{F}(V6,V4,V12), P_relation_dom-{F}(V12,V3), P_relation_dom-{F}(V5,V13), P_relation_dom-{F}(V4,V13), P_relation_dom-{F}(V14,V13), pppp1-{F}(V8,V14,V6), P_empty_set-{F}(V15) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #5703: mergings( V4 == V8, V8 == V10, V3 == V6; #5699 ), references = 1, size of lhs = 13:
% 233.82/234.06 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), pppp0-{F}(V1), relation-{F}(V2), function-{F}(V2), P_relation_composition-{F}(V2,V1,V1), P_relation_dom-{F}(V2,V3), P_relation_dom-{F}(V1,V4), P_relation_dom-{F}(V5,V4), pppp1-{F}(V6,V5,V2), pppp3-{F}(V2,V6,V4), in-{F}(V6,V4) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #5953: mergings( V12 == V15, V3 == V13; #5948 ), references = 1, size of lhs = 23:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), pppp0-{F}(V2), relation-{F}(V3), function-{F}(V3), pppp0-{F}(V3), P_relation_composition-{F}(V3,V0,V4), P_relation_dom-{F}(V4,V5), P_relation_composition-{F}(V3,V2,V6), P_relation_dom-{F}(V6,V5), P_relation_composition-{F}(V3,V1,V7), P_relation_dom-{F}(V7,V5), pppp3-{F}(V6,V8,V5), pppp3-{F}(V9,V8,V5), P_relation_dom-{F}(V2,V10), P_relation_dom-{F}(V1,V10), P_relation_dom-{F}(V0,V10), P_empty_set-{F}(V11), P_relation_dom-{F}(V3,V12) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #5957: mergings( V10 == V13, V3 == V11; #5954 ), references = 1, size of lhs = 22:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), pppp0-{F}(V2), relation-{F}(V3), function-{F}(V3), pppp0-{F}(V3), P_relation_composition-{F}(V3,V0,V4), P_relation_dom-{F}(V4,V5), P_relation_composition-{F}(V3,V2,V6), pppp15-{F}(V6,V5), P_relation_dom-{F}(V6,V5), P_relation_composition-{F}(V3,V1,V7), P_relation_dom-{F}(V7,V5), P_relation_dom-{F}(V2,V8), P_relation_dom-{F}(V1,V8), P_relation_dom-{F}(V0,V8), P_empty_set-{F}(V9), P_relation_dom-{F}(V3,V10) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #5962: mergings( V7 == V10, V2 == V8; #5959 ), references = 2, size of lhs = 22:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), relation-{F}(V3), function-{F}(V3), pppp0-{F}(V3), relation-{F}(V4), function-{F}(V4), pppp0-{F}(V4), P_relation_composition-{F}(V4,V3,V0), P_relation_composition-{F}(V4,V1,V0), P_relation_composition-{F}(V4,V2,V0), P_relation_dom-{F}(V3,V5), P_relation_dom-{F}(V2,V5), P_relation_dom-{F}(V1,V5), P_empty_set-{F}(V6), P_relation_dom-{F}(V4,V7), pppp13-{F}(V8,V9), P_relation_composition-{F}(V8,V9,V0) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #5983: exists( #81, #5981 ), references = 1, size of lhs = 6:
% 233.82/234.06 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), P_powerset-{F}(V2,V3), element-{F}(V4,V3), pppp3-{F}(V5,V0,V4) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #5986: disj( #6, #1245+#5982 ), references = 1, size of lhs = 10:
% 233.82/234.06 empty-{F}(V0), P_powerset-{F}(V0,V1), P_powerset-{F}(V1,V2), P_empty_set-{F}(V3), empty-{F}(V4), P_powerset-{F}(V4,V5), P_powerset-{F}(V5,V6), element-{F}(V7,V2), element-{F}(V7,V6), P_relation_dom-{F}(V8,V7) | pppp0-{T}(V8)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #6050: mergings( V3 == V5; #6048 ), references = 3, size of lhs = 10:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), pppp0-{F}(V0), relation-{F}(V1), function-{F}(V1), pppp0-{F}(V1), pppp13-{F}(V1,V0), P_relation_dom-{F}(V0,V2), P_empty_set-{F}(V3), P_relation_dom-{F}(V1,V4) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #6084: disj( #6, mergings( V10 == V13, V3 == V11; #5954 ) ), references = 1, size of lhs = 21:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), pppp0-{F}(V2), relation-{F}(V3), function-{F}(V3), pppp0-{F}(V3), P_relation_composition-{F}(V3,V0,V4), P_relation_dom-{F}(V4,V5), P_relation_composition-{F}(V3,V2,V6), P_relation_dom-{F}(V6,V5), P_relation_composition-{F}(V3,V1,V7), P_relation_dom-{F}(V7,V5), P_relation_dom-{F}(V2,V8), P_relation_dom-{F}(V1,V8), P_relation_dom-{F}(V0,V8), P_empty_set-{F}(V9), P_relation_dom-{F}(V3,V10) | pppp0-{T}(V6)
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #6088: mergings( V7 == V10; #6086 ), references = 1, size of lhs = 25:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), relation-{F}(V2), function-{F}(V2), pppp0-{F}(V2), relation-{F}(V3), function-{F}(V3), pppp0-{F}(V3), P_relation_composition-{F}(V3,V0,V4), P_relation_composition-{F}(V3,V2,V4), relation-{F}(V4), function-{F}(V4), P_relation_composition-{F}(V3,V1,V4), P_relation_dom-{F}(V2,V5), P_relation_dom-{F}(V1,V5), P_relation_dom-{F}(V0,V5), P_relation_dom-{F}(V3,V6), relation-{F}(V7), function-{F}(V7), pppp0-{F}(V7), pppp13-{F}(V7,V4), P_empty_set-{F}(V8), P_relation_dom-{F}(V7,V9) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #6108: mergings( V3 == V0; #6106 ), references = 1, size of lhs = 7:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), pppp0-{F}(V0), pppp13-{F}(V0,V1), P_relation_dom-{F}(V1,V2), P_empty_set-{F}(V3), P_relation_dom-{F}(V0,V4) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #6111: mergings( V2 == V3; #6109 ), references = 1, size of lhs = 6:
% 233.82/234.06 relation-{F}(V0), function-{F}(V0), pppp0-{F}(V0), pppp13-{F}(V0,V1), P_empty_set-{F}(V2), P_relation_dom-{F}(V0,V3) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #6113: exists( #67, #6109 ), references = 1, size of lhs = 6:
% 233.82/234.06 pppp14-{F}(V0), relation-{F}(V0), function-{F}(V0), pppp0-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V0,V2) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #6115: exists( #80, #6112 ), references = 2, size of lhs = 5:
% 233.82/234.06 pppp14-{F}(V0), relation-{F}(V0), function-{F}(V0), pppp0-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #6125: mergings( V0 == V2; #6123 ), references = 1, size of lhs = 1:
% 233.82/234.06 P_empty_set-{F}(V0) | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 #6127: exists( #83, #6123 ), references = 1, size of lhs = 0:
% 233.82/234.06 FALSE | FALSE
% 233.82/234.06 (used 0 times, uses = {})
% 233.82/234.06
% 233.82/234.06 number of learnt formulas = 136
% 233.82/234.06
% 233.82/234.06
% 233.82/234.06 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 233.82/234.06
% 233.82/234.06 randbase = 1
%------------------------------------------------------------------------------