TSTP Solution File: SEU030+1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : SEU030+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n019.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 06:17:06 EDT 2022
% Result : Theorem 4.00s 4.14s
% Output : Refutation 4.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU030+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Jul 22 18:36:07 EDT 2022
% 0.14/0.34 % CPUTime :
% 4.00/4.14 GeoParameters:
% 4.00/4.14
% 4.00/4.14 tptp_input = 1
% 4.00/4.14 tptp_output = 0
% 4.00/4.14 nonempty = 1
% 4.00/4.14 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.00/4.14 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 4.00/4.14
% 4.00/4.14
% 4.00/4.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.00/4.14 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.00/4.14
% 4.00/4.14 RuleSystem INPUT:
% 4.00/4.14
% 4.00/4.14 Initial Rules:
% 4.00/4.14 #0: input, references = 3, size of lhs = 2:
% 4.00/4.14 in-{F}(V0,V1), in-{F}(V1,V0) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #1: input, references = 3, size of lhs = 1:
% 4.00/4.14 empty-{F}(V0) | function-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #2: input, references = 3, size of lhs = 1:
% 4.00/4.14 empty-{F}(V0) | relation-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #3: input, references = 3, size of lhs = 3:
% 4.00/4.14 relation-{F}(V0), empty-{F}(V0), function-{F}(V0) | one_to_one-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #4: input, references = 7, size of lhs = 3:
% 4.00/4.14 P_function_inverse-{F}(V0,V1), relation-{F}(V0), function-{F}(V0) | relation-{T}(V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #5: input, references = 5, size of lhs = 3:
% 4.00/4.14 P_function_inverse-{F}(V0,V1), relation-{F}(V0), function-{F}(V0) | function-{T}(V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #6: input, references = 3, size of lhs = 3:
% 4.00/4.14 relation-{F}(V0), P_relation_composition-{F}(V1,V0,V2), relation-{F}(V1) | relation-{T}(V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #7: input, references = 3, size of lhs = 1:
% 4.00/4.14 P_identity_relation-{F}(V0,V1) | relation-{T}(V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #8: input, references = 5, size of lhs = 1:
% 4.00/4.14 #-{F} V0 | EXISTS V1: pppp0-{T}(V0,V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #9: input, references = 5, size of lhs = 1:
% 4.00/4.14 pppp0-{F}(V0,V1) | element-{T}(V1,V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #10: input, references = 5, size of lhs = 3:
% 4.00/4.14 relation-{F}(V0), P_relation_composition-{F}(V0,V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #11: input, references = 3, size of lhs = 3:
% 4.00/4.14 relation-{F}(V0), P_relation_composition-{F}(V0,V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #12: input, references = 3, size of lhs = 1:
% 4.00/4.14 P_empty_set-{F}(V0) | empty-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #13: input, references = 3, size of lhs = 1:
% 4.00/4.14 P_empty_set-{F}(V0) | relation-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #14: input, references = 3, size of lhs = 1:
% 4.00/4.14 P_empty_set-{F}(V0) | relation_empty_yielding-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #15: input, references = 3, size of lhs = 6:
% 4.00/4.14 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)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #16: input, references = 3, size of lhs = 6:
% 4.00/4.14 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)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #17: input, references = 3, size of lhs = 3:
% 4.00/4.14 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), empty-{F}(V2) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #18: input, references = 3, size of lhs = 1:
% 4.00/4.14 P_empty_set-{F}(V0) | empty-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #19: input, references = 3, size of lhs = 2:
% 4.00/4.14 P_empty_set-{F}(V0), P_identity_relation-{F}(V1,V2) | relation-{T}(V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #20: input, references = 3, size of lhs = 2:
% 4.00/4.14 P_empty_set-{F}(V0), P_identity_relation-{F}(V1,V2) | function-{T}(V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #21: input, references = 3, size of lhs = 1:
% 4.00/4.14 P_empty_set-{F}(V0) | empty-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #22: input, references = 3, size of lhs = 1:
% 4.00/4.14 P_empty_set-{F}(V0) | relation-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #23: input, references = 5, size of lhs = 4:
% 4.00/4.14 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), relation-{F}(V1), empty-{F}(V2) | empty-{T}(V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #24: input, references = 3, size of lhs = 4:
% 4.00/4.14 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), relation-{F}(V1), empty-{F}(V2) | empty-{T}(V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #25: input, references = 5, size of lhs = 3:
% 4.00/4.14 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #26: input, references = 3, size of lhs = 3:
% 4.00/4.14 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #27: input, references = 5, size of lhs = 3:
% 4.00/4.14 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #28: input, references = 3, size of lhs = 3:
% 4.00/4.14 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #29: input, references = 4, size of lhs = 4:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V2,V1,V3), empty-{F}(V2) | empty-{T}(V3)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #30: input, references = 3, size of lhs = 4:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V2,V1,V3), empty-{F}(V2) | relation-{T}(V3)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #31: input, references = 5, size of lhs = 14:
% 4.00/4.14 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V9), relation-{F}(V1), function-{F}(V1), P_relation_composition-{F}(V1,V3,V7), relation-{F}(V3), function-{F}(V3), P_relation_dom-{F}(V5,V6), P_identity_relation-{F}(V6,V7), P_relation_composition-{F}(V3,V5,V10), relation-{F}(V5), function-{F}(V5), P_identity_relation-{F}(V9,V10), V5 == V1 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #32: input, references = 3, size of lhs = 1:
% 4.00/4.14 P_empty_set-{F}(V0) | EXISTS V1: pppp1-{T}(V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #33: input, references = 3, size of lhs = 1:
% 4.00/4.14 pppp1-{F}(V0) | function-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #34: input, references = 3, size of lhs = 1:
% 4.00/4.14 pppp1-{F}(V0) | relation-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #35: input, references = 4, size of lhs = 1:
% 4.00/4.14 P_empty_set-{F}(V0) | EXISTS V1: pppp2-{T}(V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #36: input, references = 3, size of lhs = 1:
% 4.00/4.14 pppp2-{F}(V0) | relation-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #37: input, references = 5, size of lhs = 1:
% 4.00/4.14 pppp2-{F}(V0) | empty-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #38: input, references = 4, size of lhs = 2:
% 4.00/4.14 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2) | empty-{T}(V1), pppp14-{T}(V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #39: input, references = 3, size of lhs = 1:
% 4.00/4.14 pppp14-{F}(V0) | EXISTS V1: pppp3-{T}(V1,V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #40: input, references = 3, size of lhs = 2:
% 4.00/4.14 pppp3-{F}(V0,V1), empty-{F}(V0) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #41: input, references = 3, size of lhs = 1:
% 4.00/4.14 pppp3-{F}(V0,V1) | element-{T}(V0,V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #42: input, references = 4, size of lhs = 1:
% 4.00/4.14 P_empty_set-{F}(V0) | EXISTS V1: pppp4-{T}(V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #43: input, references = 5, size of lhs = 1:
% 4.00/4.14 pppp4-{F}(V0) | empty-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #44: input, references = 4, size of lhs = 1:
% 4.00/4.14 P_empty_set-{F}(V0) | EXISTS V1: pppp5-{T}(V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #45: input, references = 3, size of lhs = 1:
% 4.00/4.14 pppp5-{F}(V0) | function-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #46: input, references = 5, size of lhs = 1:
% 4.00/4.14 pppp5-{F}(V0) | empty-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #47: input, references = 3, size of lhs = 1:
% 4.00/4.14 pppp5-{F}(V0) | relation-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #48: input, references = 3, size of lhs = 1:
% 4.00/4.14 P_empty_set-{F}(V0) | EXISTS V1: pppp6-{T}(V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #49: input, references = 3, size of lhs = 1:
% 4.00/4.14 pppp6-{F}(V0) | relation-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #50: input, references = 3, size of lhs = 2:
% 4.00/4.14 pppp6-{F}(V0), empty-{F}(V0) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #51: input, references = 4, size of lhs = 2:
% 4.00/4.14 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2) | EXISTS V3: pppp7-{T}(V3,V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #52: input, references = 5, size of lhs = 1:
% 4.00/4.14 pppp7-{F}(V0,V1) | empty-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #53: input, references = 3, size of lhs = 1:
% 4.00/4.14 pppp7-{F}(V0,V1) | element-{T}(V0,V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #54: input, references = 3, size of lhs = 1:
% 4.00/4.14 P_empty_set-{F}(V0) | EXISTS V1: pppp8-{T}(V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #55: input, references = 3, size of lhs = 2:
% 4.00/4.14 pppp8-{F}(V0), empty-{F}(V0) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #56: input, references = 3, size of lhs = 1:
% 4.00/4.14 P_empty_set-{F}(V0) | EXISTS V1: pppp9-{T}(V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #57: input, references = 3, size of lhs = 1:
% 4.00/4.14 pppp9-{F}(V0) | one_to_one-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #58: input, references = 3, size of lhs = 1:
% 4.00/4.14 pppp9-{F}(V0) | function-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #59: input, references = 3, size of lhs = 1:
% 4.00/4.14 pppp9-{F}(V0) | relation-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #60: input, references = 3, size of lhs = 1:
% 4.00/4.14 P_empty_set-{F}(V0) | EXISTS V1: pppp10-{T}(V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #61: input, references = 3, size of lhs = 1:
% 4.00/4.14 pppp10-{F}(V0) | relation_empty_yielding-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #62: input, references = 3, size of lhs = 1:
% 4.00/4.14 pppp10-{F}(V0) | relation-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #63: input, references = 3, size of lhs = 2:
% 4.00/4.14 P_empty_set-{F}(V0), #-{F} V1 | subset-{T}(V1,V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #64: input, references = 3, size of lhs = 2:
% 4.00/4.14 P_empty_set-{F}(V0), in-{F}(V1,V2) | element-{T}(V1,V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #65: input, references = 4, size of lhs = 2:
% 4.00/4.14 P_empty_set-{F}(V0), element-{F}(V2,V1) | empty-{T}(V1), in-{T}(V2,V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #66: input, references = 3, size of lhs = 3:
% 4.00/4.14 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), element-{F}(V1,V3) | subset-{T}(V1,V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #67: input, references = 3, size of lhs = 3:
% 4.00/4.14 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), subset-{F}(V1,V2) | element-{T}(V1,V3)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #68: input, references = 3, size of lhs = 4:
% 4.00/4.14 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), element-{F}(V1,V3), in-{F}(V4,V1) | element-{T}(V4,V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #69: input, references = 6, size of lhs = 10:
% 4.00/4.14 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), P_function_inverse-{F}(V1,V3), P_relation_dom-{F}(V3,V4), P_relation_dom-{F}(V1,V5), P_relation_rng-{F}(V3,V6), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), V2 == V4 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #70: input, references = 6, size of lhs = 10:
% 4.00/4.14 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), P_function_inverse-{F}(V1,V3), P_relation_dom-{F}(V3,V4), P_relation_dom-{F}(V1,V5), P_relation_rng-{F}(V3,V6), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), V5 == V6 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #71: input, references = 4, size of lhs = 5:
% 4.00/4.14 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), empty-{F}(V1), element-{F}(V3,V2), in-{F}(V4,V3) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #72: input, references = 6, size of lhs = 12:
% 4.00/4.14 P_empty_set-{F}(V0), P_function_inverse-{F}(V1,V2), P_relation_composition-{F}(V1,V2,V3), P_relation_dom-{F}(V1,V4), P_identity_relation-{F}(V4,V5), P_relation_composition-{F}(V2,V1,V6), P_relation_rng-{F}(V1,V7), P_identity_relation-{F}(V7,V8), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), V3 == V5 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #73: input, references = 7, size of lhs = 12:
% 4.00/4.14 P_empty_set-{F}(V0), P_function_inverse-{F}(V1,V2), P_relation_composition-{F}(V1,V2,V3), P_relation_dom-{F}(V1,V4), P_identity_relation-{F}(V4,V5), P_relation_composition-{F}(V2,V1,V6), P_relation_rng-{F}(V1,V7), P_identity_relation-{F}(V7,V8), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), V6 == V8 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #74: input, references = 4, size of lhs = 1:
% 4.00/4.14 P_empty_set-{F}(V0) | EXISTS V1: pppp13-{T}(V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #75: input, references = 4, size of lhs = 5:
% 4.00/4.14 pppp13-{F}(V0), P_relation_rng-{F}(V0,V1), P_relation_dom-{F}(V0,V2), P_identity_relation-{F}(V2,V3), P_function_inverse-{F}(V0,V4) | EXISTS V5: pppp12-{T}(V0,V1,V3,V4,V5)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #76: input, references = 9, size of lhs = 5:
% 4.00/4.14 pppp13-{F}(V0), P_relation_rng-{F}(V0,V1), P_relation_dom-{F}(V0,V2), P_identity_relation-{F}(V2,V3), P_function_inverse-{F}(V0,V4) | one_to_one-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #77: input, references = 4, size of lhs = 5:
% 4.00/4.14 pppp13-{F}(V0), P_relation_rng-{F}(V0,V1), P_relation_dom-{F}(V0,V2), P_identity_relation-{F}(V2,V3), P_function_inverse-{F}(V0,V4) | function-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #78: input, references = 4, size of lhs = 5:
% 4.00/4.14 pppp13-{F}(V0), P_relation_rng-{F}(V0,V1), P_relation_dom-{F}(V0,V2), P_identity_relation-{F}(V2,V3), P_function_inverse-{F}(V0,V4) | relation-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #79: input, references = 8, size of lhs = 3:
% 4.00/4.14 pppp12-{F}(V0,V1,V2,V3,V4), P_relation_dom-{F}(V4,V5), P_relation_composition-{F}(V0,V4,V6) | pppp11-{T}(V4,V1,V5,V6,V2,V3)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #80: input, references = 4, size of lhs = 1:
% 4.00/4.14 pppp11-{F}(V5,V1,V2,V3,V4,V5) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #81: input, references = 4, size of lhs = 2:
% 4.00/4.14 pppp11-{F}(V0,V1,V2,V3,V4,V5), V3 == V4 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #82: input, references = 4, size of lhs = 2:
% 4.00/4.14 pppp11-{F}(V0,V1,V2,V3,V4,V5), V1 == V2 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #83: input, references = 5, size of lhs = 1:
% 4.00/4.14 pppp11-{F}(V0,V1,V2,V3,V4,V5) | function-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #84: input, references = 5, size of lhs = 1:
% 4.00/4.14 pppp11-{F}(V0,V1,V2,V3,V4,V5) | relation-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #85: input, references = 12, size of lhs = 3:
% 4.00/4.14 P_empty_set-{F}(V0), empty-{F}(V1), V1 == V0 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #86: input, references = 3, size of lhs = 3:
% 4.00/4.14 P_empty_set-{F}(V0), empty-{F}(V1), in-{F}(V2,V1) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #87: input, references = 11, size of lhs = 4:
% 4.00/4.14 P_empty_set-{F}(V0), empty-{F}(V1), empty-{F}(V2), V2 == V1 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #88: input, references = 7, size of lhs = 1:
% 4.00/4.14 #-{F} V0 | EXISTS V1: P_function_inverse-{T}(V0,V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #89: input, references = 11, size of lhs = 2:
% 4.00/4.14 #-{F} V0, #-{F} V1 | EXISTS V2: P_relation_composition-{T}(V0,V1,V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #90: input, references = 10, size of lhs = 1:
% 4.00/4.14 #-{F} V0 | EXISTS V1: P_identity_relation-{T}(V0,V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #91: input, references = 4, size of lhs = 0:
% 4.00/4.14 FALSE | EXISTS V0: P_empty_set-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #92: input, references = 3, size of lhs = 1:
% 4.00/4.14 #-{F} V0 | EXISTS V1: P_powerset-{T}(V0,V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #93: input, references = 9, size of lhs = 1:
% 4.00/4.14 #-{F} V0 | EXISTS V1: P_relation_dom-{T}(V0,V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #94: input, references = 13, size of lhs = 1:
% 4.00/4.14 #-{F} V0 | EXISTS V1: P_relation_rng-{T}(V0,V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 number of initial rules = 95
% 4.00/4.14
% 4.00/4.14 Simplifiers:
% 4.00/4.14 #95: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 P_function_inverse-{F}(V0,V1), P_function_inverse-{F}(V0,V3), V1 == V3 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #96: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 P_relation_composition-{F}(V0,V1,V2), P_relation_composition-{F}(V0,V1,V5), V2 == V5 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #97: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 P_identity_relation-{F}(V0,V1), P_identity_relation-{F}(V0,V3), V1 == V3 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #98: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 P_empty_set-{F}(V0), P_empty_set-{F}(V1), V0 == V1 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #99: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 P_powerset-{F}(V0,V1), P_powerset-{F}(V0,V3), V1 == V3 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #100: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 P_relation_dom-{F}(V0,V1), P_relation_dom-{F}(V0,V3), V1 == V3 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #101: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 P_relation_rng-{F}(V0,V1), P_relation_rng-{F}(V0,V3), V1 == V3 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #102: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 pppp0-{F}(V0,V1), pppp0-{F}(V0,V3), V1 == V3 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #103: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 pppp1-{F}(V0), pppp1-{F}(V1), V0 == V1 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #104: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 pppp2-{F}(V0), pppp2-{F}(V1), V0 == V1 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #105: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 pppp3-{F}(V0,V1), pppp3-{F}(V2,V1), V0 == V2 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #106: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 pppp4-{F}(V0), pppp4-{F}(V1), V0 == V1 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #107: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 pppp5-{F}(V0), pppp5-{F}(V1), V0 == V1 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #108: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 pppp6-{F}(V0), pppp6-{F}(V1), V0 == V1 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #109: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 pppp7-{F}(V0,V1), pppp7-{F}(V2,V1), V0 == V2 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #110: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 pppp8-{F}(V0), pppp8-{F}(V1), V0 == V1 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #111: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 pppp9-{F}(V0), pppp9-{F}(V1), V0 == V1 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #112: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 pppp10-{F}(V0), pppp10-{F}(V1), V0 == V1 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #113: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 pppp11-{F}(V0,V1,V2,V3,V4,V5), pppp11-{F}(V0,V7,V8,V9,V10,V11), V2 == V8 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #114: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V1,V2,V3,V9), V4 == V9 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #115: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V5,V6,V7,V8,V9), V0 == V5 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #116: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V6,V7,V8,V9), V1 == V6 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #117: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V6,V7,V8,V9), V3 == V8 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #118: unsound, references = 3, size of lhs = 3:
% 4.00/4.14 pppp13-{F}(V0), pppp13-{F}(V1), V0 == V1 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 number of simplifiers = 24
% 4.00/4.14
% 4.00/4.14 Learnt:
% 4.00/4.14 #124: mergings( V0 == V2; #121 ), references = 1, size of lhs = 1:
% 4.00/4.14 P_empty_set-{F}(V0) | pppp5-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #126: mergings( V0 == V2; #122 ), references = 1, size of lhs = 2:
% 4.00/4.14 P_empty_set-{F}(V0), empty-{F}(V1) | pppp5-{T}(V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #134: mergings( V0 == V2; #131 ), references = 1, size of lhs = 1:
% 4.00/4.14 P_empty_set-{F}(V0) | pppp2-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #136: mergings( V0 == V2; #132 ), references = 1, size of lhs = 2:
% 4.00/4.14 P_empty_set-{F}(V0), empty-{F}(V1) | pppp2-{T}(V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #149: mergings( V0 == V2; #146 ), references = 1, size of lhs = 1:
% 4.00/4.14 P_empty_set-{F}(V0) | pppp4-{T}(V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #151: mergings( V0 == V2; #147 ), references = 1, size of lhs = 2:
% 4.00/4.14 P_empty_set-{F}(V0), empty-{F}(V1) | pppp4-{T}(V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #160: mergings( V2 == V3; #157 ), references = 1, size of lhs = 2:
% 4.00/4.14 empty-{F}(V0), P_empty_set-{F}(V1) | P_relation_dom-{T}(V0,V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #162: mergings( V2 == V3; #158 ), references = 1, size of lhs = 3:
% 4.00/4.14 empty-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2) | P_relation_dom-{T}(V0,V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #168: exists( #94, #69 ), references = 9, size of lhs = 9:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_relation_rng-{F}(V1,V2), P_function_inverse-{F}(V1,V3), P_relation_dom-{F}(V3,V4), V2 == V4, P_relation_dom-{F}(V1,V5) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #175: mergings( V0 == V3; #171 ), references = 2, size of lhs = 3:
% 4.00/4.14 P_empty_set-{F}(V0), element-{F}(V1,V2), V2 == V0 | in-{T}(V1,V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #178: mergings( V0 == V3, V2 == V3; #172 ), references = 1, size of lhs = 4:
% 4.00/4.14 P_empty_set-{F}(V0), empty-{F}(V1), V0 == V1, element-{F}(V2,V0) | in-{T}(V2,V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #181: mergings( V0 == V3, V2 == V3; #173 ), references = 1, size of lhs = 3:
% 4.00/4.14 P_empty_set-{F}(V0), element-{F}(V1,V0), P_powerset-{F}(V2,V0) | in-{T}(V1,V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #190: exists( #94, #168 ), references = 1, size of lhs = 7:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V1,V2), P_relation_dom-{F}(V2,V3), P_relation_dom-{F}(V1,V4) | P_relation_rng-{T}(V1,V3)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #192: mergings( V3 == V4; #188 ), references = 1, size of lhs = 6:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), P_function_inverse-{F}(V1,V1), function-{F}(V1), one_to_one-{F}(V1), P_relation_dom-{F}(V1,V2) | P_relation_rng-{T}(V1,V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #198: exists( #89, #193 ), references = 1, size of lhs = 3:
% 4.00/4.14 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2) | P_relation_composition-{T}(V0,V1,V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #199: exists( #89, #194 ), references = 1, size of lhs = 4:
% 4.00/4.14 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3) | P_relation_composition-{T}(V0,V1,V3)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #213: mergings( V2 == V3; #210 ), references = 1, size of lhs = 2:
% 4.00/4.14 empty-{F}(V0), P_empty_set-{F}(V1) | P_relation_rng-{T}(V0,V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #215: mergings( V2 == V3; #211 ), references = 1, size of lhs = 3:
% 4.00/4.14 empty-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2) | P_relation_rng-{T}(V0,V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #236: mergings( V2 == V3; #234 ), references = 2, size of lhs = 5:
% 4.00/4.14 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), element-{F}(V3,V2), V3 == V0 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #240: exists( #8, #238 ), references = 1, size of lhs = 3:
% 4.00/4.14 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2) | pppp0-{T}(V2,V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #251: exists( #94, #70 ), references = 1, size of lhs = 8:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_relation_rng-{F}(V1,V2), P_function_inverse-{F}(V1,V3), P_relation_dom-{F}(V3,V4), P_relation_dom-{F}(V1,V5) | P_relation_rng-{T}(V3,V5)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #252: exists( #94, #168 ), references = 1, size of lhs = 7:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V1,V2), P_relation_dom-{F}(V2,V3), P_relation_dom-{F}(V1,V4) | P_relation_rng-{T}(V1,V3)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #253: exists( #94, #69 ), references = 1, size of lhs = 8:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V1,V2), P_relation_dom-{F}(V2,V3), P_relation_dom-{F}(V1,V4), P_relation_rng-{F}(V2,V5) | P_relation_rng-{T}(V1,V3)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #258: exists( #93, #168 ), references = 6, size of lhs = 7:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_relation_rng-{F}(V1,V2), P_function_inverse-{F}(V1,V3), P_relation_dom-{F}(V1,V4) | P_relation_dom-{T}(V3,V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #275: mergings( V2 == V5, V5 == V6; #271 ), references = 1, size of lhs = 7:
% 4.00/4.14 relation-{F}(V0), function-{F}(V0), one_to_one-{F}(V0), P_relation_rng-{F}(V0,V1), empty-{F}(V1), P_relation_dom-{F}(V0,V2), P_empty_set-{F}(V3) | P_function_inverse-{T}(V0,V3)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #278: mergings( V2 == V5, V5 == V6; #272 ), references = 1, size of lhs = 8:
% 4.00/4.14 relation-{F}(V0), function-{F}(V0), one_to_one-{F}(V0), P_relation_rng-{F}(V0,V1), empty-{F}(V1), P_relation_dom-{F}(V0,V2), P_empty_set-{F}(V3), empty-{F}(V4) | P_function_inverse-{T}(V0,V4)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #293: exists( #90, #72 ), references = 1, size of lhs = 9:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V1,V2), P_relation_composition-{F}(V1,V2,V3), P_relation_dom-{F}(V1,V4), P_relation_rng-{F}(V1,V4), P_relation_composition-{F}(V2,V1,V5) | P_identity_relation-{T}(V4,V3)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #294: exists( #90, #73 ), references = 1, size of lhs = 9:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V1,V2), P_relation_composition-{F}(V1,V2,V3), P_relation_dom-{F}(V1,V4), P_relation_rng-{F}(V1,V4), P_relation_composition-{F}(V2,V1,V5) | P_identity_relation-{T}(V4,V5)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #316: mergings( V3 == V4; #314 ), references = 1, size of lhs = 3:
% 4.00/4.14 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2) | P_relation_composition-{T}(V1,V0,V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #325: exists( #89, #72 ), references = 1, size of lhs = 9:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), P_function_inverse-{F}(V1,V1), function-{F}(V1), one_to_one-{F}(V1), P_relation_dom-{F}(V1,V2), P_identity_relation-{F}(V2,V3), P_relation_rng-{F}(V1,V4), P_identity_relation-{F}(V4,V5) | P_relation_composition-{T}(V1,V1,V3)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #326: exists( #89, #73 ), references = 1, size of lhs = 9:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), P_function_inverse-{F}(V1,V1), function-{F}(V1), one_to_one-{F}(V1), P_relation_dom-{F}(V1,V2), P_identity_relation-{F}(V2,V3), P_relation_rng-{F}(V1,V4), P_identity_relation-{F}(V4,V5) | P_relation_composition-{T}(V1,V1,V5)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #337: mergings( V0 == V3; #333 ), references = 1, size of lhs = 3:
% 4.00/4.14 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), V1 == V0 | pppp14-{T}(V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #340: mergings( V0 == V3, V1 == V3; #334 ), references = 1, size of lhs = 4:
% 4.00/4.14 P_empty_set-{F}(V0), empty-{F}(V1), V0 == V1, P_powerset-{F}(V0,V2) | pppp14-{T}(V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #344: mergings( V0 == V3, V2 == V4, V1 == V3; #335 ), references = 1, size of lhs = 4:
% 4.00/4.14 P_empty_set-{F}(V0), P_powerset-{F}(V0,V1), element-{F}(V2,V1), V2 == V0 | pppp14-{T}(V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #378: exists( #94, #70 ), references = 5, size of lhs = 9:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V1,V2), P_relation_dom-{F}(V2,V3), P_relation_dom-{F}(V1,V4), P_relation_rng-{F}(V2,V5), V4 == V5 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #379: exists( #94, #168 ), references = 1, size of lhs = 7:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V1,V2), P_relation_dom-{F}(V2,V3), P_relation_dom-{F}(V1,V4) | P_relation_rng-{T}(V1,V3)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #381: exists( #93, #376 ), references = 1, size of lhs = 7:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V1,V2), P_relation_dom-{F}(V2,V3), P_relation_rng-{F}(V2,V4) | P_relation_dom-{T}(V1,V4)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #392: exists( #94, #168 ), references = 1, size of lhs = 7:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V1,V2), P_relation_dom-{F}(V2,V3), P_relation_dom-{F}(V1,V4) | P_relation_rng-{T}(V1,V3)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #393: exists( #94, #378 ), references = 4, size of lhs = 7:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V1,V2), P_relation_dom-{F}(V2,V3), P_relation_dom-{F}(V1,V4) | P_relation_rng-{T}(V2,V4)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #405: exists( #94, #168 ), references = 1, size of lhs = 7:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V1,V2), P_relation_dom-{F}(V2,V3), P_relation_dom-{F}(V1,V4) | P_relation_rng-{T}(V1,V3)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #406: exists( #94, #378 ), references = 1, size of lhs = 7:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V1,V2), P_relation_dom-{F}(V2,V3), P_relation_dom-{F}(V1,V4) | P_relation_rng-{T}(V2,V4)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #413: mergings( V0 == V4; #410 ), references = 1, size of lhs = 2:
% 4.00/4.14 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2) | pppp7-{T}(V0,V2)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #415: mergings( V0 == V4; #411 ), references = 1, size of lhs = 3:
% 4.00/4.14 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V2,V3) | pppp7-{T}(V1,V3)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #436: exists( #89, #73 ), references = 5, size of lhs = 10:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V1,V2), P_relation_composition-{F}(V1,V2,V3), P_relation_dom-{F}(V1,V4), P_identity_relation-{F}(V4,V5), P_relation_rng-{F}(V1,V6), P_identity_relation-{F}(V6,V7) | P_relation_composition-{T}(V2,V1,V7)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #440: mergings( V3 == V8; #438 ), references = 3, size of lhs = 19:
% 4.00/4.14 one_to_one-{F}(V0), relation-{F}(V0), function-{F}(V0), P_function_inverse-{F}(V0,V1), relation-{F}(V1), function-{F}(V1), P_relation_dom-{F}(V0,V2), P_identity_relation-{F}(V2,V3), P_relation_rng-{F}(V0,V4), P_identity_relation-{F}(V4,V5), P_empty_set-{F}(V6), P_relation_rng-{F}(V1,V7), relation-{F}(V8), V8 == V1, function-{F}(V8), P_relation_dom-{F}(V8,V9), P_identity_relation-{F}(V9,V5), P_relation_composition-{F}(V0,V8,V10), P_identity_relation-{F}(V7,V10) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #461: mergings( V3 == V13, V4 == V15, V5 == V12; #457 ), references = 1, size of lhs = 22:
% 4.00/4.14 one_to_one-{F}(V0), relation-{F}(V0), function-{F}(V0), P_function_inverse-{F}(V0,V1), one_to_one-{F}(V1), relation-{F}(V1), function-{F}(V1), P_relation_rng-{F}(V0,V2), P_identity_relation-{F}(V2,V3), P_function_inverse-{F}(V1,V4), V0 == V4, relation-{F}(V4), function-{F}(V4), P_relation_dom-{F}(V1,V5), P_identity_relation-{F}(V5,V6), P_relation_rng-{F}(V1,V7), P_identity_relation-{F}(V7,V8), P_empty_set-{F}(V9), P_relation_rng-{F}(V4,V10), P_identity_relation-{F}(V10,V3), P_relation_dom-{F}(V0,V11), P_identity_relation-{F}(V11,V8) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #478: mergings( V4 == V7, V15 == V16, V5 == V9, V9 == V10, V10 == V12, V12 == V13, V13 == V17, V8 == V0, V3 == V6, V6 == V14; #467 ), references = 2, size of lhs = 15:
% 4.00/4.14 pppp13-{F}(V0), relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V0,V1), relation-{F}(V2), V0 == V2, function-{F}(V2), P_function_inverse-{F}(V1,V2), P_relation_rng-{F}(V0,V3), P_identity_relation-{F}(V3,V4), P_empty_set-{F}(V5), P_relation_dom-{F}(V0,V6) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #482: exists( #88, #480 ), references = 1, size of lhs = 11:
% 4.00/4.14 pppp13-{F}(V0), relation-{F}(V0), function-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V0,V1), P_relation_rng-{F}(V0,V2), P_identity_relation-{F}(V2,V3), P_empty_set-{F}(V4), P_relation_dom-{F}(V0,V5) | P_function_inverse-{T}(V1,V0)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #504: mergings( V3 == V4, V5 == V9, V6 == V10, V7 == V11, V8 == V12; #497 ), references = 1, size of lhs = 9:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V1,V2), P_relation_dom-{F}(V1,V3), P_identity_relation-{F}(V3,V4), P_relation_rng-{F}(V1,V5), P_identity_relation-{F}(V5,V6) | P_relation_composition-{T}(V1,V2,V4)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #506: mergings( V3 == V8; #498 ), references = 1, size of lhs = 17:
% 4.00/4.14 relation-{F}(V0), function-{F}(V0), one_to_one-{F}(V0), P_function_inverse-{F}(V0,V1), P_function_inverse-{F}(V1,V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_relation_dom-{F}(V0,V2), P_identity_relation-{F}(V2,V3), P_relation_rng-{F}(V0,V4), P_identity_relation-{F}(V4,V5), P_empty_set-{F}(V6), P_relation_dom-{F}(V1,V7), P_identity_relation-{F}(V7,V8), P_relation_rng-{F}(V1,V9), P_identity_relation-{F}(V9,V10) | P_relation_composition-{T}(V0,V1,V10)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #522: exists( #89, #520 ), references = 4, size of lhs = 2:
% 4.00/4.14 P_relation_dom-{F}(V0,V1), pppp12-{F}(V2,V3,V4,V5,V0) | P_relation_composition-{T}(V2,V0,V4)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #561: mergings( V3 == V6, V5 == V8; #558 ), references = 1, size of lhs = 2:
% 4.00/4.14 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V1,V5,V3,V4) | P_relation_dom-{T}(V4,V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #574: exists( #75, #570 ), references = 1, size of lhs = 14:
% 4.00/4.14 pppp13-{F}(V0), relation-{F}(V0), function-{F}(V0), P_relation_rng-{F}(V0,V1), P_relation_dom-{F}(V0,V2), P_identity_relation-{F}(V2,V3), P_function_inverse-{F}(V0,V4), P_empty_set-{F}(V5), relation-{F}(V6), function-{F}(V6), P_relation_rng-{F}(V6,V7), P_identity_relation-{F}(V7,V3), P_relation_composition-{F}(V6,V0,V8), P_identity_relation-{F}(V1,V8) | pppp12-{T}(V0,V1,V3,V4,V6)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #579: mergings( V4 == V6, V2 == V7, V3 == V8, V1 == V9; #573 ), references = 1, size of lhs = 14:
% 4.00/4.14 pppp13-{F}(V0), one_to_one-{F}(V0), relation-{F}(V0), function-{F}(V0), P_function_inverse-{F}(V0,V1), relation-{F}(V1), function-{F}(V1), P_relation_dom-{F}(V0,V2), P_identity_relation-{F}(V2,V3), P_relation_rng-{F}(V0,V4), P_identity_relation-{F}(V4,V5), P_empty_set-{F}(V6), P_relation_rng-{F}(V1,V7), P_identity_relation-{F}(V7,V3) | pppp12-{T}(V0,V4,V3,V1,V1)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #596: mergings( V7 == V15, V2 == V3, V3 == V4, V4 == V16, V6 == V8, V8 == V10, V9 == V11, V10 == V12, V11 == V13, V12 == V14; #585 ), references = 2, size of lhs = 12:
% 4.00/4.14 pppp13-{F}(V0), relation-{F}(V0), function-{F}(V0), P_relation_rng-{F}(V0,V1), P_identity_relation-{F}(V1,V2), P_relation_dom-{F}(V0,V3), P_function_inverse-{F}(V0,V4), relation-{F}(V4), function-{F}(V4), P_relation_rng-{F}(V4,V3), P_empty_set-{F}(V5), P_relation_dom-{F}(V4,V6) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #617: exists( #90, #596 ), references = 2, size of lhs = 11:
% 4.00/4.14 pppp13-{F}(V0), relation-{F}(V0), function-{F}(V0), P_relation_rng-{F}(V0,V1), P_relation_dom-{F}(V0,V2), P_function_inverse-{F}(V0,V3), relation-{F}(V3), function-{F}(V3), P_relation_rng-{F}(V3,V2), P_empty_set-{F}(V4), P_relation_dom-{F}(V3,V5) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #630: mergings( V4 == V6, V0 == V8; #625 ), references = 1, size of lhs = 10:
% 4.00/4.14 pppp13-{F}(V0), relation-{F}(V0), function-{F}(V0), P_relation_rng-{F}(V0,V1), P_empty_set-{F}(V2), P_function_inverse-{F}(V0,V3), P_relation_dom-{F}(V3,V4), P_relation_dom-{F}(V0,V5), P_relation_rng-{F}(V3,V6), V5 == V6 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #634: mergings( V4 == V7, V0 == V9, V3 == V6; #626 ), references = 1, size of lhs = 10:
% 4.00/4.14 pppp13-{F}(V0), relation-{F}(V0), function-{F}(V0), P_empty_set-{F}(V1), P_relation_rng-{F}(V0,V2), P_function_inverse-{F}(V0,V3), P_relation_dom-{F}(V3,V4), P_relation_dom-{F}(V0,V5), P_relation_rng-{F}(V3,V6), V5 == V6 | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #638: mergings( V4 == V7, V0 == V9, V3 == V6; #627 ), references = 1, size of lhs = 9:
% 4.00/4.14 pppp13-{F}(V0), relation-{F}(V0), function-{F}(V0), P_empty_set-{F}(V1), P_relation_rng-{F}(V0,V2), P_function_inverse-{F}(V0,V3), P_relation_dom-{F}(V3,V4), V2 == V4, P_relation_dom-{F}(V0,V5) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #656: mergings( V4 == V7, V5 == V9, V9 == V13, V0 == V8, V8 == V10, V3 == V6, V2 == V11, V6 == V12; #647 ), references = 1, size of lhs = 9:
% 4.00/4.14 relation-{F}(V0), function-{F}(V0), pppp13-{F}(V1), relation-{F}(V1), function-{F}(V1), P_function_inverse-{F}(V1,V0), P_relation_dom-{F}(V1,V2), P_relation_rng-{F}(V1,V3), P_empty_set-{F}(V4) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #663: mergings( V5 == V3, V4 == V7, V7 == V9, V2 == V6, V6 == V8; #657 ), references = 1, size of lhs = 8:
% 4.00/4.14 relation-{F}(V0), function-{F}(V0), pppp13-{F}(V1), relation-{F}(V1), function-{F}(V1), P_function_inverse-{F}(V1,V0), P_relation_dom-{F}(V1,V2), P_empty_set-{F}(V3) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #668: mergings( V3 == V5, V2 == V4, V4 == V6; #664 ), references = 2, size of lhs = 7:
% 4.00/4.14 relation-{F}(V0), function-{F}(V0), pppp13-{F}(V1), relation-{F}(V1), function-{F}(V1), P_function_inverse-{F}(V1,V0), P_empty_set-{F}(V2) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #672: exists( #88, #670 ), references = 2, size of lhs = 4:
% 4.00/4.14 pppp13-{F}(V0), relation-{F}(V0), function-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #684: exists( #94, #168 ), references = 1, size of lhs = 7:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V1,V2), P_relation_dom-{F}(V2,V3), P_relation_dom-{F}(V1,V4) | P_relation_rng-{T}(V1,V3)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #685: exists( #94, #378 ), references = 1, size of lhs = 7:
% 4.00/4.14 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_function_inverse-{F}(V1,V2), P_relation_dom-{F}(V2,V3), P_relation_dom-{F}(V1,V4) | P_relation_rng-{T}(V2,V4)
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #714: mergings( V4 == V7, V2 == V5, V3 == V6; #710 ), references = 2, size of lhs = 5:
% 4.00/4.14 pppp13-{F}(V0), P_relation_dom-{F}(V0,V1), P_identity_relation-{F}(V1,V2), P_function_inverse-{F}(V0,V3), P_empty_set-{F}(V4) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #723: exists( #90, #714 ), references = 1, size of lhs = 4:
% 4.00/4.14 pppp13-{F}(V0), P_relation_dom-{F}(V0,V1), P_function_inverse-{F}(V0,V2), P_empty_set-{F}(V3) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.14
% 4.00/4.14 #725: exists( #93, #722 ), references = 1, size of lhs = 3:
% 4.00/4.14 pppp13-{F}(V0), P_function_inverse-{F}(V0,V1), P_empty_set-{F}(V2) | FALSE
% 4.00/4.14 (used 0 times, uses = {})
% 4.00/4.15
% 4.00/4.15 #727: exists( #88, #724 ), references = 1, size of lhs = 2:
% 4.00/4.15 pppp13-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 4.00/4.15 (used 0 times, uses = {})
% 4.00/4.15
% 4.00/4.15 #730: mergings( V0 == V2; #728 ), references = 1, size of lhs = 1:
% 4.00/4.15 P_empty_set-{F}(V0) | FALSE
% 4.00/4.15 (used 0 times, uses = {})
% 4.00/4.15
% 4.00/4.15 #732: exists( #91, #728 ), references = 1, size of lhs = 0:
% 4.00/4.15 FALSE | FALSE
% 4.00/4.15 (used 0 times, uses = {})
% 4.00/4.15
% 4.00/4.15 number of learnt formulas = 71
% 4.00/4.15
% 4.00/4.15
% 4.00/4.15 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.00/4.15
% 4.00/4.15 randbase = 1
%------------------------------------------------------------------------------