TSTP Solution File: SEU032+1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : SEU032+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n007.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 1.59s 1.75s
% Output : Refutation 1.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU032+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n007.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 18:10:27 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.59/1.75 GeoParameters:
% 1.59/1.75
% 1.59/1.75 tptp_input = 1
% 1.59/1.75 tptp_output = 0
% 1.59/1.75 nonempty = 1
% 1.59/1.75 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.59/1.75 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 1.59/1.75
% 1.59/1.75
% 1.59/1.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.59/1.75 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.59/1.75
% 1.59/1.75 RuleSystem INPUT:
% 1.59/1.75
% 1.59/1.75 Initial Rules:
% 1.59/1.75 #0: input, references = 3, size of lhs = 2:
% 1.59/1.75 in-{F}(V0,V1), in-{F}(V1,V0) | FALSE
% 1.59/1.75 (used 0 times, uses = {})
% 1.59/1.75
% 1.59/1.75 #1: input, references = 3, size of lhs = 1:
% 1.59/1.75 empty-{F}(V0) | function-{T}(V0)
% 1.59/1.75 (used 0 times, uses = {})
% 1.59/1.75
% 1.59/1.75 #2: input, references = 3, size of lhs = 1:
% 1.59/1.75 empty-{F}(V0) | relation-{T}(V0)
% 1.59/1.75 (used 0 times, uses = {})
% 1.59/1.75
% 1.59/1.75 #3: input, references = 3, size of lhs = 3:
% 1.59/1.75 relation-{F}(V0), empty-{F}(V0), function-{F}(V0) | one_to_one-{T}(V0)
% 1.59/1.75 (used 0 times, uses = {})
% 1.59/1.75
% 1.59/1.75 #4: input, references = 6, size of lhs = 3:
% 1.59/1.75 P_function_inverse-{F}(V0,V1), relation-{F}(V0), function-{F}(V0) | relation-{T}(V1)
% 1.59/1.75 (used 0 times, uses = {})
% 1.59/1.75
% 1.59/1.75 #5: input, references = 4, size of lhs = 3:
% 1.59/1.75 P_function_inverse-{F}(V0,V1), relation-{F}(V0), function-{F}(V0) | function-{T}(V1)
% 1.59/1.75 (used 0 times, uses = {})
% 1.59/1.75
% 1.59/1.75 #6: input, references = 3, size of lhs = 3:
% 1.59/1.75 relation-{F}(V0), P_relation_composition-{F}(V1,V0,V2), relation-{F}(V1) | relation-{T}(V2)
% 1.59/1.75 (used 0 times, uses = {})
% 1.59/1.75
% 1.59/1.75 #7: input, references = 3, size of lhs = 1:
% 1.59/1.75 P_identity_relation-{F}(V0,V1) | relation-{T}(V1)
% 1.59/1.75 (used 0 times, uses = {})
% 1.59/1.75
% 1.59/1.75 #8: input, references = 5, size of lhs = 1:
% 1.59/1.75 #-{F} V0 | EXISTS V1: pppp0-{T}(V0,V1)
% 1.59/1.75 (used 0 times, uses = {})
% 1.59/1.75
% 1.59/1.75 #9: input, references = 5, size of lhs = 1:
% 1.59/1.75 pppp0-{F}(V0,V1) | element-{T}(V1,V0)
% 1.59/1.75 (used 0 times, uses = {})
% 1.59/1.75
% 1.59/1.75 #10: input, references = 5, size of lhs = 3:
% 1.59/1.75 relation-{F}(V0), P_relation_composition-{F}(V0,V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 1.59/1.75 (used 0 times, uses = {})
% 1.59/1.75
% 1.59/1.75 #11: input, references = 3, size of lhs = 3:
% 1.59/1.75 relation-{F}(V0), P_relation_composition-{F}(V0,V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 1.59/1.75 (used 0 times, uses = {})
% 1.59/1.75
% 1.59/1.75 #12: input, references = 3, size of lhs = 1:
% 1.59/1.75 P_empty_set-{F}(V0) | empty-{T}(V0)
% 1.59/1.75 (used 0 times, uses = {})
% 1.59/1.75
% 1.59/1.75 #13: input, references = 3, size of lhs = 1:
% 1.59/1.75 P_empty_set-{F}(V0) | relation-{T}(V0)
% 1.59/1.75 (used 0 times, uses = {})
% 1.59/1.75
% 1.59/1.75 #14: input, references = 3, size of lhs = 1:
% 1.59/1.75 P_empty_set-{F}(V0) | relation_empty_yielding-{T}(V0)
% 1.59/1.75 (used 0 times, uses = {})
% 1.59/1.75
% 1.59/1.75 #15: input, references = 3, size of lhs = 6:
% 1.59/1.75 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)
% 1.59/1.75 (used 0 times, uses = {})
% 1.59/1.75
% 1.59/1.75 #16: input, references = 3, size of lhs = 6:
% 1.59/1.75 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)
% 1.59/1.75 (used 0 times, uses = {})
% 1.59/1.75
% 1.59/1.75 #17: input, references = 3, size of lhs = 3:
% 1.59/1.75 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), empty-{F}(V2) | FALSE
% 1.59/1.75 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #18: input, references = 3, size of lhs = 1:
% 1.59/1.76 P_empty_set-{F}(V0) | empty-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #19: input, references = 3, size of lhs = 2:
% 1.59/1.76 P_empty_set-{F}(V0), P_identity_relation-{F}(V1,V2) | relation-{T}(V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #20: input, references = 3, size of lhs = 2:
% 1.59/1.76 P_empty_set-{F}(V0), P_identity_relation-{F}(V1,V2) | function-{T}(V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #21: input, references = 3, size of lhs = 1:
% 1.59/1.76 P_empty_set-{F}(V0) | empty-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #22: input, references = 3, size of lhs = 1:
% 1.59/1.76 P_empty_set-{F}(V0) | relation-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #23: input, references = 5, size of lhs = 4:
% 1.59/1.76 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), relation-{F}(V1), empty-{F}(V2) | empty-{T}(V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #24: input, references = 3, size of lhs = 4:
% 1.59/1.76 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), relation-{F}(V1), empty-{F}(V2) | empty-{T}(V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #25: input, references = 5, size of lhs = 3:
% 1.59/1.76 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #26: input, references = 3, size of lhs = 3:
% 1.59/1.76 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #27: input, references = 5, size of lhs = 3:
% 1.59/1.76 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #28: input, references = 3, size of lhs = 3:
% 1.59/1.76 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #29: input, references = 5, size of lhs = 4:
% 1.59/1.76 P_empty_set-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V2,V1,V3), empty-{F}(V2) | empty-{T}(V3)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #30: input, references = 3, size of lhs = 4:
% 1.59/1.76 P_empty_set-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V2,V1,V3), empty-{F}(V2) | relation-{T}(V3)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #31: input, references = 3, size of lhs = 1:
% 1.59/1.76 P_empty_set-{F}(V0) | EXISTS V1: pppp1-{T}(V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #32: input, references = 3, size of lhs = 1:
% 1.59/1.76 pppp1-{F}(V0) | function-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #33: input, references = 3, size of lhs = 1:
% 1.59/1.76 pppp1-{F}(V0) | relation-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #34: input, references = 4, size of lhs = 1:
% 1.59/1.76 P_empty_set-{F}(V0) | EXISTS V1: pppp2-{T}(V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #35: input, references = 3, size of lhs = 1:
% 1.59/1.76 pppp2-{F}(V0) | relation-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #36: input, references = 5, size of lhs = 1:
% 1.59/1.76 pppp2-{F}(V0) | empty-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #37: input, references = 4, size of lhs = 2:
% 1.59/1.76 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2) | empty-{T}(V1), pppp12-{T}(V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #38: input, references = 3, size of lhs = 1:
% 1.59/1.76 pppp12-{F}(V0) | EXISTS V1: pppp3-{T}(V1,V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #39: input, references = 3, size of lhs = 2:
% 1.59/1.76 pppp3-{F}(V0,V1), empty-{F}(V0) | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #40: input, references = 3, size of lhs = 1:
% 1.59/1.76 pppp3-{F}(V0,V1) | element-{T}(V0,V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #41: input, references = 4, size of lhs = 1:
% 1.59/1.76 P_empty_set-{F}(V0) | EXISTS V1: pppp4-{T}(V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #42: input, references = 5, size of lhs = 1:
% 1.59/1.76 pppp4-{F}(V0) | empty-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #43: input, references = 4, size of lhs = 1:
% 1.59/1.76 P_empty_set-{F}(V0) | EXISTS V1: pppp5-{T}(V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #44: input, references = 3, size of lhs = 1:
% 1.59/1.76 pppp5-{F}(V0) | function-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #45: input, references = 5, size of lhs = 1:
% 1.59/1.76 pppp5-{F}(V0) | empty-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #46: input, references = 3, size of lhs = 1:
% 1.59/1.76 pppp5-{F}(V0) | relation-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #47: input, references = 3, size of lhs = 1:
% 1.59/1.76 P_empty_set-{F}(V0) | EXISTS V1: pppp6-{T}(V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #48: input, references = 3, size of lhs = 1:
% 1.59/1.76 pppp6-{F}(V0) | relation-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #49: input, references = 3, size of lhs = 2:
% 1.59/1.76 pppp6-{F}(V0), empty-{F}(V0) | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #50: input, references = 4, size of lhs = 2:
% 1.59/1.76 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2) | EXISTS V3: pppp7-{T}(V3,V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #51: input, references = 4, size of lhs = 1:
% 1.59/1.76 pppp7-{F}(V0,V1) | empty-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #52: input, references = 3, size of lhs = 1:
% 1.59/1.76 pppp7-{F}(V0,V1) | element-{T}(V0,V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #53: input, references = 3, size of lhs = 1:
% 1.59/1.76 P_empty_set-{F}(V0) | EXISTS V1: pppp8-{T}(V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #54: input, references = 3, size of lhs = 2:
% 1.59/1.76 pppp8-{F}(V0), empty-{F}(V0) | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #55: input, references = 3, size of lhs = 1:
% 1.59/1.76 P_empty_set-{F}(V0) | EXISTS V1: pppp9-{T}(V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #56: input, references = 3, size of lhs = 1:
% 1.59/1.76 pppp9-{F}(V0) | one_to_one-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #57: input, references = 3, size of lhs = 1:
% 1.59/1.76 pppp9-{F}(V0) | function-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #58: input, references = 3, size of lhs = 1:
% 1.59/1.76 pppp9-{F}(V0) | relation-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #59: input, references = 3, size of lhs = 1:
% 1.59/1.76 P_empty_set-{F}(V0) | EXISTS V1: pppp10-{T}(V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #60: input, references = 3, size of lhs = 1:
% 1.59/1.76 pppp10-{F}(V0) | relation_empty_yielding-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #61: input, references = 3, size of lhs = 1:
% 1.59/1.76 pppp10-{F}(V0) | relation-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #62: input, references = 3, size of lhs = 2:
% 1.59/1.76 P_empty_set-{F}(V0), #-{F} V1 | subset-{T}(V1,V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #63: input, references = 3, size of lhs = 2:
% 1.59/1.76 P_empty_set-{F}(V0), in-{F}(V1,V2) | element-{T}(V1,V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #64: input, references = 4, size of lhs = 2:
% 1.59/1.76 P_empty_set-{F}(V0), element-{F}(V2,V1) | empty-{T}(V1), in-{T}(V2,V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #65: input, references = 3, size of lhs = 3:
% 1.59/1.76 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), element-{F}(V1,V3) | subset-{T}(V1,V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #66: input, references = 3, size of lhs = 3:
% 1.59/1.76 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), subset-{F}(V1,V2) | element-{T}(V1,V3)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #67: input, references = 3, size of lhs = 4:
% 1.59/1.76 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), element-{F}(V1,V3), in-{F}(V4,V1) | element-{T}(V4,V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #68: input, references = 5, size of lhs = 10:
% 1.59/1.76 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
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #69: input, references = 5, size of lhs = 10:
% 1.59/1.76 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
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #70: input, references = 4, size of lhs = 5:
% 1.59/1.76 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), empty-{F}(V1), element-{F}(V3,V2), in-{F}(V4,V3) | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #71: input, references = 5, size of lhs = 12:
% 1.59/1.76 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
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #72: input, references = 5, size of lhs = 12:
% 1.59/1.76 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
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #73: input, references = 4, size of lhs = 5:
% 1.59/1.76 P_empty_set-{F}(V0), P_function_inverse-{F}(V1,V2), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1) | one_to_one-{T}(V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #74: input, references = 4, size of lhs = 13:
% 1.59/1.76 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V7), P_relation_dom-{F}(V1,V3), P_identity_relation-{F}(V3,V4), P_function_inverse-{F}(V1,V5), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_relation_dom-{F}(V6,V7), P_relation_composition-{F}(V1,V6,V4), relation-{F}(V6), function-{F}(V6), V6 == V5 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #75: input, references = 4, size of lhs = 1:
% 1.59/1.76 P_empty_set-{F}(V0) | EXISTS V1: pppp11-{T}(V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #76: input, references = 4, size of lhs = 3:
% 1.59/1.76 pppp11-{F}(V0), P_function_inverse-{F}(V0,V1), P_function_inverse-{F}(V1,V0) | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #77: input, references = 5, size of lhs = 3:
% 1.59/1.76 pppp11-{F}(V0), P_function_inverse-{F}(V0,V1), P_function_inverse-{F}(V1,V2) | one_to_one-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #78: input, references = 4, size of lhs = 3:
% 1.59/1.76 pppp11-{F}(V0), P_function_inverse-{F}(V0,V1), P_function_inverse-{F}(V1,V2) | function-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #79: input, references = 4, size of lhs = 3:
% 1.59/1.76 pppp11-{F}(V0), P_function_inverse-{F}(V0,V1), P_function_inverse-{F}(V1,V2) | relation-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #80: input, references = 12, size of lhs = 3:
% 1.59/1.76 P_empty_set-{F}(V0), empty-{F}(V1), V1 == V0 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #81: input, references = 3, size of lhs = 3:
% 1.59/1.76 P_empty_set-{F}(V0), empty-{F}(V1), in-{F}(V2,V1) | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #82: input, references = 11, size of lhs = 4:
% 1.59/1.76 P_empty_set-{F}(V0), empty-{F}(V1), empty-{F}(V2), V2 == V1 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #83: input, references = 10, size of lhs = 1:
% 1.59/1.76 #-{F} V0 | EXISTS V1: P_function_inverse-{T}(V0,V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #84: input, references = 8, size of lhs = 2:
% 1.59/1.76 #-{F} V0, #-{F} V1 | EXISTS V2: P_relation_composition-{T}(V0,V1,V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #85: input, references = 6, size of lhs = 1:
% 1.59/1.76 #-{F} V0 | EXISTS V1: P_identity_relation-{T}(V0,V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #86: input, references = 4, size of lhs = 0:
% 1.59/1.76 FALSE | EXISTS V0: P_empty_set-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #87: input, references = 3, size of lhs = 1:
% 1.59/1.76 #-{F} V0 | EXISTS V1: P_powerset-{T}(V0,V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #88: input, references = 7, size of lhs = 1:
% 1.59/1.76 #-{F} V0 | EXISTS V1: P_relation_dom-{T}(V0,V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #89: input, references = 10, size of lhs = 1:
% 1.59/1.76 #-{F} V0 | EXISTS V1: P_relation_rng-{T}(V0,V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 number of initial rules = 90
% 1.59/1.76
% 1.59/1.76 Simplifiers:
% 1.59/1.76 #90: unsound, references = 3, size of lhs = 3:
% 1.59/1.76 P_function_inverse-{F}(V0,V1), P_function_inverse-{F}(V0,V3), V1 == V3 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #91: unsound, references = 3, size of lhs = 3:
% 1.59/1.76 P_relation_composition-{F}(V0,V1,V2), P_relation_composition-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #92: unsound, references = 3, size of lhs = 3:
% 1.59/1.76 P_identity_relation-{F}(V0,V1), P_identity_relation-{F}(V0,V3), V1 == V3 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #93: unsound, references = 3, size of lhs = 3:
% 1.59/1.76 P_empty_set-{F}(V0), P_empty_set-{F}(V1), V0 == V1 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #94: unsound, references = 3, size of lhs = 3:
% 1.59/1.76 P_powerset-{F}(V0,V1), P_powerset-{F}(V0,V3), V1 == V3 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #95: unsound, references = 3, size of lhs = 3:
% 1.59/1.76 P_relation_dom-{F}(V0,V1), P_relation_dom-{F}(V0,V3), V1 == V3 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #96: unsound, references = 3, size of lhs = 3:
% 1.59/1.76 P_relation_rng-{F}(V0,V1), P_relation_rng-{F}(V0,V3), V1 == V3 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #97: unsound, references = 3, size of lhs = 3:
% 1.59/1.76 pppp0-{F}(V0,V1), pppp0-{F}(V0,V3), V1 == V3 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #98: unsound, references = 3, size of lhs = 3:
% 1.59/1.76 pppp1-{F}(V0), pppp1-{F}(V1), V0 == V1 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #99: unsound, references = 3, size of lhs = 3:
% 1.59/1.76 pppp2-{F}(V0), pppp2-{F}(V1), V0 == V1 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #100: unsound, references = 3, size of lhs = 3:
% 1.59/1.76 pppp3-{F}(V0,V1), pppp3-{F}(V2,V1), V0 == V2 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #101: unsound, references = 3, size of lhs = 3:
% 1.59/1.76 pppp4-{F}(V0), pppp4-{F}(V1), V0 == V1 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #102: unsound, references = 3, size of lhs = 3:
% 1.59/1.76 pppp5-{F}(V0), pppp5-{F}(V1), V0 == V1 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #103: unsound, references = 3, size of lhs = 3:
% 1.59/1.76 pppp6-{F}(V0), pppp6-{F}(V1), V0 == V1 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #104: unsound, references = 3, size of lhs = 3:
% 1.59/1.76 pppp7-{F}(V0,V1), pppp7-{F}(V2,V1), V0 == V2 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #105: unsound, references = 3, size of lhs = 3:
% 1.59/1.76 pppp8-{F}(V0), pppp8-{F}(V1), V0 == V1 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #106: unsound, references = 3, size of lhs = 3:
% 1.59/1.76 pppp9-{F}(V0), pppp9-{F}(V1), V0 == V1 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #107: unsound, references = 3, size of lhs = 3:
% 1.59/1.76 pppp10-{F}(V0), pppp10-{F}(V1), V0 == V1 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #108: unsound, references = 3, size of lhs = 3:
% 1.59/1.76 pppp11-{F}(V0), pppp11-{F}(V1), V0 == V1 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 number of simplifiers = 19
% 1.59/1.76
% 1.59/1.76 Learnt:
% 1.59/1.76 #114: mergings( V0 == V2; #111 ), references = 1, size of lhs = 1:
% 1.59/1.76 P_empty_set-{F}(V0) | pppp5-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #116: mergings( V0 == V2; #112 ), references = 1, size of lhs = 2:
% 1.59/1.76 P_empty_set-{F}(V0), empty-{F}(V1) | pppp5-{T}(V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #124: mergings( V0 == V2; #121 ), references = 1, size of lhs = 1:
% 1.59/1.76 P_empty_set-{F}(V0) | pppp2-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #126: mergings( V0 == V2; #122 ), references = 1, size of lhs = 2:
% 1.59/1.76 P_empty_set-{F}(V0), empty-{F}(V1) | pppp2-{T}(V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #139: mergings( V0 == V2; #136 ), references = 1, size of lhs = 1:
% 1.59/1.76 P_empty_set-{F}(V0) | pppp4-{T}(V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #141: mergings( V0 == V2; #137 ), references = 1, size of lhs = 2:
% 1.59/1.76 P_empty_set-{F}(V0), empty-{F}(V1) | pppp4-{T}(V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #150: mergings( V2 == V3; #147 ), references = 1, size of lhs = 2:
% 1.59/1.76 empty-{F}(V0), P_empty_set-{F}(V1) | P_relation_dom-{T}(V0,V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #152: mergings( V2 == V3; #148 ), references = 1, size of lhs = 3:
% 1.59/1.76 empty-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2) | P_relation_dom-{T}(V0,V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #158: exists( #89, #68 ), references = 6, size of lhs = 9:
% 1.59/1.76 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
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #163: mergings( V0 == V5; #161 ), references = 1, size of lhs = 9:
% 1.59/1.76 pppp11-{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
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #168: mergings( V0 == V3; #164 ), references = 2, size of lhs = 3:
% 1.59/1.76 P_empty_set-{F}(V0), element-{F}(V1,V2), V2 == V0 | in-{T}(V1,V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #171: mergings( V0 == V3, V2 == V3; #165 ), references = 1, size of lhs = 4:
% 1.59/1.76 P_empty_set-{F}(V0), empty-{F}(V1), V0 == V1, element-{F}(V2,V0) | in-{T}(V2,V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #174: mergings( V0 == V3, V2 == V3; #166 ), references = 1, size of lhs = 3:
% 1.59/1.76 P_empty_set-{F}(V0), element-{F}(V1,V0), P_powerset-{F}(V2,V0) | in-{T}(V1,V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #183: exists( #89, #158 ), references = 1, size of lhs = 7:
% 1.59/1.76 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)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #185: mergings( V3 == V4; #181 ), references = 1, size of lhs = 6:
% 1.59/1.76 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)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #191: exists( #84, #186 ), references = 1, size of lhs = 3:
% 1.59/1.76 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2) | P_relation_composition-{T}(V0,V1,V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #192: exists( #84, #187 ), references = 1, size of lhs = 4:
% 1.59/1.76 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3) | P_relation_composition-{T}(V0,V1,V3)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #206: mergings( V2 == V3; #203 ), references = 1, size of lhs = 2:
% 1.59/1.76 empty-{F}(V0), P_empty_set-{F}(V1) | P_relation_rng-{T}(V0,V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #208: mergings( V2 == V3; #204 ), references = 1, size of lhs = 3:
% 1.59/1.76 empty-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2) | P_relation_rng-{T}(V0,V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #229: mergings( V2 == V3; #227 ), references = 2, size of lhs = 5:
% 1.59/1.76 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), element-{F}(V3,V2), V3 == V0 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #233: exists( #8, #231 ), references = 1, size of lhs = 3:
% 1.59/1.76 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2) | pppp0-{T}(V2,V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #257: exists( #89, #69 ), references = 2, size of lhs = 8:
% 1.59/1.76 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)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #262: exists( #88, #158 ), references = 4, size of lhs = 7:
% 1.59/1.76 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)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #279: mergings( V2 == V5, V5 == V6; #275 ), references = 1, size of lhs = 7:
% 1.59/1.76 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)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #282: mergings( V2 == V5, V5 == V6; #276 ), references = 1, size of lhs = 8:
% 1.59/1.76 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)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #297: exists( #85, #71 ), references = 1, size of lhs = 9:
% 1.59/1.76 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)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #298: exists( #85, #72 ), references = 1, size of lhs = 9:
% 1.59/1.76 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)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #334: exists( #89, #69 ), references = 2, size of lhs = 9:
% 1.59/1.76 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
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #335: exists( #89, #158 ), references = 1, size of lhs = 7:
% 1.59/1.76 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)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #337: exists( #88, #333 ), references = 1, size of lhs = 7:
% 1.59/1.76 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)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #356: mergings( V0 == V3; #352 ), references = 1, size of lhs = 3:
% 1.59/1.76 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), V1 == V0 | pppp12-{T}(V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #359: mergings( V0 == V3, V1 == V3; #353 ), references = 1, size of lhs = 4:
% 1.59/1.76 P_empty_set-{F}(V0), empty-{F}(V1), V0 == V1, P_powerset-{F}(V0,V2) | pppp12-{T}(V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #363: mergings( V0 == V3, V2 == V4, V1 == V3; #354 ), references = 1, size of lhs = 4:
% 1.59/1.76 P_empty_set-{F}(V0), P_powerset-{F}(V0,V1), element-{F}(V2,V1), V2 == V0 | pppp12-{T}(V1)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #399: mergings( V0 == V4; #397 ), references = 1, size of lhs = 2:
% 1.59/1.76 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2) | pppp7-{T}(V0,V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #442: mergings( V3 == V4; #439 ), references = 1, size of lhs = 3:
% 1.59/1.76 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2) | P_relation_composition-{T}(V1,V0,V2)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #444: mergings( V3 == V4; #440 ), references = 1, size of lhs = 4:
% 1.59/1.76 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3) | P_relation_composition-{T}(V1,V0,V3)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #481: exists( #84, #71 ), references = 1, size of lhs = 11:
% 1.59/1.76 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), V3 == V5, P_relation_rng-{F}(V1,V6), P_identity_relation-{F}(V6,V7) | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #483: exists( #84, #480 ), references = 1, size of lhs = 9:
% 1.59/1.76 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)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #493: exists( #84, #72 ), references = 1, size of lhs = 10:
% 1.59/1.76 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)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #502: mergings( V2 == V3, V3 == V10, V0 == V11, V5 == V8, V6 == V9; #496 ), references = 2, size of lhs = 16:
% 1.59/1.76 one_to_one-{F}(V0), relation-{F}(V0), function-{F}(V0), P_function_inverse-{F}(V0,V1), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_relation_rng-{F}(V0,V2), P_identity_relation-{F}(V2,V3), P_empty_set-{F}(V4), P_relation_rng-{F}(V1,V5), P_relation_dom-{F}(V0,V5), P_relation_dom-{F}(V1,V6), P_identity_relation-{F}(V6,V3), P_function_inverse-{F}(V1,V7), V0 == V7 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #509: mergings( V2 == V3, V3 == V10, V7 == V11, V5 == V8, V6 == V9; #503 ), references = 1, size of lhs = 14:
% 1.59/1.76 one_to_one-{F}(V0), relation-{F}(V0), function-{F}(V0), P_function_inverse-{F}(V0,V1), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_relation_rng-{F}(V0,V2), P_identity_relation-{F}(V2,V3), P_empty_set-{F}(V4), P_relation_rng-{F}(V1,V5), P_relation_dom-{F}(V0,V5), P_relation_dom-{F}(V1,V6), P_identity_relation-{F}(V6,V3) | P_function_inverse-{T}(V1,V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #526: exists( #85, #502 ), references = 1, size of lhs = 14:
% 1.59/1.76 one_to_one-{F}(V0), relation-{F}(V0), function-{F}(V0), P_function_inverse-{F}(V0,V1), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_relation_rng-{F}(V0,V2), P_relation_dom-{F}(V1,V2), P_empty_set-{F}(V3), P_relation_rng-{F}(V1,V4), P_relation_dom-{F}(V0,V4), P_function_inverse-{F}(V1,V5), V0 == V5 | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #528: exists( #83, #525 ), references = 1, size of lhs = 12:
% 1.59/1.76 one_to_one-{F}(V0), relation-{F}(V0), function-{F}(V0), P_function_inverse-{F}(V0,V1), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_relation_rng-{F}(V0,V2), P_relation_dom-{F}(V1,V2), P_empty_set-{F}(V3), P_relation_rng-{F}(V1,V4), P_relation_dom-{F}(V0,V4) | P_function_inverse-{T}(V1,V0)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #536: mergings( V2 == V5, V5 == V7, V4 == V6; #532 ), references = 1, size of lhs = 10:
% 1.59/1.76 relation-{F}(V0), function-{F}(V0), one_to_one-{F}(V0), one_to_one-{F}(V1), relation-{F}(V1), function-{F}(V1), pppp11-{F}(V1), P_function_inverse-{F}(V1,V0), P_relation_dom-{F}(V1,V2), P_empty_set-{F}(V3) | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #540: mergings( V2 == V4, V4 == V5; #537 ), references = 1, size of lhs = 9:
% 1.59/1.76 relation-{F}(V0), function-{F}(V0), one_to_one-{F}(V0), one_to_one-{F}(V1), relation-{F}(V1), function-{F}(V1), pppp11-{F}(V1), P_function_inverse-{F}(V1,V0), P_empty_set-{F}(V2) | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #548: mergings( V2 == V3, V3 == V4, V4 == V5; #544 ), references = 2, size of lhs = 5:
% 1.59/1.76 one_to_one-{F}(V0), relation-{F}(V0), function-{F}(V0), pppp11-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #561: exists( #89, #158 ), references = 1, size of lhs = 7:
% 1.59/1.76 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)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #562: exists( #89, #334 ), references = 1, size of lhs = 7:
% 1.59/1.76 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)
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #583: exists( #83, #581 ), references = 1, size of lhs = 3:
% 1.59/1.76 pppp11-{F}(V0), P_function_inverse-{F}(V0,V1), P_empty_set-{F}(V2) | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #585: exists( #83, #582 ), references = 1, size of lhs = 2:
% 1.59/1.76 pppp11-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #588: mergings( V0 == V2; #586 ), references = 1, size of lhs = 1:
% 1.59/1.76 P_empty_set-{F}(V0) | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 #590: exists( #86, #586 ), references = 1, size of lhs = 0:
% 1.59/1.76 FALSE | FALSE
% 1.59/1.76 (used 0 times, uses = {})
% 1.59/1.76
% 1.59/1.76 number of learnt formulas = 52
% 1.59/1.76
% 1.59/1.76
% 1.59/1.76 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.59/1.76
% 1.59/1.76 randbase = 1
%------------------------------------------------------------------------------