%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : SEU031+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n023.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 2.57s 2.74s
% Output : Refutation 2.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU031+1 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n023.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 19:29:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.57/2.74 GeoParameters:
% 2.57/2.74
% 2.57/2.74 tptp_input = 1
% 2.57/2.74 tptp_output = 0
% 2.57/2.74 nonempty = 1
% 2.57/2.74 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.57/2.74 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 2.57/2.74
% 2.57/2.74
% 2.57/2.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.57/2.74 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.57/2.74
% 2.57/2.74 RuleSystem INPUT:
% 2.57/2.74
% 2.57/2.74 Initial Rules:
% 2.57/2.74 #0: input, references = 3, size of lhs = 2:
% 2.57/2.74 in-{F}(V0,V1), in-{F}(V1,V0) | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #1: input, references = 3, size of lhs = 1:
% 2.57/2.74 empty-{F}(V0) | function-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #2: input, references = 3, size of lhs = 1:
% 2.57/2.74 empty-{F}(V0) | relation-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #3: input, references = 3, size of lhs = 3:
% 2.57/2.74 relation-{F}(V0), empty-{F}(V0), function-{F}(V0) | one_to_one-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #4: input, references = 6, size of lhs = 3:
% 2.57/2.74 P_function_inverse-{F}(V0,V1), relation-{F}(V0), function-{F}(V0) | relation-{T}(V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #5: input, references = 4, size of lhs = 3:
% 2.57/2.74 P_function_inverse-{F}(V0,V1), relation-{F}(V0), function-{F}(V0) | function-{T}(V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #6: input, references = 3, size of lhs = 3:
% 2.57/2.74 relation-{F}(V0), P_relation_composition-{F}(V1,V0,V2), relation-{F}(V1) | relation-{T}(V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #7: input, references = 3, size of lhs = 1:
% 2.57/2.74 P_identity_relation-{F}(V0,V1) | relation-{T}(V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #8: input, references = 5, size of lhs = 1:
% 2.57/2.74 #-{F} V0 | EXISTS V1: pppp0-{T}(V0,V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #9: input, references = 5, size of lhs = 1:
% 2.57/2.74 pppp0-{F}(V0,V1) | element-{T}(V1,V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #10: input, references = 5, size of lhs = 3:
% 2.57/2.74 relation-{F}(V0), P_relation_composition-{F}(V0,V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #11: input, references = 3, size of lhs = 3:
% 2.57/2.74 relation-{F}(V0), P_relation_composition-{F}(V0,V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #12: input, references = 3, size of lhs = 1:
% 2.57/2.74 P_empty_set-{F}(V0) | empty-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #13: input, references = 3, size of lhs = 1:
% 2.57/2.74 P_empty_set-{F}(V0) | relation-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #14: input, references = 3, size of lhs = 1:
% 2.57/2.74 P_empty_set-{F}(V0) | relation_empty_yielding-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #15: input, references = 3, size of lhs = 6:
% 2.57/2.74 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)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #16: input, references = 3, size of lhs = 6:
% 2.57/2.74 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)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #17: input, references = 3, size of lhs = 3:
% 2.57/2.74 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), empty-{F}(V2) | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #18: input, references = 3, size of lhs = 1:
% 2.57/2.74 P_empty_set-{F}(V0) | empty-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #19: input, references = 3, size of lhs = 2:
% 2.57/2.74 P_empty_set-{F}(V0), P_identity_relation-{F}(V1,V2) | relation-{T}(V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #20: input, references = 3, size of lhs = 2:
% 2.57/2.74 P_empty_set-{F}(V0), P_identity_relation-{F}(V1,V2) | function-{T}(V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #21: input, references = 3, size of lhs = 1:
% 2.57/2.74 P_empty_set-{F}(V0) | empty-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #22: input, references = 3, size of lhs = 1:
% 2.57/2.74 P_empty_set-{F}(V0) | relation-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #23: input, references = 5, size of lhs = 4:
% 2.57/2.74 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), relation-{F}(V1), empty-{F}(V2) | empty-{T}(V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #24: input, references = 3, size of lhs = 4:
% 2.57/2.74 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), relation-{F}(V1), empty-{F}(V2) | empty-{T}(V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #25: input, references = 5, size of lhs = 3:
% 2.57/2.74 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #26: input, references = 3, size of lhs = 3:
% 2.57/2.74 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #27: input, references = 5, size of lhs = 3:
% 2.57/2.74 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #28: input, references = 3, size of lhs = 3:
% 2.57/2.74 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #29: input, references = 4, size of lhs = 4:
% 2.57/2.74 P_empty_set-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V2,V1,V3), empty-{F}(V2) | empty-{T}(V3)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #30: input, references = 3, size of lhs = 4:
% 2.57/2.74 P_empty_set-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V2,V1,V3), empty-{F}(V2) | relation-{T}(V3)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #31: input, references = 4, size of lhs = 14:
% 2.57/2.74 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
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #32: input, references = 3, size of lhs = 1:
% 2.57/2.74 P_empty_set-{F}(V0) | EXISTS V1: pppp1-{T}(V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #33: input, references = 3, size of lhs = 1:
% 2.57/2.74 pppp1-{F}(V0) | function-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #34: input, references = 3, size of lhs = 1:
% 2.57/2.74 pppp1-{F}(V0) | relation-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #35: input, references = 4, size of lhs = 1:
% 2.57/2.74 P_empty_set-{F}(V0) | EXISTS V1: pppp2-{T}(V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #36: input, references = 3, size of lhs = 1:
% 2.57/2.74 pppp2-{F}(V0) | relation-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #37: input, references = 5, size of lhs = 1:
% 2.57/2.74 pppp2-{F}(V0) | empty-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #38: input, references = 4, size of lhs = 2:
% 2.57/2.74 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2) | empty-{T}(V1), pppp14-{T}(V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #39: input, references = 3, size of lhs = 1:
% 2.57/2.74 pppp14-{F}(V0) | EXISTS V1: pppp3-{T}(V1,V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #40: input, references = 3, size of lhs = 2:
% 2.57/2.74 pppp3-{F}(V0,V1), empty-{F}(V0) | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #41: input, references = 3, size of lhs = 1:
% 2.57/2.74 pppp3-{F}(V0,V1) | element-{T}(V0,V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #42: input, references = 4, size of lhs = 1:
% 2.57/2.74 P_empty_set-{F}(V0) | EXISTS V1: pppp4-{T}(V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #43: input, references = 5, size of lhs = 1:
% 2.57/2.74 pppp4-{F}(V0) | empty-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #44: input, references = 4, size of lhs = 1:
% 2.57/2.74 P_empty_set-{F}(V0) | EXISTS V1: pppp5-{T}(V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #45: input, references = 3, size of lhs = 1:
% 2.57/2.74 pppp5-{F}(V0) | function-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #46: input, references = 5, size of lhs = 1:
% 2.57/2.74 pppp5-{F}(V0) | empty-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #47: input, references = 3, size of lhs = 1:
% 2.57/2.74 pppp5-{F}(V0) | relation-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #48: input, references = 3, size of lhs = 1:
% 2.57/2.74 P_empty_set-{F}(V0) | EXISTS V1: pppp6-{T}(V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #49: input, references = 3, size of lhs = 1:
% 2.57/2.74 pppp6-{F}(V0) | relation-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #50: input, references = 3, size of lhs = 2:
% 2.57/2.74 pppp6-{F}(V0), empty-{F}(V0) | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #51: input, references = 4, size of lhs = 2:
% 2.57/2.74 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2) | EXISTS V3: pppp7-{T}(V3,V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #52: input, references = 5, size of lhs = 1:
% 2.57/2.74 pppp7-{F}(V0,V1) | empty-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #53: input, references = 3, size of lhs = 1:
% 2.57/2.74 pppp7-{F}(V0,V1) | element-{T}(V0,V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #54: input, references = 3, size of lhs = 1:
% 2.57/2.74 P_empty_set-{F}(V0) | EXISTS V1: pppp8-{T}(V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #55: input, references = 3, size of lhs = 2:
% 2.57/2.74 pppp8-{F}(V0), empty-{F}(V0) | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #56: input, references = 3, size of lhs = 1:
% 2.57/2.74 P_empty_set-{F}(V0) | EXISTS V1: pppp9-{T}(V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #57: input, references = 3, size of lhs = 1:
% 2.57/2.74 pppp9-{F}(V0) | one_to_one-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #58: input, references = 3, size of lhs = 1:
% 2.57/2.74 pppp9-{F}(V0) | function-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #59: input, references = 3, size of lhs = 1:
% 2.57/2.74 pppp9-{F}(V0) | relation-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #60: input, references = 3, size of lhs = 1:
% 2.57/2.74 P_empty_set-{F}(V0) | EXISTS V1: pppp10-{T}(V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #61: input, references = 3, size of lhs = 1:
% 2.57/2.74 pppp10-{F}(V0) | relation_empty_yielding-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #62: input, references = 3, size of lhs = 1:
% 2.57/2.74 pppp10-{F}(V0) | relation-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #63: input, references = 3, size of lhs = 2:
% 2.57/2.74 P_empty_set-{F}(V0), #-{F} V1 | subset-{T}(V1,V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #64: input, references = 3, size of lhs = 2:
% 2.57/2.74 P_empty_set-{F}(V0), in-{F}(V1,V2) | element-{T}(V1,V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #65: input, references = 4, size of lhs = 2:
% 2.57/2.74 P_empty_set-{F}(V0), element-{F}(V2,V1) | empty-{T}(V1), in-{T}(V2,V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #66: input, references = 3, size of lhs = 3:
% 2.57/2.74 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), element-{F}(V1,V3) | subset-{T}(V1,V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #67: input, references = 3, size of lhs = 3:
% 2.57/2.74 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), subset-{F}(V1,V2) | element-{T}(V1,V3)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #68: input, references = 3, size of lhs = 4:
% 2.57/2.74 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), element-{F}(V1,V3), in-{F}(V4,V1) | element-{T}(V4,V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #69: input, references = 7, size of lhs = 10:
% 2.57/2.74 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
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #70: input, references = 6, size of lhs = 10:
% 2.57/2.74 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
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #71: input, references = 4, size of lhs = 5:
% 2.57/2.74 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), empty-{F}(V1), element-{F}(V3,V2), in-{F}(V4,V3) | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #72: input, references = 7, size of lhs = 12:
% 2.57/2.74 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
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #73: input, references = 7, size of lhs = 12:
% 2.57/2.74 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
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #74: input, references = 4, size of lhs = 1:
% 2.57/2.74 P_empty_set-{F}(V0) | EXISTS V1: pppp13-{T}(V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #75: input, references = 4, size of lhs = 5:
% 2.57/2.74 pppp13-{F}(V0), P_relation_dom-{F}(V0,V1), P_relation_rng-{F}(V0,V2), P_identity_relation-{F}(V2,V3), P_function_inverse-{F}(V0,V4) | EXISTS V5: pppp12-{T}(V0,V1,V3,V4,V5)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #76: input, references = 8, size of lhs = 5:
% 2.57/2.74 pppp13-{F}(V0), P_relation_dom-{F}(V0,V1), P_relation_rng-{F}(V0,V2), P_identity_relation-{F}(V2,V3), P_function_inverse-{F}(V0,V4) | one_to_one-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #77: input, references = 6, size of lhs = 5:
% 2.57/2.74 pppp13-{F}(V0), P_relation_dom-{F}(V0,V1), P_relation_rng-{F}(V0,V2), P_identity_relation-{F}(V2,V3), P_function_inverse-{F}(V0,V4) | function-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #78: input, references = 6, size of lhs = 5:
% 2.57/2.74 pppp13-{F}(V0), P_relation_dom-{F}(V0,V1), P_relation_rng-{F}(V0,V2), P_identity_relation-{F}(V2,V3), P_function_inverse-{F}(V0,V4) | relation-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #79: input, references = 9, size of lhs = 3:
% 2.57/2.74 pppp12-{F}(V0,V1,V2,V3,V4), P_relation_rng-{F}(V4,V5), P_relation_composition-{F}(V4,V0,V6) | pppp11-{T}(V4,V5,V1,V6,V2,V3)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #80: input, references = 5, size of lhs = 1:
% 2.57/2.74 pppp11-{F}(V5,V1,V2,V3,V4,V5) | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #81: input, references = 4, size of lhs = 2:
% 2.57/2.74 pppp11-{F}(V0,V1,V2,V3,V4,V5), V3 == V4 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #82: input, references = 5, size of lhs = 2:
% 2.57/2.74 pppp11-{F}(V0,V1,V2,V3,V4,V5), V1 == V2 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #83: input, references = 4, size of lhs = 1:
% 2.57/2.74 pppp11-{F}(V0,V1,V2,V3,V4,V5) | function-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #84: input, references = 4, size of lhs = 1:
% 2.57/2.74 pppp11-{F}(V0,V1,V2,V3,V4,V5) | relation-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #85: input, references = 12, size of lhs = 3:
% 2.57/2.74 P_empty_set-{F}(V0), empty-{F}(V1), V1 == V0 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #86: input, references = 3, size of lhs = 3:
% 2.57/2.74 P_empty_set-{F}(V0), empty-{F}(V1), in-{F}(V2,V1) | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #87: input, references = 11, size of lhs = 4:
% 2.57/2.74 P_empty_set-{F}(V0), empty-{F}(V1), empty-{F}(V2), V2 == V1 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #88: input, references = 6, size of lhs = 1:
% 2.57/2.74 #-{F} V0 | EXISTS V1: P_function_inverse-{T}(V0,V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #89: input, references = 11, size of lhs = 2:
% 2.57/2.74 #-{F} V0, #-{F} V1 | EXISTS V2: P_relation_composition-{T}(V0,V1,V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #90: input, references = 9, size of lhs = 1:
% 2.57/2.74 #-{F} V0 | EXISTS V1: P_identity_relation-{T}(V0,V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #91: input, references = 4, size of lhs = 0:
% 2.57/2.74 FALSE | EXISTS V0: P_empty_set-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #92: input, references = 3, size of lhs = 1:
% 2.57/2.74 #-{F} V0 | EXISTS V1: P_powerset-{T}(V0,V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #93: input, references = 10, size of lhs = 1:
% 2.57/2.74 #-{F} V0 | EXISTS V1: P_relation_dom-{T}(V0,V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #94: input, references = 13, size of lhs = 1:
% 2.57/2.74 #-{F} V0 | EXISTS V1: P_relation_rng-{T}(V0,V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 number of initial rules = 95
% 2.57/2.74
% 2.57/2.74 Simplifiers:
% 2.57/2.74 #95: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 P_function_inverse-{F}(V0,V1), P_function_inverse-{F}(V0,V3), V1 == V3 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #96: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 P_relation_composition-{F}(V0,V1,V2), P_relation_composition-{F}(V0,V1,V5), V2 == V5 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #97: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 P_identity_relation-{F}(V0,V1), P_identity_relation-{F}(V0,V3), V1 == V3 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #98: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 P_empty_set-{F}(V0), P_empty_set-{F}(V1), V0 == V1 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #99: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 P_powerset-{F}(V0,V1), P_powerset-{F}(V0,V3), V1 == V3 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #100: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 P_relation_dom-{F}(V0,V1), P_relation_dom-{F}(V0,V3), V1 == V3 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #101: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 P_relation_rng-{F}(V0,V1), P_relation_rng-{F}(V0,V3), V1 == V3 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #102: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 pppp0-{F}(V0,V1), pppp0-{F}(V0,V3), V1 == V3 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #103: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 pppp1-{F}(V0), pppp1-{F}(V1), V0 == V1 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #104: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 pppp2-{F}(V0), pppp2-{F}(V1), V0 == V1 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #105: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 pppp3-{F}(V0,V1), pppp3-{F}(V2,V1), V0 == V2 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #106: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 pppp4-{F}(V0), pppp4-{F}(V1), V0 == V1 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #107: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 pppp5-{F}(V0), pppp5-{F}(V1), V0 == V1 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #108: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 pppp6-{F}(V0), pppp6-{F}(V1), V0 == V1 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #109: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 pppp7-{F}(V0,V1), pppp7-{F}(V2,V1), V0 == V2 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #110: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 pppp8-{F}(V0), pppp8-{F}(V1), V0 == V1 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #111: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 pppp9-{F}(V0), pppp9-{F}(V1), V0 == V1 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #112: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 pppp10-{F}(V0), pppp10-{F}(V1), V0 == V1 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #113: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 pppp11-{F}(V0,V1,V2,V3,V4,V5), pppp11-{F}(V0,V7,V8,V9,V10,V11), V1 == V7 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #114: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V1,V2,V3,V9), V4 == V9 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #115: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V5,V6,V7,V8,V9), V0 == V5 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #116: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V6,V7,V8,V9), V1 == V6 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #117: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V6,V7,V8,V9), V3 == V8 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #118: unsound, references = 3, size of lhs = 3:
% 2.57/2.74 pppp13-{F}(V0), pppp13-{F}(V1), V0 == V1 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 number of simplifiers = 24
% 2.57/2.74
% 2.57/2.74 Learnt:
% 2.57/2.74 #124: mergings( V0 == V2; #121 ), references = 1, size of lhs = 1:
% 2.57/2.74 P_empty_set-{F}(V0) | pppp5-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #126: mergings( V0 == V2; #122 ), references = 1, size of lhs = 2:
% 2.57/2.74 P_empty_set-{F}(V0), empty-{F}(V1) | pppp5-{T}(V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #134: mergings( V0 == V2; #131 ), references = 1, size of lhs = 1:
% 2.57/2.74 P_empty_set-{F}(V0) | pppp2-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #136: mergings( V0 == V2; #132 ), references = 1, size of lhs = 2:
% 2.57/2.74 P_empty_set-{F}(V0), empty-{F}(V1) | pppp2-{T}(V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #149: mergings( V0 == V2; #146 ), references = 1, size of lhs = 1:
% 2.57/2.74 P_empty_set-{F}(V0) | pppp4-{T}(V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #151: mergings( V0 == V2; #147 ), references = 1, size of lhs = 2:
% 2.57/2.74 P_empty_set-{F}(V0), empty-{F}(V1) | pppp4-{T}(V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #160: mergings( V2 == V3; #157 ), references = 1, size of lhs = 2:
% 2.57/2.74 empty-{F}(V0), P_empty_set-{F}(V1) | P_relation_dom-{T}(V0,V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #162: mergings( V2 == V3; #158 ), references = 1, size of lhs = 3:
% 2.57/2.74 empty-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2) | P_relation_dom-{T}(V0,V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #168: exists( #94, #69 ), references = 6, size of lhs = 9:
% 2.57/2.74 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
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #174: mergings( V0 == V3; #170 ), references = 2, size of lhs = 3:
% 2.57/2.74 P_empty_set-{F}(V0), element-{F}(V1,V2), V2 == V0 | in-{T}(V1,V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #177: mergings( V0 == V3, V2 == V3; #171 ), references = 1, size of lhs = 4:
% 2.57/2.74 P_empty_set-{F}(V0), empty-{F}(V1), V0 == V1, element-{F}(V2,V0) | in-{T}(V2,V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #180: mergings( V0 == V3, V2 == V3; #172 ), references = 1, size of lhs = 3:
% 2.57/2.74 P_empty_set-{F}(V0), element-{F}(V1,V0), P_powerset-{F}(V2,V0) | in-{T}(V1,V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #189: exists( #94, #168 ), references = 1, size of lhs = 7:
% 2.57/2.74 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)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #191: mergings( V3 == V4; #187 ), references = 1, size of lhs = 6:
% 2.57/2.74 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)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #197: exists( #89, #192 ), references = 1, size of lhs = 3:
% 2.57/2.74 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2) | P_relation_composition-{T}(V0,V1,V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #198: exists( #89, #193 ), references = 1, size of lhs = 4:
% 2.57/2.74 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3) | P_relation_composition-{T}(V0,V1,V3)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #212: mergings( V2 == V3; #209 ), references = 1, size of lhs = 2:
% 2.57/2.74 empty-{F}(V0), P_empty_set-{F}(V1) | P_relation_rng-{T}(V0,V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #214: mergings( V2 == V3; #210 ), references = 1, size of lhs = 3:
% 2.57/2.74 empty-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2) | P_relation_rng-{T}(V0,V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #235: mergings( V2 == V3; #233 ), references = 2, size of lhs = 5:
% 2.57/2.74 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), element-{F}(V3,V2), V3 == V0 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #239: exists( #8, #237 ), references = 1, size of lhs = 3:
% 2.57/2.74 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2) | pppp0-{T}(V2,V0)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #250: exists( #94, #70 ), references = 2, size of lhs = 8:
% 2.57/2.74 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)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #251: exists( #94, #168 ), references = 1, size of lhs = 7:
% 2.57/2.74 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)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #252: exists( #94, #69 ), references = 1, size of lhs = 8:
% 2.57/2.74 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)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #257: exists( #93, #168 ), references = 4, size of lhs = 7:
% 2.57/2.74 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)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #274: mergings( V2 == V5, V5 == V6; #270 ), references = 1, size of lhs = 7:
% 2.57/2.74 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)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #277: mergings( V2 == V5, V5 == V6; #271 ), references = 1, size of lhs = 8:
% 2.57/2.74 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)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #292: exists( #90, #72 ), references = 1, size of lhs = 9:
% 2.57/2.74 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)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #293: exists( #90, #73 ), references = 1, size of lhs = 9:
% 2.57/2.74 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)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #315: mergings( V3 == V4; #313 ), references = 1, size of lhs = 3:
% 2.57/2.74 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2) | P_relation_composition-{T}(V1,V0,V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #324: exists( #89, #72 ), references = 1, size of lhs = 9:
% 2.57/2.74 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)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #325: exists( #89, #73 ), references = 1, size of lhs = 9:
% 2.57/2.74 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)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #336: mergings( V0 == V3; #332 ), references = 1, size of lhs = 3:
% 2.57/2.74 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), V1 == V0 | pppp14-{T}(V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #339: mergings( V0 == V3, V1 == V3; #333 ), references = 1, size of lhs = 4:
% 2.57/2.74 P_empty_set-{F}(V0), empty-{F}(V1), V0 == V1, P_powerset-{F}(V0,V2) | pppp14-{T}(V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #343: mergings( V0 == V3, V2 == V4, V1 == V3; #334 ), references = 1, size of lhs = 4:
% 2.57/2.74 P_empty_set-{F}(V0), P_powerset-{F}(V0,V1), element-{F}(V2,V1), V2 == V0 | pppp14-{T}(V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #389: mergings( V4 == V6, V6 == V8, V8 == V11, V3 == V5, V5 == V7, V7 == V13, V0 == V10; #379 ), references = 3, size of lhs = 7:
% 2.57/2.74 pppp13-{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
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #398: mergings( V4 == V6, V6 == V8, V8 == V11, V3 == V5, V5 == V7, V7 == V13, V0 == V10, V10 == V12; #381 ), references = 3, size of lhs = 8:
% 2.57/2.74 pppp13-{F}(V0), P_empty_set-{F}(V1), P_relation_rng-{F}(V0,V2), P_function_inverse-{F}(V0,V3), P_relation_dom-{F}(V3,V2), P_relation_dom-{F}(V0,V4), P_relation_rng-{F}(V3,V5), V4 == V5 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #415: exists( #94, #168 ), references = 1, size of lhs = 7:
% 2.57/2.74 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)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #416: exists( #94, #389 ), references = 2, size of lhs = 5:
% 2.57/2.74 pppp13-{F}(V0), P_empty_set-{F}(V1), P_function_inverse-{F}(V0,V2), P_relation_dom-{F}(V2,V3), P_relation_dom-{F}(V0,V4) | P_relation_rng-{T}(V0,V3)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #417: exists( #94, #69 ), references = 1, size of lhs = 8:
% 2.57/2.74 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)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #425: mergings( V4 == V6, V2 == V3, V5 == V7; #420 ), references = 1, size of lhs = 7:
% 2.57/2.74 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)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #428: mergings( V3 == V6, V2 == V5; #421 ), references = 1, size of lhs = 8:
% 2.57/2.74 relation-{F}(V0), function-{F}(V0), one_to_one-{F}(V0), pppp13-{F}(V0), P_empty_set-{F}(V1), P_function_inverse-{F}(V0,V2), P_relation_dom-{F}(V2,V3), P_relation_rng-{F}(V2,V4) | P_relation_dom-{T}(V0,V4)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #445: mergings( V0 == V4; #442 ), references = 1, size of lhs = 2:
% 2.57/2.74 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2) | pppp7-{T}(V0,V2)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #447: mergings( V0 == V4; #443 ), references = 1, size of lhs = 3:
% 2.57/2.74 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V2,V3) | pppp7-{T}(V1,V3)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #493: exists( #94, #491 ), references = 1, size of lhs = 2:
% 2.57/2.74 P_relation_composition-{F}(V0,V1,V2), pppp12-{F}(V1,V3,V4,V5,V0) | P_relation_rng-{T}(V0,V3)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #535: exists( #89, #532 ), references = 1, size of lhs = 3:
% 2.57/2.74 P_relation_rng-{F}(V0,V1), pppp12-{F}(V2,V3,V4,V5,V0), V1 == V3 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #537: mergings( V3 == V4; #533 ), references = 2, size of lhs = 2:
% 2.57/2.74 P_relation_rng-{F}(V0,V1), pppp12-{F}(V2,V1,V3,V4,V0) | P_relation_composition-{T}(V0,V2,V3)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #539: exists( #94, #534 ), references = 1, size of lhs = 1:
% 2.57/2.74 pppp12-{F}(V0,V1,V2,V3,V4) | P_relation_rng-{T}(V4,V1)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #546: exists( #75, #544 ), references = 3, size of lhs = 14:
% 2.57/2.74 pppp13-{F}(V0), relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), P_relation_rng-{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_dom-{F}(V6,V7), P_identity_relation-{F}(V7,V3), P_relation_composition-{F}(V0,V6,V8), P_identity_relation-{F}(V1,V8) | pppp12-{T}(V0,V1,V3,V4,V6)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #575: mergings( V4 == V6, V3 == V0; #571 ), references = 1, size of lhs = 9:
% 2.57/2.74 pppp13-{F}(V0), relation-{F}(V0), function-{F}(V0), P_empty_set-{F}(V1), P_function_inverse-{F}(V0,V2), P_relation_composition-{F}(V0,V2,V3), P_relation_dom-{F}(V0,V4), P_relation_rng-{F}(V0,V4), P_relation_composition-{F}(V2,V0,V5) | P_identity_relation-{T}(V4,V3)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #578: mergings( V4 == V6, V3 == V0; #572 ), references = 1, size of lhs = 9:
% 2.57/2.74 pppp13-{F}(V0), relation-{F}(V0), function-{F}(V0), P_empty_set-{F}(V1), P_function_inverse-{F}(V0,V2), P_relation_composition-{F}(V0,V2,V3), P_relation_dom-{F}(V0,V4), P_relation_rng-{F}(V0,V4), P_relation_composition-{F}(V2,V0,V5) | P_identity_relation-{T}(V4,V5)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #587: mergings( V0 == V3, V4 == V6, V2 == V5, V5 == V7; #582 ), references = 1, size of lhs = 7:
% 2.57/2.74 pppp13-{F}(V0), relation-{F}(V0), function-{F}(V0), P_function_inverse-{F}(V0,V0), P_relation_dom-{F}(V0,V1), P_relation_rng-{F}(V0,V1), P_empty_set-{F}(V2) | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #593: mergings( V0 == V4, V2 == V3, V3 == V5; #589 ), references = 1, size of lhs = 5:
% 2.57/2.74 pppp13-{F}(V0), relation-{F}(V0), function-{F}(V0), P_function_inverse-{F}(V0,V0), P_empty_set-{F}(V1) | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #609: mergings( V3 == V6, V2 == V5; #606 ), references = 1, size of lhs = 5:
% 2.57/2.74 pppp13-{F}(V0), P_empty_set-{F}(V1), P_function_inverse-{F}(V0,V2), P_relation_dom-{F}(V2,V3), P_relation_rng-{F}(V2,V4) | P_relation_dom-{T}(V0,V4)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #630: exists( #89, #73 ), references = 1, size of lhs = 11:
% 2.57/2.74 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_composition-{F}(V2,V1,V5), P_relation_rng-{F}(V1,V6), P_identity_relation-{F}(V6,V7), V5 == V7 | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #632: exists( #89, #629 ), references = 2, size of lhs = 9:
% 2.57/2.74 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}(V2,V1,V6)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #652: exists( #89, #72 ), references = 2, size of lhs = 10:
% 2.57/2.74 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_composition-{F}(V2,V1,V5), P_relation_rng-{F}(V1,V6), P_identity_relation-{F}(V6,V7) | P_relation_composition-{T}(V1,V2,V4)
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #686: mergings( V2 == V3, V3 == V12, V5 == V7, V6 == V8, V7 == V9, V8 == V10, V9 == V13; #678 ), references = 2, size of lhs = 13:
% 2.57/2.74 one_to_one-{F}(V0), pppp13-{F}(V0), relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), P_relation_rng-{F}(V0,V2), P_function_inverse-{F}(V0,V3), relation-{F}(V3), function-{F}(V3), P_relation_dom-{F}(V3,V2), P_empty_set-{F}(V4), P_identity_relation-{F}(V2,V5), P_relation_rng-{F}(V3,V6) | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #705: mergings( V3 == V7, V2 == V4, V4 == V12, V6 == V8, V8 == V10, V10 == V11, V9 == V0; #697 ), references = 1, size of lhs = 9:
% 2.57/2.74 relation-{F}(V0), function-{F}(V0), pppp13-{F}(V1), relation-{F}(V1), function-{F}(V1), P_function_inverse-{F}(V1,V0), P_relation_rng-{F}(V1,V2), P_relation_dom-{F}(V1,V3), P_empty_set-{F}(V4) | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #713: mergings( V3 == V6, V2 == V4, V4 == V10, V5 == V7, V7 == V8, V8 == V9; #706 ), references = 1, size of lhs = 8:
% 2.57/2.74 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
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #718: mergings( V3 == V5, V2 == V4, V4 == V6; #714 ), references = 1, size of lhs = 7:
% 2.57/2.74 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
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #724: mergings( V2 == V3, V3 == V4; #721 ), references = 2, size of lhs = 4:
% 2.57/2.74 pppp13-{F}(V0), relation-{F}(V0), function-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #760: mergings( V4 == V6, V3 == V5; #755 ), references = 2, size of lhs = 5:
% 2.57/2.74 pppp13-{F}(V0), P_relation_dom-{F}(V0,V1), P_relation_rng-{F}(V0,V2), P_function_inverse-{F}(V0,V3), P_empty_set-{F}(V4) | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #772: exists( #94, #760 ), references = 1, size of lhs = 4:
% 2.57/2.74 pppp13-{F}(V0), P_relation_dom-{F}(V0,V1), P_function_inverse-{F}(V0,V2), P_empty_set-{F}(V3) | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #774: exists( #93, #771 ), references = 1, size of lhs = 3:
% 2.57/2.74 pppp13-{F}(V0), P_function_inverse-{F}(V0,V1), P_empty_set-{F}(V2) | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #776: exists( #88, #773 ), references = 1, size of lhs = 2:
% 2.57/2.74 pppp13-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #779: mergings( V0 == V2; #777 ), references = 1, size of lhs = 1:
% 2.57/2.74 P_empty_set-{F}(V0) | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 #781: exists( #91, #777 ), references = 1, size of lhs = 0:
% 2.57/2.74 FALSE | FALSE
% 2.57/2.74 (used 0 times, uses = {})
% 2.57/2.74
% 2.57/2.74 number of learnt formulas = 67
% 2.57/2.74
% 2.57/2.74
% 2.57/2.74 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.57/2.74
% 2.57/2.74 randbase = 1
%------------------------------------------------------------------------------