TSTP Solution File: SEU221+1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : SEU221+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n015.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 06:17:31 EDT 2022
% Result : Theorem 1.95s 2.12s
% Output : Refutation 1.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU221+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n015.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 19:17:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.95/2.12 GeoParameters:
% 1.95/2.12
% 1.95/2.12 tptp_input = 1
% 1.95/2.12 tptp_output = 0
% 1.95/2.12 nonempty = 1
% 1.95/2.12 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.95/2.12 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 1.95/2.12
% 1.95/2.12
% 1.95/2.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.95/2.12 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.95/2.12
% 1.95/2.12 RuleSystem INPUT:
% 1.95/2.12
% 1.95/2.12 Initial Rules:
% 1.95/2.12 #0: input, references = 6, size of lhs = 2:
% 1.95/2.12 in-{F}(V0,V1), in-{F}(V1,V0) | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #1: input, references = 3, size of lhs = 1:
% 1.95/2.12 empty-{F}(V0) | function-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #2: input, references = 3, size of lhs = 1:
% 1.95/2.12 empty-{F}(V0) | relation-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #3: input, references = 3, size of lhs = 3:
% 1.95/2.12 relation-{F}(V0), empty-{F}(V0), function-{F}(V0) | one_to_one-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #4: input, references = 3, size of lhs = 3:
% 1.95/2.12 relation-{F}(V0), function-{F}(V0), one_to_one-{F}(V0) | pppp0-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #5: input, references = 5, size of lhs = 3:
% 1.95/2.12 relation-{F}(V0), function-{F}(V0), pppp0-{F}(V0) | one_to_one-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #6: input, references = 3, size of lhs = 7:
% 1.95/2.12 P_relation_dom-{F}(V0,V1), pppp0-{F}(V0), P_apply-{F}(V0,V2,V3), in-{F}(V2,V1), P_apply-{F}(V0,V4,V3), in-{F}(V4,V1), V4 == V2 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #7: input, references = 5, size of lhs = 1:
% 1.95/2.12 P_relation_dom-{F}(V0,V1) | pppp0-{T}(V0), pppp18-{T}(V0,V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #8: input, references = 4, size of lhs = 1:
% 1.95/2.12 pppp18-{F}(V0,V1) | EXISTS V2: pppp3-{T}(V0,V2,V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #9: input, references = 4, size of lhs = 2:
% 1.95/2.12 pppp3-{F}(V0,V1,V2), P_apply-{F}(V0,V1,V3) | EXISTS V4: pppp2-{T}(V0,V4,V1,V2,V3)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #10: input, references = 5, size of lhs = 2:
% 1.95/2.12 pppp3-{F}(V0,V1,V2), P_apply-{F}(V0,V1,V3) | in-{T}(V1,V2)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #11: input, references = 4, size of lhs = 2:
% 1.95/2.12 pppp2-{F}(V0,V2,V2,V3,V4), P_apply-{F}(V0,V2,V5) | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #12: input, references = 4, size of lhs = 3:
% 1.95/2.12 pppp2-{F}(V0,V1,V2,V3,V4), P_apply-{F}(V0,V1,V5), V5 == V4 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #13: input, references = 4, size of lhs = 2:
% 1.95/2.12 pppp2-{F}(V0,V1,V2,V3,V4), P_apply-{F}(V0,V1,V5) | in-{T}(V1,V3)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #14: input, references = 6, size of lhs = 3:
% 1.95/2.12 P_function_inverse-{F}(V0,V1), relation-{F}(V0), function-{F}(V0) | relation-{T}(V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #15: input, references = 6, size of lhs = 3:
% 1.95/2.12 P_function_inverse-{F}(V0,V1), relation-{F}(V0), function-{F}(V0) | function-{T}(V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #16: input, references = 3, size of lhs = 3:
% 1.95/2.12 relation-{F}(V0), P_relation_composition-{F}(V1,V0,V2), relation-{F}(V1) | relation-{T}(V2)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #17: input, references = 3, size of lhs = 1:
% 1.95/2.12 #-{F} V0 | EXISTS V1: pppp4-{T}(V0,V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #18: input, references = 3, size of lhs = 1:
% 1.95/2.12 pppp4-{F}(V0,V1) | element-{T}(V1,V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #19: input, references = 5, size of lhs = 3:
% 1.95/2.12 relation-{F}(V0), P_relation_composition-{F}(V0,V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #20: input, references = 3, size of lhs = 3:
% 1.95/2.12 relation-{F}(V0), P_relation_composition-{F}(V0,V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #21: input, references = 3, size of lhs = 1:
% 1.95/2.12 P_empty_set-{F}(V0) | empty-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #22: input, references = 3, size of lhs = 1:
% 1.95/2.12 P_empty_set-{F}(V0) | relation-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #23: input, references = 3, size of lhs = 1:
% 1.95/2.12 P_empty_set-{F}(V0) | relation_empty_yielding-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #24: input, references = 3, size of lhs = 6:
% 1.95/2.12 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)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #25: input, references = 3, size of lhs = 6:
% 1.95/2.12 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)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #26: input, references = 3, size of lhs = 1:
% 1.95/2.12 P_empty_set-{F}(V0) | empty-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #27: input, references = 3, size of lhs = 1:
% 1.95/2.12 P_empty_set-{F}(V0) | empty-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #28: input, references = 3, size of lhs = 1:
% 1.95/2.12 P_empty_set-{F}(V0) | relation-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #29: input, references = 5, size of lhs = 4:
% 1.95/2.12 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), relation-{F}(V1), empty-{F}(V2) | empty-{T}(V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #30: input, references = 3, size of lhs = 4:
% 1.95/2.12 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), relation-{F}(V1), empty-{F}(V2) | empty-{T}(V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #31: input, references = 5, size of lhs = 3:
% 1.95/2.12 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #32: input, references = 3, size of lhs = 3:
% 1.95/2.12 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #33: input, references = 5, size of lhs = 3:
% 1.95/2.12 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #34: input, references = 3, size of lhs = 3:
% 1.95/2.12 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #35: input, references = 5, size of lhs = 4:
% 1.95/2.12 P_empty_set-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V2,V1,V3), empty-{F}(V2) | empty-{T}(V3)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #36: input, references = 3, size of lhs = 4:
% 1.95/2.12 P_empty_set-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V2,V1,V3), empty-{F}(V2) | relation-{T}(V3)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #37: input, references = 3, size of lhs = 1:
% 1.95/2.12 P_empty_set-{F}(V0) | EXISTS V1: pppp5-{T}(V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #38: input, references = 3, size of lhs = 1:
% 1.95/2.12 pppp5-{F}(V0) | function-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #39: input, references = 3, size of lhs = 1:
% 1.95/2.12 pppp5-{F}(V0) | relation-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #40: input, references = 4, size of lhs = 1:
% 1.95/2.12 P_empty_set-{F}(V0) | EXISTS V1: pppp6-{T}(V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #41: input, references = 3, size of lhs = 1:
% 1.95/2.12 pppp6-{F}(V0) | relation-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #42: input, references = 5, size of lhs = 1:
% 1.95/2.12 pppp6-{F}(V0) | empty-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #43: input, references = 4, size of lhs = 1:
% 1.95/2.12 P_empty_set-{F}(V0) | EXISTS V1: pppp7-{T}(V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #44: input, references = 5, size of lhs = 1:
% 1.95/2.12 pppp7-{F}(V0) | empty-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #45: input, references = 4, size of lhs = 1:
% 1.95/2.12 P_empty_set-{F}(V0) | EXISTS V1: pppp8-{T}(V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #46: input, references = 3, size of lhs = 1:
% 1.95/2.12 pppp8-{F}(V0) | function-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #47: input, references = 5, size of lhs = 1:
% 1.95/2.12 pppp8-{F}(V0) | empty-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #48: input, references = 3, size of lhs = 1:
% 1.95/2.12 pppp8-{F}(V0) | relation-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #49: input, references = 3, size of lhs = 1:
% 1.95/2.12 P_empty_set-{F}(V0) | EXISTS V1: pppp9-{T}(V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #50: input, references = 3, size of lhs = 1:
% 1.95/2.12 pppp9-{F}(V0) | relation-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #51: input, references = 3, size of lhs = 2:
% 1.95/2.12 pppp9-{F}(V0), empty-{F}(V0) | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #52: input, references = 3, size of lhs = 1:
% 1.95/2.12 P_empty_set-{F}(V0) | EXISTS V1: pppp10-{T}(V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #53: input, references = 3, size of lhs = 2:
% 1.95/2.12 pppp10-{F}(V0), empty-{F}(V0) | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #54: input, references = 3, size of lhs = 1:
% 1.95/2.12 P_empty_set-{F}(V0) | EXISTS V1: pppp11-{T}(V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #55: input, references = 3, size of lhs = 1:
% 1.95/2.12 pppp11-{F}(V0) | one_to_one-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #56: input, references = 3, size of lhs = 1:
% 1.95/2.12 pppp11-{F}(V0) | function-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #57: input, references = 3, size of lhs = 1:
% 1.95/2.12 pppp11-{F}(V0) | relation-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #58: input, references = 3, size of lhs = 1:
% 1.95/2.12 P_empty_set-{F}(V0) | EXISTS V1: pppp12-{T}(V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #59: input, references = 3, size of lhs = 1:
% 1.95/2.12 pppp12-{F}(V0) | relation_empty_yielding-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #60: input, references = 3, size of lhs = 1:
% 1.95/2.12 pppp12-{F}(V0) | relation-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #61: input, references = 3, size of lhs = 2:
% 1.95/2.12 P_empty_set-{F}(V0), in-{F}(V1,V2) | element-{T}(V1,V2)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #62: input, references = 5, size of lhs = 2:
% 1.95/2.12 P_empty_set-{F}(V0), element-{F}(V2,V1) | empty-{T}(V1), in-{T}(V2,V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #63: input, references = 7, size of lhs = 7:
% 1.95/2.12 P_empty_set-{F}(V0), P_function_inverse-{F}(V1,V2), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), relation-{F}(V2), function-{F}(V2) | pppp1-{T}(V1,V2)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #64: input, references = 3, size of lhs = 9:
% 1.95/2.12 P_empty_set-{F}(V0), P_function_inverse-{F}(V1,V2), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), relation-{F}(V3), function-{F}(V3), pppp1-{F}(V1,V3), V3 == V2 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #65: input, references = 9, size of lhs = 5:
% 1.95/2.12 P_empty_set-{F}(V0), P_relation_dom-{F}(V2,V3), P_relation_rng-{F}(V1,V4), P_relation_dom-{F}(V1,V5), pppp1-{F}(V1,V2) | pppp13-{T}(V1,V2,V3,V4,V5)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #66: input, references = 5, size of lhs = 4:
% 1.95/2.12 P_empty_set-{F}(V0), P_relation_dom-{F}(V2,V4), P_relation_rng-{F}(V1,V4), P_relation_dom-{F}(V1,V5) | pppp1-{T}(V1,V2), pppp19-{T}(V1,V2,V4,V5)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #67: input, references = 3, size of lhs = 1:
% 1.95/2.12 pppp19-{F}(V0,V1,V2,V3) | EXISTS V4: pppp16-{T}(V0,V1,V2,V3,V4)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #68: input, references = 5, size of lhs = 1:
% 1.95/2.12 pppp16-{F}(V0,V1,V2,V3,V4) | EXISTS V5: pppp15-{T}(V0,V1,V4,V5,V2,V3)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #69: input, references = 3, size of lhs = 4:
% 1.95/2.12 pppp15-{F}(V0,V1,V2,V6,V4,V5), P_apply-{F}(V1,V2,V6), P_apply-{F}(V0,V6,V7), in-{F}(V2,V4) | pppp14-{T}(V2,V6,V4,V5,V6,V7)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #70: input, references = 4, size of lhs = 4:
% 1.95/2.12 pppp15-{F}(V0,V1,V2,V3,V4,V5), P_apply-{F}(V1,V2,V6), P_apply-{F}(V0,V3,V7), V2 == V7 | pppp14-{T}(V2,V3,V4,V5,V6,V7)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #71: input, references = 5, size of lhs = 3:
% 1.95/2.12 pppp15-{F}(V0,V1,V2,V3,V4,V5), P_apply-{F}(V1,V2,V6), P_apply-{F}(V0,V3,V7) | pppp14-{T}(V2,V3,V4,V5,V6,V7), in-{T}(V3,V5)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #72: input, references = 3, size of lhs = 2:
% 1.95/2.12 pppp14-{F}(V5,V1,V2,V3,V4,V5), in-{F}(V1,V3) | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #73: input, references = 6, size of lhs = 2:
% 1.95/2.12 pppp14-{F}(V0,V1,V2,V3,V4,V5), V1 == V4 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #74: input, references = 5, size of lhs = 1:
% 1.95/2.12 pppp14-{F}(V0,V1,V2,V3,V4,V5) | in-{T}(V0,V2)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #75: input, references = 5, size of lhs = 5:
% 1.95/2.12 pppp13-{F}(V0,V1,V2,V3,V4), P_apply-{F}(V1,V8,V7), P_apply-{F}(V0,V6,V8), in-{F}(V6,V4), V6 == V7 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #76: input, references = 4, size of lhs = 4:
% 1.95/2.12 pppp13-{F}(V0,V1,V2,V3,V4), P_apply-{F}(V1,V8,V7), P_apply-{F}(V0,V6,V8), in-{F}(V6,V4) | in-{T}(V8,V3)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #77: input, references = 5, size of lhs = 5:
% 1.95/2.12 pppp13-{F}(V0,V1,V2,V3,V4), P_apply-{F}(V1,V5,V7), P_apply-{F}(V0,V7,V8), in-{F}(V5,V3), V5 == V8 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #78: input, references = 3, size of lhs = 4:
% 1.95/2.12 pppp13-{F}(V0,V1,V2,V3,V4), P_apply-{F}(V1,V5,V7), P_apply-{F}(V0,V7,V8), in-{F}(V5,V3) | in-{T}(V7,V4)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #79: input, references = 6, size of lhs = 2:
% 1.95/2.12 pppp13-{F}(V0,V1,V2,V3,V4), V2 == V3 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #80: input, references = 3, size of lhs = 12:
% 1.95/2.12 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), P_function_inverse-{F}(V1,V3), P_relation_composition-{F}(V3,V1,V4), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_apply-{F}(V3,V5,V6), P_apply-{F}(V1,V6,V7), P_apply-{F}(V4,V5,V8), in-{F}(V5,V2), V5 == V7 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #81: input, references = 4, size of lhs = 12:
% 1.95/2.12 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), P_function_inverse-{F}(V1,V3), P_relation_composition-{F}(V3,V1,V4), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_apply-{F}(V3,V5,V6), P_apply-{F}(V1,V6,V7), P_apply-{F}(V4,V5,V8), in-{F}(V5,V2), V5 == V8 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #82: input, references = 4, size of lhs = 1:
% 1.95/2.12 P_empty_set-{F}(V0) | EXISTS V1: pppp17-{T}(V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #83: input, references = 4, size of lhs = 3:
% 1.95/2.12 pppp17-{F}(V0), P_function_inverse-{F}(V0,V1), one_to_one-{F}(V1) | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #84: input, references = 4, size of lhs = 2:
% 1.95/2.12 pppp17-{F}(V0), P_function_inverse-{F}(V0,V1) | one_to_one-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #85: input, references = 4, size of lhs = 2:
% 1.95/2.12 pppp17-{F}(V0), P_function_inverse-{F}(V0,V1) | function-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #86: input, references = 4, size of lhs = 2:
% 1.95/2.12 pppp17-{F}(V0), P_function_inverse-{F}(V0,V1) | relation-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #87: input, references = 11, size of lhs = 3:
% 1.95/2.12 P_empty_set-{F}(V0), empty-{F}(V1), V1 == V0 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #88: input, references = 4, size of lhs = 3:
% 1.95/2.12 P_empty_set-{F}(V0), empty-{F}(V1), in-{F}(V2,V1) | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #89: input, references = 11, size of lhs = 4:
% 1.95/2.12 P_empty_set-{F}(V0), empty-{F}(V1), empty-{F}(V2), V2 == V1 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #90: input, references = 6, size of lhs = 1:
% 1.95/2.12 #-{F} V0 | EXISTS V1: P_relation_dom-{T}(V0,V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #91: input, references = 12, size of lhs = 2:
% 1.95/2.12 #-{F} V0, #-{F} V1 | EXISTS V2: P_apply-{T}(V0,V1,V2)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #92: input, references = 7, size of lhs = 1:
% 1.95/2.12 #-{F} V0 | EXISTS V1: P_function_inverse-{T}(V0,V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #93: input, references = 5, size of lhs = 2:
% 1.95/2.12 #-{F} V0, #-{F} V1 | EXISTS V2: P_relation_composition-{T}(V0,V1,V2)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #94: input, references = 4, size of lhs = 0:
% 1.95/2.12 FALSE | EXISTS V0: P_empty_set-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #95: input, references = 6, size of lhs = 1:
% 1.95/2.12 #-{F} V0 | EXISTS V1: P_relation_rng-{T}(V0,V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 number of initial rules = 96
% 1.95/2.12
% 1.95/2.12 Simplifiers:
% 1.95/2.12 #96: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 P_relation_dom-{F}(V0,V1), P_relation_dom-{F}(V0,V3), V1 == V3 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #97: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 P_apply-{F}(V0,V1,V2), P_apply-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #98: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 P_function_inverse-{F}(V0,V1), P_function_inverse-{F}(V0,V3), V1 == V3 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #99: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 P_relation_composition-{F}(V0,V1,V2), P_relation_composition-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #100: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 P_empty_set-{F}(V0), P_empty_set-{F}(V1), V0 == V1 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #101: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 P_relation_rng-{F}(V0,V1), P_relation_rng-{F}(V0,V3), V1 == V3 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #102: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp2-{F}(V0,V1,V2,V3,V4), pppp2-{F}(V0,V6,V2,V3,V4), V1 == V6 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #103: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp2-{F}(V0,V1,V2,V3,V4), pppp2-{F}(V0,V6,V7,V3,V9), V2 == V7 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #104: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp2-{F}(V0,V1,V2,V3,V4), pppp2-{F}(V0,V6,V7,V8,V9), V3 == V8 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #105: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp2-{F}(V0,V1,V2,V3,V4), pppp2-{F}(V0,V6,V2,V8,V9), V4 == V9 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #106: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp3-{F}(V0,V1,V2), pppp3-{F}(V0,V4,V2), V1 == V4 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #107: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp3-{F}(V0,V1,V2), pppp3-{F}(V0,V4,V5), V2 == V5 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #108: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp4-{F}(V0,V1), pppp4-{F}(V0,V3), V1 == V3 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #109: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp5-{F}(V0), pppp5-{F}(V1), V0 == V1 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #110: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp6-{F}(V0), pppp6-{F}(V1), V0 == V1 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #111: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp7-{F}(V0), pppp7-{F}(V1), V0 == V1 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #112: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp8-{F}(V0), pppp8-{F}(V1), V0 == V1 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #113: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp9-{F}(V0), pppp9-{F}(V1), V0 == V1 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #114: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp10-{F}(V0), pppp10-{F}(V1), V0 == V1 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #115: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp11-{F}(V0), pppp11-{F}(V1), V0 == V1 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #116: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp12-{F}(V0), pppp12-{F}(V1), V0 == V1 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #117: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp13-{F}(V0,V1,V2,V3,V4), pppp13-{F}(V5,V1,V7,V8,V9), V2 == V7 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #118: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp13-{F}(V0,V1,V2,V3,V4), pppp13-{F}(V0,V6,V7,V8,V9), V3 == V8 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #119: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp13-{F}(V0,V1,V2,V3,V4), pppp13-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #120: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp15-{F}(V0,V1,V2,V3,V4,V5), pppp15-{F}(V0,V1,V2,V9,V4,V5), V3 == V9 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #121: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp15-{F}(V0,V1,V2,V3,V4,V5), pppp15-{F}(V0,V1,V8,V9,V4,V5), V2 == V8 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #122: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp15-{F}(V0,V1,V2,V3,V4,V5), pppp15-{F}(V6,V1,V8,V9,V10,V11), V4 == V10 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #123: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp15-{F}(V0,V1,V2,V3,V4,V5), pppp15-{F}(V0,V7,V8,V9,V10,V11), V4 == V10 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #124: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp15-{F}(V0,V1,V2,V3,V4,V5), pppp15-{F}(V0,V7,V8,V9,V10,V11), V5 == V11 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #125: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp16-{F}(V0,V1,V2,V3,V4), pppp16-{F}(V0,V1,V2,V3,V9), V4 == V9 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #126: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp16-{F}(V0,V1,V2,V3,V4), pppp16-{F}(V5,V1,V7,V8,V9), V2 == V7 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #127: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp16-{F}(V0,V1,V2,V3,V4), pppp16-{F}(V0,V6,V7,V8,V9), V2 == V7 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #128: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp16-{F}(V0,V1,V2,V3,V4), pppp16-{F}(V0,V6,V7,V8,V9), V3 == V8 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #129: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp17-{F}(V0), pppp17-{F}(V1), V0 == V1 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #130: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp18-{F}(V0,V1), pppp18-{F}(V0,V3), V1 == V3 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #131: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp19-{F}(V0,V1,V2,V3), pppp19-{F}(V4,V1,V6,V7), V2 == V6 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #132: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp19-{F}(V0,V1,V2,V3), pppp19-{F}(V0,V5,V6,V7), V2 == V6 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #133: unsound, references = 3, size of lhs = 3:
% 1.95/2.12 pppp19-{F}(V0,V1,V2,V3), pppp19-{F}(V0,V5,V6,V7), V3 == V7 | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 number of simplifiers = 38
% 1.95/2.12
% 1.95/2.12 Learnt:
% 1.95/2.12 #139: mergings( V0 == V2; #136 ), references = 1, size of lhs = 1:
% 1.95/2.12 P_empty_set-{F}(V0) | pppp6-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #141: mergings( V0 == V2; #137 ), references = 1, size of lhs = 2:
% 1.95/2.12 P_empty_set-{F}(V0), empty-{F}(V1) | pppp6-{T}(V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #147: mergings( V0 == V2; #144 ), references = 1, size of lhs = 1:
% 1.95/2.12 P_empty_set-{F}(V0) | pppp7-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #149: mergings( V0 == V2; #145 ), references = 1, size of lhs = 2:
% 1.95/2.12 P_empty_set-{F}(V0), empty-{F}(V1) | pppp7-{T}(V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #162: mergings( V2 == V3; #159 ), references = 1, size of lhs = 2:
% 1.95/2.12 empty-{F}(V0), P_empty_set-{F}(V1) | P_relation_dom-{T}(V0,V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #164: mergings( V2 == V3; #160 ), references = 1, size of lhs = 3:
% 1.95/2.12 empty-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2) | P_relation_dom-{T}(V0,V2)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #185: exists( #93, #181 ), references = 1, size of lhs = 3:
% 1.95/2.12 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2) | P_relation_composition-{T}(V0,V1,V2)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #186: exists( #93, #182 ), references = 1, size of lhs = 4:
% 1.95/2.12 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3) | P_relation_composition-{T}(V0,V1,V3)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #192: mergings( V0 == V2; #189 ), references = 1, size of lhs = 1:
% 1.95/2.12 P_empty_set-{F}(V0) | pppp8-{T}(V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #194: mergings( V0 == V2; #190 ), references = 1, size of lhs = 2:
% 1.95/2.12 P_empty_set-{F}(V0), empty-{F}(V1) | pppp8-{T}(V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #214: mergings( V2 == V3; #211 ), references = 1, size of lhs = 2:
% 1.95/2.12 empty-{F}(V0), P_empty_set-{F}(V1) | P_relation_rng-{T}(V0,V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #216: mergings( V2 == V3; #212 ), references = 1, size of lhs = 3:
% 1.95/2.12 empty-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2) | P_relation_rng-{T}(V0,V2)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #235: mergings( V0 == V5; #233 ), references = 1, size of lhs = 11:
% 1.95/2.12 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), one_to_one-{F}(V1), P_relation_rng-{F}(V1,V2), P_relation_dom-{F}(V1,V3), P_function_inverse-{F}(V1,V4), relation-{F}(V5), V5 == V4, P_relation_dom-{F}(V5,V2), function-{F}(V5) | pppp19-{T}(V1,V5,V2,V3)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #237: disj( #62, input ), references = 1, size of lhs = 2:
% 1.95/2.12 P_empty_set-{F}(V0), element-{F}(V1,V1) | empty-{T}(V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #256: exists( #90, #254 ), references = 4, size of lhs = 4:
% 1.95/2.12 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), P_relation_dom-{F}(V1,V3), pppp1-{F}(V1,V4) | P_relation_dom-{T}(V4,V2)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #282: mergings( V3 == V4; #279 ), references = 1, size of lhs = 3:
% 1.95/2.12 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2) | P_relation_composition-{T}(V1,V0,V2)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #284: mergings( V3 == V4; #280 ), references = 1, size of lhs = 4:
% 1.95/2.12 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3) | P_relation_composition-{T}(V1,V0,V3)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #327: mergings( V2 == V3, V3 == V4, V4 == V7; #322 ), references = 1, size of lhs = 7:
% 1.95/2.12 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)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #331: mergings( V2 == V3, V3 == V4, V4 == V7; #323 ), references = 1, size of lhs = 8:
% 1.95/2.12 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)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #348: mergings( V0 == V3; #344 ), references = 1, size of lhs = 3:
% 1.95/2.12 P_empty_set-{F}(V0), element-{F}(V1,V2), V2 == V0 | in-{T}(V1,V2)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #351: mergings( V0 == V3, V2 == V3; #345 ), references = 1, size of lhs = 4:
% 1.95/2.12 P_empty_set-{F}(V0), empty-{F}(V1), V0 == V1, element-{F}(V2,V0) | in-{T}(V2,V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #353: mergings( V2 == V0; #346 ), references = 1, size of lhs = 3:
% 1.95/2.12 P_empty_set-{F}(V0), pppp10-{F}(V0), element-{F}(V1,V0) | in-{T}(V1,V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #386: disj( #7, #5+#83 ), references = 1, size of lhs = 5:
% 1.95/2.12 relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), pppp17-{F}(V2), P_function_inverse-{F}(V2,V0) | pppp18-{T}(V0,V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #394: exists( #91, #390 ), references = 2, size of lhs = 3:
% 1.95/2.12 in-{F}(V0,V1), P_apply-{F}(V2,V0,V3), pppp13-{F}(V2,V4,V5,V3,V1) | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #402: exists( #91, #75 ), references = 1, size of lhs = 3:
% 1.95/2.12 in-{F}(V0,V1), P_apply-{F}(V2,V0,V3), pppp13-{F}(V2,V4,V5,V6,V1) | P_apply-{T}(V4,V3,V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #411: mergings( V2 == V8, V4 == V7, V0 == V5, V8 == V6; #405 ), references = 1, size of lhs = 6:
% 1.95/2.12 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), P_relation_dom-{F}(V1,V3), P_relation_dom-{F}(V4,V2), in-{F}(V5,V3), P_apply-{F}(V1,V5,V2) | pppp19-{T}(V1,V4,V2,V3)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #416: mergings( V2 == V8, V4 == V7, V0 == V5, V8 == V6; #406 ), references = 1, size of lhs = 8:
% 1.95/2.12 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), P_relation_dom-{F}(V1,V3), P_relation_dom-{F}(V4,V2), in-{F}(V5,V3), P_apply-{F}(V1,V5,V6), P_apply-{F}(V4,V6,V7), V5 == V7 | pppp19-{T}(V1,V4,V2,V3)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #428: disj( #71, input ), references = 3, size of lhs = 3:
% 1.95/2.12 P_apply-{F}(V0,V1,V2), pppp15-{F}(V3,V0,V1,V4,V5,V4), P_apply-{F}(V3,V4,V6) | pppp14-{T}(V1,V4,V5,V4,V2,V6)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #429: disj( #71, input ), references = 2, size of lhs = 9:
% 1.95/2.12 pppp0-{F}(V0), P_relation_dom-{F}(V0,V1), in-{F}(V2,V1), P_apply-{F}(V0,V2,V3), P_apply-{F}(V0,V4,V3), V2 == V4, P_apply-{F}(V5,V4,V6), pppp15-{F}(V5,V7,V8,V4,V9,V1), P_apply-{F}(V7,V8,V10) | pppp14-{T}(V8,V4,V9,V1,V10,V6)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #447: exists( #91, #445 ), references = 2, size of lhs = 3:
% 1.95/2.12 P_apply-{F}(V0,V1,V2), pppp15-{F}(V3,V0,V1,V4,V5,V6), V4 == V2 | P_apply-{T}(V3,V4,V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #452: mergings( V7 == V8; #450 ), references = 1, size of lhs = 6:
% 1.95/2.12 pppp0-{F}(V0), P_relation_dom-{F}(V0,V1), in-{F}(V2,V1), P_apply-{F}(V0,V2,V3), pppp16-{F}(V0,V4,V5,V1,V3), P_apply-{F}(V4,V3,V6) | pppp15-{T}(V0,V4,V3,V6,V5,V1), pppp15-{T}(V0,V4,V3,V2,V5,V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #471: mergings( V1 == V5, V5 == V7, V6 == V8; #459 ), references = 1, size of lhs = 7:
% 1.95/2.12 pppp0-{F}(V0), P_relation_dom-{F}(V0,V1), in-{F}(V2,V1), P_apply-{F}(V0,V2,V3), pppp16-{F}(V0,V4,V3,V1,V3), P_apply-{F}(V4,V3,V1), P_apply-{F}(V0,V1,V5) | pppp15-{T}(V0,V4,V3,V2,V3,V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #475: mergings( V1 == V5, V5 == V8, V6 == V9; #460 ), references = 1, size of lhs = 9:
% 1.95/2.12 pppp0-{F}(V0), P_relation_dom-{F}(V0,V1), in-{F}(V2,V1), P_apply-{F}(V0,V2,V3), empty-{F}(V3), pppp16-{F}(V0,V4,V3,V1,V3), P_apply-{F}(V4,V3,V1), P_empty_set-{F}(V5), P_apply-{F}(V0,V1,V6) | pppp15-{T}(V0,V4,V3,V2,V3,V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #479: mergings( V1 == V6, V6 == V8, V7 == V9; #462 ), references = 1, size of lhs = 9:
% 1.95/2.12 pppp0-{F}(V0), P_relation_dom-{F}(V0,V1), in-{F}(V2,V1), P_apply-{F}(V0,V2,V3), empty-{F}(V3), pppp16-{F}(V0,V4,V3,V1,V3), P_apply-{F}(V4,V3,V1), P_empty_set-{F}(V5), P_apply-{F}(V0,V1,V6) | pppp15-{T}(V0,V4,V3,V2,V3,V1)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #505: exists( #91, #502 ), references = 1, size of lhs = 1:
% 1.95/2.12 pppp3-{F}(V0,V1,V1) | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #540: mergings( V1 == V6, V2 == V4; #537 ), references = 1, size of lhs = 10:
% 1.95/2.12 relation-{F}(V0), function-{F}(V0), P_function_inverse-{F}(V0,V1), relation-{F}(V1), function-{F}(V1), P_empty_set-{F}(V2), P_relation_rng-{F}(V0,V3), P_relation_dom-{F}(V0,V4), P_relation_dom-{F}(V1,V5), V5 == V3 | pppp18-{T}(V0,V4)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #542: exists( #91, #77 ), references = 2, size of lhs = 3:
% 1.95/2.12 in-{F}(V0,V1), P_apply-{F}(V2,V0,V3), pppp13-{F}(V4,V2,V5,V1,V6) | P_apply-{T}(V4,V3,V0)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #563: exists( #91, #81 ), references = 1, size of lhs = 10:
% 1.95/2.12 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_composition-{F}(V3,V1,V4), in-{F}(V5,V2), P_apply-{F}(V3,V5,V6), P_apply-{F}(V1,V6,V7) | P_apply-{T}(V4,V5,V5)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #565: disj( #71, input ), references = 1, size of lhs = 7:
% 1.95/2.12 P_apply-{F}(V0,V1,V2), P_apply-{F}(V3,V4,V5), pppp15-{F}(V3,V0,V1,V4,V6,V7), P_apply-{F}(V8,V4,V9), P_apply-{F}(V10,V9,V11), V4 == V11, pppp13-{F}(V10,V8,V12,V7,V13) | pppp14-{T}(V1,V4,V6,V7,V2,V5)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #570: mergings( V6 == V9; #568 ), references = 1, size of lhs = 4:
% 1.95/2.12 P_apply-{F}(V0,V1,V2), P_apply-{F}(V3,V1,V4), pppp16-{F}(V5,V0,V6,V7,V1), pppp13-{F}(V3,V5,V8,V7,V9) | pppp15-{T}(V5,V0,V1,V2,V6,V7), pppp15-{T}(V5,V0,V1,V4,V6,V7)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #587: exists( #91, #12 ), references = 1, size of lhs = 1:
% 1.95/2.12 pppp2-{F}(V0,V1,V2,V3,V4) | P_apply-{T}(V0,V1,V4)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #591: exists( #9, #589 ), references = 2, size of lhs = 4:
% 1.95/2.12 pppp3-{F}(V0,V1,V2), P_apply-{F}(V0,V1,V3), P_apply-{F}(V4,V3,V5), pppp13-{F}(V4,V0,V6,V2,V7) | pppp2-{T}(V0,V5,V1,V2,V3)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #599: mergings( V6 == V8, V3 == V4, V7 == V9; #595 ), references = 2, size of lhs = 3:
% 1.95/2.12 in-{F}(V0,V1), pppp3-{F}(V2,V0,V1), pppp13-{F}(V3,V2,V4,V1,V5) | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #622: exists( #91, #619 ), references = 1, size of lhs = 3:
% 1.95/2.12 pppp3-{F}(V0,V1,V2), pppp3-{F}(V3,V1,V2), pppp13-{F}(V4,V3,V5,V2,V6) | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #624: exists( #8, #621 ), references = 1, size of lhs = 2:
% 1.95/2.12 pppp18-{F}(V0,V1), pppp13-{F}(V2,V0,V3,V1,V4) | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #631: mergings( V5 == V6, V2 == V3; #628 ), references = 1, size of lhs = 7:
% 1.95/2.12 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), pppp1-{F}(V2,V1), P_relation_dom-{F}(V2,V3), pppp17-{F}(V4), P_function_inverse-{F}(V4,V1) | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #639: mergings( V5 == V6, V2 == V3, V3 == V4; #635 ), references = 1, size of lhs = 6:
% 1.95/2.12 relation-{F}(V0), function-{F}(V0), one_to_one-{F}(V0), pppp17-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V0,V2) | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #643: mergings( V2 == V3, V3 == V4; #640 ), references = 2, size of lhs = 5:
% 1.95/2.12 relation-{F}(V0), function-{F}(V0), one_to_one-{F}(V0), pppp17-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #646: exists( #95, #644 ), references = 1, size of lhs = 4:
% 1.95/2.12 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), pppp1-{F}(V1,V3), P_relation_dom-{F}(V3,V4) | P_relation_rng-{T}(V1,V4)
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #679: exists( #92, #675 ), references = 2, size of lhs = 4:
% 1.95/2.12 relation-{F}(V0), function-{F}(V0), pppp17-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #690: exists( #92, #684 ), references = 1, size of lhs = 2:
% 1.95/2.12 pppp17-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #694: mergings( V0 == V2; #691 ), references = 1, size of lhs = 1:
% 1.95/2.12 P_empty_set-{F}(V0) | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 #697: exists( #94, #691 ), references = 1, size of lhs = 0:
% 1.95/2.12 FALSE | FALSE
% 1.95/2.12 (used 0 times, uses = {})
% 1.95/2.12
% 1.95/2.12 number of learnt formulas = 53
% 1.95/2.12
% 1.95/2.12
% 1.95/2.12 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.95/2.12
% 1.95/2.12 randbase = 1
%------------------------------------------------------------------------------