TSTP Solution File: SEU221+3 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : SEU221+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n028.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 10.82s 11.01s
% Output : Refutation 10.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU221+3 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n028.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 19:44:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 10.82/11.01 GeoParameters:
% 10.82/11.01
% 10.82/11.01 tptp_input = 1
% 10.82/11.01 tptp_output = 0
% 10.82/11.01 nonempty = 1
% 10.82/11.01 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.82/11.01 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 10.82/11.01
% 10.82/11.01
% 10.82/11.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.82/11.01 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.82/11.01
% 10.82/11.01 RuleSystem INPUT:
% 10.82/11.01
% 10.82/11.01 Initial Rules:
% 10.82/11.01 #0: input, references = 3, size of lhs = 2:
% 10.82/11.01 in-{F}(V0,V1), in-{F}(V1,V0) | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #1: input, references = 3, size of lhs = 1:
% 10.82/11.01 empty-{F}(V0) | function-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #2: input, references = 3, size of lhs = 1:
% 10.82/11.01 empty-{F}(V0) | relation-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #3: input, references = 3, size of lhs = 3:
% 10.82/11.01 relation-{F}(V0), empty-{F}(V0), function-{F}(V0) | one_to_one-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #4: input, references = 3, size of lhs = 3:
% 10.82/11.01 relation-{F}(V0), function-{F}(V0), one_to_one-{F}(V0) | pppp0-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #5: input, references = 8, size of lhs = 3:
% 10.82/11.01 relation-{F}(V0), function-{F}(V0), pppp0-{F}(V0) | one_to_one-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #6: input, references = 3, size of lhs = 7:
% 10.82/11.01 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
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #7: input, references = 8, size of lhs = 1:
% 10.82/11.01 P_relation_dom-{F}(V0,V1) | pppp0-{T}(V0), pppp20-{T}(V0,V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #8: input, references = 4, size of lhs = 1:
% 10.82/11.01 pppp20-{F}(V0,V1) | EXISTS V2: pppp3-{T}(V0,V2,V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #9: input, references = 4, size of lhs = 2:
% 10.82/11.01 pppp3-{F}(V0,V1,V2), P_apply-{F}(V0,V1,V3) | EXISTS V4: pppp2-{T}(V0,V4,V1,V2,V3)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #10: input, references = 7, size of lhs = 2:
% 10.82/11.01 pppp3-{F}(V0,V1,V2), P_apply-{F}(V0,V1,V3) | in-{T}(V1,V2)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #11: input, references = 4, size of lhs = 2:
% 10.82/11.01 pppp2-{F}(V0,V2,V2,V3,V4), P_apply-{F}(V0,V2,V5) | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #12: input, references = 4, size of lhs = 3:
% 10.82/11.01 pppp2-{F}(V0,V1,V2,V3,V4), P_apply-{F}(V0,V1,V5), V5 == V4 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #13: input, references = 4, size of lhs = 2:
% 10.82/11.01 pppp2-{F}(V0,V1,V2,V3,V4), P_apply-{F}(V0,V1,V5) | in-{T}(V1,V3)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #14: input, references = 6, size of lhs = 3:
% 10.82/11.01 P_function_inverse-{F}(V0,V1), relation-{F}(V0), function-{F}(V0) | relation-{T}(V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #15: input, references = 6, size of lhs = 3:
% 10.82/11.01 P_function_inverse-{F}(V0,V1), relation-{F}(V0), function-{F}(V0) | function-{T}(V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #16: input, references = 3, size of lhs = 3:
% 10.82/11.01 relation-{F}(V0), P_relation_composition-{F}(V1,V0,V2), relation-{F}(V1) | relation-{T}(V2)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #17: input, references = 7, size of lhs = 1:
% 10.82/11.01 #-{F} V0 | EXISTS V1: pppp4-{T}(V0,V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #18: input, references = 7, size of lhs = 1:
% 10.82/11.01 pppp4-{F}(V0,V1) | element-{T}(V1,V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #19: input, references = 5, size of lhs = 3:
% 10.82/11.01 relation-{F}(V0), P_relation_composition-{F}(V0,V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #20: input, references = 3, size of lhs = 3:
% 10.82/11.01 relation-{F}(V0), P_relation_composition-{F}(V0,V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #21: input, references = 3, size of lhs = 1:
% 10.82/11.01 P_empty_set-{F}(V0) | empty-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #22: input, references = 3, size of lhs = 1:
% 10.82/11.01 P_empty_set-{F}(V0) | relation-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #23: input, references = 3, size of lhs = 1:
% 10.82/11.01 P_empty_set-{F}(V0) | relation_empty_yielding-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #24: input, references = 3, size of lhs = 6:
% 10.82/11.01 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)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #25: input, references = 3, size of lhs = 6:
% 10.82/11.01 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)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #26: input, references = 3, size of lhs = 3:
% 10.82/11.01 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), empty-{F}(V2) | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #27: input, references = 3, size of lhs = 1:
% 10.82/11.01 P_empty_set-{F}(V0) | empty-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #28: input, references = 3, size of lhs = 1:
% 10.82/11.01 P_empty_set-{F}(V0) | empty-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #29: input, references = 3, size of lhs = 1:
% 10.82/11.01 P_empty_set-{F}(V0) | relation-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #30: input, references = 5, size of lhs = 4:
% 10.82/11.01 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), relation-{F}(V1), empty-{F}(V2) | empty-{T}(V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #31: input, references = 3, size of lhs = 4:
% 10.82/11.01 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), relation-{F}(V1), empty-{F}(V2) | empty-{T}(V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #32: input, references = 5, size of lhs = 3:
% 10.82/11.01 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #33: input, references = 3, size of lhs = 3:
% 10.82/11.01 P_empty_set-{F}(V0), P_relation_dom-{F}(V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #34: input, references = 5, size of lhs = 3:
% 10.82/11.01 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), empty-{F}(V1) | empty-{T}(V2)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #35: input, references = 3, size of lhs = 3:
% 10.82/11.01 P_empty_set-{F}(V0), P_relation_rng-{F}(V1,V2), empty-{F}(V1) | relation-{T}(V2)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #36: input, references = 5, size of lhs = 4:
% 10.82/11.01 P_empty_set-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V2,V1,V3), empty-{F}(V2) | empty-{T}(V3)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #37: input, references = 3, size of lhs = 4:
% 10.82/11.01 P_empty_set-{F}(V0), relation-{F}(V1), P_relation_composition-{F}(V2,V1,V3), empty-{F}(V2) | relation-{T}(V3)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #38: input, references = 3, size of lhs = 1:
% 10.82/11.01 P_empty_set-{F}(V0) | EXISTS V1: pppp5-{T}(V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #39: input, references = 3, size of lhs = 1:
% 10.82/11.01 pppp5-{F}(V0) | function-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #40: input, references = 3, size of lhs = 1:
% 10.82/11.01 pppp5-{F}(V0) | relation-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #41: input, references = 4, size of lhs = 1:
% 10.82/11.01 P_empty_set-{F}(V0) | EXISTS V1: pppp6-{T}(V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #42: input, references = 3, size of lhs = 1:
% 10.82/11.01 pppp6-{F}(V0) | relation-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #43: input, references = 5, size of lhs = 1:
% 10.82/11.01 pppp6-{F}(V0) | empty-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #44: input, references = 4, size of lhs = 2:
% 10.82/11.01 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2) | empty-{T}(V1), pppp21-{T}(V2)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #45: input, references = 3, size of lhs = 1:
% 10.82/11.01 pppp21-{F}(V0) | EXISTS V1: pppp7-{T}(V1,V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #46: input, references = 3, size of lhs = 2:
% 10.82/11.01 pppp7-{F}(V0,V1), empty-{F}(V0) | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #47: input, references = 3, size of lhs = 1:
% 10.82/11.01 pppp7-{F}(V0,V1) | element-{T}(V0,V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #48: input, references = 4, size of lhs = 1:
% 10.82/11.01 P_empty_set-{F}(V0) | EXISTS V1: pppp8-{T}(V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #49: input, references = 5, size of lhs = 1:
% 10.82/11.01 pppp8-{F}(V0) | empty-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #50: input, references = 4, size of lhs = 1:
% 10.82/11.01 P_empty_set-{F}(V0) | EXISTS V1: pppp9-{T}(V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #51: input, references = 3, size of lhs = 1:
% 10.82/11.01 pppp9-{F}(V0) | function-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #52: input, references = 5, size of lhs = 1:
% 10.82/11.01 pppp9-{F}(V0) | empty-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #53: input, references = 3, size of lhs = 1:
% 10.82/11.01 pppp9-{F}(V0) | relation-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #54: input, references = 3, size of lhs = 1:
% 10.82/11.01 P_empty_set-{F}(V0) | EXISTS V1: pppp10-{T}(V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #55: input, references = 3, size of lhs = 1:
% 10.82/11.01 pppp10-{F}(V0) | relation-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #56: input, references = 3, size of lhs = 2:
% 10.82/11.01 pppp10-{F}(V0), empty-{F}(V0) | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #57: input, references = 4, size of lhs = 2:
% 10.82/11.01 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2) | EXISTS V3: pppp11-{T}(V3,V2)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #58: input, references = 4, size of lhs = 1:
% 10.82/11.01 pppp11-{F}(V0,V1) | empty-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #59: input, references = 3, size of lhs = 1:
% 10.82/11.01 pppp11-{F}(V0,V1) | element-{T}(V0,V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #60: input, references = 3, size of lhs = 1:
% 10.82/11.01 P_empty_set-{F}(V0) | EXISTS V1: pppp12-{T}(V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #61: input, references = 3, size of lhs = 2:
% 10.82/11.01 pppp12-{F}(V0), empty-{F}(V0) | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #62: input, references = 3, size of lhs = 1:
% 10.82/11.01 P_empty_set-{F}(V0) | EXISTS V1: pppp13-{T}(V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #63: input, references = 3, size of lhs = 1:
% 10.82/11.01 pppp13-{F}(V0) | one_to_one-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #64: input, references = 3, size of lhs = 1:
% 10.82/11.01 pppp13-{F}(V0) | function-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #65: input, references = 3, size of lhs = 1:
% 10.82/11.01 pppp13-{F}(V0) | relation-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #66: input, references = 3, size of lhs = 1:
% 10.82/11.01 P_empty_set-{F}(V0) | EXISTS V1: pppp14-{T}(V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #67: input, references = 3, size of lhs = 1:
% 10.82/11.01 pppp14-{F}(V0) | relation_empty_yielding-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #68: input, references = 3, size of lhs = 1:
% 10.82/11.01 pppp14-{F}(V0) | relation-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #69: input, references = 3, size of lhs = 2:
% 10.82/11.01 P_empty_set-{F}(V0), #-{F} V1 | subset-{T}(V1,V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #70: input, references = 5, size of lhs = 2:
% 10.82/11.01 P_empty_set-{F}(V0), in-{F}(V1,V2) | element-{T}(V1,V2)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #71: input, references = 4, size of lhs = 2:
% 10.82/11.01 P_empty_set-{F}(V0), element-{F}(V2,V1) | empty-{T}(V1), in-{T}(V2,V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #72: input, references = 3, size of lhs = 3:
% 10.82/11.01 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), element-{F}(V1,V3) | subset-{T}(V1,V2)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #73: input, references = 3, size of lhs = 3:
% 10.82/11.01 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), subset-{F}(V1,V2) | element-{T}(V1,V3)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #74: input, references = 6, size of lhs = 4:
% 10.82/11.01 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), element-{F}(V1,V3), in-{F}(V4,V1) | element-{T}(V4,V2)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #75: input, references = 7, size of lhs = 7:
% 10.82/11.01 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)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #76: input, references = 3, size of lhs = 9:
% 10.82/11.01 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
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #77: input, references = 11, size of lhs = 5:
% 10.82/11.01 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) | pppp15-{T}(V1,V2,V3,V4,V5)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #78: input, references = 6, size of lhs = 4:
% 10.82/11.01 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), pppp22-{T}(V1,V2,V4,V5)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #79: input, references = 3, size of lhs = 1:
% 10.82/11.01 pppp22-{F}(V0,V1,V2,V3) | EXISTS V4: pppp18-{T}(V0,V1,V2,V3,V4)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #80: input, references = 3, size of lhs = 1:
% 10.82/11.01 pppp18-{F}(V0,V1,V2,V3,V4) | EXISTS V5: pppp17-{T}(V0,V1,V4,V5,V2,V3)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #81: input, references = 3, size of lhs = 4:
% 10.82/11.01 pppp17-{F}(V0,V1,V2,V6,V4,V5), P_apply-{F}(V1,V2,V6), P_apply-{F}(V0,V6,V7), in-{F}(V2,V4) | pppp16-{T}(V2,V6,V4,V5,V6,V7)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #82: input, references = 4, size of lhs = 4:
% 10.82/11.01 pppp17-{F}(V0,V1,V2,V3,V4,V5), P_apply-{F}(V1,V2,V6), P_apply-{F}(V0,V3,V7), V2 == V7 | pppp16-{T}(V2,V3,V4,V5,V6,V7)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #83: input, references = 3, size of lhs = 3:
% 10.82/11.01 pppp17-{F}(V0,V1,V2,V3,V4,V5), P_apply-{F}(V1,V2,V6), P_apply-{F}(V0,V3,V7) | pppp16-{T}(V2,V3,V4,V5,V6,V7), in-{T}(V3,V5)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #84: input, references = 3, size of lhs = 2:
% 10.82/11.01 pppp16-{F}(V5,V1,V2,V3,V4,V5), in-{F}(V1,V3) | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #85: input, references = 4, size of lhs = 2:
% 10.82/11.01 pppp16-{F}(V0,V1,V2,V3,V4,V5), V1 == V4 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #86: input, references = 3, size of lhs = 1:
% 10.82/11.01 pppp16-{F}(V0,V1,V2,V3,V4,V5) | in-{T}(V0,V2)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #87: input, references = 5, size of lhs = 5:
% 10.82/11.01 pppp15-{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
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #88: input, references = 5, size of lhs = 4:
% 10.82/11.01 pppp15-{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)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #89: input, references = 6, size of lhs = 5:
% 10.82/11.01 pppp15-{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
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #90: input, references = 3, size of lhs = 4:
% 10.82/11.01 pppp15-{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)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #91: input, references = 6, size of lhs = 2:
% 10.82/11.01 pppp15-{F}(V0,V1,V2,V3,V4), V2 == V3 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #92: input, references = 5, size of lhs = 12:
% 10.82/11.01 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
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #93: input, references = 6, size of lhs = 12:
% 10.82/11.01 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
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #94: input, references = 6, size of lhs = 5:
% 10.82/11.01 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), empty-{F}(V1), element-{F}(V3,V2), in-{F}(V4,V3) | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #95: input, references = 4, size of lhs = 1:
% 10.82/11.01 P_empty_set-{F}(V0) | EXISTS V1: pppp19-{T}(V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #96: input, references = 4, size of lhs = 3:
% 10.82/11.01 pppp19-{F}(V0), P_function_inverse-{F}(V0,V1), one_to_one-{F}(V1) | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #97: input, references = 4, size of lhs = 2:
% 10.82/11.01 pppp19-{F}(V0), P_function_inverse-{F}(V0,V1) | one_to_one-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #98: input, references = 4, size of lhs = 2:
% 10.82/11.01 pppp19-{F}(V0), P_function_inverse-{F}(V0,V1) | function-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #99: input, references = 4, size of lhs = 2:
% 10.82/11.01 pppp19-{F}(V0), P_function_inverse-{F}(V0,V1) | relation-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #100: input, references = 12, size of lhs = 3:
% 10.82/11.01 P_empty_set-{F}(V0), empty-{F}(V1), V1 == V0 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #101: input, references = 4, size of lhs = 3:
% 10.82/11.01 P_empty_set-{F}(V0), empty-{F}(V1), in-{F}(V2,V1) | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #102: input, references = 11, size of lhs = 4:
% 10.82/11.01 P_empty_set-{F}(V0), empty-{F}(V1), empty-{F}(V2), V2 == V1 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #103: input, references = 6, size of lhs = 1:
% 10.82/11.01 #-{F} V0 | EXISTS V1: P_relation_dom-{T}(V0,V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #104: input, references = 13, size of lhs = 2:
% 10.82/11.01 #-{F} V0, #-{F} V1 | EXISTS V2: P_apply-{T}(V0,V1,V2)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #105: input, references = 7, size of lhs = 1:
% 10.82/11.01 #-{F} V0 | EXISTS V1: P_function_inverse-{T}(V0,V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #106: input, references = 5, size of lhs = 2:
% 10.82/11.01 #-{F} V0, #-{F} V1 | EXISTS V2: P_relation_composition-{T}(V0,V1,V2)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #107: input, references = 4, size of lhs = 0:
% 10.82/11.01 FALSE | EXISTS V0: P_empty_set-{T}(V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #108: input, references = 3, size of lhs = 1:
% 10.82/11.01 #-{F} V0 | EXISTS V1: P_powerset-{T}(V0,V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #109: input, references = 6, size of lhs = 1:
% 10.82/11.01 #-{F} V0 | EXISTS V1: P_relation_rng-{T}(V0,V1)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 number of initial rules = 110
% 10.82/11.01
% 10.82/11.01 Simplifiers:
% 10.82/11.01 #110: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 P_relation_dom-{F}(V0,V1), P_relation_dom-{F}(V0,V3), V1 == V3 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #111: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 P_apply-{F}(V0,V1,V2), P_apply-{F}(V0,V1,V5), V2 == V5 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #112: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 P_function_inverse-{F}(V0,V1), P_function_inverse-{F}(V0,V3), V1 == V3 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #113: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 P_relation_composition-{F}(V0,V1,V2), P_relation_composition-{F}(V0,V1,V5), V2 == V5 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #114: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 P_empty_set-{F}(V0), P_empty_set-{F}(V1), V0 == V1 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #115: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 P_powerset-{F}(V0,V1), P_powerset-{F}(V0,V3), V1 == V3 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #116: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 P_relation_rng-{F}(V0,V1), P_relation_rng-{F}(V0,V3), V1 == V3 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #117: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp2-{F}(V0,V1,V2,V3,V4), pppp2-{F}(V0,V6,V2,V3,V4), V1 == V6 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #118: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp2-{F}(V0,V1,V2,V3,V4), pppp2-{F}(V0,V6,V7,V3,V9), V2 == V7 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #119: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp2-{F}(V0,V1,V2,V3,V4), pppp2-{F}(V0,V6,V7,V8,V9), V3 == V8 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #120: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp2-{F}(V0,V1,V2,V3,V4), pppp2-{F}(V0,V6,V2,V8,V9), V4 == V9 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #121: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp3-{F}(V0,V1,V2), pppp3-{F}(V0,V4,V2), V1 == V4 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #122: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp3-{F}(V0,V1,V2), pppp3-{F}(V0,V4,V5), V2 == V5 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #123: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp4-{F}(V0,V1), pppp4-{F}(V0,V3), V1 == V3 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #124: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp5-{F}(V0), pppp5-{F}(V1), V0 == V1 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #125: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp6-{F}(V0), pppp6-{F}(V1), V0 == V1 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #126: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp7-{F}(V0,V1), pppp7-{F}(V2,V1), V0 == V2 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #127: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp8-{F}(V0), pppp8-{F}(V1), V0 == V1 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #128: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp9-{F}(V0), pppp9-{F}(V1), V0 == V1 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #129: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp10-{F}(V0), pppp10-{F}(V1), V0 == V1 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #130: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp11-{F}(V0,V1), pppp11-{F}(V2,V1), V0 == V2 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #131: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp12-{F}(V0), pppp12-{F}(V1), V0 == V1 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #132: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp13-{F}(V0), pppp13-{F}(V1), V0 == V1 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #133: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp14-{F}(V0), pppp14-{F}(V1), V0 == V1 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #134: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp15-{F}(V0,V1,V2,V3,V4), pppp15-{F}(V5,V1,V7,V8,V9), V2 == V7 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #135: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp15-{F}(V0,V1,V2,V3,V4), pppp15-{F}(V0,V6,V7,V8,V9), V3 == V8 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #136: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp15-{F}(V0,V1,V2,V3,V4), pppp15-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #137: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp17-{F}(V0,V1,V2,V3,V4,V5), pppp17-{F}(V0,V1,V2,V9,V4,V5), V3 == V9 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #138: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp17-{F}(V0,V1,V2,V3,V4,V5), pppp17-{F}(V0,V1,V8,V9,V4,V5), V2 == V8 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #139: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp17-{F}(V0,V1,V2,V3,V4,V5), pppp17-{F}(V6,V1,V8,V9,V10,V11), V4 == V10 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #140: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp17-{F}(V0,V1,V2,V3,V4,V5), pppp17-{F}(V0,V7,V8,V9,V10,V11), V4 == V10 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #141: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp17-{F}(V0,V1,V2,V3,V4,V5), pppp17-{F}(V0,V7,V8,V9,V10,V11), V5 == V11 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #142: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp18-{F}(V0,V1,V2,V3,V4), pppp18-{F}(V0,V1,V2,V3,V9), V4 == V9 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #143: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp18-{F}(V0,V1,V2,V3,V4), pppp18-{F}(V5,V1,V7,V8,V9), V2 == V7 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #144: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp18-{F}(V0,V1,V2,V3,V4), pppp18-{F}(V0,V6,V7,V8,V9), V2 == V7 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #145: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp18-{F}(V0,V1,V2,V3,V4), pppp18-{F}(V0,V6,V7,V8,V9), V3 == V8 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #146: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp19-{F}(V0), pppp19-{F}(V1), V0 == V1 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #147: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp20-{F}(V0,V1), pppp20-{F}(V0,V3), V1 == V3 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #148: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp22-{F}(V0,V1,V2,V3), pppp22-{F}(V4,V1,V6,V7), V2 == V6 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #149: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp22-{F}(V0,V1,V2,V3), pppp22-{F}(V0,V5,V6,V7), V2 == V6 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #150: unsound, references = 3, size of lhs = 3:
% 10.82/11.01 pppp22-{F}(V0,V1,V2,V3), pppp22-{F}(V0,V5,V6,V7), V3 == V7 | FALSE
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 number of simplifiers = 41
% 10.82/11.01
% 10.82/11.01 Learnt:
% 10.82/11.01 #173: mergings( V0 == V3; #169 ), references = 4, size of lhs = 3:
% 10.82/11.01 P_empty_set-{F}(V0), element-{F}(V1,V2), V2 == V0 | in-{T}(V1,V2)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.01
% 10.82/11.01 #176: mergings( V0 == V3, V2 == V3; #170 ), references = 1, size of lhs = 4:
% 10.82/11.01 P_empty_set-{F}(V0), empty-{F}(V1), V0 == V1, element-{F}(V2,V0) | in-{T}(V2,V0)
% 10.82/11.01 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #179: mergings( V0 == V3, V2 == V3; #171 ), references = 1, size of lhs = 3:
% 10.82/11.02 P_empty_set-{F}(V0), element-{F}(V1,V0), P_powerset-{F}(V2,V0) | in-{T}(V1,V0)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #186: mergings( V0 == V2; #183 ), references = 1, size of lhs = 1:
% 10.82/11.02 P_empty_set-{F}(V0) | pppp8-{T}(V0)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #188: mergings( V0 == V2; #184 ), references = 1, size of lhs = 2:
% 10.82/11.02 P_empty_set-{F}(V0), empty-{F}(V1) | pppp8-{T}(V1)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #197: mergings( V0 == V2; #194 ), references = 1, size of lhs = 1:
% 10.82/11.02 P_empty_set-{F}(V0) | pppp9-{T}(V0)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #199: mergings( V0 == V2; #195 ), references = 1, size of lhs = 2:
% 10.82/11.02 P_empty_set-{F}(V0), empty-{F}(V1) | pppp9-{T}(V1)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #216: mergings( V2 == V3; #213 ), references = 1, size of lhs = 2:
% 10.82/11.02 empty-{F}(V0), P_empty_set-{F}(V1) | P_relation_dom-{T}(V0,V1)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #218: mergings( V2 == V3; #214 ), references = 1, size of lhs = 3:
% 10.82/11.02 empty-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2) | P_relation_dom-{T}(V0,V2)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #230: mergings( V0 == V2; #227 ), references = 1, size of lhs = 1:
% 10.82/11.02 P_empty_set-{F}(V0) | pppp6-{T}(V0)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #232: mergings( V0 == V2; #228 ), references = 1, size of lhs = 2:
% 10.82/11.02 P_empty_set-{F}(V0), empty-{F}(V1) | pppp6-{T}(V1)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #258: mergings( V2 == V3; #255 ), references = 1, size of lhs = 2:
% 10.82/11.02 empty-{F}(V0), P_empty_set-{F}(V1) | P_relation_rng-{T}(V0,V1)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #260: mergings( V2 == V3; #256 ), references = 1, size of lhs = 3:
% 10.82/11.02 empty-{F}(V0), P_empty_set-{F}(V1), empty-{F}(V2) | P_relation_rng-{T}(V0,V2)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #271: exists( #106, #266 ), references = 1, size of lhs = 3:
% 10.82/11.02 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2) | P_relation_composition-{T}(V0,V1,V2)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #272: exists( #106, #267 ), references = 1, size of lhs = 4:
% 10.82/11.02 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3) | P_relation_composition-{T}(V0,V1,V3)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #283: mergings( V0 == V5; #281 ), references = 1, size of lhs = 11:
% 10.82/11.02 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) | pppp22-{T}(V1,V5,V2,V3)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #288: mergings( V2 == V3; #286 ), references = 4, size of lhs = 5:
% 10.82/11.02 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), element-{F}(V3,V2), V3 == V0 | FALSE
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #292: exists( #17, #290 ), references = 1, size of lhs = 3:
% 10.82/11.02 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2) | pppp4-{T}(V2,V0)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #299: mergings( V3 == V4; #296 ), references = 1, size of lhs = 3:
% 10.82/11.02 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2) | P_relation_composition-{T}(V1,V0,V2)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #301: mergings( V3 == V4; #297 ), references = 1, size of lhs = 4:
% 10.82/11.02 relation-{F}(V0), empty-{F}(V1), P_empty_set-{F}(V2), empty-{F}(V3) | P_relation_composition-{T}(V1,V0,V3)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #308: exists( #103, #306 ), references = 2, size of lhs = 4:
% 10.82/11.02 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)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #324: mergings( V2 == V3, V3 == V4, V4 == V7; #319 ), references = 1, size of lhs = 7:
% 10.82/11.02 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)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #328: mergings( V2 == V3, V3 == V4, V4 == V7; #320 ), references = 1, size of lhs = 8:
% 10.82/11.02 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)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #356: mergings( V0 == V3; #352 ), references = 1, size of lhs = 3:
% 10.82/11.02 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), V1 == V0 | pppp21-{T}(V2)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #359: mergings( V0 == V3, V1 == V3; #353 ), references = 1, size of lhs = 4:
% 10.82/11.02 P_empty_set-{F}(V0), empty-{F}(V1), V0 == V1, P_powerset-{F}(V0,V2) | pppp21-{T}(V2)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #363: mergings( V0 == V3, V2 == V4, V1 == V3; #354 ), references = 1, size of lhs = 4:
% 10.82/11.02 P_empty_set-{F}(V0), P_powerset-{F}(V0,V1), element-{F}(V2,V1), V2 == V0 | pppp21-{T}(V1)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #381: mergings( V0 == V4; #379 ), references = 1, size of lhs = 2:
% 10.82/11.02 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2) | pppp11-{T}(V0,V2)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #427: mergings( V2 == V3, V3 == V4; #424 ), references = 1, size of lhs = 6:
% 10.82/11.02 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), P_powerset-{F}(V2,V3), element-{F}(V4,V3), V4 == V0 | pppp4-{T}(V4,V0)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #432: exists( #109, #430 ), references = 1, size of lhs = 4:
% 10.82/11.02 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)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #439: disj( #7, #5+#96 ), references = 2, size of lhs = 5:
% 10.82/11.02 relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), pppp19-{F}(V2), P_function_inverse-{F}(V2,V0) | pppp20-{T}(V0,V1)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #445: exists( #104, #89 ), references = 3, size of lhs = 3:
% 10.82/11.02 in-{F}(V0,V1), P_apply-{F}(V2,V0,V3), pppp15-{F}(V4,V2,V5,V1,V6) | P_apply-{T}(V4,V3,V0)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #525: exists( #104, #93 ), references = 2, size of lhs = 10:
% 10.82/11.02 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)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #567: exists( #104, #87 ), references = 3, size of lhs = 3:
% 10.82/11.02 in-{F}(V0,V1), P_apply-{F}(V2,V0,V3), pppp15-{F}(V2,V4,V5,V6,V1) | P_apply-{T}(V4,V3,V0)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #677: disj( #7, #5+#92 ), references = 1, size of lhs = 12:
% 10.82/11.02 relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), P_empty_set-{F}(V2), P_relation_rng-{F}(V0,V3), P_function_inverse-{F}(V0,V4), P_relation_composition-{F}(V4,V0,V5), in-{F}(V6,V3), P_apply-{F}(V4,V6,V7), P_apply-{F}(V0,V7,V8), V6 == V8, P_apply-{F}(V5,V6,V9) | pppp20-{T}(V0,V1)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #678: disj( #7, #5+#93 ), references = 1, size of lhs = 12:
% 10.82/11.02 relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), P_empty_set-{F}(V2), P_relation_rng-{F}(V0,V3), P_function_inverse-{F}(V0,V4), P_relation_composition-{F}(V4,V0,V5), in-{F}(V6,V3), P_apply-{F}(V4,V6,V7), P_apply-{F}(V0,V7,V8), P_apply-{F}(V5,V6,V9), V6 == V9 | pppp20-{T}(V0,V1)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #699: mergings( V2 == V8, V4 == V7, V0 == V5, V8 == V6; #693 ), references = 1, size of lhs = 8:
% 10.82/11.02 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,V2), P_apply-{F}(V4,V5,V6), P_apply-{F}(V1,V6,V7), V5 == V7 | pppp22-{T}(V1,V4,V2,V3)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #704: mergings( V2 == V8, V4 == V7, V0 == V5, V8 == V6; #694 ), references = 1, size of lhs = 8:
% 10.82/11.02 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 | pppp22-{T}(V1,V4,V2,V3)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #798: mergings( V1 == V2; #796 ), references = 1, size of lhs = 6:
% 10.82/11.02 P_relation_dom-{F}(V0,V1), in-{F}(V2,V1), P_apply-{F}(V0,V2,V3), P_apply-{F}(V0,V4,V3), V4 == V2, in-{F}(V4,V1) | pppp20-{T}(V0,V1)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #835: exists( #104, #12 ), references = 2, size of lhs = 1:
% 10.82/11.02 pppp2-{F}(V0,V1,V2,V3,V4) | P_apply-{T}(V0,V1,V4)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #839: exists( #9, #837 ), references = 2, size of lhs = 4:
% 10.82/11.02 pppp3-{F}(V0,V1,V2), P_apply-{F}(V0,V1,V3), P_apply-{F}(V4,V3,V5), pppp15-{F}(V4,V0,V6,V2,V7) | pppp2-{T}(V0,V5,V1,V2,V3)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #898: exists( #104, #896 ), references = 1, size of lhs = 11:
% 10.82/11.02 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), pppp3-{F}(V3,V5,V2), P_apply-{F}(V4,V5,V6), V5 == V6, pppp15-{F}(V1,V3,V7,V2,V8) | FALSE
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #900: exists( #104, #897 ), references = 1, size of lhs = 9:
% 10.82/11.02 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), pppp3-{F}(V3,V5,V2), pppp15-{F}(V1,V3,V6,V2,V7) | P_apply-{T}(V4,V5,V5)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #974: mergings( V3 == V4, V4 == V5; #970 ), references = 2, size of lhs = 7:
% 10.82/11.02 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), P_powerset-{F}(V2,V3), in-{F}(V4,V5), V4 == V0, pppp3-{F}(V6,V5,V3) | FALSE
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #978: mergings( V3 == V4, V4 == V5, V10 == V5; #971 ), references = 1, size of lhs = 7:
% 10.82/11.02 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), P_powerset-{F}(V2,V3), in-{F}(V4,V0), in-{F}(V0,V5), pppp3-{F}(V6,V5,V3) | FALSE
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #1061: mergings( V2 == V3; #1059 ), references = 1, size of lhs = 6:
% 10.82/11.02 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), P_powerset-{F}(V2,V3), pppp3-{F}(V4,V5,V3), V5 == V0 | pppp4-{T}(V5,V0)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #1166: exists( #104, #1164 ), references = 1, size of lhs = 3:
% 10.82/11.02 P_apply-{F}(V0,V1,V2), pppp17-{F}(V3,V0,V1,V4,V5,V6), V4 == V2 | P_apply-{T}(V3,V4,V1)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #1193: mergings( V4 == V11, V7 == V12, V8 == V13, V2 == V9, V3 == V10; #1187 ), references = 1, size of lhs = 11:
% 10.82/11.02 relation-{F}(V0), function-{F}(V0), P_relation_dom-{F}(V0,V1), P_empty_set-{F}(V2), P_relation_rng-{F}(V0,V3), in-{F}(V4,V3), P_function_inverse-{F}(V0,V5), P_relation_composition-{F}(V5,V0,V6), P_apply-{F}(V5,V4,V7), P_apply-{F}(V0,V7,V8), V4 == V8 | pppp20-{T}(V0,V1)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #1213: mergings( V1 == V6, V2 == V4; #1209 ), references = 1, size of lhs = 10:
% 10.82/11.02 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 | pppp20-{T}(V0,V4)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #1306: mergings( V6 == V8, V3 == V4, V7 == V9; #1302 ), references = 2, size of lhs = 3:
% 10.82/11.02 in-{F}(V0,V1), pppp3-{F}(V2,V0,V1), pppp15-{F}(V3,V2,V4,V1,V5) | FALSE
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #1424: exists( #104, #1421 ), references = 1, size of lhs = 3:
% 10.82/11.02 pppp3-{F}(V0,V1,V2), pppp3-{F}(V3,V1,V2), pppp15-{F}(V4,V3,V5,V2,V6) | FALSE
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #1426: exists( #8, #1423 ), references = 2, size of lhs = 2:
% 10.82/11.02 pppp20-{F}(V0,V1), pppp15-{F}(V2,V0,V3,V1,V4) | FALSE
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #1459: mergings( V5 == V6, V2 == V3; #1456 ), references = 1, size of lhs = 7:
% 10.82/11.02 P_empty_set-{F}(V0), relation-{F}(V1), function-{F}(V1), pppp1-{F}(V2,V1), P_relation_dom-{F}(V2,V3), pppp19-{F}(V4), P_function_inverse-{F}(V4,V1) | FALSE
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #1468: mergings( V5 == V6, V2 == V3, V3 == V4; #1464 ), references = 1, size of lhs = 5:
% 10.82/11.02 relation-{F}(V0), function-{F}(V0), pppp19-{F}(V0), P_empty_set-{F}(V1), P_relation_dom-{F}(V0,V2) | FALSE
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #1472: mergings( V2 == V3, V3 == V4; #1469 ), references = 2, size of lhs = 4:
% 10.82/11.02 relation-{F}(V0), function-{F}(V0), pppp19-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #1493: mergings( V2 == V9, V4 == V8, V0 == V5, V5 == V6, V7 == V9; #1485 ), references = 1, size of lhs = 9:
% 10.82/11.02 P_empty_set-{F}(V0), empty-{F}(V1), P_relation_rng-{F}(V2,V1), P_relation_dom-{F}(V2,V3), P_relation_dom-{F}(V4,V1), in-{F}(V5,V3), P_apply-{F}(V2,V5,V6), in-{F}(V7,V3), P_apply-{F}(V2,V7,V6) | pppp22-{T}(V2,V4,V1,V3)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #1500: mergings( V2 == V11, V4 == V10, V0 == V5, V5 == V6, V9 == V11, V11 == V6; #1486 ), references = 1, size of lhs = 11:
% 10.82/11.02 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), element-{F}(V0,V2), P_relation_rng-{F}(V3,V0), P_relation_dom-{F}(V3,V4), P_relation_dom-{F}(V5,V0), in-{F}(V6,V4), P_apply-{F}(V3,V6,V7), in-{F}(V8,V4), P_apply-{F}(V3,V8,V7) | pppp22-{T}(V3,V5,V0,V4)
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #1532: exists( #105, #1528 ), references = 2, size of lhs = 3:
% 10.82/11.02 relation-{F}(V0), pppp19-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #1555: exists( #105, #1547 ), references = 1, size of lhs = 2:
% 10.82/11.02 pppp19-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #1559: mergings( V0 == V2; #1556 ), references = 1, size of lhs = 1:
% 10.82/11.02 P_empty_set-{F}(V0) | FALSE
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 #1562: exists( #107, #1556 ), references = 1, size of lhs = 0:
% 10.82/11.02 FALSE | FALSE
% 10.82/11.02 (used 0 times, uses = {})
% 10.82/11.02
% 10.82/11.02 number of learnt formulas = 60
% 10.82/11.02
% 10.82/11.02
% 10.82/11.02 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.82/11.02
% 10.82/11.02 randbase = 1
%------------------------------------------------------------------------------