TSTP Solution File: NUM404+1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : NUM404+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n011.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 06:12:23 EDT 2022
% Result : Theorem 5.91s 6.13s
% Output : Refutation 5.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM404+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n011.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 23:31:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 5.91/6.13 GeoParameters:
% 5.91/6.13
% 5.91/6.13 tptp_input = 1
% 5.91/6.13 tptp_output = 0
% 5.91/6.13 nonempty = 1
% 5.91/6.13 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.91/6.13 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 5.91/6.13
% 5.91/6.13
% 5.91/6.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.91/6.13 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.91/6.13
% 5.91/6.13 RuleSystem INPUT:
% 5.91/6.13
% 5.91/6.13 Initial Rules:
% 5.91/6.13 #0: input, references = 10, size of lhs = 2:
% 5.91/6.13 in-{F}(V0,V1), in-{F}(V1,V0) | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #1: input, references = 3, size of lhs = 1:
% 5.91/6.13 empty-{F}(V0) | function-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #2: input, references = 5, size of lhs = 1:
% 5.91/6.13 ordinal-{F}(V0) | epsilon_transitive-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #3: input, references = 4, size of lhs = 1:
% 5.91/6.13 ordinal-{F}(V0) | epsilon_connected-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #4: input, references = 3, size of lhs = 1:
% 5.91/6.13 empty-{F}(V0) | relation-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #5: input, references = 3, size of lhs = 3:
% 5.91/6.13 relation-{F}(V0), empty-{F}(V0), function-{F}(V0) | one_to_one-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #6: input, references = 4, size of lhs = 2:
% 5.91/6.13 epsilon_transitive-{F}(V0), epsilon_connected-{F}(V0) | ordinal-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #7: input, references = 3, size of lhs = 1:
% 5.91/6.13 empty-{F}(V0) | epsilon_transitive-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #8: input, references = 3, size of lhs = 1:
% 5.91/6.13 empty-{F}(V0) | epsilon_connected-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #9: input, references = 3, size of lhs = 1:
% 5.91/6.13 empty-{F}(V0) | ordinal-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #10: input, references = 5, size of lhs = 1:
% 5.91/6.13 epsilon_transitive-{F}(V0) | pppp0-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #11: input, references = 4, size of lhs = 1:
% 5.91/6.13 pppp0-{F}(V0) | epsilon_transitive-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #12: input, references = 6, size of lhs = 2:
% 5.91/6.13 pppp0-{F}(V0), in-{F}(V1,V0) | subset-{T}(V1,V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #13: input, references = 5, size of lhs = 1:
% 5.91/6.13 #-{F} V0 | pppp0-{T}(V0), pppp25-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #14: input, references = 4, size of lhs = 1:
% 5.91/6.13 pppp25-{F}(V0) | EXISTS V1: pppp4-{T}(V0,V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #15: input, references = 6, size of lhs = 2:
% 5.91/6.13 pppp4-{F}(V0,V1), subset-{F}(V1,V0) | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #16: input, references = 4, size of lhs = 1:
% 5.91/6.13 pppp4-{F}(V0,V1) | in-{T}(V1,V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #17: input, references = 4, size of lhs = 1:
% 5.91/6.13 epsilon_connected-{F}(V0) | pppp1-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #18: input, references = 4, size of lhs = 1:
% 5.91/6.13 pppp1-{F}(V0) | epsilon_connected-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #19: input, references = 4, size of lhs = 4:
% 5.91/6.13 pppp1-{F}(V0), in-{F}(V1,V0), in-{F}(V2,V0), V2 == V1 | in-{T}(V2,V1), in-{T}(V1,V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #20: input, references = 6, size of lhs = 1:
% 5.91/6.13 #-{F} V0 | pppp1-{T}(V0), pppp26-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #21: input, references = 6, size of lhs = 1:
% 5.91/6.13 pppp26-{F}(V0) | EXISTS V1: pppp6-{T}(V0,V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #22: input, references = 5, size of lhs = 1:
% 5.91/6.13 pppp6-{F}(V0,V1) | EXISTS V2: pppp5-{T}(V0,V2,V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #23: input, references = 6, size of lhs = 1:
% 5.91/6.13 pppp6-{F}(V0,V1) | in-{T}(V1,V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #24: input, references = 5, size of lhs = 2:
% 5.91/6.13 pppp5-{F}(V0,V1,V2), in-{F}(V2,V1) | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #25: input, references = 5, size of lhs = 1:
% 5.91/6.13 pppp5-{F}(V0,V2,V2) | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #26: input, references = 3, size of lhs = 2:
% 5.91/6.13 pppp5-{F}(V0,V1,V2), in-{F}(V1,V2) | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #27: input, references = 5, size of lhs = 1:
% 5.91/6.13 pppp5-{F}(V0,V1,V2) | in-{T}(V1,V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #28: input, references = 7, size of lhs = 1:
% 5.91/6.13 subset-{F}(V0,V1) | pppp2-{T}(V0,V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #29: input, references = 7, size of lhs = 1:
% 5.91/6.13 pppp2-{F}(V0,V1) | subset-{T}(V0,V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #30: input, references = 19, size of lhs = 2:
% 5.91/6.13 pppp2-{F}(V0,V1), in-{F}(V2,V0) | in-{T}(V2,V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #31: input, references = 14, size of lhs = 2:
% 5.91/6.13 #-{F} V0, #-{F} V1 | pppp2-{T}(V0,V1), pppp27-{T}(V0,V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #32: input, references = 9, size of lhs = 1:
% 5.91/6.13 pppp27-{F}(V0,V1) | EXISTS V2: pppp7-{T}(V0,V1,V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #33: input, references = 8, size of lhs = 2:
% 5.91/6.13 pppp7-{F}(V0,V1,V2), in-{F}(V2,V1) | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #34: input, references = 10, size of lhs = 1:
% 5.91/6.13 pppp7-{F}(V0,V1,V2) | in-{T}(V2,V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #35: input, references = 3, size of lhs = 1:
% 5.91/6.13 ordinal-{F}(V0) | pppp3-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #36: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp3-{F}(V0) | ordinal-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #37: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp3-{F}(V0) | epsilon_transitive-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #38: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp3-{F}(V0) | epsilon_connected-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #39: input, references = 3, size of lhs = 2:
% 5.91/6.13 epsilon_transitive-{F}(V0), epsilon_connected-{F}(V0) | pppp3-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #40: input, references = 5, size of lhs = 1:
% 5.91/6.13 #-{F} V0 | EXISTS V1: pppp8-{T}(V0,V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #41: input, references = 6, size of lhs = 1:
% 5.91/6.13 pppp8-{F}(V0,V1) | element-{T}(V1,V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #42: input, references = 3, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | empty-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #43: input, references = 3, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | relation-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #44: input, references = 3, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | relation_empty_yielding-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #45: input, references = 3, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | empty-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #46: input, references = 3, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | pppp9-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #47: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp9-{F}(V0) | ordinal-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #48: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp9-{F}(V0) | epsilon_connected-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #49: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp9-{F}(V0) | epsilon_transitive-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #50: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp9-{F}(V0) | empty-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #51: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp9-{F}(V0) | one_to_one-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #52: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp9-{F}(V0) | function-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #53: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp9-{F}(V0) | relation_empty_yielding-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #54: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp9-{F}(V0) | relation-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #55: input, references = 3, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | empty-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #56: input, references = 3, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | relation-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #57: input, references = 3, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | EXISTS V1: pppp10-{T}(V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #58: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp10-{F}(V0) | function-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #59: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp10-{F}(V0) | relation-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #60: input, references = 3, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | EXISTS V1: pppp11-{T}(V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #61: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp11-{F}(V0) | ordinal-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #62: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp11-{F}(V0) | epsilon_connected-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #63: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp11-{F}(V0) | epsilon_transitive-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #64: input, references = 4, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | EXISTS V1: pppp12-{T}(V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #65: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp12-{F}(V0) | relation-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #66: input, references = 5, size of lhs = 1:
% 5.91/6.13 pppp12-{F}(V0) | empty-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #67: input, references = 4, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | EXISTS V1: pppp13-{T}(V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #68: input, references = 5, size of lhs = 1:
% 5.91/6.13 pppp13-{F}(V0) | empty-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #69: input, references = 4, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | EXISTS V1: pppp14-{T}(V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #70: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp14-{F}(V0) | function-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #71: input, references = 5, size of lhs = 1:
% 5.91/6.13 pppp14-{F}(V0) | empty-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #72: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp14-{F}(V0) | relation-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #73: input, references = 4, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | EXISTS V1: pppp16-{T}(V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #74: input, references = 5, size of lhs = 1:
% 5.91/6.13 pppp16-{F}(V0) | pppp15-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #75: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp15-{F}(V0) | ordinal-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #76: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp15-{F}(V0) | epsilon_connected-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #77: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp15-{F}(V0) | epsilon_transitive-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #78: input, references = 5, size of lhs = 1:
% 5.91/6.13 pppp15-{F}(V0) | empty-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #79: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp15-{F}(V0) | one_to_one-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #80: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp15-{F}(V0) | function-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #81: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp15-{F}(V0) | relation-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #82: input, references = 3, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | EXISTS V1: pppp17-{T}(V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #83: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp17-{F}(V0) | relation-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #84: input, references = 4, size of lhs = 2:
% 5.91/6.13 pppp17-{F}(V0), empty-{F}(V0) | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #85: input, references = 3, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | EXISTS V1: pppp18-{T}(V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #86: input, references = 3, size of lhs = 2:
% 5.91/6.13 pppp18-{F}(V0), empty-{F}(V0) | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #87: input, references = 3, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | EXISTS V1: pppp19-{T}(V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #88: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp19-{F}(V0) | one_to_one-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #89: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp19-{F}(V0) | function-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #90: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp19-{F}(V0) | relation-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #91: input, references = 3, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | EXISTS V1: pppp20-{T}(V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #92: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp20-{F}(V0) | ordinal-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #93: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp20-{F}(V0) | epsilon_connected-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #94: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp20-{F}(V0) | epsilon_transitive-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #95: input, references = 4, size of lhs = 2:
% 5.91/6.13 pppp20-{F}(V0), empty-{F}(V0) | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #96: input, references = 3, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | EXISTS V1: pppp21-{T}(V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #97: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp21-{F}(V0) | relation_empty_yielding-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #98: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp21-{F}(V0) | relation-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #99: input, references = 3, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | EXISTS V1: pppp22-{T}(V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #100: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp22-{F}(V0) | function-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #101: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp22-{F}(V0) | relation_empty_yielding-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #102: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp22-{F}(V0) | relation-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #103: input, references = 3, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | EXISTS V1: pppp23-{T}(V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #104: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp23-{F}(V0) | function-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #105: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp23-{F}(V0) | relation_non_empty-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #106: input, references = 3, size of lhs = 1:
% 5.91/6.13 pppp23-{F}(V0) | relation-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #107: input, references = 4, size of lhs = 2:
% 5.91/6.13 P_empty_set-{F}(V0), #-{F} V1 | subset-{T}(V1,V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #108: input, references = 12, size of lhs = 2:
% 5.91/6.13 P_empty_set-{F}(V0), in-{F}(V1,V2) | element-{T}(V1,V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #109: input, references = 4, size of lhs = 3:
% 5.91/6.13 P_empty_set-{F}(V0), ordinal-{F}(V1), in-{F}(V2,V1) | ordinal-{T}(V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #110: input, references = 4, size of lhs = 4:
% 5.91/6.13 P_empty_set-{F}(V0), ordinal-{F}(V1), ordinal-{F}(V2), V1 == V2 | in-{T}(V1,V2), in-{T}(V2,V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #111: input, references = 5, size of lhs = 2:
% 5.91/6.13 P_empty_set-{F}(V0), element-{F}(V2,V1) | empty-{T}(V1), in-{T}(V2,V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #112: input, references = 4, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | EXISTS V1: pppp24-{T}(V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #113: input, references = 5, size of lhs = 2:
% 5.91/6.13 pppp24-{F}(V0), ordinal-{F}(V1) | in-{T}(V1,V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #114: input, references = 11, size of lhs = 2:
% 5.91/6.13 pppp24-{F}(V0), in-{F}(V1,V0) | ordinal-{T}(V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #115: input, references = 7, size of lhs = 3:
% 5.91/6.13 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), element-{F}(V1,V3) | subset-{T}(V1,V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #116: input, references = 8, size of lhs = 3:
% 5.91/6.13 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), subset-{F}(V1,V2) | element-{T}(V1,V3)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #117: input, references = 6, size of lhs = 4:
% 5.91/6.13 P_empty_set-{F}(V0), P_powerset-{F}(V2,V3), element-{F}(V1,V3), in-{F}(V4,V1) | element-{T}(V4,V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #118: input, references = 5, size of lhs = 5:
% 5.91/6.13 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), empty-{F}(V1), element-{F}(V3,V2), in-{F}(V4,V3) | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #119: input, references = 9, size of lhs = 3:
% 5.91/6.13 P_empty_set-{F}(V0), empty-{F}(V1), V1 == V0 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #120: input, references = 5, size of lhs = 3:
% 5.91/6.13 P_empty_set-{F}(V0), empty-{F}(V1), in-{F}(V2,V1) | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #121: input, references = 8, size of lhs = 4:
% 5.91/6.13 P_empty_set-{F}(V0), empty-{F}(V1), empty-{F}(V2), V2 == V1 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #122: input, references = 4, size of lhs = 0:
% 5.91/6.13 FALSE | EXISTS V0: P_empty_set-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #123: input, references = 4, size of lhs = 1:
% 5.91/6.13 #-{F} V0 | EXISTS V1: P_powerset-{T}(V0,V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 number of initial rules = 124
% 5.91/6.13
% 5.91/6.13 Simplifiers:
% 5.91/6.13 #124: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 relation_non_empty-{F}(V0), relation_non_empty-{F}(V1), V0 == V1 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #125: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 P_empty_set-{F}(V0), P_empty_set-{F}(V1), V0 == V1 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #126: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 P_powerset-{F}(V0,V1), P_powerset-{F}(V0,V3), V1 == V3 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #127: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp4-{F}(V0,V1), pppp4-{F}(V0,V3), V1 == V3 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #128: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp5-{F}(V0,V1,V2), pppp5-{F}(V0,V4,V2), V1 == V4 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #129: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp5-{F}(V0,V1,V2), pppp5-{F}(V0,V4,V5), V2 == V5 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #130: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp6-{F}(V0,V1), pppp6-{F}(V0,V3), V1 == V3 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #131: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp7-{F}(V0,V1,V2), pppp7-{F}(V0,V1,V5), V2 == V5 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #132: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp8-{F}(V0,V1), pppp8-{F}(V0,V3), V1 == V3 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #133: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp9-{F}(V0), pppp9-{F}(V1), V0 == V1 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #134: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp10-{F}(V0), pppp10-{F}(V1), V0 == V1 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #135: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp11-{F}(V0), pppp11-{F}(V1), V0 == V1 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #136: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp12-{F}(V0), pppp12-{F}(V1), V0 == V1 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #137: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp13-{F}(V0), pppp13-{F}(V1), V0 == V1 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #138: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp14-{F}(V0), pppp14-{F}(V1), V0 == V1 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #139: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp15-{F}(V0), pppp15-{F}(V1), V0 == V1 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #140: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp16-{F}(V0), pppp16-{F}(V1), V0 == V1 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #141: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp17-{F}(V0), pppp17-{F}(V1), V0 == V1 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #142: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp18-{F}(V0), pppp18-{F}(V1), V0 == V1 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #143: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp19-{F}(V0), pppp19-{F}(V1), V0 == V1 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #144: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp20-{F}(V0), pppp20-{F}(V1), V0 == V1 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #145: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp21-{F}(V0), pppp21-{F}(V1), V0 == V1 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #146: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp22-{F}(V0), pppp22-{F}(V1), V0 == V1 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #147: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp23-{F}(V0), pppp23-{F}(V1), V0 == V1 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #148: unsound, references = 3, size of lhs = 3:
% 5.91/6.13 pppp24-{F}(V0), pppp24-{F}(V1), V0 == V1 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 number of simplifiers = 25
% 5.91/6.13
% 5.91/6.13 Learnt:
% 5.91/6.13 #154: mergings( V0 == V2; #151 ), references = 1, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | pppp14-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #156: mergings( V0 == V2; #152 ), references = 1, size of lhs = 2:
% 5.91/6.13 P_empty_set-{F}(V0), empty-{F}(V1) | pppp14-{T}(V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #162: mergings( V0 == V2; #159 ), references = 1, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | pppp12-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #164: mergings( V0 == V2; #160 ), references = 1, size of lhs = 2:
% 5.91/6.13 P_empty_set-{F}(V0), empty-{F}(V1) | pppp12-{T}(V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #168: mergings( V0 == V3; #166 ), references = 6, size of lhs = 5:
% 5.91/6.13 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), element-{F}(V3,V2), element-{F}(V4,V3) | empty-{T}(V3)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #186: mergings( V2 == V3, V3 == V5; #181 ), references = 1, size of lhs = 5:
% 5.91/6.13 empty-{F}(V0), P_powerset-{F}(V0,V1), P_powerset-{F}(V2,V1), P_empty_set-{F}(V3), V1 == V3 | pppp27-{T}(V1,V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #190: mergings( V2 == V3, V3 == V5, V0 == V5; #182 ), references = 1, size of lhs = 6:
% 5.91/6.13 empty-{F}(V0), P_powerset-{F}(V0,V1), P_empty_set-{F}(V1), P_powerset-{F}(V2,V1), empty-{F}(V3), V1 == V3 | pppp27-{T}(V1,V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #194: mergings( V2 == V3, V0 == V3, V3 == V4; #183 ), references = 1, size of lhs = 5:
% 5.91/6.13 P_empty_set-{F}(V0), empty-{F}(V0), P_powerset-{F}(V0,V0), pppp20-{F}(V0), P_powerset-{F}(V1,V0) | pppp27-{T}(V0,V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #199: mergings( V0 == V3; #195 ), references = 5, size of lhs = 3:
% 5.91/6.13 P_empty_set-{F}(V0), element-{F}(V1,V2), V2 == V0 | in-{T}(V1,V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #202: mergings( V0 == V3, V2 == V3; #196 ), references = 1, size of lhs = 4:
% 5.91/6.13 P_empty_set-{F}(V0), empty-{F}(V1), V0 == V1, element-{F}(V2,V0) | in-{T}(V2,V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #204: mergings( V2 == V0; #197 ), references = 1, size of lhs = 3:
% 5.91/6.13 P_empty_set-{F}(V0), pppp20-{F}(V0), element-{F}(V1,V0) | in-{T}(V1,V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #216: exists( #40, #210 ), references = 1, size of lhs = 5:
% 5.91/6.13 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), pppp17-{F}(V3), element-{F}(V3,V2) | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #218: mergings( V2 == V5; #214 ), references = 4, size of lhs = 5:
% 5.91/6.13 empty-{F}(V0), P_powerset-{F}(V0,V1), P_empty_set-{F}(V2), element-{F}(V3,V1), V3 == V2 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #229: mergings( V2 == V3, V3 == V5; #225 ), references = 1, size of lhs = 4:
% 5.91/6.13 pppp26-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V0), P_empty_set-{F}(V2) | pppp6-{T}(V0,V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #243: disj( #31, #30+#120 ), references = 1, size of lhs = 3:
% 5.91/6.13 P_empty_set-{F}(V0), empty-{F}(V1), in-{F}(V2,V3) | pppp27-{T}(V3,V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #244: disj( #31, #30+#0 ), references = 1, size of lhs = 2:
% 5.91/6.13 in-{F}(V0,V1), in-{F}(V1,V2) | pppp27-{T}(V2,V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #246: mergings( V1 == V2; #242 ), references = 1, size of lhs = 5:
% 5.91/6.13 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), element-{F}(V0,V2), in-{F}(V3,V4) | pppp27-{T}(V4,V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #257: disj( #31, #30+#0 ), references = 1, size of lhs = 1:
% 5.91/6.13 in-{F}(V0,V1) | pppp27-{T}(V1,V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #267: mergings( V0 == V2; #264 ), references = 1, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | pppp16-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #269: mergings( V0 == V2; #265 ), references = 1, size of lhs = 2:
% 5.91/6.13 P_empty_set-{F}(V0), empty-{F}(V1) | pppp16-{T}(V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #279: exists( #40, #276 ), references = 1, size of lhs = 3:
% 5.91/6.13 empty-{F}(V0), P_powerset-{F}(V0,V1), P_empty_set-{F}(V2) | pppp8-{T}(V1,V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #293: mergings( V3 == V5; #291 ), references = 2, size of lhs = 4:
% 5.91/6.13 empty-{F}(V0), P_powerset-{F}(V0,V1), pppp27-{F}(V1,V2), P_empty_set-{F}(V3) | pppp7-{T}(V1,V2,V3)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #298: disj( #20, #18+#6+#113+#0 ), references = 2, size of lhs = 2:
% 5.91/6.13 epsilon_transitive-{F}(V0), pppp24-{F}(V0) | pppp26-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #321: disj( #19, input ), references = 1, size of lhs = 5:
% 5.91/6.13 pppp1-{F}(V0), in-{F}(V1,V0), in-{F}(V2,V0), V2 == V1, pppp5-{F}(V3,V1,V2) | in-{T}(V2,V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #322: disj( #19, input ), references = 5, size of lhs = 5:
% 5.91/6.13 pppp1-{F}(V0), in-{F}(V1,V0), in-{F}(V2,V0), V1 == V2, pppp7-{F}(V3,V1,V2) | in-{T}(V1,V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #326: exists( #22, #324 ), references = 1, size of lhs = 3:
% 5.91/6.13 pppp1-{F}(V0), pppp6-{F}(V0,V1), in-{F}(V1,V0) | pppp5-{T}(V0,V1,V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #330: exists( #21, #328 ), references = 2, size of lhs = 2:
% 5.91/6.13 pppp26-{F}(V0), pppp1-{F}(V0) | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #339: mergings( V0 == V2; #336 ), references = 1, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | pppp13-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #341: mergings( V0 == V2; #337 ), references = 1, size of lhs = 2:
% 5.91/6.13 P_empty_set-{F}(V0), empty-{F}(V1) | pppp13-{T}(V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #362: disj( #31, #29+#15 ), references = 2, size of lhs = 1:
% 5.91/6.13 pppp4-{F}(V0,V1) | pppp27-{T}(V1,V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #378: disj( #31, #293+#33 ), references = 1, size of lhs = 4:
% 5.91/6.13 empty-{F}(V0), P_powerset-{F}(V0,V1), P_empty_set-{F}(V2), in-{F}(V2,V3) | pppp2-{T}(V1,V3)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #389: mergings( V3 == V4; #387 ), references = 1, size of lhs = 5:
% 5.91/6.13 P_empty_set-{F}(V0), pppp1-{F}(V1), pppp27-{F}(V1,V2), in-{F}(V2,V1), P_powerset-{F}(V2,V1) | pppp7-{T}(V1,V2,V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #408: mergings( V2 == V3; #406 ), references = 1, size of lhs = 4:
% 5.91/6.13 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), pppp4-{F}(V1,V3), in-{F}(V3,V4) | pppp27-{T}(V4,V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #420: mergings( V1 == V2; #418 ), references = 1, size of lhs = 5:
% 5.91/6.13 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), pppp4-{F}(V1,V3), in-{F}(V3,V4), in-{F}(V4,V2) | pppp25-{T}(V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #444: exists( #32, #442 ), references = 1, size of lhs = 4:
% 5.91/6.13 P_empty_set-{F}(V0), ordinal-{F}(V1), pppp27-{F}(V1,V2), pppp24-{F}(V2) | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #449: exists( #14, #447 ), references = 1, size of lhs = 3:
% 5.91/6.13 pppp25-{F}(V0), pppp24-{F}(V0), P_empty_set-{F}(V1) | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #487: mergings( V3 == V4; #485 ), references = 2, size of lhs = 5:
% 5.91/6.13 pppp0-{F}(V0), pppp27-{F}(V0,V1), P_powerset-{F}(V0,V1), P_empty_set-{F}(V2), V1 == V2 | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #501: mergings( V3 == V4; #499 ), references = 2, size of lhs = 6:
% 5.91/6.13 pppp0-{F}(V0), pppp27-{F}(V0,V1), P_empty_set-{F}(V2), P_powerset-{F}(V0,V3), V3 == V2, pppp2-{F}(V3,V1) | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #505: mergings( V2 == V3; #503 ), references = 1, size of lhs = 5:
% 5.91/6.13 pppp0-{F}(V0), P_empty_set-{F}(V1), P_powerset-{F}(V0,V2), V2 == V1, pppp2-{F}(V2,V3) | pppp2-{T}(V0,V3)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #522: disj( #13, exists( #14, #447 ) ), references = 1, size of lhs = 2:
% 5.91/6.13 pppp24-{F}(V0), P_empty_set-{F}(V1) | pppp0-{T}(V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #596: disj( #31, #30+#114+#3+#17+#330 ), references = 1, size of lhs = 3:
% 5.91/6.13 pppp24-{F}(V0), pppp26-{F}(V1), in-{F}(V1,V2) | pppp27-{T}(V2,V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #597: disj( #31, #30+#114+#2+#10+#487 ), references = 1, size of lhs = 6:
% 5.91/6.13 pppp24-{F}(V0), P_empty_set-{F}(V1), in-{F}(V2,V3), pppp27-{F}(V2,V4), V4 == V1, P_powerset-{F}(V2,V4) | pppp27-{T}(V3,V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #598: disj( #31, #30+#114+#2+#10+#501 ), references = 1, size of lhs = 7:
% 5.91/6.13 pppp24-{F}(V0), P_empty_set-{F}(V1), in-{F}(V2,V3), pppp27-{F}(V2,V4), P_powerset-{F}(V2,V5), V5 == V1, pppp2-{F}(V5,V4) | pppp27-{T}(V3,V0)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #614: disj( #20, #322+#120 ), references = 1, size of lhs = 6:
% 5.91/6.13 P_empty_set-{F}(V0), empty-{F}(V1), in-{F}(V1,V2), in-{F}(V3,V2), V3 == V1, pppp7-{F}(V4,V3,V1) | pppp26-{T}(V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #616: mergings( V5 == V2; #613 ), references = 1, size of lhs = 8:
% 5.91/6.13 P_empty_set-{F}(V0), empty-{F}(V1), P_powerset-{F}(V1,V2), element-{F}(V0,V2), in-{F}(V0,V3), in-{F}(V4,V3), V4 == V0, pppp7-{F}(V5,V4,V0) | pppp26-{T}(V3)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #755: disj( #31, mergings( V3 == V4; #499 ) ), references = 1, size of lhs = 5:
% 5.91/6.13 pppp0-{F}(V0), pppp27-{F}(V0,V1), P_empty_set-{F}(V2), P_powerset-{F}(V0,V3), V3 == V2 | pppp27-{T}(V3,V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #777: disj( #20, #322+#30+#0 ), references = 1, size of lhs = 5:
% 5.91/6.13 in-{F}(V0,V1), in-{F}(V2,V1), V0 == V2, pppp2-{F}(V2,V0), pppp7-{F}(V3,V0,V2) | pppp26-{T}(V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #895: mergings( V2 == V3, V3 == V4; #891 ), references = 1, size of lhs = 6:
% 5.91/6.13 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), V1 == V0, in-{F}(V1,V3), in-{F}(V3,V4), in-{F}(V4,V5) | pppp27-{T}(V5,V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #1080: mergings( V2 == V3, V3 == V4; #1077 ), references = 1, size of lhs = 6:
% 5.91/6.13 P_empty_set-{F}(V0), P_powerset-{F}(V1,V2), V1 == V0, pppp7-{F}(V3,V1,V4), in-{F}(V4,V5), in-{F}(V5,V6) | pppp27-{T}(V6,V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #1164: disj( #110, input ), references = 1, size of lhs = 5:
% 5.91/6.13 P_empty_set-{F}(V0), ordinal-{F}(V1), ordinal-{F}(V2), V1 == V2, pppp7-{F}(V3,V1,V2) | in-{T}(V1,V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #1165: disj( #110, input ), references = 2, size of lhs = 5:
% 5.91/6.13 P_empty_set-{F}(V0), ordinal-{F}(V1), ordinal-{F}(V2), V1 == V2, pppp5-{F}(V3,V2,V1) | in-{T}(V1,V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #1191: mergings( V3 == V4, V4 == V5; #1186 ), references = 1, size of lhs = 5:
% 5.91/6.13 pppp24-{F}(V0), pppp27-{F}(V0,V1), ordinal-{F}(V1), P_powerset-{F}(V1,V0), P_empty_set-{F}(V2) | pppp7-{T}(V0,V1,V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #1195: mergings( V3 == V4, V4 == V5, V5 == V8; #1187 ), references = 1, size of lhs = 8:
% 5.91/6.13 pppp24-{F}(V0), pppp27-{F}(V0,V1), ordinal-{F}(V1), empty-{F}(V2), P_powerset-{F}(V2,V3), P_powerset-{F}(V3,V0), P_empty_set-{F}(V4), V1 == V4 | pppp7-{T}(V0,V1,V1)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #1230: exists( #22, #1228 ), references = 2, size of lhs = 5:
% 5.91/6.13 pppp24-{F}(V0), P_empty_set-{F}(V1), ordinal-{F}(V2), pppp6-{F}(V3,V2), pppp2-{F}(V3,V0) | pppp5-{T}(V3,V2,V2)
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #1252: mergings( V0 == V2; #1250 ), references = 1, size of lhs = 4:
% 5.91/6.13 pppp26-{F}(V0), pppp24-{F}(V0), pppp2-{F}(V0,V0), P_empty_set-{F}(V1) | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #1262: mergings( V0 == V2, V2 == V3, V3 == V4; #1258 ), references = 1, size of lhs = 1:
% 5.91/6.13 P_empty_set-{F}(V0) | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 #1264: exists( #122, #1258 ), references = 1, size of lhs = 0:
% 5.91/6.13 FALSE | FALSE
% 5.91/6.13 (used 0 times, uses = {})
% 5.91/6.13
% 5.91/6.13 number of learnt formulas = 57
% 5.91/6.13
% 5.91/6.13
% 5.91/6.13 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.91/6.13
% 5.91/6.13 randbase = 1
%------------------------------------------------------------------------------