TSTP Solution File: LCL536+1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : LCL536+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n027.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 06:09:25 EDT 2022
% Result : Theorem 30.01s 30.17s
% Output : Refutation 30.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL536+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.13/0.32 % Computer : n027.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Fri Jul 22 22:59:31 EDT 2022
% 0.13/0.32 % CPUTime :
% 30.01/30.17 GeoParameters:
% 30.01/30.17
% 30.01/30.17 tptp_input = 1
% 30.01/30.17 tptp_output = 0
% 30.01/30.17 nonempty = 1
% 30.01/30.17 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.01/30.17 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 30.01/30.17
% 30.01/30.17
% 30.01/30.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.01/30.17 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.01/30.17
% 30.01/30.17 RuleSystem INPUT:
% 30.01/30.17
% 30.01/30.17 Initial Rules:
% 30.01/30.17 #0: input, references = 3, size of lhs = 1:
% 30.01/30.17 modus_ponens-{F}() | pppp0-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #1: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp0-{F}() | modus_ponens-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #2: input, references = 7, size of lhs = 4:
% 30.01/30.17 pppp0-{F}(), P_implies-{F}(V1,V0,V2), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2) | is_a_theorem-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #3: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp0-{T}(), pppp143-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #4: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp143-{F}() | EXISTS V0: pppp50-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #5: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp50-{F}(V0) | EXISTS V1: pppp49-{T}(V1,V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #6: input, references = 3, size of lhs = 2:
% 30.01/30.17 pppp50-{F}(V0), is_a_theorem-{F}(V0) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #7: input, references = 3, size of lhs = 2:
% 30.01/30.17 pppp49-{F}(V0,V1), P_implies-{F}(V0,V1,V2) | is_a_theorem-{T}(V2)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #8: input, references = 3, size of lhs = 2:
% 30.01/30.17 pppp49-{F}(V0,V1), P_implies-{F}(V0,V1,V2) | is_a_theorem-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #9: input, references = 3, size of lhs = 1:
% 30.01/30.17 substitution_of_equivalents-{F}() | pppp1-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #10: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp1-{F}() | substitution_of_equivalents-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #11: input, references = 8, size of lhs = 4:
% 30.01/30.17 pppp1-{F}(), P_equiv-{F}(V0,V1,V2), is_a_theorem-{F}(V2), V0 == V1 | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #12: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp1-{T}(), pppp144-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #13: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp144-{F}() | EXISTS V0: pppp52-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #14: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp52-{F}(V0) | EXISTS V1: pppp51-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #15: input, references = 3, size of lhs = 2:
% 30.01/30.17 pppp51-{F}(V1,V1), P_equiv-{F}(V1,V1,V2) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #16: input, references = 3, size of lhs = 2:
% 30.01/30.17 pppp51-{F}(V0,V1), P_equiv-{F}(V0,V1,V2) | is_a_theorem-{T}(V2)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #17: input, references = 3, size of lhs = 1:
% 30.01/30.17 modus_tollens-{F}() | pppp2-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #18: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp2-{F}() | modus_tollens-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #19: input, references = 3, size of lhs = 6:
% 30.01/30.17 pppp2-{F}(), P_not-{F}(V1,V2), P_not-{F}(V0,V3), P_implies-{F}(V2,V3,V4), P_implies-{F}(V0,V1,V5), P_implies-{F}(V4,V5,V6) | is_a_theorem-{T}(V6)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #20: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp2-{T}(), pppp145-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #21: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp145-{F}() | EXISTS V0: pppp54-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #22: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp54-{F}(V0) | EXISTS V1: pppp53-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #23: input, references = 3, size of lhs = 7:
% 30.01/30.17 pppp53-{F}(V0,V1), P_not-{F}(V1,V2), P_not-{F}(V0,V3), P_implies-{F}(V2,V3,V4), P_implies-{F}(V0,V1,V5), P_implies-{F}(V4,V5,V6), is_a_theorem-{F}(V6) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #24: input, references = 3, size of lhs = 1:
% 30.01/30.17 implies_1-{F}() | pppp3-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #25: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp3-{F}() | implies_1-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #26: input, references = 7, size of lhs = 3:
% 30.01/30.17 pppp3-{F}(), P_implies-{F}(V1,V0,V2), P_implies-{F}(V0,V2,V3) | is_a_theorem-{T}(V3)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #27: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp3-{T}(), pppp146-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #28: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp146-{F}() | EXISTS V0: pppp56-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #29: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp56-{F}(V0) | EXISTS V1: pppp55-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #30: input, references = 3, size of lhs = 4:
% 30.01/30.17 pppp55-{F}(V0,V1), P_implies-{F}(V1,V0,V2), P_implies-{F}(V0,V2,V3), is_a_theorem-{F}(V3) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #31: input, references = 3, size of lhs = 1:
% 30.01/30.17 implies_2-{F}() | pppp4-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #32: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp4-{F}() | implies_2-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #33: input, references = 5, size of lhs = 4:
% 30.01/30.17 pppp4-{F}(), P_implies-{F}(V0,V1,V2), P_implies-{F}(V0,V2,V3), P_implies-{F}(V3,V2,V4) | is_a_theorem-{T}(V4)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #34: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp4-{T}(), pppp147-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #35: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp147-{F}() | EXISTS V0: pppp58-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #36: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp58-{F}(V0) | EXISTS V1: pppp57-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #37: input, references = 3, size of lhs = 5:
% 30.01/30.17 pppp57-{F}(V0,V1), P_implies-{F}(V0,V1,V2), P_implies-{F}(V0,V2,V3), P_implies-{F}(V3,V2,V4), is_a_theorem-{F}(V4) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #38: input, references = 3, size of lhs = 1:
% 30.01/30.17 implies_3-{F}() | pppp5-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #39: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp5-{F}() | implies_3-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #40: input, references = 8, size of lhs = 6:
% 30.01/30.17 pppp5-{F}(), P_implies-{F}(V0,V1,V3), P_implies-{F}(V1,V2,V4), P_implies-{F}(V0,V2,V5), P_implies-{F}(V4,V5,V6), P_implies-{F}(V3,V6,V7) | is_a_theorem-{T}(V7)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #41: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp5-{T}(), pppp148-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #42: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp148-{F}() | EXISTS V0: pppp61-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #43: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp61-{F}(V0) | EXISTS V1: pppp60-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #44: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp60-{F}(V0,V1) | EXISTS V2: pppp59-{T}(V0,V1,V2)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #45: input, references = 3, size of lhs = 7:
% 30.01/30.17 pppp59-{F}(V0,V1,V2), P_implies-{F}(V0,V1,V3), P_implies-{F}(V1,V2,V4), P_implies-{F}(V0,V2,V5), P_implies-{F}(V4,V5,V6), P_implies-{F}(V3,V6,V7), is_a_theorem-{F}(V7) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #46: input, references = 3, size of lhs = 1:
% 30.01/30.17 and_1-{F}() | pppp6-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #47: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp6-{F}() | and_1-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #48: input, references = 7, size of lhs = 3:
% 30.01/30.17 pppp6-{F}(), P_and-{F}(V0,V1,V2), P_implies-{F}(V2,V0,V3) | is_a_theorem-{T}(V3)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #49: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp6-{T}(), pppp149-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #50: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp149-{F}() | EXISTS V0: pppp63-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #51: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp63-{F}(V0) | EXISTS V1: pppp62-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #52: input, references = 3, size of lhs = 4:
% 30.01/30.17 pppp62-{F}(V0,V1), P_and-{F}(V0,V1,V2), P_implies-{F}(V2,V0,V3), is_a_theorem-{F}(V3) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #53: input, references = 3, size of lhs = 1:
% 30.01/30.17 and_2-{F}() | pppp7-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #54: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp7-{F}() | and_2-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #55: input, references = 5, size of lhs = 3:
% 30.01/30.17 pppp7-{F}(), P_and-{F}(V0,V1,V2), P_implies-{F}(V2,V1,V3) | is_a_theorem-{T}(V3)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #56: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp7-{T}(), pppp150-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #57: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp150-{F}() | EXISTS V0: pppp65-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #58: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp65-{F}(V0) | EXISTS V1: pppp64-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #59: input, references = 3, size of lhs = 4:
% 30.01/30.17 pppp64-{F}(V0,V1), P_and-{F}(V0,V1,V2), P_implies-{F}(V2,V1,V3), is_a_theorem-{F}(V3) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #60: input, references = 3, size of lhs = 1:
% 30.01/30.17 and_3-{F}() | pppp8-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #61: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp8-{F}() | and_3-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #62: input, references = 8, size of lhs = 4:
% 30.01/30.17 pppp8-{F}(), P_and-{F}(V0,V1,V2), P_implies-{F}(V1,V2,V3), P_implies-{F}(V0,V3,V4) | is_a_theorem-{T}(V4)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #63: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp8-{T}(), pppp151-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #64: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp151-{F}() | EXISTS V0: pppp67-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #65: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp67-{F}(V0) | EXISTS V1: pppp66-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #66: input, references = 3, size of lhs = 5:
% 30.01/30.17 pppp66-{F}(V0,V1), P_and-{F}(V0,V1,V2), P_implies-{F}(V1,V2,V3), P_implies-{F}(V0,V3,V4), is_a_theorem-{F}(V4) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #67: input, references = 3, size of lhs = 1:
% 30.01/30.17 or_1-{F}() | pppp9-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #68: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp9-{F}() | or_1-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #69: input, references = 3, size of lhs = 3:
% 30.01/30.17 pppp9-{F}(), P_or-{F}(V0,V1,V2), P_implies-{F}(V0,V2,V3) | is_a_theorem-{T}(V3)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #70: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp9-{T}(), pppp152-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #71: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp152-{F}() | EXISTS V0: pppp69-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #72: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp69-{F}(V0) | EXISTS V1: pppp68-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #73: input, references = 3, size of lhs = 4:
% 30.01/30.17 pppp68-{F}(V0,V1), P_or-{F}(V0,V1,V2), P_implies-{F}(V0,V2,V3), is_a_theorem-{F}(V3) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #74: input, references = 3, size of lhs = 1:
% 30.01/30.17 or_2-{F}() | pppp10-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #75: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp10-{F}() | or_2-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #76: input, references = 3, size of lhs = 3:
% 30.01/30.17 pppp10-{F}(), P_or-{F}(V0,V1,V2), P_implies-{F}(V1,V2,V3) | is_a_theorem-{T}(V3)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #77: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp10-{T}(), pppp153-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #78: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp153-{F}() | EXISTS V0: pppp71-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #79: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp71-{F}(V0) | EXISTS V1: pppp70-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #80: input, references = 3, size of lhs = 4:
% 30.01/30.17 pppp70-{F}(V0,V1), P_or-{F}(V0,V1,V2), P_implies-{F}(V1,V2,V3), is_a_theorem-{F}(V3) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #81: input, references = 3, size of lhs = 1:
% 30.01/30.17 or_3-{F}() | pppp11-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #82: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp11-{F}() | or_3-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #83: input, references = 3, size of lhs = 7:
% 30.01/30.17 pppp11-{F}(), P_implies-{F}(V0,V2,V3), P_implies-{F}(V1,V2,V4), P_or-{F}(V0,V1,V5), P_implies-{F}(V5,V2,V6), P_implies-{F}(V4,V6,V7), P_implies-{F}(V3,V7,V8) | is_a_theorem-{T}(V8)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #84: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp11-{T}(), pppp154-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #85: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp154-{F}() | EXISTS V0: pppp74-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #86: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp74-{F}(V0) | EXISTS V1: pppp73-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #87: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp73-{F}(V0,V1) | EXISTS V2: pppp72-{T}(V0,V1,V2)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #88: input, references = 3, size of lhs = 8:
% 30.01/30.17 pppp72-{F}(V0,V1,V2), P_implies-{F}(V0,V2,V3), P_implies-{F}(V1,V2,V4), P_or-{F}(V0,V1,V5), P_implies-{F}(V5,V2,V6), P_implies-{F}(V4,V6,V7), P_implies-{F}(V3,V7,V8), is_a_theorem-{F}(V8) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #89: input, references = 3, size of lhs = 1:
% 30.01/30.17 equivalence_1-{F}() | pppp12-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #90: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp12-{F}() | equivalence_1-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #91: input, references = 5, size of lhs = 4:
% 30.01/30.17 pppp12-{F}(), P_equiv-{F}(V0,V1,V2), P_implies-{F}(V0,V1,V3), P_implies-{F}(V2,V3,V4) | is_a_theorem-{T}(V4)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #92: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp12-{T}(), pppp155-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #93: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp155-{F}() | EXISTS V0: pppp76-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #94: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp76-{F}(V0) | EXISTS V1: pppp75-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #95: input, references = 3, size of lhs = 5:
% 30.01/30.17 pppp75-{F}(V0,V1), P_equiv-{F}(V0,V1,V2), P_implies-{F}(V0,V1,V3), P_implies-{F}(V2,V3,V4), is_a_theorem-{F}(V4) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #96: input, references = 3, size of lhs = 1:
% 30.01/30.17 equivalence_2-{F}() | pppp13-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #97: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp13-{F}() | equivalence_2-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #98: input, references = 5, size of lhs = 4:
% 30.01/30.17 pppp13-{F}(), P_equiv-{F}(V0,V1,V2), P_implies-{F}(V1,V0,V3), P_implies-{F}(V2,V3,V4) | is_a_theorem-{T}(V4)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #99: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp13-{T}(), pppp156-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #100: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp156-{F}() | EXISTS V0: pppp78-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #101: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp78-{F}(V0) | EXISTS V1: pppp77-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #102: input, references = 3, size of lhs = 5:
% 30.01/30.17 pppp77-{F}(V0,V1), P_equiv-{F}(V0,V1,V2), P_implies-{F}(V1,V0,V3), P_implies-{F}(V2,V3,V4), is_a_theorem-{F}(V4) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #103: input, references = 3, size of lhs = 1:
% 30.01/30.17 equivalence_3-{F}() | pppp14-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #104: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp14-{F}() | equivalence_3-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #105: input, references = 3, size of lhs = 6:
% 30.01/30.17 pppp14-{F}(), P_implies-{F}(V0,V1,V2), P_implies-{F}(V1,V0,V3), P_equiv-{F}(V0,V1,V4), P_implies-{F}(V3,V4,V5), P_implies-{F}(V2,V5,V6) | is_a_theorem-{T}(V6)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #106: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp14-{T}(), pppp157-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #107: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp157-{F}() | EXISTS V0: pppp80-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #108: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp80-{F}(V0) | EXISTS V1: pppp79-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #109: input, references = 3, size of lhs = 7:
% 30.01/30.17 pppp79-{F}(V0,V1), P_implies-{F}(V0,V1,V2), P_implies-{F}(V1,V0,V3), P_equiv-{F}(V0,V1,V4), P_implies-{F}(V3,V4,V5), P_implies-{F}(V2,V5,V6), is_a_theorem-{F}(V6) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #110: input, references = 3, size of lhs = 1:
% 30.01/30.17 kn1-{F}() | pppp15-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #111: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp15-{F}() | kn1-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #112: input, references = 3, size of lhs = 3:
% 30.01/30.17 pppp15-{F}(), P_and-{F}(V0,V0,V1), P_implies-{F}(V0,V1,V2) | is_a_theorem-{T}(V2)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #113: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp15-{T}(), pppp158-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #114: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp158-{F}() | EXISTS V0: pppp81-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #115: input, references = 6, size of lhs = 4:
% 30.01/30.17 pppp81-{F}(V0), P_and-{F}(V0,V0,V1), P_implies-{F}(V0,V1,V2), is_a_theorem-{F}(V2) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #116: input, references = 3, size of lhs = 1:
% 30.01/30.17 kn2-{F}() | pppp16-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #117: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp16-{F}() | kn2-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #118: input, references = 3, size of lhs = 3:
% 30.01/30.17 pppp16-{F}(), P_and-{F}(V0,V1,V2), P_implies-{F}(V2,V0,V3) | is_a_theorem-{T}(V3)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #119: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp16-{T}(), pppp159-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #120: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp159-{F}() | EXISTS V0: pppp83-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #121: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp83-{F}(V0) | EXISTS V1: pppp82-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #122: input, references = 3, size of lhs = 4:
% 30.01/30.17 pppp82-{F}(V0,V1), P_and-{F}(V0,V1,V2), P_implies-{F}(V2,V0,V3), is_a_theorem-{F}(V3) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #123: input, references = 3, size of lhs = 1:
% 30.01/30.17 kn3-{F}() | pppp17-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #124: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp17-{F}() | kn3-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #125: input, references = 3, size of lhs = 8:
% 30.01/30.17 pppp17-{F}(), P_implies-{F}(V0,V1,V3), P_and-{F}(V1,V2,V4), P_not-{F}(V4,V5), P_and-{F}(V2,V0,V6), P_not-{F}(V6,V7), P_implies-{F}(V5,V7,V8), P_implies-{F}(V3,V8,V9) | is_a_theorem-{T}(V9)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #126: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp17-{T}(), pppp160-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #127: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp160-{F}() | EXISTS V0: pppp86-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #128: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp86-{F}(V0) | EXISTS V1: pppp85-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #129: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp85-{F}(V0,V1) | EXISTS V2: pppp84-{T}(V0,V1,V2)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #130: input, references = 3, size of lhs = 9:
% 30.01/30.17 pppp84-{F}(V0,V1,V2), P_implies-{F}(V0,V1,V3), P_and-{F}(V1,V2,V4), P_not-{F}(V4,V5), P_and-{F}(V2,V0,V6), P_not-{F}(V6,V7), P_implies-{F}(V5,V7,V8), P_implies-{F}(V3,V8,V9), is_a_theorem-{F}(V9) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #131: input, references = 3, size of lhs = 1:
% 30.01/30.17 cn1-{F}() | pppp18-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #132: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp18-{F}() | cn1-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #133: input, references = 3, size of lhs = 6:
% 30.01/30.17 pppp18-{F}(), P_implies-{F}(V0,V1,V3), P_implies-{F}(V1,V2,V4), P_implies-{F}(V0,V2,V5), P_implies-{F}(V4,V5,V6), P_implies-{F}(V3,V6,V7) | is_a_theorem-{T}(V7)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #134: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp18-{T}(), pppp161-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #135: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp161-{F}() | EXISTS V0: pppp89-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #136: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp89-{F}(V0) | EXISTS V1: pppp88-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #137: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp88-{F}(V0,V1) | EXISTS V2: pppp87-{T}(V0,V1,V2)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #138: input, references = 3, size of lhs = 7:
% 30.01/30.17 pppp87-{F}(V0,V1,V2), P_implies-{F}(V0,V1,V3), P_implies-{F}(V1,V2,V4), P_implies-{F}(V0,V2,V5), P_implies-{F}(V4,V5,V6), P_implies-{F}(V3,V6,V7), is_a_theorem-{F}(V7) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #139: input, references = 3, size of lhs = 1:
% 30.01/30.17 cn2-{F}() | pppp19-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #140: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp19-{F}() | cn2-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #141: input, references = 3, size of lhs = 4:
% 30.01/30.17 pppp19-{F}(), P_not-{F}(V0,V2), P_implies-{F}(V2,V1,V3), P_implies-{F}(V0,V3,V4) | is_a_theorem-{T}(V4)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #142: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp19-{T}(), pppp162-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #143: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp162-{F}() | EXISTS V0: pppp91-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #144: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp91-{F}(V0) | EXISTS V1: pppp90-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #145: input, references = 3, size of lhs = 5:
% 30.01/30.17 pppp90-{F}(V0,V1), P_not-{F}(V0,V2), P_implies-{F}(V2,V1,V3), P_implies-{F}(V0,V3,V4), is_a_theorem-{F}(V4) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #146: input, references = 3, size of lhs = 1:
% 30.01/30.17 cn3-{F}() | pppp20-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #147: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp20-{F}() | cn3-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #148: input, references = 3, size of lhs = 4:
% 30.01/30.17 pppp20-{F}(), P_not-{F}(V0,V1), P_implies-{F}(V1,V0,V2), P_implies-{F}(V2,V0,V3) | is_a_theorem-{T}(V3)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #149: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp20-{T}(), pppp163-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #150: input, references = 4, size of lhs = 1:
% 30.01/30.17 pppp163-{F}() | EXISTS V0: pppp92-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #151: input, references = 10, size of lhs = 5:
% 30.01/30.17 pppp92-{F}(V0), P_not-{F}(V0,V1), P_implies-{F}(V1,V0,V2), P_implies-{F}(V2,V0,V3), is_a_theorem-{F}(V3) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #152: input, references = 3, size of lhs = 1:
% 30.01/30.17 r1-{F}() | pppp21-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #153: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp21-{F}() | r1-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #154: input, references = 4, size of lhs = 3:
% 30.01/30.17 pppp21-{F}(), P_or-{F}(V0,V0,V1), P_implies-{F}(V1,V0,V2) | is_a_theorem-{T}(V2)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #155: input, references = 4, size of lhs = 0:
% 30.01/30.17 FALSE | pppp21-{T}(), pppp164-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #156: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp164-{F}() | EXISTS V0: pppp93-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #157: input, references = 7, size of lhs = 4:
% 30.01/30.17 pppp93-{F}(V0), P_or-{F}(V0,V0,V1), P_implies-{F}(V1,V0,V2), is_a_theorem-{F}(V2) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #158: input, references = 3, size of lhs = 1:
% 30.01/30.17 r2-{F}() | pppp22-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #159: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp22-{F}() | r2-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #160: input, references = 3, size of lhs = 3:
% 30.01/30.17 pppp22-{F}(), P_or-{F}(V0,V1,V2), P_implies-{F}(V1,V2,V3) | is_a_theorem-{T}(V3)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #161: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp22-{T}(), pppp165-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #162: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp165-{F}() | EXISTS V0: pppp95-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #163: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp95-{F}(V0) | EXISTS V1: pppp94-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #164: input, references = 3, size of lhs = 4:
% 30.01/30.17 pppp94-{F}(V0,V1), P_or-{F}(V0,V1,V2), P_implies-{F}(V1,V2,V3), is_a_theorem-{F}(V3) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #165: input, references = 3, size of lhs = 1:
% 30.01/30.17 r3-{F}() | pppp23-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #166: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp23-{F}() | r3-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #167: input, references = 3, size of lhs = 4:
% 30.01/30.17 pppp23-{F}(), P_or-{F}(V0,V1,V2), P_or-{F}(V1,V0,V3), P_implies-{F}(V2,V3,V4) | is_a_theorem-{T}(V4)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #168: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp23-{T}(), pppp166-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #169: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp166-{F}() | EXISTS V0: pppp97-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #170: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp97-{F}(V0) | EXISTS V1: pppp96-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #171: input, references = 3, size of lhs = 5:
% 30.01/30.17 pppp96-{F}(V0,V1), P_or-{F}(V0,V1,V2), P_or-{F}(V1,V0,V3), P_implies-{F}(V2,V3,V4), is_a_theorem-{F}(V4) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #172: input, references = 3, size of lhs = 1:
% 30.01/30.17 r4-{F}() | pppp24-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #173: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp24-{F}() | r4-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #174: input, references = 3, size of lhs = 6:
% 30.01/30.17 pppp24-{F}(), P_or-{F}(V1,V2,V3), P_or-{F}(V0,V3,V4), P_or-{F}(V0,V2,V5), P_or-{F}(V1,V5,V6), P_implies-{F}(V4,V6,V7) | is_a_theorem-{T}(V7)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #175: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp24-{T}(), pppp167-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #176: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp167-{F}() | EXISTS V0: pppp100-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #177: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp100-{F}(V0) | EXISTS V1: pppp99-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #178: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp99-{F}(V0,V1) | EXISTS V2: pppp98-{T}(V0,V1,V2)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #179: input, references = 3, size of lhs = 7:
% 30.01/30.17 pppp98-{F}(V0,V1,V2), P_or-{F}(V1,V2,V3), P_or-{F}(V0,V3,V4), P_or-{F}(V0,V2,V5), P_or-{F}(V1,V5,V6), P_implies-{F}(V4,V6,V7), is_a_theorem-{F}(V7) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #180: input, references = 3, size of lhs = 1:
% 30.01/30.17 r5-{F}() | pppp25-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #181: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp25-{F}() | r5-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #182: input, references = 3, size of lhs = 6:
% 30.01/30.17 pppp25-{F}(), P_implies-{F}(V1,V2,V3), P_or-{F}(V0,V1,V4), P_or-{F}(V0,V2,V5), P_implies-{F}(V4,V5,V6), P_implies-{F}(V3,V6,V7) | is_a_theorem-{T}(V7)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #183: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | pppp25-{T}(), pppp168-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #184: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp168-{F}() | EXISTS V0: pppp103-{T}(V0)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #185: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp103-{F}(V0) | EXISTS V1: pppp102-{T}(V0,V1)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #186: input, references = 3, size of lhs = 1:
% 30.01/30.17 pppp102-{F}(V0,V1) | EXISTS V2: pppp101-{T}(V0,V1,V2)
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #187: input, references = 3, size of lhs = 7:
% 30.01/30.17 pppp101-{F}(V0,V1,V2), P_implies-{F}(V1,V2,V3), P_or-{F}(V0,V1,V4), P_or-{F}(V0,V2,V5), P_implies-{F}(V4,V5,V6), P_implies-{F}(V3,V6,V7), is_a_theorem-{F}(V7) | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #188: input, references = 5, size of lhs = 7:
% 30.01/30.17 op_or-{F}(), P_or-{F}(V0,V1,V2), P_not-{F}(V0,V3), P_not-{F}(V1,V4), P_and-{F}(V3,V4,V5), P_not-{F}(V5,V6), V2 == V6 | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #189: input, references = 3, size of lhs = 7:
% 30.01/30.17 op_and-{F}(), P_and-{F}(V0,V1,V2), P_not-{F}(V0,V3), P_not-{F}(V1,V4), P_or-{F}(V3,V4,V5), P_not-{F}(V5,V6), V2 == V6 | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #190: input, references = 7, size of lhs = 6:
% 30.01/30.17 op_implies_and-{F}(), P_implies-{F}(V0,V1,V2), P_not-{F}(V1,V3), P_and-{F}(V0,V3,V4), P_not-{F}(V4,V5), V2 == V5 | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #191: input, references = 3, size of lhs = 5:
% 30.01/30.17 op_implies_or-{F}(), P_implies-{F}(V0,V1,V2), P_not-{F}(V0,V3), P_or-{F}(V3,V1,V4), V2 == V4 | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #192: input, references = 5, size of lhs = 6:
% 30.01/30.17 op_equiv-{F}(), P_equiv-{F}(V0,V1,V2), P_implies-{F}(V0,V1,V3), P_implies-{F}(V1,V0,V4), P_and-{F}(V3,V4,V5), V2 == V5 | FALSE
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #193: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | op_or-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #194: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | op_implies_and-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #195: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | op_equiv-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #196: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | modus_ponens-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #197: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | modus_tollens-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #198: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | implies_1-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #199: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | implies_2-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #200: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | implies_3-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #201: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | and_1-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #202: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | and_2-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #203: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | and_3-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #204: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | or_1-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #205: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | or_2-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #206: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | or_3-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #207: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | equivalence_1-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #208: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | equivalence_2-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #209: input, references = 3, size of lhs = 0:
% 30.01/30.17 FALSE | equivalence_3-{T}()
% 30.01/30.17 (used 0 times, uses = {})
% 30.01/30.17
% 30.01/30.17 #210: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | substitution_of_equivalents-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #211: input, references = 4, size of lhs = 1:
% 30.01/30.18 necessitation-{F}() | pppp26-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #212: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp26-{F}() | necessitation-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #213: input, references = 8, size of lhs = 3:
% 30.01/30.18 pppp26-{F}(), P_necessarily-{F}(V0,V1), is_a_theorem-{F}(V0) | is_a_theorem-{T}(V1)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #214: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp26-{T}(), pppp169-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #215: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp169-{F}() | EXISTS V0: pppp104-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #216: input, references = 3, size of lhs = 3:
% 30.01/30.18 pppp104-{F}(V0), P_necessarily-{F}(V0,V1), is_a_theorem-{F}(V1) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #217: input, references = 3, size of lhs = 2:
% 30.01/30.18 pppp104-{F}(V0), P_necessarily-{F}(V0,V1) | is_a_theorem-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #218: input, references = 3, size of lhs = 1:
% 30.01/30.18 modus_ponens_strict_implies-{F}() | pppp27-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #219: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp27-{F}() | modus_ponens_strict_implies-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #220: input, references = 6, size of lhs = 4:
% 30.01/30.18 pppp27-{F}(), P_strict_implies-{F}(V1,V0,V2), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2) | is_a_theorem-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #221: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp27-{T}(), pppp170-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #222: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp170-{F}() | EXISTS V0: pppp106-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #223: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp106-{F}(V0) | EXISTS V1: pppp105-{T}(V1,V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #224: input, references = 3, size of lhs = 2:
% 30.01/30.18 pppp106-{F}(V0), is_a_theorem-{F}(V0) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #225: input, references = 3, size of lhs = 2:
% 30.01/30.18 pppp105-{F}(V0,V1), P_strict_implies-{F}(V0,V1,V2) | is_a_theorem-{T}(V2)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #226: input, references = 3, size of lhs = 2:
% 30.01/30.18 pppp105-{F}(V0,V1), P_strict_implies-{F}(V0,V1,V2) | is_a_theorem-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #227: input, references = 3, size of lhs = 1:
% 30.01/30.18 adjunction-{F}() | pppp28-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #228: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp28-{F}() | adjunction-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #229: input, references = 3, size of lhs = 4:
% 30.01/30.18 pppp28-{F}(), is_a_theorem-{F}(V0), P_and-{F}(V1,V0,V2), is_a_theorem-{F}(V1) | is_a_theorem-{T}(V2)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #230: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp28-{T}(), pppp171-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #231: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp171-{F}() | EXISTS V0: pppp108-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #232: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp108-{F}(V0) | EXISTS V1: pppp107-{T}(V1,V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #233: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp108-{F}(V0) | is_a_theorem-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #234: input, references = 3, size of lhs = 3:
% 30.01/30.18 pppp107-{F}(V0,V1), P_and-{F}(V0,V1,V2), is_a_theorem-{F}(V2) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #235: input, references = 3, size of lhs = 2:
% 30.01/30.18 pppp107-{F}(V0,V1), P_and-{F}(V0,V1,V2) | is_a_theorem-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #236: input, references = 3, size of lhs = 1:
% 30.01/30.18 substitution_strict_equiv-{F}() | pppp29-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #237: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp29-{F}() | substitution_strict_equiv-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #238: input, references = 4, size of lhs = 4:
% 30.01/30.18 pppp29-{F}(), P_strict_equiv-{F}(V0,V1,V2), is_a_theorem-{F}(V2), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #239: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp29-{T}(), pppp172-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #240: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp172-{F}() | EXISTS V0: pppp110-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #241: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp110-{F}(V0) | EXISTS V1: pppp109-{T}(V0,V1)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #242: input, references = 3, size of lhs = 2:
% 30.01/30.18 pppp109-{F}(V1,V1), P_strict_equiv-{F}(V1,V1,V2) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #243: input, references = 3, size of lhs = 2:
% 30.01/30.18 pppp109-{F}(V0,V1), P_strict_equiv-{F}(V0,V1,V2) | is_a_theorem-{T}(V2)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #244: input, references = 3, size of lhs = 1:
% 30.01/30.18 axiom_K-{F}() | pppp30-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #245: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp30-{F}() | axiom_K-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #246: input, references = 5, size of lhs = 7:
% 30.01/30.18 pppp30-{F}(), P_implies-{F}(V0,V1,V2), P_necessarily-{F}(V2,V3), P_necessarily-{F}(V0,V4), P_necessarily-{F}(V1,V5), P_implies-{F}(V4,V5,V6), P_implies-{F}(V3,V6,V7) | is_a_theorem-{T}(V7)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #247: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp30-{T}(), pppp173-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #248: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp173-{F}() | EXISTS V0: pppp112-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #249: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp112-{F}(V0) | EXISTS V1: pppp111-{T}(V0,V1)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #250: input, references = 3, size of lhs = 8:
% 30.01/30.18 pppp111-{F}(V0,V1), P_implies-{F}(V0,V1,V2), P_necessarily-{F}(V2,V3), P_necessarily-{F}(V0,V4), P_necessarily-{F}(V1,V5), P_implies-{F}(V4,V5,V6), P_implies-{F}(V3,V6,V7), is_a_theorem-{F}(V7) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #251: input, references = 3, size of lhs = 1:
% 30.01/30.18 axiom_M-{F}() | pppp31-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #252: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp31-{F}() | axiom_M-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #253: input, references = 4, size of lhs = 3:
% 30.01/30.18 pppp31-{F}(), P_necessarily-{F}(V0,V1), P_implies-{F}(V1,V0,V2) | is_a_theorem-{T}(V2)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #254: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp31-{T}(), pppp174-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #255: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp174-{F}() | EXISTS V0: pppp113-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #256: input, references = 3, size of lhs = 4:
% 30.01/30.18 pppp113-{F}(V0), P_necessarily-{F}(V0,V1), P_implies-{F}(V1,V0,V2), is_a_theorem-{F}(V2) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #257: input, references = 3, size of lhs = 1:
% 30.01/30.18 axiom_4-{F}() | pppp32-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #258: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp32-{F}() | axiom_4-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #259: input, references = 3, size of lhs = 4:
% 30.01/30.18 pppp32-{F}(), P_necessarily-{F}(V0,V1), P_necessarily-{F}(V1,V2), P_implies-{F}(V1,V2,V3) | is_a_theorem-{T}(V3)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #260: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp32-{T}(), pppp175-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #261: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp175-{F}() | EXISTS V0: pppp114-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #262: input, references = 4, size of lhs = 5:
% 30.01/30.18 pppp114-{F}(V0), P_necessarily-{F}(V0,V1), P_necessarily-{F}(V1,V2), P_implies-{F}(V1,V2,V3), is_a_theorem-{F}(V3) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #263: input, references = 3, size of lhs = 1:
% 30.01/30.18 axiom_B-{F}() | pppp33-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #264: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp33-{F}() | axiom_B-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #265: input, references = 3, size of lhs = 4:
% 30.01/30.18 pppp33-{F}(), P_possibly-{F}(V0,V1), P_necessarily-{F}(V1,V2), P_implies-{F}(V0,V2,V3) | is_a_theorem-{T}(V3)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #266: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp33-{T}(), pppp176-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #267: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp176-{F}() | EXISTS V0: pppp115-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #268: input, references = 3, size of lhs = 5:
% 30.01/30.18 pppp115-{F}(V0), P_possibly-{F}(V0,V1), P_necessarily-{F}(V1,V2), P_implies-{F}(V0,V2,V3), is_a_theorem-{F}(V3) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #269: input, references = 4, size of lhs = 1:
% 30.01/30.18 axiom_5-{F}() | pppp34-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #270: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp34-{F}() | axiom_5-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #271: input, references = 7, size of lhs = 4:
% 30.01/30.18 pppp34-{F}(), P_possibly-{F}(V0,V1), P_necessarily-{F}(V1,V2), P_implies-{F}(V1,V2,V3) | is_a_theorem-{T}(V3)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #272: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp34-{T}(), pppp177-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #273: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp177-{F}() | EXISTS V0: pppp116-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #274: input, references = 3, size of lhs = 5:
% 30.01/30.18 pppp116-{F}(V0), P_possibly-{F}(V0,V1), P_necessarily-{F}(V1,V2), P_implies-{F}(V1,V2,V3), is_a_theorem-{F}(V3) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #275: input, references = 3, size of lhs = 1:
% 30.01/30.18 axiom_s1-{F}() | pppp35-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #276: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp35-{F}() | axiom_s1-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #277: input, references = 3, size of lhs = 9:
% 30.01/30.18 pppp35-{F}(), P_implies-{F}(V0,V1,V3), P_necessarily-{F}(V3,V4), P_implies-{F}(V1,V2,V5), P_necessarily-{F}(V5,V6), P_and-{F}(V4,V6,V7), P_implies-{F}(V0,V2,V8), P_necessarily-{F}(V8,V9), P_implies-{F}(V7,V9,V10) | is_a_theorem-{T}(V10)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #278: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp35-{T}(), pppp178-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #279: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp178-{F}() | EXISTS V0: pppp119-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #280: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp119-{F}(V0) | EXISTS V1: pppp118-{T}(V0,V1)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #281: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp118-{F}(V0,V1) | EXISTS V2: pppp117-{T}(V0,V1,V2)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #282: input, references = 3, size of lhs = 10:
% 30.01/30.18 pppp117-{F}(V0,V1,V2), P_implies-{F}(V0,V1,V3), P_necessarily-{F}(V3,V4), P_implies-{F}(V1,V2,V5), P_necessarily-{F}(V5,V6), P_and-{F}(V4,V6,V7), P_implies-{F}(V0,V2,V8), P_necessarily-{F}(V8,V9), P_implies-{F}(V7,V9,V10), is_a_theorem-{F}(V10) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #283: input, references = 3, size of lhs = 1:
% 30.01/30.18 axiom_s2-{F}() | pppp36-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #284: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp36-{F}() | axiom_s2-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #285: input, references = 3, size of lhs = 7:
% 30.01/30.18 pppp36-{F}(), P_and-{F}(V0,V1,V2), P_possibly-{F}(V2,V3), P_possibly-{F}(V0,V4), P_possibly-{F}(V1,V5), P_and-{F}(V4,V5,V6), P_strict_implies-{F}(V3,V6,V7) | is_a_theorem-{T}(V7)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #286: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp36-{T}(), pppp179-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #287: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp179-{F}() | EXISTS V0: pppp121-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #288: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp121-{F}(V0) | EXISTS V1: pppp120-{T}(V0,V1)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #289: input, references = 3, size of lhs = 8:
% 30.01/30.18 pppp120-{F}(V0,V1), P_and-{F}(V0,V1,V2), P_possibly-{F}(V2,V3), P_possibly-{F}(V0,V4), P_possibly-{F}(V1,V5), P_and-{F}(V4,V5,V6), P_strict_implies-{F}(V3,V6,V7), is_a_theorem-{F}(V7) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #290: input, references = 3, size of lhs = 1:
% 30.01/30.18 axiom_s3-{F}() | pppp37-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #291: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp37-{F}() | axiom_s3-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #292: input, references = 3, size of lhs = 8:
% 30.01/30.18 pppp37-{F}(), P_strict_implies-{F}(V0,V1,V2), P_possibly-{F}(V1,V3), P_not-{F}(V3,V4), P_possibly-{F}(V0,V5), P_not-{F}(V5,V6), P_strict_implies-{F}(V4,V6,V7), P_strict_implies-{F}(V2,V7,V8) | is_a_theorem-{T}(V8)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #293: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp37-{T}(), pppp180-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #294: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp180-{F}() | EXISTS V0: pppp123-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #295: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp123-{F}(V0) | EXISTS V1: pppp122-{T}(V0,V1)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #296: input, references = 3, size of lhs = 9:
% 30.01/30.18 pppp122-{F}(V0,V1), P_strict_implies-{F}(V0,V1,V2), P_possibly-{F}(V1,V3), P_not-{F}(V3,V4), P_possibly-{F}(V0,V5), P_not-{F}(V5,V6), P_strict_implies-{F}(V4,V6,V7), P_strict_implies-{F}(V2,V7,V8), is_a_theorem-{F}(V8) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #297: input, references = 3, size of lhs = 1:
% 30.01/30.18 axiom_s4-{F}() | pppp38-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #298: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp38-{F}() | axiom_s4-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #299: input, references = 3, size of lhs = 4:
% 30.01/30.18 pppp38-{F}(), P_necessarily-{F}(V0,V1), P_necessarily-{F}(V1,V2), P_strict_implies-{F}(V1,V2,V3) | is_a_theorem-{T}(V3)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #300: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp38-{T}(), pppp181-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #301: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp181-{F}() | EXISTS V0: pppp124-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #302: input, references = 4, size of lhs = 5:
% 30.01/30.18 pppp124-{F}(V0), P_necessarily-{F}(V0,V1), P_necessarily-{F}(V1,V2), P_strict_implies-{F}(V1,V2,V3), is_a_theorem-{F}(V3) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #303: input, references = 3, size of lhs = 1:
% 30.01/30.18 axiom_m1-{F}() | pppp39-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #304: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp39-{F}() | axiom_m1-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #305: input, references = 3, size of lhs = 4:
% 30.01/30.18 pppp39-{F}(), P_and-{F}(V0,V1,V2), P_and-{F}(V1,V0,V3), P_strict_implies-{F}(V2,V3,V4) | is_a_theorem-{T}(V4)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #306: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp39-{T}(), pppp182-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #307: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp182-{F}() | EXISTS V0: pppp126-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #308: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp126-{F}(V0) | EXISTS V1: pppp125-{T}(V0,V1)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #309: input, references = 3, size of lhs = 5:
% 30.01/30.18 pppp125-{F}(V0,V1), P_and-{F}(V0,V1,V2), P_and-{F}(V1,V0,V3), P_strict_implies-{F}(V2,V3,V4), is_a_theorem-{F}(V4) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #310: input, references = 3, size of lhs = 1:
% 30.01/30.18 axiom_m2-{F}() | pppp40-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #311: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp40-{F}() | axiom_m2-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #312: input, references = 3, size of lhs = 3:
% 30.01/30.18 pppp40-{F}(), P_and-{F}(V0,V1,V2), P_strict_implies-{F}(V2,V0,V3) | is_a_theorem-{T}(V3)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #313: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp40-{T}(), pppp183-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #314: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp183-{F}() | EXISTS V0: pppp128-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #315: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp128-{F}(V0) | EXISTS V1: pppp127-{T}(V0,V1)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #316: input, references = 3, size of lhs = 4:
% 30.01/30.18 pppp127-{F}(V0,V1), P_and-{F}(V0,V1,V2), P_strict_implies-{F}(V2,V0,V3), is_a_theorem-{F}(V3) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #317: input, references = 3, size of lhs = 1:
% 30.01/30.18 axiom_m3-{F}() | pppp41-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #318: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp41-{F}() | axiom_m3-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #319: input, references = 3, size of lhs = 6:
% 30.01/30.18 pppp41-{F}(), P_and-{F}(V0,V1,V3), P_and-{F}(V3,V2,V4), P_and-{F}(V1,V2,V5), P_and-{F}(V0,V5,V6), P_strict_implies-{F}(V4,V6,V7) | is_a_theorem-{T}(V7)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #320: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp41-{T}(), pppp184-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #321: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp184-{F}() | EXISTS V0: pppp131-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #322: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp131-{F}(V0) | EXISTS V1: pppp130-{T}(V0,V1)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #323: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp130-{F}(V0,V1) | EXISTS V2: pppp129-{T}(V0,V1,V2)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #324: input, references = 3, size of lhs = 7:
% 30.01/30.18 pppp129-{F}(V0,V1,V2), P_and-{F}(V0,V1,V3), P_and-{F}(V3,V2,V4), P_and-{F}(V1,V2,V5), P_and-{F}(V0,V5,V6), P_strict_implies-{F}(V4,V6,V7), is_a_theorem-{F}(V7) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #325: input, references = 3, size of lhs = 1:
% 30.01/30.18 axiom_m4-{F}() | pppp42-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #326: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp42-{F}() | axiom_m4-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #327: input, references = 3, size of lhs = 3:
% 30.01/30.18 pppp42-{F}(), P_and-{F}(V0,V0,V1), P_strict_implies-{F}(V0,V1,V2) | is_a_theorem-{T}(V2)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #328: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp42-{T}(), pppp185-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #329: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp185-{F}() | EXISTS V0: pppp132-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #330: input, references = 3, size of lhs = 4:
% 30.01/30.18 pppp132-{F}(V0), P_and-{F}(V0,V0,V1), P_strict_implies-{F}(V0,V1,V2), is_a_theorem-{F}(V2) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #331: input, references = 3, size of lhs = 1:
% 30.01/30.18 axiom_m5-{F}() | pppp43-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #332: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp43-{F}() | axiom_m5-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #333: input, references = 3, size of lhs = 6:
% 30.01/30.18 pppp43-{F}(), P_strict_implies-{F}(V0,V1,V3), P_strict_implies-{F}(V1,V2,V4), P_and-{F}(V3,V4,V5), P_strict_implies-{F}(V0,V2,V6), P_strict_implies-{F}(V5,V6,V7) | is_a_theorem-{T}(V7)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #334: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp43-{T}(), pppp186-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #335: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp186-{F}() | EXISTS V0: pppp135-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #336: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp135-{F}(V0) | EXISTS V1: pppp134-{T}(V0,V1)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #337: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp134-{F}(V0,V1) | EXISTS V2: pppp133-{T}(V0,V1,V2)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #338: input, references = 3, size of lhs = 7:
% 30.01/30.18 pppp133-{F}(V0,V1,V2), P_strict_implies-{F}(V0,V1,V3), P_strict_implies-{F}(V1,V2,V4), P_and-{F}(V3,V4,V5), P_strict_implies-{F}(V0,V2,V6), P_strict_implies-{F}(V5,V6,V7), is_a_theorem-{F}(V7) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #339: input, references = 3, size of lhs = 1:
% 30.01/30.18 axiom_m6-{F}() | pppp44-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #340: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp44-{F}() | axiom_m6-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #341: input, references = 3, size of lhs = 3:
% 30.01/30.18 pppp44-{F}(), P_possibly-{F}(V0,V1), P_strict_implies-{F}(V0,V1,V2) | is_a_theorem-{T}(V2)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #342: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp44-{T}(), pppp187-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #343: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp187-{F}() | EXISTS V0: pppp136-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #344: input, references = 4, size of lhs = 4:
% 30.01/30.18 pppp136-{F}(V0), P_possibly-{F}(V0,V1), P_strict_implies-{F}(V0,V1,V2), is_a_theorem-{F}(V2) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #345: input, references = 3, size of lhs = 1:
% 30.01/30.18 axiom_m7-{F}() | pppp45-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #346: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp45-{F}() | axiom_m7-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #347: input, references = 3, size of lhs = 4:
% 30.01/30.18 pppp45-{F}(), P_and-{F}(V0,V1,V2), P_possibly-{F}(V2,V3), P_strict_implies-{F}(V3,V0,V4) | is_a_theorem-{T}(V4)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #348: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp45-{T}(), pppp188-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #349: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp188-{F}() | EXISTS V0: pppp138-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #350: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp138-{F}(V0) | EXISTS V1: pppp137-{T}(V0,V1)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #351: input, references = 3, size of lhs = 5:
% 30.01/30.18 pppp137-{F}(V0,V1), P_and-{F}(V0,V1,V2), P_possibly-{F}(V2,V3), P_strict_implies-{F}(V3,V0,V4), is_a_theorem-{F}(V4) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #352: input, references = 3, size of lhs = 1:
% 30.01/30.18 axiom_m8-{F}() | pppp46-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #353: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp46-{F}() | axiom_m8-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #354: input, references = 3, size of lhs = 6:
% 30.01/30.18 pppp46-{F}(), P_strict_implies-{F}(V0,V1,V2), P_possibly-{F}(V0,V3), P_possibly-{F}(V1,V4), P_strict_implies-{F}(V3,V4,V5), P_strict_implies-{F}(V2,V5,V6) | is_a_theorem-{T}(V6)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #355: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp46-{T}(), pppp189-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #356: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp189-{F}() | EXISTS V0: pppp140-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #357: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp140-{F}(V0) | EXISTS V1: pppp139-{T}(V0,V1)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #358: input, references = 3, size of lhs = 7:
% 30.01/30.18 pppp139-{F}(V0,V1), P_strict_implies-{F}(V0,V1,V2), P_possibly-{F}(V0,V3), P_possibly-{F}(V1,V4), P_strict_implies-{F}(V3,V4,V5), P_strict_implies-{F}(V2,V5,V6), is_a_theorem-{F}(V6) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #359: input, references = 3, size of lhs = 1:
% 30.01/30.18 axiom_m9-{F}() | pppp47-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #360: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp47-{F}() | axiom_m9-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #361: input, references = 7, size of lhs = 4:
% 30.01/30.18 pppp47-{F}(), P_possibly-{F}(V0,V1), P_possibly-{F}(V1,V2), P_strict_implies-{F}(V2,V1,V3) | is_a_theorem-{T}(V3)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #362: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | pppp47-{T}(), pppp190-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #363: input, references = 3, size of lhs = 1:
% 30.01/30.18 pppp190-{F}() | EXISTS V0: pppp141-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #364: input, references = 4, size of lhs = 5:
% 30.01/30.18 pppp141-{F}(V0), P_possibly-{F}(V0,V1), P_possibly-{F}(V1,V2), P_strict_implies-{F}(V2,V1,V3), is_a_theorem-{F}(V3) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #365: input, references = 3, size of lhs = 1:
% 30.01/30.18 axiom_m10-{F}() | pppp48-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #366: input, references = 4, size of lhs = 1:
% 30.01/30.18 pppp48-{F}() | axiom_m10-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #367: input, references = 3, size of lhs = 4:
% 30.01/30.18 pppp48-{F}(), P_possibly-{F}(V0,V1), P_necessarily-{F}(V1,V2), P_strict_implies-{F}(V1,V2,V3) | is_a_theorem-{T}(V3)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #368: input, references = 4, size of lhs = 0:
% 30.01/30.18 FALSE | pppp48-{T}(), pppp191-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #369: input, references = 4, size of lhs = 1:
% 30.01/30.18 pppp191-{F}() | EXISTS V0: pppp142-{T}(V0)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #370: input, references = 5, size of lhs = 5:
% 30.01/30.18 pppp142-{F}(V0), P_possibly-{F}(V0,V1), P_necessarily-{F}(V1,V2), P_strict_implies-{F}(V1,V2,V3), is_a_theorem-{F}(V3) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #371: input, references = 5, size of lhs = 6:
% 30.01/30.18 op_possibly-{F}(), P_possibly-{F}(V0,V1), P_not-{F}(V0,V2), P_necessarily-{F}(V2,V3), P_not-{F}(V3,V4), V1 == V4 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #372: input, references = 3, size of lhs = 6:
% 30.01/30.18 op_necessarily-{F}(), P_necessarily-{F}(V0,V1), P_not-{F}(V0,V2), P_possibly-{F}(V2,V3), P_not-{F}(V3,V4), V1 == V4 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #373: input, references = 5, size of lhs = 5:
% 30.01/30.18 op_strict_implies-{F}(), P_strict_implies-{F}(V0,V1,V2), P_implies-{F}(V0,V1,V3), P_necessarily-{F}(V3,V4), V2 == V4 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #374: input, references = 6, size of lhs = 6:
% 30.01/30.18 op_strict_equiv-{F}(), P_strict_equiv-{F}(V0,V1,V2), P_strict_implies-{F}(V0,V1,V3), P_strict_implies-{F}(V1,V0,V4), P_and-{F}(V3,V4,V5), V2 == V5 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #375: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | op_possibly-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #376: input, references = 4, size of lhs = 0:
% 30.01/30.18 FALSE | necessitation-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #377: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | axiom_K-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #378: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | axiom_M-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #379: input, references = 4, size of lhs = 0:
% 30.01/30.18 FALSE | axiom_5-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #380: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | op_possibly-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #381: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | op_or-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #382: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | op_implies-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #383: input, references = 4, size of lhs = 0:
% 30.01/30.18 FALSE | op_strict_implies-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #384: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | op_equiv-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #385: input, references = 3, size of lhs = 0:
% 30.01/30.18 FALSE | op_strict_equiv-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #386: input, references = 4, size of lhs = 1:
% 30.01/30.18 axiom_m10-{F}() | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #387: input, references = 18, size of lhs = 2:
% 30.01/30.18 #-{F} V0, #-{F} V1 | EXISTS V2: P_implies-{T}(V0,V1,V2)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #388: input, references = 7, size of lhs = 2:
% 30.01/30.18 #-{F} V0, #-{F} V1 | EXISTS V2: P_equiv-{T}(V0,V1,V2)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #389: input, references = 6, size of lhs = 1:
% 30.01/30.18 #-{F} V0 | EXISTS V1: P_not-{T}(V0,V1)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #390: input, references = 12, size of lhs = 2:
% 30.01/30.18 #-{F} V0, #-{F} V1 | EXISTS V2: P_and-{T}(V0,V1,V2)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #391: input, references = 15, size of lhs = 2:
% 30.01/30.18 #-{F} V0, #-{F} V1 | EXISTS V2: P_or-{T}(V0,V1,V2)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #392: input, references = 10, size of lhs = 1:
% 30.01/30.18 #-{F} V0 | EXISTS V1: P_necessarily-{T}(V0,V1)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #393: input, references = 12, size of lhs = 2:
% 30.01/30.18 #-{F} V0, #-{F} V1 | EXISTS V2: P_strict_implies-{T}(V0,V1,V2)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #394: input, references = 6, size of lhs = 2:
% 30.01/30.18 #-{F} V0, #-{F} V1 | EXISTS V2: P_strict_equiv-{T}(V0,V1,V2)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #395: input, references = 5, size of lhs = 1:
% 30.01/30.18 #-{F} V0 | EXISTS V1: P_possibly-{T}(V0,V1)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 number of initial rules = 396
% 30.01/30.18
% 30.01/30.18 Simplifiers:
% 30.01/30.18 #396: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 P_implies-{F}(V0,V1,V2), P_implies-{F}(V0,V1,V5), V2 == V5 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #397: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 P_equiv-{F}(V0,V1,V2), P_equiv-{F}(V0,V1,V5), V2 == V5 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #398: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 P_not-{F}(V0,V1), P_not-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #399: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 P_and-{F}(V0,V1,V2), P_and-{F}(V0,V1,V5), V2 == V5 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #400: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 P_or-{F}(V0,V1,V2), P_or-{F}(V0,V1,V5), V2 == V5 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #401: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 P_necessarily-{F}(V0,V1), P_necessarily-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #402: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 P_strict_implies-{F}(V0,V1,V2), P_strict_implies-{F}(V0,V1,V5), V2 == V5 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #403: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 P_strict_equiv-{F}(V0,V1,V2), P_strict_equiv-{F}(V0,V1,V5), V2 == V5 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #404: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 P_possibly-{F}(V0,V1), P_possibly-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #405: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp49-{F}(V0,V1), pppp49-{F}(V2,V1), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #406: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp49-{F}(V0,V1), pppp49-{F}(V2,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #407: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp50-{F}(V0), pppp50-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #408: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp51-{F}(V0,V1), pppp51-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #409: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp51-{F}(V0,V1), pppp51-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #410: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp52-{F}(V0), pppp52-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #411: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp53-{F}(V0,V1), pppp53-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #412: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp53-{F}(V0,V1), pppp53-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #413: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp54-{F}(V0), pppp54-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #414: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp55-{F}(V0,V1), pppp55-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #415: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp55-{F}(V0,V1), pppp55-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #416: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp56-{F}(V0), pppp56-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #417: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp57-{F}(V0,V1), pppp57-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #418: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp57-{F}(V0,V1), pppp57-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #419: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp58-{F}(V0), pppp58-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #420: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp59-{F}(V0,V1,V2), pppp59-{F}(V0,V1,V5), V2 == V5 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #421: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp59-{F}(V0,V1,V2), pppp59-{F}(V0,V4,V5), V1 == V4 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #422: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp59-{F}(V0,V1,V2), pppp59-{F}(V3,V4,V5), V0 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #423: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp60-{F}(V0,V1), pppp60-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #424: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp60-{F}(V0,V1), pppp60-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #425: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp61-{F}(V0), pppp61-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #426: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp62-{F}(V0,V1), pppp62-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #427: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp62-{F}(V0,V1), pppp62-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #428: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp63-{F}(V0), pppp63-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #429: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp64-{F}(V0,V1), pppp64-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #430: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp64-{F}(V0,V1), pppp64-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #431: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp65-{F}(V0), pppp65-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #432: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp66-{F}(V0,V1), pppp66-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #433: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp66-{F}(V0,V1), pppp66-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #434: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp67-{F}(V0), pppp67-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #435: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp68-{F}(V0,V1), pppp68-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #436: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp68-{F}(V0,V1), pppp68-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #437: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp69-{F}(V0), pppp69-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #438: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp70-{F}(V0,V1), pppp70-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #439: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp70-{F}(V0,V1), pppp70-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #440: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp71-{F}(V0), pppp71-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #441: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp72-{F}(V0,V1,V2), pppp72-{F}(V0,V1,V5), V2 == V5 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #442: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp72-{F}(V0,V1,V2), pppp72-{F}(V0,V4,V5), V1 == V4 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #443: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp72-{F}(V0,V1,V2), pppp72-{F}(V3,V4,V5), V0 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #444: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp73-{F}(V0,V1), pppp73-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #445: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp73-{F}(V0,V1), pppp73-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #446: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp74-{F}(V0), pppp74-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #447: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp75-{F}(V0,V1), pppp75-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #448: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp75-{F}(V0,V1), pppp75-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #449: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp76-{F}(V0), pppp76-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #450: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp77-{F}(V0,V1), pppp77-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #451: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp77-{F}(V0,V1), pppp77-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #452: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp78-{F}(V0), pppp78-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #453: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp79-{F}(V0,V1), pppp79-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #454: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp79-{F}(V0,V1), pppp79-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #455: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp80-{F}(V0), pppp80-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #456: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp81-{F}(V0), pppp81-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #457: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp82-{F}(V0,V1), pppp82-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #458: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp82-{F}(V0,V1), pppp82-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #459: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp83-{F}(V0), pppp83-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #460: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp84-{F}(V0,V1,V2), pppp84-{F}(V0,V1,V5), V2 == V5 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #461: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp84-{F}(V0,V1,V2), pppp84-{F}(V0,V4,V5), V1 == V4 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #462: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp84-{F}(V0,V1,V2), pppp84-{F}(V3,V4,V5), V0 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #463: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp85-{F}(V0,V1), pppp85-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #464: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp85-{F}(V0,V1), pppp85-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #465: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp86-{F}(V0), pppp86-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #466: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp87-{F}(V0,V1,V2), pppp87-{F}(V0,V1,V5), V2 == V5 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #467: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp87-{F}(V0,V1,V2), pppp87-{F}(V0,V4,V5), V1 == V4 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #468: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp87-{F}(V0,V1,V2), pppp87-{F}(V3,V4,V5), V0 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #469: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp88-{F}(V0,V1), pppp88-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #470: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp88-{F}(V0,V1), pppp88-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #471: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp89-{F}(V0), pppp89-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #472: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp90-{F}(V0,V1), pppp90-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #473: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp90-{F}(V0,V1), pppp90-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #474: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp91-{F}(V0), pppp91-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #475: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp92-{F}(V0), pppp92-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #476: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp93-{F}(V0), pppp93-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #477: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp94-{F}(V0,V1), pppp94-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #478: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp94-{F}(V0,V1), pppp94-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #479: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp95-{F}(V0), pppp95-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #480: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp96-{F}(V0,V1), pppp96-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #481: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp96-{F}(V0,V1), pppp96-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #482: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp97-{F}(V0), pppp97-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #483: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp98-{F}(V0,V1,V2), pppp98-{F}(V0,V1,V5), V2 == V5 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #484: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp98-{F}(V0,V1,V2), pppp98-{F}(V0,V4,V5), V1 == V4 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #485: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp98-{F}(V0,V1,V2), pppp98-{F}(V3,V4,V5), V0 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #486: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp99-{F}(V0,V1), pppp99-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #487: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp99-{F}(V0,V1), pppp99-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #488: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp100-{F}(V0), pppp100-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #489: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp101-{F}(V0,V1,V2), pppp101-{F}(V0,V1,V5), V2 == V5 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #490: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp101-{F}(V0,V1,V2), pppp101-{F}(V0,V4,V5), V1 == V4 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #491: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp101-{F}(V0,V1,V2), pppp101-{F}(V3,V4,V5), V0 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #492: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp102-{F}(V0,V1), pppp102-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #493: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp102-{F}(V0,V1), pppp102-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #494: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp103-{F}(V0), pppp103-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #495: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp104-{F}(V0), pppp104-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #496: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp105-{F}(V0,V1), pppp105-{F}(V2,V1), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #497: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp105-{F}(V0,V1), pppp105-{F}(V2,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #498: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp106-{F}(V0), pppp106-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #499: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp107-{F}(V0,V1), pppp107-{F}(V2,V1), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #500: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp107-{F}(V0,V1), pppp107-{F}(V2,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #501: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp108-{F}(V0), pppp108-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #502: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp109-{F}(V0,V1), pppp109-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #503: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp109-{F}(V0,V1), pppp109-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #504: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp110-{F}(V0), pppp110-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #505: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp111-{F}(V0,V1), pppp111-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #506: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp111-{F}(V0,V1), pppp111-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #507: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp112-{F}(V0), pppp112-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #508: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp113-{F}(V0), pppp113-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #509: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp114-{F}(V0), pppp114-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #510: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp115-{F}(V0), pppp115-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #511: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp116-{F}(V0), pppp116-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #512: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp117-{F}(V0,V1,V2), pppp117-{F}(V0,V1,V5), V2 == V5 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #513: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp117-{F}(V0,V1,V2), pppp117-{F}(V0,V4,V5), V1 == V4 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #514: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp117-{F}(V0,V1,V2), pppp117-{F}(V3,V4,V5), V0 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #515: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp118-{F}(V0,V1), pppp118-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #516: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp118-{F}(V0,V1), pppp118-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #517: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp119-{F}(V0), pppp119-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #518: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp120-{F}(V0,V1), pppp120-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #519: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp120-{F}(V0,V1), pppp120-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #520: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp121-{F}(V0), pppp121-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #521: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp122-{F}(V0,V1), pppp122-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #522: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp122-{F}(V0,V1), pppp122-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #523: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp123-{F}(V0), pppp123-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #524: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp124-{F}(V0), pppp124-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #525: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp125-{F}(V0,V1), pppp125-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #526: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp125-{F}(V0,V1), pppp125-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #527: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp126-{F}(V0), pppp126-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #528: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp127-{F}(V0,V1), pppp127-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #529: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp127-{F}(V0,V1), pppp127-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #530: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp128-{F}(V0), pppp128-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #531: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp129-{F}(V0,V1,V2), pppp129-{F}(V0,V1,V5), V2 == V5 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #532: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp129-{F}(V0,V1,V2), pppp129-{F}(V0,V4,V5), V1 == V4 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #533: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp129-{F}(V0,V1,V2), pppp129-{F}(V3,V4,V5), V0 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #534: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp130-{F}(V0,V1), pppp130-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #535: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp130-{F}(V0,V1), pppp130-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #536: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp131-{F}(V0), pppp131-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #537: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp132-{F}(V0), pppp132-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #538: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp133-{F}(V0,V1,V2), pppp133-{F}(V0,V1,V5), V2 == V5 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #539: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp133-{F}(V0,V1,V2), pppp133-{F}(V0,V4,V5), V1 == V4 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #540: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp133-{F}(V0,V1,V2), pppp133-{F}(V3,V4,V5), V0 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #541: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp134-{F}(V0,V1), pppp134-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #542: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp134-{F}(V0,V1), pppp134-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #543: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp135-{F}(V0), pppp135-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #544: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp136-{F}(V0), pppp136-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #545: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp137-{F}(V0,V1), pppp137-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #546: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp137-{F}(V0,V1), pppp137-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #547: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp138-{F}(V0), pppp138-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #548: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp139-{F}(V0,V1), pppp139-{F}(V0,V3), V1 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #549: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp139-{F}(V0,V1), pppp139-{F}(V2,V3), V0 == V2 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #550: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp140-{F}(V0), pppp140-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #551: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp141-{F}(V0), pppp141-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #552: unsound, references = 3, size of lhs = 3:
% 30.01/30.18 pppp142-{F}(V0), pppp142-{F}(V1), V0 == V1 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 number of simplifiers = 157
% 30.01/30.18
% 30.01/30.18 Learnt:
% 30.01/30.18 #554: exists( #394, #374 ), references = 1, size of lhs = 4:
% 30.01/30.18 op_strict_equiv-{F}(), P_strict_implies-{F}(V0,V1,V2), P_strict_implies-{F}(V1,V0,V3), P_and-{F}(V2,V3,V4) | P_strict_equiv-{T}(V0,V1,V4)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #588: exists( #393, #582 ), references = 1, size of lhs = 10:
% 30.01/30.18 pppp47-{F}(), pppp27-{F}(), pppp26-{F}(), is_a_theorem-{F}(V0), pppp81-{F}(V1), P_and-{F}(V1,V1,V2), P_implies-{F}(V1,V2,V3), P_necessarily-{F}(V4,V3), P_possibly-{F}(V4,V0), P_possibly-{F}(V5,V4) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #602: exists( #393, #600 ), references = 1, size of lhs = 8:
% 30.01/30.18 pppp47-{F}(), pppp27-{F}(), pppp1-{F}(), is_a_theorem-{F}(V0), P_possibly-{F}(V1,V0), P_possibly-{F}(V2,V1), P_equiv-{F}(V3,V4,V1), V3 == V4 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #606: exists( #393, #373 ), references = 4, size of lhs = 3:
% 30.01/30.18 op_strict_implies-{F}(), P_necessarily-{F}(V0,V1), P_implies-{F}(V2,V3,V0) | P_strict_implies-{T}(V2,V3,V1)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #622: exists( #393, #620 ), references = 1, size of lhs = 10:
% 30.01/30.18 pppp47-{F}(), pppp27-{F}(), pppp26-{F}(), pppp1-{F}(), is_a_theorem-{F}(V0), P_possibly-{F}(V1,V0), P_possibly-{F}(V2,V1), P_necessarily-{F}(V1,V3), P_equiv-{F}(V4,V5,V3), V4 == V5 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #629: exists( #393, #625 ), references = 2, size of lhs = 5:
% 30.01/30.18 pppp47-{F}(), pppp136-{F}(V0), P_possibly-{F}(V0,V1), P_possibly-{F}(V1,V0), P_possibly-{F}(V2,V1) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #631: exists( #390, #192 ), references = 4, size of lhs = 4:
% 30.01/30.18 op_equiv-{F}(), P_equiv-{F}(V0,V1,V2), P_implies-{F}(V0,V1,V3), P_implies-{F}(V1,V0,V4) | P_and-{T}(V3,V4,V2)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #636: exists( #388, #192 ), references = 1, size of lhs = 4:
% 30.01/30.18 op_equiv-{F}(), P_implies-{F}(V0,V1,V2), P_implies-{F}(V1,V0,V3), P_and-{F}(V2,V3,V4) | P_equiv-{T}(V0,V1,V4)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #647: exists( #389, #371 ), references = 9, size of lhs = 4:
% 30.01/30.18 op_possibly-{F}(), P_possibly-{F}(V0,V1), P_not-{F}(V0,V2), P_necessarily-{F}(V2,V3) | P_not-{T}(V3,V1)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #648: exists( #389, #190 ), references = 15, size of lhs = 4:
% 30.01/30.18 op_implies_and-{F}(), P_not-{F}(V0,V1), P_implies-{F}(V2,V0,V3), P_and-{F}(V2,V1,V4) | P_not-{T}(V4,V3)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #649: exists( #389, #188 ), references = 6, size of lhs = 5:
% 30.01/30.18 op_or-{F}(), P_not-{F}(V0,V1), P_or-{F}(V0,V2,V3), P_not-{F}(V2,V4), P_and-{F}(V1,V4,V5) | P_not-{T}(V5,V3)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #651: exists( #395, #371 ), references = 4, size of lhs = 4:
% 30.01/30.18 op_possibly-{F}(), P_not-{F}(V0,V1), P_necessarily-{F}(V1,V2), P_not-{F}(V2,V3) | P_possibly-{T}(V0,V3)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #655: exists( #392, #653 ), references = 1, size of lhs = 7:
% 30.01/30.18 op_possibly-{F}(), pppp47-{F}(), pppp136-{F}(V0), P_possibly-{F}(V1,V0), P_not-{F}(V1,V2), P_not-{F}(V0,V2), P_possibly-{F}(V3,V0) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #668: exists( #390, #665 ), references = 2, size of lhs = 8:
% 30.01/30.18 op_or-{F}(), op_implies_and-{F}(), P_not-{F}(V0,V1), P_or-{F}(V0,V2,V3), P_not-{F}(V2,V4), P_not-{F}(V5,V4), P_implies-{F}(V1,V5,V6), V6 == V3 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #669: exists( #390, #664 ), references = 1, size of lhs = 8:
% 30.01/30.18 op_implies_and-{F}(), op_or-{F}(), P_not-{F}(V0,V1), P_not-{F}(V2,V1), P_not-{F}(V3,V4), P_implies-{F}(V4,V0,V5), P_or-{F}(V3,V2,V6), V6 == V5 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #672: exists( #387, #666 ), references = 26, size of lhs = 6:
% 30.01/30.18 op_or-{F}(), op_implies_and-{F}(), P_not-{F}(V0,V1), P_or-{F}(V0,V2,V3), P_not-{F}(V2,V4), P_not-{F}(V5,V4) | P_implies-{T}(V1,V5,V3)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #675: exists( #387, #190 ), references = 9, size of lhs = 4:
% 30.01/30.18 op_implies_and-{F}(), P_not-{F}(V0,V1), P_and-{F}(V2,V1,V3), P_not-{F}(V3,V4) | P_implies-{T}(V2,V0,V4)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #683: exists( #392, #681 ), references = 1, size of lhs = 13:
% 30.01/30.18 op_possibly-{F}(), pppp26-{F}(), op_or-{F}(), op_implies_and-{F}(), op_strict_implies-{F}(), is_a_theorem-{F}(V0), pppp142-{F}(V1), P_possibly-{F}(V1,V0), P_not-{F}(V2,V0), P_not-{F}(V3,V0), P_possibly-{F}(V3,V4), P_not-{F}(V5,V4), P_or-{F}(V2,V5,V0) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #698: exists( #391, #668 ), references = 1, size of lhs = 6:
% 30.01/30.18 op_or-{F}(), op_implies_and-{F}(), P_not-{F}(V0,V1), P_not-{F}(V2,V3), P_not-{F}(V4,V3), P_implies-{F}(V1,V4,V5) | P_or-{T}(V0,V2,V5)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #711: exists( #388, #709 ), references = 4, size of lhs = 13:
% 30.01/30.18 op_equiv-{F}(), op_implies_and-{F}(), pppp0-{F}(), pppp1-{F}(), is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), P_not-{F}(V2,V1), P_and-{F}(V0,V3,V2), P_not-{F}(V4,V5), P_implies-{F}(V6,V4,V3), P_implies-{F}(V7,V8,V6), V7 == V8, P_implies-{F}(V8,V7,V5) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #722: exists( #390, #720 ), references = 1, size of lhs = 5:
% 30.01/30.18 op_implies_and-{F}(), pppp81-{F}(V0), is_a_theorem-{F}(V0), P_not-{F}(V1,V0), P_implies-{F}(V0,V1,V0) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #726: exists( #387, #724 ), references = 1, size of lhs = 5:
% 30.01/30.18 pppp3-{F}(), pppp92-{F}(V0), P_not-{F}(V0,V1), P_implies-{F}(V1,V0,V2), P_implies-{F}(V3,V2,V0) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #731: exists( #388, #729 ), references = 3, size of lhs = 15:
% 30.01/30.18 op_equiv-{F}(), op_implies_and-{F}(), pppp0-{F}(), pppp1-{F}(), is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), P_implies-{F}(V0,V2,V1), P_not-{F}(V2,V3), P_implies-{F}(V4,V5,V0), P_implies-{F}(V5,V4,V3), P_not-{F}(V6,V7), P_implies-{F}(V8,V6,V3), P_implies-{F}(V9,V10,V8), V9 == V10, P_implies-{F}(V10,V9,V7) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #740: exists( #390, #738 ), references = 1, size of lhs = 8:
% 30.01/30.18 op_implies_and-{F}(), pppp8-{F}(), pppp1-{F}(), P_not-{F}(V0,V1), P_implies-{F}(V1,V0,V1), P_implies-{F}(V1,V1,V2), P_equiv-{F}(V3,V4,V2), V3 == V4 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #751: exists( #392, #373 ), references = 5, size of lhs = 3:
% 30.01/30.18 op_strict_implies-{F}(), P_strict_implies-{F}(V0,V1,V2), P_implies-{F}(V0,V1,V3) | P_necessarily-{T}(V3,V2)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #760: exists( #387, #756 ), references = 1, size of lhs = 7:
% 30.01/30.18 pppp5-{F}(), pppp81-{F}(V0), P_and-{F}(V0,V0,V1), P_implies-{F}(V2,V3,V0), P_implies-{F}(V3,V4,V5), P_implies-{F}(V2,V4,V6), P_implies-{F}(V5,V6,V1) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #804: mergings( V4 == V8, V5 == V9; #800 ), references = 2, size of lhs = 18:
% 30.01/30.18 op_or-{F}(), pppp6-{F}(), op_equiv-{F}(), op_implies_and-{F}(), pppp0-{F}(), pppp1-{F}(), is_a_theorem-{F}(V0), P_not-{F}(V1,V2), P_not-{F}(V3,V4), P_and-{F}(V3,V5,V2), P_not-{F}(V6,V4), P_and-{F}(V2,V4,V7), P_and-{F}(V0,V8,V7), P_not-{F}(V9,V10), P_implies-{F}(V11,V9,V8), P_implies-{F}(V12,V13,V10), V13 == V12, P_implies-{F}(V13,V12,V11) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #808: mergings( V4 == V8, V5 == V9, V11 == V13; #801 ), references = 2, size of lhs = 21:
% 30.01/30.18 op_or-{F}(), pppp6-{F}(), op_equiv-{F}(), op_implies_and-{F}(), pppp0-{F}(), pppp1-{F}(), is_a_theorem-{F}(V0), P_not-{F}(V1,V2), P_not-{F}(V3,V4), P_and-{F}(V3,V5,V2), P_not-{F}(V6,V4), P_and-{F}(V2,V4,V7), P_and-{F}(V0,V8,V7), P_not-{F}(V9,V8), P_implies-{F}(V10,V11,V0), P_implies-{F}(V11,V10,V8), P_not-{F}(V12,V13), P_implies-{F}(V14,V12,V8), P_implies-{F}(V15,V16,V14), V15 == V16, P_implies-{F}(V16,V15,V13) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #822: exists( #390, #818 ), references = 1, size of lhs = 21:
% 30.01/30.18 pppp8-{F}(), op_or-{F}(), pppp6-{F}(), op_equiv-{F}(), op_implies_and-{F}(), pppp0-{F}(), pppp1-{F}(), P_not-{F}(V0,V1), P_implies-{F}(V1,V0,V1), P_implies-{F}(V1,V1,V2), P_not-{F}(V3,V4), P_not-{F}(V5,V6), P_and-{F}(V5,V7,V4), P_not-{F}(V8,V6), P_and-{F}(V4,V6,V9), P_and-{F}(V2,V10,V9), P_not-{F}(V11,V12), P_implies-{F}(V13,V11,V10), P_implies-{F}(V14,V15,V12), V15 == V14, P_implies-{F}(V15,V14,V13) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #823: exists( #390, #819 ), references = 1, size of lhs = 24:
% 30.01/30.18 pppp8-{F}(), op_or-{F}(), pppp6-{F}(), op_equiv-{F}(), op_implies_and-{F}(), pppp0-{F}(), pppp1-{F}(), P_not-{F}(V0,V1), P_implies-{F}(V1,V0,V1), P_implies-{F}(V1,V1,V2), P_not-{F}(V3,V4), P_not-{F}(V5,V6), P_and-{F}(V5,V7,V4), P_not-{F}(V8,V6), P_and-{F}(V4,V6,V9), P_and-{F}(V2,V10,V9), P_not-{F}(V11,V10), P_implies-{F}(V12,V13,V2), P_implies-{F}(V13,V12,V10), P_not-{F}(V14,V15), P_implies-{F}(V16,V14,V10), P_implies-{F}(V17,V18,V16), V17 == V18, P_implies-{F}(V18,V17,V15) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #862: exists( #387, #860 ), references = 1, size of lhs = 8:
% 30.01/30.18 pppp5-{F}(), pppp114-{F}(V0), P_necessarily-{F}(V0,V1), P_necessarily-{F}(V1,V2), P_implies-{F}(V3,V4,V1), P_implies-{F}(V4,V5,V6), P_implies-{F}(V3,V5,V7), P_implies-{F}(V6,V7,V2) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #896: exists( #387, #894 ), references = 1, size of lhs = 6:
% 30.01/30.18 pppp4-{F}(), pppp92-{F}(V0), P_not-{F}(V0,V1), P_implies-{F}(V1,V0,V2), P_implies-{F}(V3,V0,V2), P_implies-{F}(V3,V4,V0) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #958: mergings( V4 == V5; #955 ), references = 2, size of lhs = 9:
% 30.01/30.18 op_or-{F}(), op_implies_and-{F}(), pppp21-{F}(), pppp92-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V2,V1), P_implies-{F}(V1,V0,V3), P_or-{F}(V0,V0,V3), P_not-{F}(V4,V3) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #963: exists( #388, #961 ), references = 1, size of lhs = 7:
% 30.01/30.18 op_equiv-{F}(), op_strict_equiv-{F}(), P_implies-{F}(V0,V1,V2), P_implies-{F}(V1,V0,V3), P_strict_implies-{F}(V4,V5,V2), P_strict_implies-{F}(V5,V4,V3), P_strict_equiv-{F}(V4,V5,V6) | P_equiv-{T}(V0,V1,V6)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1088: exists( #390, #1085 ), references = 1, size of lhs = 10:
% 30.01/30.18 op_or-{F}(), op_implies_and-{F}(), pppp21-{F}(), pppp92-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V2,V1), P_implies-{F}(V1,V0,V3), P_or-{F}(V0,V0,V3), P_not-{F}(V4,V5), P_implies-{F}(V6,V4,V3) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1093: mergings( V2 == V3, V3 == V5; #1090 ), references = 1, size of lhs = 6:
% 30.01/30.18 op_or-{F}(), op_implies_and-{F}(), pppp21-{F}(), pppp92-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V2,V1) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1095: exists( #389, #1090 ), references = 1, size of lhs = 4:
% 30.01/30.18 op_or-{F}(), op_implies_and-{F}(), pppp21-{F}(), pppp92-{F}(V0) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1097: exists( #150, #1094 ), references = 1, size of lhs = 4:
% 30.01/30.18 pppp163-{F}(), op_or-{F}(), op_implies_and-{F}(), pppp21-{F}() | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1099: disj( #155, exists( #150, #1094 ) ), references = 1, size of lhs = 3:
% 30.01/30.18 pppp163-{F}(), op_or-{F}(), op_implies_and-{F}() | pppp164-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1125: mergings( V4 == V8, V5 == V9; #1121 ), references = 1, size of lhs = 21:
% 30.01/30.18 op_or-{F}(), pppp5-{F}(), op_equiv-{F}(), op_implies_and-{F}(), pppp0-{F}(), pppp1-{F}(), is_a_theorem-{F}(V0), P_not-{F}(V1,V2), P_not-{F}(V3,V4), P_and-{F}(V2,V4,V5), P_and-{F}(V0,V6,V5), P_not-{F}(V7,V4), P_not-{F}(V8,V9), P_implies-{F}(V10,V8,V6), P_implies-{F}(V11,V12,V9), V12 == V11, P_implies-{F}(V12,V11,V10), P_implies-{F}(V13,V14,V2), P_implies-{F}(V14,V15,V16), P_implies-{F}(V13,V15,V17), P_implies-{F}(V16,V17,V7) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1129: mergings( V4 == V10, V5 == V11, V7 == V9; #1122 ), references = 1, size of lhs = 24:
% 30.01/30.18 op_or-{F}(), pppp5-{F}(), op_equiv-{F}(), op_implies_and-{F}(), pppp0-{F}(), pppp1-{F}(), is_a_theorem-{F}(V0), P_not-{F}(V1,V2), P_not-{F}(V3,V4), P_and-{F}(V2,V4,V5), P_not-{F}(V6,V4), P_and-{F}(V0,V7,V5), P_not-{F}(V8,V7), P_implies-{F}(V9,V10,V0), P_implies-{F}(V10,V9,V7), P_not-{F}(V11,V12), P_implies-{F}(V13,V11,V7), P_implies-{F}(V14,V15,V13), V14 == V15, P_implies-{F}(V15,V14,V12), P_implies-{F}(V16,V17,V2), P_implies-{F}(V17,V18,V19), P_implies-{F}(V16,V18,V20), P_implies-{F}(V19,V20,V6) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1148: exists( #390, #374 ), references = 3, size of lhs = 4:
% 30.01/30.18 op_strict_equiv-{F}(), P_strict_equiv-{F}(V0,V1,V2), P_strict_implies-{F}(V0,V1,V3), P_strict_implies-{F}(V1,V0,V4) | P_and-{T}(V3,V4,V2)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1247: exists( #393, #1245 ), references = 4, size of lhs = 8:
% 30.01/30.18 pppp26-{F}(), op_strict_implies-{F}(), is_a_theorem-{F}(V0), pppp142-{F}(V1), P_possibly-{F}(V1,V2), P_necessarily-{F}(V2,V3), P_implies-{F}(V2,V3,V0), P_implies-{F}(V4,V5,V0) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1249: exists( #387, #1246 ), references = 2, size of lhs = 8:
% 30.01/30.18 pppp26-{F}(), op_strict_implies-{F}(), is_a_theorem-{F}(V0), pppp142-{F}(V1), P_possibly-{F}(V1,V2), P_necessarily-{F}(V2,V3), P_implies-{F}(V2,V3,V0), P_implies-{F}(V4,V5,V0) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1254: exists( #393, #1252 ), references = 1, size of lhs = 14:
% 30.01/30.18 op_possibly-{F}(), op_or-{F}(), op_implies_and-{F}(), pppp26-{F}(), op_strict_implies-{F}(), is_a_theorem-{F}(V0), pppp142-{F}(V1), P_possibly-{F}(V1,V2), P_not-{F}(V3,V2), P_or-{F}(V3,V4,V0), P_not-{F}(V4,V5), P_possibly-{F}(V6,V5), P_not-{F}(V6,V2), P_implies-{F}(V7,V8,V2) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1260: mergings( V4 == V7, V6 == V8; #1257 ), references = 1, size of lhs = 16:
% 30.01/30.18 pppp4-{F}(), op_possibly-{F}(), op_or-{F}(), op_implies_and-{F}(), pppp26-{F}(), op_strict_implies-{F}(), pppp142-{F}(V0), P_possibly-{F}(V0,V1), P_not-{F}(V2,V1), P_possibly-{F}(V2,V3), P_not-{F}(V4,V1), P_not-{F}(V5,V3), P_not-{F}(V6,V3), P_implies-{F}(V7,V6,V1), P_implies-{F}(V7,V8,V6), P_implies-{F}(V9,V10,V1) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1278: exists( #393, #1275 ), references = 3, size of lhs = 7:
% 30.01/30.18 op_strict_implies-{F}(), pppp26-{F}(), is_a_theorem-{F}(V0), pppp124-{F}(V1), P_necessarily-{F}(V1,V2), P_necessarily-{F}(V2,V3), P_implies-{F}(V2,V3,V0) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1281: exists( #387, #1279 ), references = 1, size of lhs = 10:
% 30.01/30.18 pppp5-{F}(), op_strict_implies-{F}(), pppp26-{F}(), pppp124-{F}(V0), P_necessarily-{F}(V0,V1), P_necessarily-{F}(V1,V2), P_implies-{F}(V3,V4,V1), P_implies-{F}(V4,V5,V6), P_implies-{F}(V3,V5,V7), P_implies-{F}(V6,V7,V2) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1308: exists( #392, #1303 ), references = 4, size of lhs = 13:
% 30.01/30.18 op_possibly-{F}(), op_or-{F}(), op_implies_and-{F}(), pppp26-{F}(), op_strict_implies-{F}(), is_a_theorem-{F}(V0), pppp142-{F}(V1), P_possibly-{F}(V1,V2), P_not-{F}(V3,V2), P_or-{F}(V3,V4,V0), P_not-{F}(V4,V5), P_possibly-{F}(V6,V5), P_not-{F}(V6,V2) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1309: exists( #392, #1304 ), references = 4, size of lhs = 13:
% 30.01/30.18 op_possibly-{F}(), op_or-{F}(), op_implies_and-{F}(), pppp26-{F}(), op_strict_implies-{F}(), is_a_theorem-{F}(V0), pppp142-{F}(V1), P_possibly-{F}(V1,V2), P_not-{F}(V3,V2), P_or-{F}(V3,V4,V0), P_not-{F}(V4,V5), P_possibly-{F}(V6,V5), P_not-{F}(V6,V2) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1318: mergings( V4 == V7, V6 == V8; #1314 ), references = 1, size of lhs = 15:
% 30.01/30.18 pppp13-{F}(), op_possibly-{F}(), op_or-{F}(), op_implies_and-{F}(), pppp26-{F}(), op_strict_implies-{F}(), pppp142-{F}(V0), P_possibly-{F}(V0,V1), P_not-{F}(V2,V1), P_possibly-{F}(V2,V3), P_not-{F}(V4,V1), P_not-{F}(V5,V3), P_not-{F}(V6,V3), P_equiv-{F}(V7,V8,V1), P_implies-{F}(V8,V7,V6) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1321: mergings( V4 == V7, V6 == V8; #1315 ), references = 1, size of lhs = 15:
% 30.01/30.18 pppp13-{F}(), op_possibly-{F}(), op_or-{F}(), op_implies_and-{F}(), pppp26-{F}(), op_strict_implies-{F}(), pppp142-{F}(V0), P_possibly-{F}(V0,V1), P_not-{F}(V2,V1), P_possibly-{F}(V2,V3), P_not-{F}(V4,V1), P_not-{F}(V5,V3), P_not-{F}(V6,V3), P_equiv-{F}(V7,V8,V1), P_implies-{F}(V8,V7,V6) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1335: mergings( V4 == V7, V6 == V8; #1331 ), references = 1, size of lhs = 15:
% 30.01/30.18 pppp12-{F}(), op_possibly-{F}(), op_or-{F}(), op_implies_and-{F}(), pppp26-{F}(), op_strict_implies-{F}(), pppp142-{F}(V0), P_possibly-{F}(V0,V1), P_not-{F}(V2,V1), P_possibly-{F}(V2,V3), P_not-{F}(V4,V1), P_not-{F}(V5,V3), P_not-{F}(V6,V3), P_equiv-{F}(V7,V8,V1), P_implies-{F}(V7,V8,V6) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1338: mergings( V4 == V7, V6 == V8; #1332 ), references = 1, size of lhs = 15:
% 30.01/30.18 pppp12-{F}(), op_possibly-{F}(), op_or-{F}(), op_implies_and-{F}(), pppp26-{F}(), op_strict_implies-{F}(), pppp142-{F}(V0), P_possibly-{F}(V0,V1), P_not-{F}(V2,V1), P_possibly-{F}(V2,V3), P_not-{F}(V4,V1), P_not-{F}(V5,V3), P_not-{F}(V6,V3), P_equiv-{F}(V7,V8,V1), P_implies-{F}(V7,V8,V6) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1352: mergings( V4 == V7, V6 == V8; #1348 ), references = 1, size of lhs = 14:
% 30.01/30.18 pppp7-{F}(), op_possibly-{F}(), op_or-{F}(), op_implies_and-{F}(), pppp26-{F}(), op_strict_implies-{F}(), pppp142-{F}(V0), P_possibly-{F}(V0,V1), P_not-{F}(V2,V1), P_possibly-{F}(V2,V3), P_not-{F}(V4,V1), P_not-{F}(V5,V3), P_not-{F}(V6,V3), P_and-{F}(V7,V6,V1) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1355: mergings( V4 == V7, V6 == V8; #1349 ), references = 1, size of lhs = 14:
% 30.01/30.18 pppp7-{F}(), op_possibly-{F}(), op_or-{F}(), op_implies_and-{F}(), pppp26-{F}(), op_strict_implies-{F}(), pppp142-{F}(V0), P_possibly-{F}(V0,V1), P_not-{F}(V2,V1), P_possibly-{F}(V2,V3), P_not-{F}(V4,V1), P_not-{F}(V5,V3), P_not-{F}(V6,V3), P_and-{F}(V7,V6,V1) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1366: mergings( V4 == V7, V6 == V8; #1362 ), references = 1, size of lhs = 14:
% 30.01/30.18 pppp6-{F}(), op_possibly-{F}(), op_or-{F}(), op_implies_and-{F}(), pppp26-{F}(), op_strict_implies-{F}(), pppp142-{F}(V0), P_possibly-{F}(V0,V1), P_not-{F}(V2,V1), P_possibly-{F}(V2,V3), P_not-{F}(V4,V1), P_not-{F}(V5,V3), P_not-{F}(V6,V3), P_and-{F}(V6,V7,V1) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1369: mergings( V4 == V7, V6 == V8; #1363 ), references = 1, size of lhs = 14:
% 30.01/30.18 pppp6-{F}(), op_possibly-{F}(), op_or-{F}(), op_implies_and-{F}(), pppp26-{F}(), op_strict_implies-{F}(), pppp142-{F}(V0), P_possibly-{F}(V0,V1), P_not-{F}(V2,V1), P_possibly-{F}(V2,V3), P_not-{F}(V4,V1), P_not-{F}(V5,V3), P_not-{F}(V6,V3), P_and-{F}(V6,V7,V1) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1446: exists( #392, #1443 ), references = 1, size of lhs = 16:
% 30.01/30.18 op_possibly-{F}(), op_strict_implies-{F}(), op_or-{F}(), op_implies_and-{F}(), pppp0-{F}(), is_a_theorem-{F}(V0), P_not-{F}(V1,V0), is_a_theorem-{F}(V2), P_or-{F}(V1,V3,V2), P_not-{F}(V3,V4), P_possibly-{F}(V5,V4), P_not-{F}(V5,V6), pppp141-{F}(V7), P_possibly-{F}(V7,V8), P_possibly-{F}(V8,V9), P_implies-{F}(V9,V8,V6) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1477: exists( #392, #1471 ), references = 1, size of lhs = 13:
% 30.01/30.18 op_possibly-{F}(), op_or-{F}(), op_implies_and-{F}(), pppp34-{F}(), pppp92-{F}(V0), P_not-{F}(V0,V1), P_implies-{F}(V1,V0,V2), P_implies-{F}(V2,V0,V3), P_possibly-{F}(V4,V5), P_not-{F}(V4,V5), P_not-{F}(V6,V5), P_or-{F}(V6,V7,V3), P_not-{F}(V7,V5) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1478: exists( #392, #1472 ), references = 1, size of lhs = 12:
% 30.01/30.18 op_possibly-{F}(), op_or-{F}(), op_implies_and-{F}(), pppp34-{F}(), pppp93-{F}(V0), P_or-{F}(V0,V0,V1), P_implies-{F}(V1,V0,V2), P_possibly-{F}(V3,V4), P_not-{F}(V3,V4), P_not-{F}(V5,V4), P_or-{F}(V5,V6,V2), P_not-{F}(V6,V4) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1479: exists( #392, #1473 ), references = 1, size of lhs = 13:
% 30.01/30.18 op_possibly-{F}(), op_or-{F}(), op_implies_and-{F}(), pppp34-{F}(), pppp26-{F}(), op_strict_implies-{F}(), pppp142-{F}(V0), P_possibly-{F}(V0,V1), P_possibly-{F}(V2,V1), P_not-{F}(V2,V1), P_not-{F}(V3,V1), P_not-{F}(V4,V1), P_or-{F}(V3,V4,V5) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1483: exists( #391, #1476 ), references = 1, size of lhs = 12:
% 30.01/30.18 op_possibly-{F}(), op_or-{F}(), op_implies_and-{F}(), pppp34-{F}(), pppp26-{F}(), op_strict_implies-{F}(), pppp142-{F}(V0), P_possibly-{F}(V0,V1), P_possibly-{F}(V2,V1), P_not-{F}(V2,V1), P_not-{F}(V3,V1), P_not-{F}(V4,V1) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1507: exists( #387, #1503 ), references = 1, size of lhs = 7:
% 30.01/30.18 pppp31-{F}(), op_strict_implies-{F}(), pppp26-{F}(), pppp124-{F}(V0), P_necessarily-{F}(V0,V1), P_necessarily-{F}(V1,V2), P_necessarily-{F}(V2,V1) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1532: mergings( V3 == V4, V5 == V6; #1528 ), references = 2, size of lhs = 13:
% 30.01/30.18 op_or-{F}(), op_implies_and-{F}(), pppp3-{F}(), pppp0-{F}(), pppp1-{F}(), is_a_theorem-{F}(V0), P_not-{F}(V1,V0), P_not-{F}(V2,V3), P_not-{F}(V4,V3), P_implies-{F}(V5,V0,V4), P_not-{F}(V6,V3), P_equiv-{F}(V7,V8,V6), V7 == V8 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1550: exists( #387, #1545 ), references = 1, size of lhs = 8:
% 30.01/30.18 pppp30-{F}(), pppp93-{F}(V0), P_or-{F}(V0,V0,V1), P_necessarily-{F}(V2,V1), P_necessarily-{F}(V3,V4), P_implies-{F}(V3,V5,V2), P_necessarily-{F}(V5,V6), P_implies-{F}(V4,V6,V0) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1551: exists( #387, #1546 ), references = 1, size of lhs = 9:
% 30.01/30.18 pppp30-{F}(), pppp92-{F}(V0), P_not-{F}(V0,V1), P_implies-{F}(V1,V0,V2), P_necessarily-{F}(V3,V2), P_necessarily-{F}(V4,V5), P_implies-{F}(V4,V6,V3), P_necessarily-{F}(V6,V7), P_implies-{F}(V5,V7,V0) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1590: exists( #390, #1586 ), references = 1, size of lhs = 6:
% 30.01/30.18 op_implies_and-{F}(), P_not-{F}(V0,V1), P_not-{F}(V2,V1), P_implies-{F}(V3,V0,V4), P_implies-{F}(V3,V2,V5), V5 == V4 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1592: exists( #387, #1589 ), references = 4, size of lhs = 4:
% 30.01/30.18 op_implies_and-{F}(), P_not-{F}(V0,V1), P_not-{F}(V2,V1), P_implies-{F}(V3,V0,V4) | P_implies-{T}(V3,V2,V4)
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1603: mergings( V4 == V5; #1600 ), references = 1, size of lhs = 7:
% 30.01/30.18 op_implies_and-{F}(), pppp3-{F}(), pppp92-{F}(V0), P_not-{F}(V0,V1), P_implies-{F}(V1,V0,V2), P_not-{F}(V3,V1), P_implies-{F}(V4,V2,V3) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1604: exists( #387, #1599 ), references = 1, size of lhs = 7:
% 30.01/30.18 op_implies_and-{F}(), pppp3-{F}(), pppp93-{F}(V0), P_not-{F}(V0,V1), P_or-{F}(V0,V0,V2), P_not-{F}(V3,V1), P_implies-{F}(V4,V2,V3) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1623: exists( #387, #1619 ), references = 1, size of lhs = 5:
% 30.01/30.18 pppp8-{F}(), pppp93-{F}(V0), P_or-{F}(V0,V0,V1), P_and-{F}(V1,V2,V3), P_implies-{F}(V2,V3,V0) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1624: exists( #387, #1620 ), references = 1, size of lhs = 6:
% 30.01/30.18 pppp8-{F}(), pppp92-{F}(V0), P_not-{F}(V0,V1), P_implies-{F}(V1,V0,V2), P_and-{F}(V2,V3,V4), P_implies-{F}(V3,V4,V0) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1640: exists( #394, #1638 ), references = 2, size of lhs = 13:
% 30.01/30.18 op_strict_equiv-{F}(), op_implies_and-{F}(), pppp0-{F}(), pppp29-{F}(), is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), P_implies-{F}(V0,V2,V1), P_not-{F}(V2,V3), P_not-{F}(V4,V5), P_implies-{F}(V6,V4,V3), P_strict_implies-{F}(V7,V8,V6), V7 == V8, P_strict_implies-{F}(V8,V7,V5) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1650: exists( #387, #1647 ), references = 2, size of lhs = 12:
% 30.01/30.18 op_or-{F}(), op_implies_and-{F}(), pppp3-{F}(), pppp0-{F}(), pppp1-{F}(), is_a_theorem-{F}(V0), P_not-{F}(V1,V0), P_not-{F}(V2,V3), P_and-{F}(V4,V3,V5), P_implies-{F}(V6,V0,V5), P_equiv-{F}(V7,V8,V5), V7 == V8 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1652: exists( #389, #1649 ), references = 2, size of lhs = 12:
% 30.01/30.18 op_or-{F}(), op_implies_and-{F}(), pppp3-{F}(), pppp0-{F}(), pppp1-{F}(), is_a_theorem-{F}(V0), P_not-{F}(V1,V0), P_not-{F}(V2,V3), P_and-{F}(V4,V3,V5), P_implies-{F}(V6,V0,V5), P_equiv-{F}(V7,V8,V5), V7 == V8 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1698: exists( #390, #1694 ), references = 1, size of lhs = 13:
% 30.01/30.18 op_or-{F}(), op_implies_and-{F}(), pppp3-{F}(), pppp0-{F}(), pppp1-{F}(), is_a_theorem-{F}(V0), P_not-{F}(V1,V0), P_not-{F}(V2,V3), P_implies-{F}(V4,V2,V5), P_and-{F}(V6,V5,V7), P_implies-{F}(V8,V0,V7), P_equiv-{F}(V9,V10,V7), V9 == V10 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1699: exists( #390, #1695 ), references = 1, size of lhs = 13:
% 30.01/30.18 op_or-{F}(), op_implies_and-{F}(), pppp3-{F}(), pppp0-{F}(), pppp1-{F}(), is_a_theorem-{F}(V0), P_not-{F}(V1,V0), P_not-{F}(V2,V3), P_implies-{F}(V4,V2,V5), P_and-{F}(V6,V5,V7), P_implies-{F}(V8,V0,V7), P_equiv-{F}(V9,V10,V7), V9 == V10 | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1808: exists( #387, #1801 ), references = 2, size of lhs = 7:
% 30.01/30.18 pppp34-{F}(), pppp26-{F}(), op_strict_implies-{F}(), pppp142-{F}(V0), P_possibly-{F}(V0,V1), P_possibly-{F}(V2,V1), P_necessarily-{F}(V1,V3) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1816: exists( #393, #1811 ), references = 1, size of lhs = 7:
% 30.01/30.18 pppp34-{F}(), pppp26-{F}(), op_strict_implies-{F}(), pppp142-{F}(V0), P_possibly-{F}(V0,V1), P_possibly-{F}(V2,V1), P_implies-{F}(V3,V4,V1) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1915: exists( #394, #1913 ), references = 1, size of lhs = 17:
% 30.01/30.18 op_strict_equiv-{F}(), op_implies_and-{F}(), pppp0-{F}(), pppp29-{F}(), is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), P_not-{F}(V2,V1), P_and-{F}(V0,V3,V2), P_not-{F}(V4,V5), P_implies-{F}(V6,V4,V3), P_strict_implies-{F}(V7,V8,V6), P_strict_implies-{F}(V8,V7,V5), P_not-{F}(V9,V10), P_implies-{F}(V11,V9,V3), P_strict_implies-{F}(V12,V13,V11), V12 == V13, P_strict_implies-{F}(V13,V12,V10) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1924: exists( #392, #1808 ), references = 1, size of lhs = 6:
% 30.01/30.18 pppp34-{F}(), pppp26-{F}(), op_strict_implies-{F}(), pppp142-{F}(V0), P_possibly-{F}(V0,V1), P_possibly-{F}(V2,V1) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1926: exists( #395, #1923 ), references = 1, size of lhs = 4:
% 30.01/30.18 pppp34-{F}(), pppp26-{F}(), op_strict_implies-{F}(), pppp142-{F}(V0) | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1928: exists( #369, #1925 ), references = 1, size of lhs = 4:
% 30.01/30.18 pppp191-{F}(), pppp34-{F}(), pppp26-{F}(), op_strict_implies-{F}() | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1930: disj( #368, exists( #369, #1925 ) ), references = 1, size of lhs = 3:
% 30.01/30.18 pppp34-{F}(), pppp26-{F}(), op_strict_implies-{F}() | pppp48-{T}()
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 #1938: #376+#379+#383+#211+#269+#1929+#366+#386, references = 1, size of lhs = 0:
% 30.01/30.18 FALSE | FALSE
% 30.01/30.18 (used 0 times, uses = {})
% 30.01/30.18
% 30.01/30.18 number of learnt formulas = 86
% 30.01/30.18
% 30.01/30.18
% 30.01/30.18 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.01/30.18
% 30.01/30.18 randbase = 1
%------------------------------------------------------------------------------