TSTP Solution File: LCL536+1 by Geo-III---2018C

View Problem - 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
%------------------------------------------------------------------------------