%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : LCL469+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:06:20 PM UTC 2026
% Result : Theorem 23.78s 24.06s
% Output : Refutation 23.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL469+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 4 18:43:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 23.78/24.06 GeoParameters:
% 23.78/24.06
% 23.78/24.06 tptp_input = 1
% 23.78/24.06 tptp_output = 0
% 23.78/24.06 nonempty = 1
% 23.78/24.06 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.78/24.06 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 23.78/24.06
% 23.78/24.06
% 23.78/24.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.78/24.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.78/24.06
% 23.78/24.06 RuleSystem INPUT:
% 23.78/24.06
% 23.78/24.06 Initial Rules:
% 23.78/24.06 #0: input, references = 3, size of lhs = 1:
% 23.78/24.06 modus_ponens-{F}() | pppp0-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #1: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp0-{F}() | modus_ponens-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #2: input, references = 4, size of lhs = 4:
% 23.78/24.06 pppp0-{F}(), P_implies-{F}(V1,V0,V2), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2) | is_a_theorem-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #3: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp0-{T}(), pppp81-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #4: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp81-{F}() | EXISTS V0: pppp27-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #5: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp27-{F}(V0) | EXISTS V1: pppp26-{T}(V1,V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #6: input, references = 3, size of lhs = 2:
% 23.78/24.06 pppp27-{F}(V0), is_a_theorem-{F}(V0) | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #7: input, references = 3, size of lhs = 2:
% 23.78/24.06 pppp26-{F}(V0,V1), P_implies-{F}(V0,V1,V2) | is_a_theorem-{T}(V2)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #8: input, references = 3, size of lhs = 2:
% 23.78/24.06 pppp26-{F}(V0,V1), P_implies-{F}(V0,V1,V2) | is_a_theorem-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #9: input, references = 3, size of lhs = 1:
% 23.78/24.06 substitution_of_equivalents-{F}() | pppp1-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #10: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp1-{F}() | substitution_of_equivalents-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #11: input, references = 4, size of lhs = 4:
% 23.78/24.06 pppp1-{F}(), P_equiv-{F}(V0,V1,V2), is_a_theorem-{F}(V2), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #12: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp1-{T}(), pppp82-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #13: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp82-{F}() | EXISTS V0: pppp29-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #14: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp29-{F}(V0) | EXISTS V1: pppp28-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #15: input, references = 3, size of lhs = 2:
% 23.78/24.06 pppp28-{F}(V1,V1), P_equiv-{F}(V1,V1,V2) | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #16: input, references = 3, size of lhs = 2:
% 23.78/24.06 pppp28-{F}(V0,V1), P_equiv-{F}(V0,V1,V2) | is_a_theorem-{T}(V2)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #17: input, references = 3, size of lhs = 1:
% 23.78/24.06 modus_tollens-{F}() | pppp2-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #18: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp2-{F}() | modus_tollens-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #19: input, references = 3, size of lhs = 6:
% 23.78/24.06 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)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #20: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp2-{T}(), pppp83-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #21: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp83-{F}() | EXISTS V0: pppp31-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #22: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp31-{F}(V0) | EXISTS V1: pppp30-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #23: input, references = 3, size of lhs = 7:
% 23.78/24.06 pppp30-{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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #24: input, references = 3, size of lhs = 1:
% 23.78/24.06 implies_1-{F}() | pppp3-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #25: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp3-{F}() | implies_1-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #26: input, references = 3, size of lhs = 3:
% 23.78/24.06 pppp3-{F}(), P_implies-{F}(V1,V0,V2), P_implies-{F}(V0,V2,V3) | is_a_theorem-{T}(V3)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #27: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp3-{T}(), pppp84-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #28: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp84-{F}() | EXISTS V0: pppp33-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #29: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp33-{F}(V0) | EXISTS V1: pppp32-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #30: input, references = 3, size of lhs = 4:
% 23.78/24.06 pppp32-{F}(V0,V1), P_implies-{F}(V1,V0,V2), P_implies-{F}(V0,V2,V3), is_a_theorem-{F}(V3) | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #31: input, references = 3, size of lhs = 1:
% 23.78/24.06 implies_2-{F}() | pppp4-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #32: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp4-{F}() | implies_2-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #33: input, references = 3, size of lhs = 4:
% 23.78/24.06 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)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #34: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp4-{T}(), pppp85-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #35: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp85-{F}() | EXISTS V0: pppp35-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #36: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp35-{F}(V0) | EXISTS V1: pppp34-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #37: input, references = 3, size of lhs = 5:
% 23.78/24.06 pppp34-{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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #38: input, references = 3, size of lhs = 1:
% 23.78/24.06 implies_3-{F}() | pppp5-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #39: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp5-{F}() | implies_3-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #40: input, references = 3, size of lhs = 6:
% 23.78/24.06 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)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #41: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp5-{T}(), pppp86-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #42: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp86-{F}() | EXISTS V0: pppp38-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #43: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp38-{F}(V0) | EXISTS V1: pppp37-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #44: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp37-{F}(V0,V1) | EXISTS V2: pppp36-{T}(V0,V1,V2)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #45: input, references = 3, size of lhs = 7:
% 23.78/24.06 pppp36-{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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #46: input, references = 3, size of lhs = 1:
% 23.78/24.06 and_1-{F}() | pppp6-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #47: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp6-{F}() | and_1-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #48: input, references = 3, size of lhs = 3:
% 23.78/24.06 pppp6-{F}(), P_and-{F}(V0,V1,V2), P_implies-{F}(V2,V0,V3) | is_a_theorem-{T}(V3)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #49: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp6-{T}(), pppp87-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #50: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp87-{F}() | EXISTS V0: pppp40-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #51: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp40-{F}(V0) | EXISTS V1: pppp39-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #52: input, references = 3, size of lhs = 4:
% 23.78/24.06 pppp39-{F}(V0,V1), P_and-{F}(V0,V1,V2), P_implies-{F}(V2,V0,V3), is_a_theorem-{F}(V3) | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #53: input, references = 3, size of lhs = 1:
% 23.78/24.06 and_2-{F}() | pppp7-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #54: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp7-{F}() | and_2-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #55: input, references = 5, size of lhs = 3:
% 23.78/24.06 pppp7-{F}(), P_and-{F}(V0,V1,V2), P_implies-{F}(V2,V1,V3) | is_a_theorem-{T}(V3)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #56: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp7-{T}(), pppp88-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #57: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp88-{F}() | EXISTS V0: pppp42-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #58: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp42-{F}(V0) | EXISTS V1: pppp41-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #59: input, references = 3, size of lhs = 4:
% 23.78/24.06 pppp41-{F}(V0,V1), P_and-{F}(V0,V1,V2), P_implies-{F}(V2,V1,V3), is_a_theorem-{F}(V3) | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #60: input, references = 3, size of lhs = 1:
% 23.78/24.06 and_3-{F}() | pppp8-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #61: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp8-{F}() | and_3-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #62: input, references = 3, size of lhs = 4:
% 23.78/24.06 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)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #63: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp8-{T}(), pppp89-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #64: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp89-{F}() | EXISTS V0: pppp44-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #65: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp44-{F}(V0) | EXISTS V1: pppp43-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #66: input, references = 3, size of lhs = 5:
% 23.78/24.06 pppp43-{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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #67: input, references = 3, size of lhs = 1:
% 23.78/24.06 or_1-{F}() | pppp9-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #68: input, references = 4, size of lhs = 1:
% 23.78/24.06 pppp9-{F}() | or_1-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #69: input, references = 3, size of lhs = 3:
% 23.78/24.06 pppp9-{F}(), P_or-{F}(V0,V1,V2), P_implies-{F}(V0,V2,V3) | is_a_theorem-{T}(V3)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #70: input, references = 4, size of lhs = 0:
% 23.78/24.06 FALSE | pppp9-{T}(), pppp90-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #71: input, references = 4, size of lhs = 1:
% 23.78/24.06 pppp90-{F}() | EXISTS V0: pppp46-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #72: input, references = 4, size of lhs = 1:
% 23.78/24.06 pppp46-{F}(V0) | EXISTS V1: pppp45-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #73: input, references = 6, size of lhs = 4:
% 23.78/24.06 pppp45-{F}(V0,V1), P_or-{F}(V0,V1,V2), P_implies-{F}(V0,V2,V3), is_a_theorem-{F}(V3) | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #74: input, references = 3, size of lhs = 1:
% 23.78/24.06 or_2-{F}() | pppp10-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #75: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp10-{F}() | or_2-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #76: input, references = 4, size of lhs = 3:
% 23.78/24.06 pppp10-{F}(), P_or-{F}(V0,V1,V2), P_implies-{F}(V1,V2,V3) | is_a_theorem-{T}(V3)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #77: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp10-{T}(), pppp91-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #78: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp91-{F}() | EXISTS V0: pppp48-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #79: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp48-{F}(V0) | EXISTS V1: pppp47-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #80: input, references = 3, size of lhs = 4:
% 23.78/24.06 pppp47-{F}(V0,V1), P_or-{F}(V0,V1,V2), P_implies-{F}(V1,V2,V3), is_a_theorem-{F}(V3) | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #81: input, references = 3, size of lhs = 1:
% 23.78/24.06 or_3-{F}() | pppp11-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #82: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp11-{F}() | or_3-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #83: input, references = 4, size of lhs = 7:
% 23.78/24.06 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)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #84: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp11-{T}(), pppp92-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #85: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp92-{F}() | EXISTS V0: pppp51-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #86: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp51-{F}(V0) | EXISTS V1: pppp50-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #87: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp50-{F}(V0,V1) | EXISTS V2: pppp49-{T}(V0,V1,V2)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #88: input, references = 3, size of lhs = 8:
% 23.78/24.06 pppp49-{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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #89: input, references = 3, size of lhs = 1:
% 23.78/24.06 equivalence_1-{F}() | pppp12-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #90: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp12-{F}() | equivalence_1-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #91: input, references = 3, size of lhs = 4:
% 23.78/24.06 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)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #92: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp12-{T}(), pppp93-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #93: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp93-{F}() | EXISTS V0: pppp53-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #94: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp53-{F}(V0) | EXISTS V1: pppp52-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #95: input, references = 3, size of lhs = 5:
% 23.78/24.06 pppp52-{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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #96: input, references = 3, size of lhs = 1:
% 23.78/24.06 equivalence_2-{F}() | pppp13-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #97: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp13-{F}() | equivalence_2-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #98: input, references = 3, size of lhs = 4:
% 23.78/24.06 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)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #99: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp13-{T}(), pppp94-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #100: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp94-{F}() | EXISTS V0: pppp55-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #101: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp55-{F}(V0) | EXISTS V1: pppp54-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #102: input, references = 3, size of lhs = 5:
% 23.78/24.06 pppp54-{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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #103: input, references = 3, size of lhs = 1:
% 23.78/24.06 equivalence_3-{F}() | pppp14-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #104: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp14-{F}() | equivalence_3-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #105: input, references = 3, size of lhs = 6:
% 23.78/24.06 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)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #106: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp14-{T}(), pppp95-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #107: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp95-{F}() | EXISTS V0: pppp57-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #108: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp57-{F}(V0) | EXISTS V1: pppp56-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #109: input, references = 3, size of lhs = 7:
% 23.78/24.06 pppp56-{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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #110: input, references = 3, size of lhs = 1:
% 23.78/24.06 kn1-{F}() | pppp15-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #111: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp15-{F}() | kn1-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #112: input, references = 3, size of lhs = 3:
% 23.78/24.06 pppp15-{F}(), P_and-{F}(V0,V0,V1), P_implies-{F}(V0,V1,V2) | is_a_theorem-{T}(V2)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #113: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp15-{T}(), pppp96-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #114: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp96-{F}() | EXISTS V0: pppp58-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #115: input, references = 5, size of lhs = 4:
% 23.78/24.06 pppp58-{F}(V0), P_and-{F}(V0,V0,V1), P_implies-{F}(V0,V1,V2), is_a_theorem-{F}(V2) | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #116: input, references = 3, size of lhs = 1:
% 23.78/24.06 kn2-{F}() | pppp16-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #117: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp16-{F}() | kn2-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #118: input, references = 3, size of lhs = 3:
% 23.78/24.06 pppp16-{F}(), P_and-{F}(V0,V1,V2), P_implies-{F}(V2,V0,V3) | is_a_theorem-{T}(V3)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #119: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp16-{T}(), pppp97-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #120: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp97-{F}() | EXISTS V0: pppp60-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #121: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp60-{F}(V0) | EXISTS V1: pppp59-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #122: input, references = 3, size of lhs = 4:
% 23.78/24.06 pppp59-{F}(V0,V1), P_and-{F}(V0,V1,V2), P_implies-{F}(V2,V0,V3), is_a_theorem-{F}(V3) | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #123: input, references = 3, size of lhs = 1:
% 23.78/24.06 kn3-{F}() | pppp17-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #124: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp17-{F}() | kn3-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #125: input, references = 3, size of lhs = 8:
% 23.78/24.06 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)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #126: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp17-{T}(), pppp98-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #127: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp98-{F}() | EXISTS V0: pppp63-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #128: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp63-{F}(V0) | EXISTS V1: pppp62-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #129: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp62-{F}(V0,V1) | EXISTS V2: pppp61-{T}(V0,V1,V2)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #130: input, references = 3, size of lhs = 9:
% 23.78/24.06 pppp61-{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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #131: input, references = 3, size of lhs = 1:
% 23.78/24.06 cn1-{F}() | pppp18-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #132: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp18-{F}() | cn1-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #133: input, references = 3, size of lhs = 6:
% 23.78/24.06 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)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #134: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp18-{T}(), pppp99-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #135: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp99-{F}() | EXISTS V0: pppp66-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #136: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp66-{F}(V0) | EXISTS V1: pppp65-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #137: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp65-{F}(V0,V1) | EXISTS V2: pppp64-{T}(V0,V1,V2)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #138: input, references = 3, size of lhs = 7:
% 23.78/24.06 pppp64-{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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #139: input, references = 4, size of lhs = 1:
% 23.78/24.06 cn2-{F}() | pppp19-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #140: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp19-{F}() | cn2-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #141: input, references = 7, size of lhs = 4:
% 23.78/24.06 pppp19-{F}(), P_not-{F}(V0,V2), P_implies-{F}(V2,V1,V3), P_implies-{F}(V0,V3,V4) | is_a_theorem-{T}(V4)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #142: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp19-{T}(), pppp100-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #143: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp100-{F}() | EXISTS V0: pppp68-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #144: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp68-{F}(V0) | EXISTS V1: pppp67-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #145: input, references = 3, size of lhs = 5:
% 23.78/24.06 pppp67-{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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #146: input, references = 3, size of lhs = 1:
% 23.78/24.06 cn3-{F}() | pppp20-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #147: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp20-{F}() | cn3-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #148: input, references = 4, size of lhs = 4:
% 23.78/24.06 pppp20-{F}(), P_not-{F}(V0,V1), P_implies-{F}(V1,V0,V2), P_implies-{F}(V2,V0,V3) | is_a_theorem-{T}(V3)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #149: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp20-{T}(), pppp101-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #150: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp101-{F}() | EXISTS V0: pppp69-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #151: input, references = 3, size of lhs = 5:
% 23.78/24.06 pppp69-{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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #152: input, references = 3, size of lhs = 1:
% 23.78/24.06 r1-{F}() | pppp21-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #153: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp21-{F}() | r1-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #154: input, references = 6, size of lhs = 3:
% 23.78/24.06 pppp21-{F}(), P_or-{F}(V0,V0,V1), P_implies-{F}(V1,V0,V2) | is_a_theorem-{T}(V2)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #155: input, references = 4, size of lhs = 0:
% 23.78/24.06 FALSE | pppp21-{T}(), pppp102-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #156: input, references = 4, size of lhs = 1:
% 23.78/24.06 pppp102-{F}() | EXISTS V0: pppp70-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #157: input, references = 4, size of lhs = 4:
% 23.78/24.06 pppp70-{F}(V0), P_or-{F}(V0,V0,V1), P_implies-{F}(V1,V0,V2), is_a_theorem-{F}(V2) | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #158: input, references = 3, size of lhs = 1:
% 23.78/24.06 r2-{F}() | pppp22-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #159: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp22-{F}() | r2-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #160: input, references = 3, size of lhs = 3:
% 23.78/24.06 pppp22-{F}(), P_or-{F}(V0,V1,V2), P_implies-{F}(V1,V2,V3) | is_a_theorem-{T}(V3)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #161: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp22-{T}(), pppp103-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #162: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp103-{F}() | EXISTS V0: pppp72-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #163: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp72-{F}(V0) | EXISTS V1: pppp71-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #164: input, references = 3, size of lhs = 4:
% 23.78/24.06 pppp71-{F}(V0,V1), P_or-{F}(V0,V1,V2), P_implies-{F}(V1,V2,V3), is_a_theorem-{F}(V3) | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #165: input, references = 3, size of lhs = 1:
% 23.78/24.06 r3-{F}() | pppp23-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #166: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp23-{F}() | r3-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #167: input, references = 3, size of lhs = 4:
% 23.78/24.06 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)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #168: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp23-{T}(), pppp104-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #169: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp104-{F}() | EXISTS V0: pppp74-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #170: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp74-{F}(V0) | EXISTS V1: pppp73-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #171: input, references = 3, size of lhs = 5:
% 23.78/24.06 pppp73-{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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #172: input, references = 3, size of lhs = 1:
% 23.78/24.06 r4-{F}() | pppp24-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #173: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp24-{F}() | r4-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #174: input, references = 3, size of lhs = 6:
% 23.78/24.06 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)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #175: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp24-{T}(), pppp105-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #176: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp105-{F}() | EXISTS V0: pppp77-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #177: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp77-{F}(V0) | EXISTS V1: pppp76-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #178: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp76-{F}(V0,V1) | EXISTS V2: pppp75-{T}(V0,V1,V2)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #179: input, references = 3, size of lhs = 7:
% 23.78/24.06 pppp75-{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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #180: input, references = 3, size of lhs = 1:
% 23.78/24.06 r5-{F}() | pppp25-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #181: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp25-{F}() | r5-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #182: input, references = 3, size of lhs = 6:
% 23.78/24.06 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)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #183: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | pppp25-{T}(), pppp106-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #184: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp106-{F}() | EXISTS V0: pppp80-{T}(V0)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #185: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp80-{F}(V0) | EXISTS V1: pppp79-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #186: input, references = 3, size of lhs = 1:
% 23.78/24.06 pppp79-{F}(V0,V1) | EXISTS V2: pppp78-{T}(V0,V1,V2)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #187: input, references = 3, size of lhs = 7:
% 23.78/24.06 pppp78-{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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #188: input, references = 6, size of lhs = 7:
% 23.78/24.06 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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #189: input, references = 3, size of lhs = 7:
% 23.78/24.06 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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #190: input, references = 7, size of lhs = 6:
% 23.78/24.06 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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #191: input, references = 3, size of lhs = 5:
% 23.78/24.06 op_implies_or-{F}(), P_implies-{F}(V0,V1,V2), P_not-{F}(V0,V3), P_or-{F}(V3,V1,V4), V2 == V4 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #192: input, references = 5, size of lhs = 6:
% 23.78/24.06 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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #193: input, references = 4, size of lhs = 0:
% 23.78/24.06 FALSE | op_or-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #194: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | op_implies-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #195: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | op_equiv-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #196: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | modus_ponens-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #197: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | cn1-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #198: input, references = 4, size of lhs = 0:
% 23.78/24.06 FALSE | cn2-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #199: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | cn3-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #200: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | substitution_of_equivalents-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #201: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | op_or-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #202: input, references = 4, size of lhs = 0:
% 23.78/24.06 FALSE | op_implies_and-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #203: input, references = 3, size of lhs = 0:
% 23.78/24.06 FALSE | op_equiv-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #204: input, references = 4, size of lhs = 1:
% 23.78/24.06 or_1-{F}() | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #205: input, references = 14, size of lhs = 2:
% 23.78/24.06 #-{F} V0, #-{F} V1 | EXISTS V2: P_implies-{T}(V0,V1,V2)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #206: input, references = 8, size of lhs = 2:
% 23.78/24.06 #-{F} V0, #-{F} V1 | EXISTS V2: P_equiv-{T}(V0,V1,V2)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #207: input, references = 8, size of lhs = 1:
% 23.78/24.06 #-{F} V0 | EXISTS V1: P_not-{T}(V0,V1)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #208: input, references = 7, size of lhs = 2:
% 23.78/24.06 #-{F} V0, #-{F} V1 | EXISTS V2: P_and-{T}(V0,V1,V2)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #209: input, references = 7, size of lhs = 2:
% 23.78/24.06 #-{F} V0, #-{F} V1 | EXISTS V2: P_or-{T}(V0,V1,V2)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 number of initial rules = 210
% 23.78/24.06
% 23.78/24.06 Simplifiers:
% 23.78/24.06 #210: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 P_implies-{F}(V0,V1,V2), P_implies-{F}(V0,V1,V5), V2 == V5 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #211: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 P_equiv-{F}(V0,V1,V2), P_equiv-{F}(V0,V1,V5), V2 == V5 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #212: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 P_not-{F}(V0,V1), P_not-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #213: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 P_and-{F}(V0,V1,V2), P_and-{F}(V0,V1,V5), V2 == V5 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #214: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 P_or-{F}(V0,V1,V2), P_or-{F}(V0,V1,V5), V2 == V5 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #215: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp26-{F}(V0,V1), pppp26-{F}(V2,V1), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #216: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp26-{F}(V0,V1), pppp26-{F}(V2,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #217: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp27-{F}(V0), pppp27-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #218: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp28-{F}(V0,V1), pppp28-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #219: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp28-{F}(V0,V1), pppp28-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #220: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp29-{F}(V0), pppp29-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #221: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp30-{F}(V0,V1), pppp30-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #222: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp30-{F}(V0,V1), pppp30-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #223: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp31-{F}(V0), pppp31-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #224: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp32-{F}(V0,V1), pppp32-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #225: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp32-{F}(V0,V1), pppp32-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #226: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp33-{F}(V0), pppp33-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #227: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp34-{F}(V0,V1), pppp34-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #228: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp34-{F}(V0,V1), pppp34-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #229: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp35-{F}(V0), pppp35-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #230: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp36-{F}(V0,V1,V2), pppp36-{F}(V0,V1,V5), V2 == V5 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #231: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp36-{F}(V0,V1,V2), pppp36-{F}(V0,V4,V5), V1 == V4 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #232: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp36-{F}(V0,V1,V2), pppp36-{F}(V3,V4,V5), V0 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #233: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp37-{F}(V0,V1), pppp37-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #234: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp37-{F}(V0,V1), pppp37-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #235: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp38-{F}(V0), pppp38-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #236: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp39-{F}(V0,V1), pppp39-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #237: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp39-{F}(V0,V1), pppp39-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #238: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp40-{F}(V0), pppp40-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #239: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp41-{F}(V0,V1), pppp41-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #240: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp41-{F}(V0,V1), pppp41-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #241: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp42-{F}(V0), pppp42-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #242: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp43-{F}(V0,V1), pppp43-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #243: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp43-{F}(V0,V1), pppp43-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #244: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp44-{F}(V0), pppp44-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #245: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp45-{F}(V0,V1), pppp45-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #246: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp45-{F}(V0,V1), pppp45-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #247: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp46-{F}(V0), pppp46-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #248: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp47-{F}(V0,V1), pppp47-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #249: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp47-{F}(V0,V1), pppp47-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #250: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp48-{F}(V0), pppp48-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #251: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp49-{F}(V0,V1,V2), pppp49-{F}(V0,V1,V5), V2 == V5 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #252: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp49-{F}(V0,V1,V2), pppp49-{F}(V0,V4,V5), V1 == V4 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #253: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp49-{F}(V0,V1,V2), pppp49-{F}(V3,V4,V5), V0 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #254: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp50-{F}(V0,V1), pppp50-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #255: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp50-{F}(V0,V1), pppp50-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #256: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp51-{F}(V0), pppp51-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #257: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp52-{F}(V0,V1), pppp52-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #258: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp52-{F}(V0,V1), pppp52-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #259: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp53-{F}(V0), pppp53-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #260: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp54-{F}(V0,V1), pppp54-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #261: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp54-{F}(V0,V1), pppp54-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #262: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp55-{F}(V0), pppp55-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #263: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp56-{F}(V0,V1), pppp56-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #264: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp56-{F}(V0,V1), pppp56-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #265: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp57-{F}(V0), pppp57-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #266: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp58-{F}(V0), pppp58-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #267: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp59-{F}(V0,V1), pppp59-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #268: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp59-{F}(V0,V1), pppp59-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #269: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp60-{F}(V0), pppp60-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #270: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp61-{F}(V0,V1,V2), pppp61-{F}(V0,V1,V5), V2 == V5 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #271: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp61-{F}(V0,V1,V2), pppp61-{F}(V0,V4,V5), V1 == V4 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #272: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp61-{F}(V0,V1,V2), pppp61-{F}(V3,V4,V5), V0 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #273: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp62-{F}(V0,V1), pppp62-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #274: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp62-{F}(V0,V1), pppp62-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #275: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp63-{F}(V0), pppp63-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #276: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp64-{F}(V0,V1,V2), pppp64-{F}(V0,V1,V5), V2 == V5 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #277: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp64-{F}(V0,V1,V2), pppp64-{F}(V0,V4,V5), V1 == V4 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #278: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp64-{F}(V0,V1,V2), pppp64-{F}(V3,V4,V5), V0 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #279: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp65-{F}(V0,V1), pppp65-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #280: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp65-{F}(V0,V1), pppp65-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #281: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp66-{F}(V0), pppp66-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #282: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp67-{F}(V0,V1), pppp67-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #283: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp67-{F}(V0,V1), pppp67-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #284: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp68-{F}(V0), pppp68-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #285: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp69-{F}(V0), pppp69-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #286: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp70-{F}(V0), pppp70-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #287: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp71-{F}(V0,V1), pppp71-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #288: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp71-{F}(V0,V1), pppp71-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #289: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp72-{F}(V0), pppp72-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #290: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp73-{F}(V0,V1), pppp73-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #291: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp73-{F}(V0,V1), pppp73-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #292: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp74-{F}(V0), pppp74-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #293: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp75-{F}(V0,V1,V2), pppp75-{F}(V0,V1,V5), V2 == V5 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #294: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp75-{F}(V0,V1,V2), pppp75-{F}(V0,V4,V5), V1 == V4 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #295: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp75-{F}(V0,V1,V2), pppp75-{F}(V3,V4,V5), V0 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #296: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp76-{F}(V0,V1), pppp76-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #297: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp76-{F}(V0,V1), pppp76-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #298: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp77-{F}(V0), pppp77-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #299: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp78-{F}(V0,V1,V2), pppp78-{F}(V0,V1,V5), V2 == V5 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #300: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp78-{F}(V0,V1,V2), pppp78-{F}(V0,V4,V5), V1 == V4 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #301: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp78-{F}(V0,V1,V2), pppp78-{F}(V3,V4,V5), V0 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #302: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp79-{F}(V0,V1), pppp79-{F}(V0,V3), V1 == V3 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #303: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp79-{F}(V0,V1), pppp79-{F}(V2,V3), V0 == V2 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #304: unsound, references = 3, size of lhs = 3:
% 23.78/24.06 pppp80-{F}(V0), pppp80-{F}(V1), V0 == V1 | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 number of simplifiers = 95
% 23.78/24.06
% 23.78/24.06 Learnt:
% 23.78/24.06 #307: disj( #70, #68+#204 ), references = 1, size of lhs = 0:
% 23.78/24.06 FALSE | pppp90-{T}()
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #310: exists( #205, #308 ), references = 3, size of lhs = 5:
% 23.78/24.06 pppp20-{F}(), pppp70-{F}(V0), P_or-{F}(V0,V0,V1), P_not-{F}(V0,V2), P_implies-{F}(V2,V0,V1) | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #312: exists( #206, #192 ), references = 1, size of lhs = 4:
% 23.78/24.06 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)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #314: exists( #208, #192 ), references = 6, size of lhs = 4:
% 23.78/24.06 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)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #317: exists( #207, #190 ), references = 12, size of lhs = 4:
% 23.78/24.06 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)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #318: exists( #207, #188 ), references = 5, size of lhs = 5:
% 23.78/24.06 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)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #321: exists( #205, #190 ), references = 12, size of lhs = 4:
% 23.78/24.06 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)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #329: exists( #206, #327 ), references = 5, size of lhs = 13:
% 23.78/24.06 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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #346: exists( #209, #188 ), references = 2, size of lhs = 5:
% 23.78/24.06 op_or-{F}(), P_not-{F}(V0,V1), P_not-{F}(V2,V3), P_and-{F}(V1,V3,V4), P_not-{F}(V4,V5) | P_or-{T}(V0,V2,V5)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #353: mergings( V3 == V4, V4 == V5, V5 == V6; #349 ), references = 2, size of lhs = 6:
% 23.78/24.06 op_implies_and-{F}(), op_or-{F}(), pppp20-{F}(), pppp70-{F}(V0), P_not-{F}(V0,V1), P_and-{F}(V1,V1,V2) | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #357: exists( #206, #355 ), references = 4, size of lhs = 15:
% 23.78/24.06 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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #360: exists( #206, #358 ), references = 1, size of lhs = 8:
% 23.78/24.06 op_equiv-{F}(), op_implies_and-{F}(), op_or-{F}(), pppp20-{F}(), pppp70-{F}(V0), P_not-{F}(V0,V1), P_implies-{F}(V2,V3,V1), P_implies-{F}(V3,V2,V1) | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #379: exists( #208, #374 ), references = 2, size of lhs = 8:
% 23.78/24.06 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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #380: exists( #208, #375 ), references = 1, size of lhs = 8:
% 23.78/24.06 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
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #383: exists( #209, #377 ), references = 4, size of lhs = 6:
% 23.78/24.06 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)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #394: exists( #205, #392 ), references = 2, size of lhs = 4:
% 23.78/24.06 pppp10-{F}(), pppp45-{F}(V0,V1), P_or-{F}(V0,V1,V2), P_or-{F}(V3,V0,V2) | FALSE
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #399: exists( #205, #379 ), references = 2, size of lhs = 6:
% 23.78/24.06 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)
% 23.78/24.06 (used 0 times, uses = {})
% 23.78/24.06
% 23.78/24.06 #404: mergings( V2 == V3; #402 ), references = 1, size of lhs = 5:
% 23.78/24.06 op_or-{F}(), op_implies_and-{F}(), pppp20-{F}(), pppp70-{F}(V0), P_not-{F}(V0,V1) | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #406: exists( #207, #402 ), references = 1, size of lhs = 4:
% 23.78/24.07 op_or-{F}(), op_implies_and-{F}(), pppp20-{F}(), pppp70-{F}(V0) | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #408: exists( #156, #405 ), references = 1, size of lhs = 4:
% 23.78/24.07 pppp102-{F}(), op_or-{F}(), op_implies_and-{F}(), pppp20-{F}() | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #410: disj( #155, exists( #156, #405 ) ), references = 1, size of lhs = 3:
% 23.78/24.07 op_or-{F}(), op_implies_and-{F}(), pppp20-{F}() | pppp21-{T}()
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #422: exists( #208, #420 ), references = 1, size of lhs = 6:
% 23.78/24.07 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
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #424: exists( #205, #421 ), references = 2, size of lhs = 4:
% 23.78/24.07 op_implies_and-{F}(), P_not-{F}(V0,V1), P_not-{F}(V2,V1), P_implies-{F}(V3,V2,V4) | P_implies-{T}(V3,V0,V4)
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #437: exists( #205, #435 ), references = 1, size of lhs = 11:
% 23.78/24.07 op_implies_and-{F}(), pppp11-{F}(), pppp58-{F}(V0), P_and-{F}(V0,V0,V1), P_not-{F}(V1,V2), P_not-{F}(V3,V2), P_implies-{F}(V4,V5,V0), P_implies-{F}(V6,V5,V7), P_or-{F}(V4,V6,V8), P_implies-{F}(V8,V5,V9), P_implies-{F}(V7,V9,V3) | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #449: exists( #208, #447 ), references = 1, size of lhs = 10:
% 23.78/24.07 op_or-{F}(), op_implies_and-{F}(), pppp10-{F}(), P_not-{F}(V0,V1), P_implies-{F}(V2,V0,V3), P_not-{F}(V4,V5), P_not-{F}(V6,V5), P_implies-{F}(V3,V6,V7), pppp45-{F}(V4,V8), P_or-{F}(V4,V8,V7) | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #457: mergings( V0 == V4, V4 == V6, V8 == V9; #453 ), references = 1, size of lhs = 12:
% 23.78/24.07 op_or-{F}(), op_implies_and-{F}(), pppp10-{F}(), P_not-{F}(V0,V1), P_not-{F}(V2,V1), pppp45-{F}(V0,V3), P_not-{F}(V3,V4), P_not-{F}(V5,V4), P_and-{F}(V1,V4,V6), P_and-{F}(V7,V1,V6), P_not-{F}(V8,V9), P_implies-{F}(V10,V8,V7) | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #493: mergings( V3 == V7, V4 == V8, V8 == V6; #488 ), references = 1, size of lhs = 22:
% 23.78/24.07 op_or-{F}(), pppp19-{F}(), op_equiv-{F}(), op_implies_and-{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_and-{F}(V0,V3,V5), P_not-{F}(V6,V7), P_and-{F}(V6,V8,V5), P_not-{F}(V9,V8), P_implies-{F}(V7,V10,V9), P_implies-{F}(V11,V12,V0), P_implies-{F}(V12,V11,V3), P_not-{F}(V13,V14), P_implies-{F}(V15,V13,V3), P_implies-{F}(V16,V17,V15), V16 == V17, P_implies-{F}(V17,V16,V14) | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #494: exists( #209, #483 ), references = 1, size of lhs = 20:
% 23.78/24.07 op_or-{F}(), pppp19-{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,V8), P_and-{F}(V7,V9,V5), P_not-{F}(V10,V9), P_implies-{F}(V8,V11,V10), P_not-{F}(V12,V13), P_implies-{F}(V14,V12,V6), P_implies-{F}(V15,V16,V14), V15 == V16, P_implies-{F}(V16,V15,V13) | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #495: exists( #209, #485 ), references = 1, size of lhs = 12:
% 23.78/24.07 op_or-{F}(), op_implies_and-{F}(), pppp19-{F}(), P_not-{F}(V0,V1), P_not-{F}(V2,V3), P_and-{F}(V1,V3,V4), P_not-{F}(V5,V6), pppp45-{F}(V5,V7), P_or-{F}(V5,V7,V8), P_not-{F}(V8,V9), P_and-{F}(V5,V9,V4), P_implies-{F}(V6,V10,V8) | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #529: exists( #205, #523 ), references = 1, size of lhs = 9:
% 23.78/24.07 op_implies_and-{F}(), pppp21-{F}(), pppp58-{F}(V0), P_and-{F}(V0,V0,V1), P_not-{F}(V1,V2), P_and-{F}(V0,V2,V3), P_not-{F}(V4,V5), P_or-{F}(V4,V4,V6), P_and-{F}(V6,V5,V3) | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #530: exists( #205, #524 ), references = 1, size of lhs = 17:
% 23.78/24.07 pppp21-{F}(), op_equiv-{F}(), op_implies_and-{F}(), pppp0-{F}(), pppp1-{F}(), is_a_theorem-{F}(V0), P_not-{F}(V1,V2), P_and-{F}(V3,V2,V4), P_and-{F}(V0,V5,V4), P_not-{F}(V6,V7), P_or-{F}(V6,V6,V8), P_and-{F}(V8,V7,V4), P_not-{F}(V9,V10), P_implies-{F}(V11,V9,V5), P_implies-{F}(V12,V13,V11), V12 == V13, P_implies-{F}(V13,V12,V10) | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #532: mergings( V3 == V5; #528 ), references = 1, size of lhs = 18:
% 23.78/24.07 pppp21-{F}(), op_equiv-{F}(), op_implies_and-{F}(), pppp0-{F}(), pppp1-{F}(), is_a_theorem-{F}(V0), P_not-{F}(V1,V2), P_and-{F}(V0,V2,V3), P_not-{F}(V4,V5), P_or-{F}(V4,V4,V6), P_and-{F}(V6,V5,V3), P_implies-{F}(V7,V8,V0), P_implies-{F}(V8,V7,V2), P_not-{F}(V9,V10), P_implies-{F}(V11,V9,V2), P_implies-{F}(V12,V13,V11), V12 == V13, P_implies-{F}(V13,V12,V10) | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #562: exists( #205, #558 ), references = 2, size of lhs = 17:
% 23.78/24.07 pppp7-{F}(), op_equiv-{F}(), op_implies_and-{F}(), pppp0-{F}(), pppp1-{F}(), is_a_theorem-{F}(V0), P_not-{F}(V1,V2), P_and-{F}(V3,V2,V4), P_and-{F}(V0,V5,V4), P_not-{F}(V6,V7), P_and-{F}(V8,V7,V4), P_and-{F}(V9,V6,V8), P_not-{F}(V10,V11), P_implies-{F}(V12,V10,V5), P_implies-{F}(V13,V14,V11), V14 == V13, P_implies-{F}(V14,V13,V12) | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #564: mergings( V3 == V5; #561 ), references = 2, size of lhs = 18:
% 23.78/24.07 pppp7-{F}(), op_equiv-{F}(), op_implies_and-{F}(), pppp0-{F}(), pppp1-{F}(), is_a_theorem-{F}(V0), P_not-{F}(V1,V2), P_and-{F}(V0,V2,V3), P_not-{F}(V4,V5), P_and-{F}(V6,V5,V3), P_and-{F}(V7,V4,V6), P_implies-{F}(V8,V9,V0), P_implies-{F}(V9,V8,V2), P_not-{F}(V10,V11), P_implies-{F}(V12,V10,V2), P_implies-{F}(V13,V14,V12), V13 == V14, P_implies-{F}(V14,V13,V11) | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #603: exists( #206, #598 ), references = 1, size of lhs = 16:
% 23.78/24.07 pppp7-{F}(), op_equiv-{F}(), op_implies_and-{F}(), pppp0-{F}(), pppp1-{F}(), is_a_theorem-{F}(V0), P_implies-{F}(V1,V2,V0), P_implies-{F}(V2,V1,V3), P_not-{F}(V4,V3), P_not-{F}(V5,V3), P_and-{F}(V6,V5,V0), P_not-{F}(V7,V8), P_implies-{F}(V9,V7,V3), P_implies-{F}(V10,V11,V8), V11 == V10, P_implies-{F}(V11,V10,V9) | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #604: exists( #206, #599 ), references = 1, size of lhs = 18:
% 23.78/24.07 pppp7-{F}(), op_equiv-{F}(), op_implies_and-{F}(), pppp0-{F}(), pppp1-{F}(), is_a_theorem-{F}(V0), P_implies-{F}(V1,V2,V0), P_implies-{F}(V2,V1,V3), P_not-{F}(V4,V3), P_not-{F}(V5,V3), P_and-{F}(V6,V5,V0), P_implies-{F}(V7,V8,V0), P_implies-{F}(V8,V7,V3), P_not-{F}(V9,V10), P_implies-{F}(V11,V9,V3), P_implies-{F}(V12,V13,V11), V12 == V13, P_implies-{F}(V13,V12,V10) | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #642: exists( #205, #639 ), references = 1, size of lhs = 5:
% 23.78/24.07 pppp19-{F}(), P_not-{F}(V0,V1), pppp45-{F}(V0,V2), P_or-{F}(V0,V2,V3), P_implies-{F}(V1,V4,V3) | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #645: exists( #205, #643 ), references = 1, size of lhs = 7:
% 23.78/24.07 op_or-{F}(), op_implies_and-{F}(), pppp19-{F}(), P_not-{F}(V0,V1), pppp45-{F}(V0,V2), P_not-{F}(V2,V3), P_not-{F}(V4,V3) | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #647: exists( #207, #644 ), references = 1, size of lhs = 5:
% 23.78/24.07 op_or-{F}(), op_implies_and-{F}(), pppp19-{F}(), P_not-{F}(V0,V1), pppp45-{F}(V0,V2) | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #649: exists( #207, #646 ), references = 1, size of lhs = 4:
% 23.78/24.07 op_or-{F}(), op_implies_and-{F}(), pppp19-{F}(), pppp45-{F}(V0,V1) | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #651: exists( #72, #648 ), references = 1, size of lhs = 4:
% 23.78/24.07 op_or-{F}(), op_implies_and-{F}(), pppp19-{F}(), pppp46-{F}(V0) | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #653: exists( #71, #650 ), references = 1, size of lhs = 4:
% 23.78/24.07 pppp90-{F}(), op_or-{F}(), op_implies_and-{F}(), pppp19-{F}() | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 #659: #193+#198+#202+#139+#306+#652, references = 1, size of lhs = 0:
% 23.78/24.07 FALSE | FALSE
% 23.78/24.07 (used 0 times, uses = {})
% 23.78/24.07
% 23.78/24.07 number of learnt formulas = 43
% 23.78/24.07
% 23.78/24.07
% 23.78/24.07 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.78/24.07
% 23.78/24.07 randbase = 1
%------------------------------------------------------------------------------