TSTP Solution File: LCL013-1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : LCL013-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n013.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 06:08:38 EDT 2022
% Result : Unsatisfiable 3.91s 4.09s
% Output : Refutation 3.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL013-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jul 22 22:15:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.91/4.09 GeoParameters:
% 3.91/4.09
% 3.91/4.09 tptp_input = 1
% 3.91/4.09 tptp_output = 0
% 3.91/4.09 nonempty = 1
% 3.91/4.09 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.91/4.09 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 3.91/4.09
% 3.91/4.09
% 3.91/4.09 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.91/4.09 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.91/4.09
% 3.91/4.09 RuleSystem INPUT:
% 3.91/4.09
% 3.91/4.09 Initial Rules:
% 3.91/4.09 #0: input, references = 22, size of lhs = 3:
% 3.91/4.09 P_equivalent-{F}(V1,V0,V2), is_a_theorem-{F}(V2), is_a_theorem-{F}(V1) | is_a_theorem-{T}(V0)
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #1: input, references = 19, size of lhs = 5:
% 3.91/4.09 P_equivalent-{F}(V0,V2,V3), P_equivalent-{F}(V1,V3,V4), P_equivalent-{F}(V2,V1,V5), P_equivalent-{F}(V4,V5,V6), P_equivalent-{F}(V0,V6,V7) | is_a_theorem-{T}(V7)
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #2: input, references = 4, size of lhs = 9:
% 3.91/4.09 P_a-{F}(V0), P_b-{F}(V1), P_equivalent-{F}(V0,V1,V2), P_c-{F}(V3), P_equivalent-{F}(V2,V3,V4), P_equivalent-{F}(V3,V0,V5), P_equivalent-{F}(V1,V5,V6), P_equivalent-{F}(V4,V6,V7), is_a_theorem-{F}(V7) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #3: input, references = 45, size of lhs = 2:
% 3.91/4.09 #-{F} V0, #-{F} V1 | EXISTS V2: P_equivalent-{T}(V0,V1,V2)
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #4: input, references = 4, size of lhs = 0:
% 3.91/4.09 FALSE | EXISTS V0: P_a-{T}(V0)
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #5: input, references = 4, size of lhs = 0:
% 3.91/4.09 FALSE | EXISTS V0: P_b-{T}(V0)
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #6: input, references = 4, size of lhs = 0:
% 3.91/4.09 FALSE | EXISTS V0: P_c-{T}(V0)
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 number of initial rules = 7
% 3.91/4.09
% 3.91/4.09 Simplifiers:
% 3.91/4.09 #7: unsound, references = 3, size of lhs = 3:
% 3.91/4.09 P_equivalent-{F}(V0,V1,V2), P_equivalent-{F}(V0,V1,V5), V2 == V5 | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #8: unsound, references = 3, size of lhs = 3:
% 3.91/4.09 P_a-{F}(V0), P_a-{F}(V1), V0 == V1 | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #9: unsound, references = 3, size of lhs = 3:
% 3.91/4.09 P_b-{F}(V0), P_b-{F}(V1), V0 == V1 | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #10: unsound, references = 3, size of lhs = 3:
% 3.91/4.09 P_c-{F}(V0), P_c-{F}(V1), V0 == V1 | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 number of simplifiers = 4
% 3.91/4.09
% 3.91/4.09 Learnt:
% 3.91/4.09 #22: exists( #3, #20 ), references = 1, size of lhs = 15:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), P_a-{F}(V2), P_b-{F}(V3), P_equivalent-{F}(V2,V3,V4), P_c-{F}(V5), P_equivalent-{F}(V4,V5,V6), P_equivalent-{F}(V5,V2,V7), P_equivalent-{F}(V3,V7,V8), P_equivalent-{F}(V6,V8,V9), P_equivalent-{F}(V1,V9,V10), P_equivalent-{F}(V0,V11,V12), P_equivalent-{F}(V13,V12,V14), P_equivalent-{F}(V11,V13,V15), P_equivalent-{F}(V14,V15,V10) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #24: exists( #3, #21 ), references = 4, size of lhs = 13:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), P_a-{F}(V2), P_b-{F}(V3), P_equivalent-{F}(V2,V3,V4), P_c-{F}(V5), P_equivalent-{F}(V4,V5,V6), P_equivalent-{F}(V5,V2,V7), P_equivalent-{F}(V3,V7,V8), P_equivalent-{F}(V6,V8,V9), P_equivalent-{F}(V0,V10,V11), P_equivalent-{F}(V12,V11,V1), P_equivalent-{F}(V10,V12,V9) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #32: exists( #3, #30 ), references = 2, size of lhs = 17:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), P_a-{F}(V2), P_b-{F}(V3), P_equivalent-{F}(V2,V3,V4), P_c-{F}(V5), P_equivalent-{F}(V4,V5,V6), P_equivalent-{F}(V5,V2,V7), P_equivalent-{F}(V3,V7,V8), P_equivalent-{F}(V6,V8,V9), P_equivalent-{F}(V1,V10,V11), P_equivalent-{F}(V10,V12,V9), P_equivalent-{F}(V12,V11,V13), P_equivalent-{F}(V0,V14,V15), P_equivalent-{F}(V16,V15,V17), P_equivalent-{F}(V14,V16,V18), P_equivalent-{F}(V17,V18,V13) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #35: exists( #3, #32 ), references = 2, size of lhs = 15:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), P_a-{F}(V2), P_b-{F}(V3), P_equivalent-{F}(V2,V3,V4), P_c-{F}(V5), P_equivalent-{F}(V4,V5,V6), P_equivalent-{F}(V5,V2,V7), P_equivalent-{F}(V3,V7,V8), P_equivalent-{F}(V6,V8,V9), P_equivalent-{F}(V1,V10,V11), P_equivalent-{F}(V10,V12,V9), P_equivalent-{F}(V0,V13,V14), P_equivalent-{F}(V15,V14,V12), P_equivalent-{F}(V13,V15,V11) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #37: exists( #3, #34 ), references = 2, size of lhs = 15:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), P_a-{F}(V2), P_b-{F}(V3), P_equivalent-{F}(V2,V3,V4), P_c-{F}(V5), P_equivalent-{F}(V4,V5,V6), P_equivalent-{F}(V5,V2,V7), P_equivalent-{F}(V3,V7,V8), P_equivalent-{F}(V6,V8,V9), P_equivalent-{F}(V1,V10,V11), P_equivalent-{F}(V10,V12,V9), P_equivalent-{F}(V0,V13,V14), P_equivalent-{F}(V15,V14,V12), P_equivalent-{F}(V13,V15,V11) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #74: exists( #3, #68 ), references = 1, size of lhs = 19:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V2,V11,V12), P_equivalent-{F}(V11,V13,V10), P_equivalent-{F}(V13,V12,V14), P_equivalent-{F}(V1,V14,V15), P_equivalent-{F}(V0,V16,V17), P_equivalent-{F}(V18,V17,V19), P_equivalent-{F}(V16,V18,V20), P_equivalent-{F}(V19,V20,V15) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #76: exists( #3, #71 ), references = 2, size of lhs = 17:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V2,V11,V12), P_equivalent-{F}(V11,V13,V10), P_equivalent-{F}(V13,V12,V14), P_equivalent-{F}(V0,V15,V16), P_equivalent-{F}(V17,V16,V1), P_equivalent-{F}(V15,V17,V14) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #78: exists( #3, #75 ), references = 2, size of lhs = 17:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V2,V11,V12), P_equivalent-{F}(V11,V13,V10), P_equivalent-{F}(V13,V12,V14), P_equivalent-{F}(V0,V15,V16), P_equivalent-{F}(V17,V16,V1), P_equivalent-{F}(V15,V17,V14) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #80: exists( #3, #77 ), references = 1, size of lhs = 15:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V2,V11,V12), P_equivalent-{F}(V11,V13,V10), P_equivalent-{F}(V0,V13,V14), P_equivalent-{F}(V12,V14,V1) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #97: exists( #3, #91 ), references = 1, size of lhs = 21:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V2,V11,V12), P_equivalent-{F}(V11,V13,V10), P_equivalent-{F}(V13,V12,V14), P_equivalent-{F}(V1,V15,V16), P_equivalent-{F}(V15,V17,V14), P_equivalent-{F}(V17,V16,V18), P_equivalent-{F}(V0,V19,V20), P_equivalent-{F}(V21,V20,V22), P_equivalent-{F}(V19,V21,V23), P_equivalent-{F}(V22,V23,V18) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #98: exists( #3, #92 ), references = 1, size of lhs = 21:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V2,V11,V12), P_equivalent-{F}(V11,V13,V10), P_equivalent-{F}(V13,V12,V14), P_equivalent-{F}(V1,V15,V16), P_equivalent-{F}(V15,V17,V14), P_equivalent-{F}(V17,V16,V18), P_equivalent-{F}(V0,V19,V20), P_equivalent-{F}(V21,V20,V22), P_equivalent-{F}(V19,V21,V23), P_equivalent-{F}(V22,V23,V18) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #101: exists( #3, #94 ), references = 2, size of lhs = 19:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V2,V11,V12), P_equivalent-{F}(V11,V13,V10), P_equivalent-{F}(V13,V12,V14), P_equivalent-{F}(V1,V15,V16), P_equivalent-{F}(V15,V17,V14), P_equivalent-{F}(V0,V18,V19), P_equivalent-{F}(V20,V19,V17), P_equivalent-{F}(V18,V20,V16) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #102: exists( #3, #95 ), references = 2, size of lhs = 19:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V2,V11,V12), P_equivalent-{F}(V11,V13,V10), P_equivalent-{F}(V13,V12,V14), P_equivalent-{F}(V1,V15,V16), P_equivalent-{F}(V15,V17,V14), P_equivalent-{F}(V0,V18,V19), P_equivalent-{F}(V20,V19,V17), P_equivalent-{F}(V18,V20,V16) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #105: exists( #3, #101 ), references = 3, size of lhs = 17:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V2,V11,V12), P_equivalent-{F}(V11,V13,V10), P_equivalent-{F}(V1,V13,V14), P_equivalent-{F}(V0,V15,V16), P_equivalent-{F}(V17,V16,V12), P_equivalent-{F}(V15,V17,V14) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #106: exists( #3, #102 ), references = 3, size of lhs = 17:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V2,V11,V12), P_equivalent-{F}(V11,V13,V10), P_equivalent-{F}(V1,V13,V14), P_equivalent-{F}(V0,V15,V16), P_equivalent-{F}(V17,V16,V12), P_equivalent-{F}(V15,V17,V14) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #109: exists( #3, #103 ), references = 3, size of lhs = 17:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V2,V11,V12), P_equivalent-{F}(V11,V13,V10), P_equivalent-{F}(V1,V13,V14), P_equivalent-{F}(V0,V15,V16), P_equivalent-{F}(V17,V16,V12), P_equivalent-{F}(V15,V17,V14) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #110: exists( #3, #104 ), references = 1, size of lhs = 17:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V2,V11,V12), P_equivalent-{F}(V11,V13,V10), P_equivalent-{F}(V1,V13,V14), P_equivalent-{F}(V0,V15,V16), P_equivalent-{F}(V17,V16,V12), P_equivalent-{F}(V15,V17,V14) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #141: exists( #3, #135 ), references = 2, size of lhs = 23:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), is_a_theorem-{F}(V3), P_a-{F}(V4), P_b-{F}(V5), P_equivalent-{F}(V4,V5,V6), P_c-{F}(V7), P_equivalent-{F}(V6,V7,V8), P_equivalent-{F}(V7,V4,V9), P_equivalent-{F}(V5,V9,V10), P_equivalent-{F}(V8,V10,V11), P_equivalent-{F}(V1,V12,V13), P_equivalent-{F}(V12,V14,V15), P_equivalent-{F}(V14,V16,V11), P_equivalent-{F}(V3,V16,V17), P_equivalent-{F}(V2,V18,V19), P_equivalent-{F}(V20,V19,V15), P_equivalent-{F}(V18,V20,V17), P_equivalent-{F}(V0,V21,V22), P_equivalent-{F}(V23,V22,V24), P_equivalent-{F}(V21,V23,V25), P_equivalent-{F}(V24,V25,V13) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #142: exists( #3, #136 ), references = 2, size of lhs = 23:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), is_a_theorem-{F}(V3), P_a-{F}(V4), P_b-{F}(V5), P_equivalent-{F}(V4,V5,V6), P_c-{F}(V7), P_equivalent-{F}(V6,V7,V8), P_equivalent-{F}(V7,V4,V9), P_equivalent-{F}(V5,V9,V10), P_equivalent-{F}(V8,V10,V11), P_equivalent-{F}(V1,V12,V13), P_equivalent-{F}(V12,V14,V15), P_equivalent-{F}(V14,V16,V11), P_equivalent-{F}(V3,V16,V17), P_equivalent-{F}(V2,V18,V19), P_equivalent-{F}(V20,V19,V15), P_equivalent-{F}(V18,V20,V17), P_equivalent-{F}(V0,V21,V22), P_equivalent-{F}(V23,V22,V24), P_equivalent-{F}(V21,V23,V25), P_equivalent-{F}(V24,V25,V13) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #143: exists( #3, #137 ), references = 2, size of lhs = 23:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), is_a_theorem-{F}(V3), P_a-{F}(V4), P_b-{F}(V5), P_equivalent-{F}(V4,V5,V6), P_c-{F}(V7), P_equivalent-{F}(V6,V7,V8), P_equivalent-{F}(V7,V4,V9), P_equivalent-{F}(V5,V9,V10), P_equivalent-{F}(V8,V10,V11), P_equivalent-{F}(V1,V12,V13), P_equivalent-{F}(V12,V14,V15), P_equivalent-{F}(V14,V16,V11), P_equivalent-{F}(V3,V16,V17), P_equivalent-{F}(V2,V18,V19), P_equivalent-{F}(V20,V19,V15), P_equivalent-{F}(V18,V20,V17), P_equivalent-{F}(V0,V21,V22), P_equivalent-{F}(V23,V22,V24), P_equivalent-{F}(V21,V23,V25), P_equivalent-{F}(V24,V25,V13) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #147: exists( #3, #138 ), references = 1, size of lhs = 21:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), is_a_theorem-{F}(V3), P_a-{F}(V4), P_b-{F}(V5), P_equivalent-{F}(V4,V5,V6), P_c-{F}(V7), P_equivalent-{F}(V6,V7,V8), P_equivalent-{F}(V7,V4,V9), P_equivalent-{F}(V5,V9,V10), P_equivalent-{F}(V8,V10,V11), P_equivalent-{F}(V1,V12,V13), P_equivalent-{F}(V3,V14,V15), P_equivalent-{F}(V16,V12,V15), P_equivalent-{F}(V2,V16,V17), P_equivalent-{F}(V17,V14,V11), P_equivalent-{F}(V0,V18,V19), P_equivalent-{F}(V20,V19,V21), P_equivalent-{F}(V18,V20,V22), P_equivalent-{F}(V21,V22,V13) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #148: exists( #3, #139 ), references = 1, size of lhs = 21:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), is_a_theorem-{F}(V3), P_a-{F}(V4), P_b-{F}(V5), P_equivalent-{F}(V4,V5,V6), P_c-{F}(V7), P_equivalent-{F}(V6,V7,V8), P_equivalent-{F}(V7,V4,V9), P_equivalent-{F}(V5,V9,V10), P_equivalent-{F}(V8,V10,V11), P_equivalent-{F}(V1,V12,V13), P_equivalent-{F}(V3,V14,V15), P_equivalent-{F}(V16,V12,V15), P_equivalent-{F}(V2,V16,V17), P_equivalent-{F}(V17,V14,V11), P_equivalent-{F}(V0,V18,V19), P_equivalent-{F}(V20,V19,V21), P_equivalent-{F}(V18,V20,V22), P_equivalent-{F}(V21,V22,V13) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #149: exists( #3, #140 ), references = 1, size of lhs = 21:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), is_a_theorem-{F}(V3), P_a-{F}(V4), P_b-{F}(V5), P_equivalent-{F}(V4,V5,V6), P_c-{F}(V7), P_equivalent-{F}(V6,V7,V8), P_equivalent-{F}(V7,V4,V9), P_equivalent-{F}(V5,V9,V10), P_equivalent-{F}(V8,V10,V11), P_equivalent-{F}(V1,V12,V13), P_equivalent-{F}(V3,V14,V15), P_equivalent-{F}(V16,V12,V15), P_equivalent-{F}(V2,V16,V17), P_equivalent-{F}(V17,V14,V11), P_equivalent-{F}(V0,V18,V19), P_equivalent-{F}(V20,V19,V21), P_equivalent-{F}(V18,V20,V22), P_equivalent-{F}(V21,V22,V13) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #153: exists( #3, #144 ), references = 1, size of lhs = 16:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V1,V2,V11), P_equivalent-{F}(V11,V12,V10), P_equivalent-{F}(V0,V13,V14), P_equivalent-{F}(V15,V14,V2), P_equivalent-{F}(V13,V15,V12) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #154: exists( #3, #145 ), references = 1, size of lhs = 16:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V1,V2,V11), P_equivalent-{F}(V11,V12,V10), P_equivalent-{F}(V0,V13,V14), P_equivalent-{F}(V15,V14,V2), P_equivalent-{F}(V13,V15,V12) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #155: exists( #3, #146 ), references = 1, size of lhs = 16:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V1,V2,V11), P_equivalent-{F}(V11,V12,V10), P_equivalent-{F}(V0,V13,V14), P_equivalent-{F}(V15,V14,V2), P_equivalent-{F}(V13,V15,V12) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #159: exists( #3, #150 ), references = 2, size of lhs = 14:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V1,V2,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V0,V10,V11), P_equivalent-{F}(V12,V11,V2), P_equivalent-{F}(V10,V12,V9) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #160: exists( #3, #151 ), references = 2, size of lhs = 14:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V1,V2,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V0,V10,V11), P_equivalent-{F}(V12,V11,V2), P_equivalent-{F}(V10,V12,V9) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #161: exists( #3, #152 ), references = 2, size of lhs = 14:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V1,V2,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V0,V10,V11), P_equivalent-{F}(V12,V11,V2), P_equivalent-{F}(V10,V12,V9) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #165: exists( #3, #156 ), references = 2, size of lhs = 12:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V1,V2,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V0,V4,V9), P_equivalent-{F}(V8,V9,V2) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #166: exists( #3, #157 ), references = 2, size of lhs = 12:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V1,V2,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V0,V4,V9), P_equivalent-{F}(V8,V9,V2) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #167: exists( #3, #158 ), references = 2, size of lhs = 12:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V1,V2,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V0,V4,V9), P_equivalent-{F}(V8,V9,V2) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #171: exists( #3, #165 ), references = 1, size of lhs = 10:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_c-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V1), P_equivalent-{F}(V2,V3,V5), P_equivalent-{F}(V0,V4,V6), P_equivalent-{F}(V5,V6,V2) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #172: exists( #3, #166 ), references = 1, size of lhs = 10:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_c-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V1), P_equivalent-{F}(V2,V3,V5), P_equivalent-{F}(V0,V4,V6), P_equivalent-{F}(V5,V6,V2) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #173: exists( #3, #167 ), references = 1, size of lhs = 10:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_c-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V1), P_equivalent-{F}(V2,V3,V5), P_equivalent-{F}(V0,V4,V6), P_equivalent-{F}(V5,V6,V2) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #177: exists( #3, #159 ), references = 1, size of lhs = 12:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_c-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V1), P_equivalent-{F}(V2,V3,V5), P_equivalent-{F}(V4,V5,V6), P_equivalent-{F}(V0,V7,V8), P_equivalent-{F}(V9,V8,V2), P_equivalent-{F}(V7,V9,V6) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #178: exists( #3, #160 ), references = 1, size of lhs = 12:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_c-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V1), P_equivalent-{F}(V2,V3,V5), P_equivalent-{F}(V4,V5,V6), P_equivalent-{F}(V0,V7,V8), P_equivalent-{F}(V9,V8,V2), P_equivalent-{F}(V7,V9,V6) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #179: exists( #3, #161 ), references = 1, size of lhs = 12:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_c-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V1), P_equivalent-{F}(V2,V3,V5), P_equivalent-{F}(V4,V5,V6), P_equivalent-{F}(V0,V7,V8), P_equivalent-{F}(V9,V8,V2), P_equivalent-{F}(V7,V9,V6) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #182: exists( #3, #35 ), references = 1, size of lhs = 13:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), P_a-{F}(V2), P_b-{F}(V3), P_equivalent-{F}(V2,V3,V4), P_c-{F}(V5), P_equivalent-{F}(V4,V5,V6), P_equivalent-{F}(V5,V2,V7), P_equivalent-{F}(V3,V7,V8), P_equivalent-{F}(V1,V6,V9), P_equivalent-{F}(V0,V10,V11), P_equivalent-{F}(V12,V11,V8), P_equivalent-{F}(V10,V12,V9) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #183: exists( #3, #37 ), references = 1, size of lhs = 13:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), P_a-{F}(V2), P_b-{F}(V3), P_equivalent-{F}(V2,V3,V4), P_c-{F}(V5), P_equivalent-{F}(V4,V5,V6), P_equivalent-{F}(V5,V2,V7), P_equivalent-{F}(V3,V7,V8), P_equivalent-{F}(V1,V6,V9), P_equivalent-{F}(V0,V10,V11), P_equivalent-{F}(V12,V11,V8), P_equivalent-{F}(V10,V12,V9) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #187: exists( #3, #105 ), references = 2, size of lhs = 15:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V1,V11,V12), P_equivalent-{F}(V13,V2,V12), P_equivalent-{F}(V0,V13,V14), P_equivalent-{F}(V14,V11,V10) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #188: exists( #3, #106 ), references = 2, size of lhs = 15:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V1,V11,V12), P_equivalent-{F}(V13,V2,V12), P_equivalent-{F}(V0,V13,V14), P_equivalent-{F}(V14,V11,V10) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #189: exists( #3, #109 ), references = 2, size of lhs = 15:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V1,V11,V12), P_equivalent-{F}(V13,V2,V12), P_equivalent-{F}(V0,V13,V14), P_equivalent-{F}(V14,V11,V10) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #193: exists( #3, #184 ), references = 1, size of lhs = 15:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V1,V11,V12), P_equivalent-{F}(V13,V2,V12), P_equivalent-{F}(V0,V13,V14), P_equivalent-{F}(V14,V11,V10) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #194: exists( #3, #185 ), references = 1, size of lhs = 15:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V1,V11,V12), P_equivalent-{F}(V13,V2,V12), P_equivalent-{F}(V0,V13,V14), P_equivalent-{F}(V14,V11,V10) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #195: exists( #3, #186 ), references = 1, size of lhs = 15:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V7,V9,V10), P_equivalent-{F}(V1,V11,V12), P_equivalent-{F}(V13,V2,V12), P_equivalent-{F}(V0,V13,V14), P_equivalent-{F}(V14,V11,V10) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #199: exists( #3, #190 ), references = 1, size of lhs = 11:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), P_equivalent-{F}(V0,V1,V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V1), P_equivalent-{F}(V6,V3,V7), P_equivalent-{F}(V4,V7,V2) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #200: exists( #3, #191 ), references = 1, size of lhs = 11:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), P_equivalent-{F}(V0,V1,V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V1), P_equivalent-{F}(V6,V3,V7), P_equivalent-{F}(V4,V7,V2) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #201: exists( #3, #192 ), references = 1, size of lhs = 11:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), P_equivalent-{F}(V0,V1,V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V1), P_equivalent-{F}(V6,V3,V7), P_equivalent-{F}(V4,V7,V2) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #205: exists( #3, #187 ), references = 2, size of lhs = 13:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V1,V9,V10), P_equivalent-{F}(V11,V2,V10), P_equivalent-{F}(V0,V11,V7) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #206: exists( #3, #188 ), references = 2, size of lhs = 13:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V1,V9,V10), P_equivalent-{F}(V11,V2,V10), P_equivalent-{F}(V0,V11,V7) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #207: exists( #3, #189 ), references = 2, size of lhs = 13:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V9), P_equivalent-{F}(V1,V9,V10), P_equivalent-{F}(V11,V2,V10), P_equivalent-{F}(V0,V11,V7) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #211: exists( #3, #205 ), references = 1, size of lhs = 11:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V0,V1,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V2) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #212: exists( #3, #206 ), references = 1, size of lhs = 11:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V0,V1,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V2) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #213: exists( #3, #207 ), references = 1, size of lhs = 11:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_c-{F}(V6), P_equivalent-{F}(V5,V6,V7), P_equivalent-{F}(V0,V1,V7), P_equivalent-{F}(V6,V3,V8), P_equivalent-{F}(V4,V8,V2) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #217: exists( #3, #208 ), references = 2, size of lhs = 9:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), P_c-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V0), P_equivalent-{F}(V1,V3,V5), P_equivalent-{F}(V4,V5,V2) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #218: exists( #3, #209 ), references = 2, size of lhs = 9:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), P_c-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V0), P_equivalent-{F}(V1,V3,V5), P_equivalent-{F}(V4,V5,V2) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #219: exists( #3, #210 ), references = 2, size of lhs = 9:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), P_c-{F}(V1), is_a_theorem-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V0), P_equivalent-{F}(V1,V3,V5), P_equivalent-{F}(V4,V5,V2) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #226: exists( #3, #220 ), references = 1, size of lhs = 11:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), P_c-{F}(V1), P_a-{F}(V2), P_b-{F}(V3), P_equivalent-{F}(V2,V3,V0), P_equivalent-{F}(V1,V2,V4), P_equivalent-{F}(V3,V5,V6), P_equivalent-{F}(V7,V6,V8), P_equivalent-{F}(V5,V7,V9), P_equivalent-{F}(V8,V9,V4) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #227: exists( #3, #221 ), references = 1, size of lhs = 11:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), P_c-{F}(V1), P_a-{F}(V2), P_b-{F}(V3), P_equivalent-{F}(V2,V3,V0), P_equivalent-{F}(V1,V2,V4), P_equivalent-{F}(V3,V5,V6), P_equivalent-{F}(V7,V6,V8), P_equivalent-{F}(V5,V7,V9), P_equivalent-{F}(V8,V9,V4) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #228: exists( #3, #222 ), references = 1, size of lhs = 11:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), P_c-{F}(V1), P_a-{F}(V2), P_b-{F}(V3), P_equivalent-{F}(V2,V3,V0), P_equivalent-{F}(V1,V2,V4), P_equivalent-{F}(V3,V5,V6), P_equivalent-{F}(V7,V6,V8), P_equivalent-{F}(V5,V7,V9), P_equivalent-{F}(V8,V9,V4) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #274: exists( #3, #268 ), references = 1, size of lhs = 14:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_c-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_equivalent-{F}(V1,V5,V6), P_equivalent-{F}(V2,V3,V7), P_equivalent-{F}(V4,V7,V6), P_equivalent-{F}(V0,V8,V9), P_equivalent-{F}(V10,V9,V11), P_equivalent-{F}(V8,V10,V12), P_equivalent-{F}(V11,V12,V6) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #275: exists( #3, #269 ), references = 1, size of lhs = 14:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_c-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_equivalent-{F}(V1,V5,V6), P_equivalent-{F}(V2,V3,V7), P_equivalent-{F}(V4,V7,V6), P_equivalent-{F}(V0,V8,V9), P_equivalent-{F}(V10,V9,V11), P_equivalent-{F}(V8,V10,V12), P_equivalent-{F}(V11,V12,V6) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #276: exists( #3, #270 ), references = 1, size of lhs = 14:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), P_c-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_equivalent-{F}(V1,V5,V6), P_equivalent-{F}(V2,V3,V7), P_equivalent-{F}(V4,V7,V6), P_equivalent-{F}(V0,V8,V9), P_equivalent-{F}(V10,V9,V11), P_equivalent-{F}(V8,V10,V12), P_equivalent-{F}(V11,V12,V6) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #310: exists( #3, #141 ), references = 1, size of lhs = 21:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), is_a_theorem-{F}(V3), P_a-{F}(V4), P_b-{F}(V5), P_equivalent-{F}(V4,V5,V6), P_c-{F}(V7), P_equivalent-{F}(V6,V7,V8), P_equivalent-{F}(V7,V4,V9), P_equivalent-{F}(V5,V9,V10), P_equivalent-{F}(V3,V10,V11), P_equivalent-{F}(V1,V12,V13), P_equivalent-{F}(V12,V8,V14), P_equivalent-{F}(V2,V15,V16), P_equivalent-{F}(V17,V16,V14), P_equivalent-{F}(V15,V17,V11), P_equivalent-{F}(V0,V18,V19), P_equivalent-{F}(V20,V19,V21), P_equivalent-{F}(V18,V20,V22), P_equivalent-{F}(V21,V22,V13) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #311: exists( #3, #142 ), references = 1, size of lhs = 21:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), is_a_theorem-{F}(V3), P_a-{F}(V4), P_b-{F}(V5), P_equivalent-{F}(V4,V5,V6), P_c-{F}(V7), P_equivalent-{F}(V6,V7,V8), P_equivalent-{F}(V7,V4,V9), P_equivalent-{F}(V5,V9,V10), P_equivalent-{F}(V3,V10,V11), P_equivalent-{F}(V1,V12,V13), P_equivalent-{F}(V12,V8,V14), P_equivalent-{F}(V2,V15,V16), P_equivalent-{F}(V17,V16,V14), P_equivalent-{F}(V15,V17,V11), P_equivalent-{F}(V0,V18,V19), P_equivalent-{F}(V20,V19,V21), P_equivalent-{F}(V18,V20,V22), P_equivalent-{F}(V21,V22,V13) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #312: exists( #3, #143 ), references = 1, size of lhs = 21:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), is_a_theorem-{F}(V3), P_a-{F}(V4), P_b-{F}(V5), P_equivalent-{F}(V4,V5,V6), P_c-{F}(V7), P_equivalent-{F}(V6,V7,V8), P_equivalent-{F}(V7,V4,V9), P_equivalent-{F}(V5,V9,V10), P_equivalent-{F}(V3,V10,V11), P_equivalent-{F}(V1,V12,V13), P_equivalent-{F}(V12,V8,V14), P_equivalent-{F}(V2,V15,V16), P_equivalent-{F}(V17,V16,V14), P_equivalent-{F}(V15,V17,V11), P_equivalent-{F}(V0,V18,V19), P_equivalent-{F}(V20,V19,V21), P_equivalent-{F}(V18,V20,V22), P_equivalent-{F}(V21,V22,V13) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #316: exists( #3, #307 ), references = 1, size of lhs = 19:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), is_a_theorem-{F}(V3), P_a-{F}(V4), P_b-{F}(V5), P_equivalent-{F}(V4,V5,V6), P_c-{F}(V7), P_equivalent-{F}(V6,V7,V8), P_equivalent-{F}(V7,V4,V9), P_equivalent-{F}(V5,V9,V10), P_equivalent-{F}(V3,V10,V11), P_equivalent-{F}(V2,V12,V13), P_equivalent-{F}(V12,V14,V11), P_equivalent-{F}(V14,V13,V15), P_equivalent-{F}(V16,V8,V15), P_equivalent-{F}(V0,V17,V18), P_equivalent-{F}(V19,V18,V1), P_equivalent-{F}(V17,V19,V16) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #317: exists( #3, #308 ), references = 1, size of lhs = 19:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), is_a_theorem-{F}(V3), P_a-{F}(V4), P_b-{F}(V5), P_equivalent-{F}(V4,V5,V6), P_c-{F}(V7), P_equivalent-{F}(V6,V7,V8), P_equivalent-{F}(V7,V4,V9), P_equivalent-{F}(V5,V9,V10), P_equivalent-{F}(V3,V10,V11), P_equivalent-{F}(V2,V12,V13), P_equivalent-{F}(V12,V14,V11), P_equivalent-{F}(V14,V13,V15), P_equivalent-{F}(V16,V8,V15), P_equivalent-{F}(V0,V17,V18), P_equivalent-{F}(V19,V18,V1), P_equivalent-{F}(V17,V19,V16) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #318: exists( #3, #309 ), references = 1, size of lhs = 19:
% 3.91/4.09 is_a_theorem-{F}(V0), is_a_theorem-{F}(V1), is_a_theorem-{F}(V2), is_a_theorem-{F}(V3), P_a-{F}(V4), P_b-{F}(V5), P_equivalent-{F}(V4,V5,V6), P_c-{F}(V7), P_equivalent-{F}(V6,V7,V8), P_equivalent-{F}(V7,V4,V9), P_equivalent-{F}(V5,V9,V10), P_equivalent-{F}(V3,V10,V11), P_equivalent-{F}(V2,V12,V13), P_equivalent-{F}(V12,V14,V11), P_equivalent-{F}(V14,V13,V15), P_equivalent-{F}(V16,V8,V15), P_equivalent-{F}(V0,V17,V18), P_equivalent-{F}(V19,V18,V1), P_equivalent-{F}(V17,V19,V16) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #351: exists( #3, #349 ), references = 2, size of lhs = 15:
% 3.91/4.09 is_a_theorem-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_equivalent-{F}(V1,V2,V3), P_c-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_equivalent-{F}(V4,V1,V6), P_equivalent-{F}(V2,V6,V7), P_equivalent-{F}(V5,V7,V8), P_equivalent-{F}(V0,V9,V10), P_equivalent-{F}(V9,V11,V8), P_equivalent-{F}(V11,V12,V13), P_equivalent-{F}(V14,V13,V15), P_equivalent-{F}(V12,V14,V16), P_equivalent-{F}(V15,V16,V10) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #376: exists( #3, #351 ), references = 1, size of lhs = 13:
% 3.91/4.09 is_a_theorem-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_equivalent-{F}(V1,V2,V3), P_c-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_equivalent-{F}(V4,V1,V6), P_equivalent-{F}(V2,V6,V7), P_equivalent-{F}(V5,V7,V8), P_equivalent-{F}(V9,V10,V8), P_equivalent-{F}(V10,V11,V12), P_equivalent-{F}(V13,V12,V0), P_equivalent-{F}(V11,V13,V9) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #378: exists( #3, #375 ), references = 1, size of lhs = 11:
% 3.91/4.09 is_a_theorem-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_equivalent-{F}(V1,V2,V3), P_c-{F}(V4), P_equivalent-{F}(V3,V4,V5), P_equivalent-{F}(V4,V1,V6), P_equivalent-{F}(V2,V6,V7), P_equivalent-{F}(V7,V8,V9), P_equivalent-{F}(V10,V9,V0), P_equivalent-{F}(V8,V10,V5) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #381: exists( #3, #379 ), references = 2, size of lhs = 13:
% 3.91/4.09 P_a-{F}(V0), P_b-{F}(V1), P_equivalent-{F}(V0,V1,V2), P_c-{F}(V3), P_equivalent-{F}(V2,V3,V4), P_equivalent-{F}(V3,V0,V5), P_equivalent-{F}(V1,V5,V6), P_equivalent-{F}(V6,V7,V8), P_equivalent-{F}(V7,V9,V4), P_equivalent-{F}(V9,V10,V11), P_equivalent-{F}(V12,V11,V13), P_equivalent-{F}(V10,V12,V14), P_equivalent-{F}(V13,V14,V8) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #383: exists( #3, #380 ), references = 2, size of lhs = 13:
% 3.91/4.09 P_a-{F}(V0), P_b-{F}(V1), P_equivalent-{F}(V0,V1,V2), P_c-{F}(V3), P_equivalent-{F}(V2,V3,V4), P_equivalent-{F}(V3,V0,V5), P_equivalent-{F}(V1,V5,V6), P_equivalent-{F}(V6,V7,V8), P_equivalent-{F}(V7,V9,V4), P_equivalent-{F}(V9,V10,V11), P_equivalent-{F}(V12,V11,V13), P_equivalent-{F}(V10,V12,V14), P_equivalent-{F}(V13,V14,V8) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #386: exists( #3, #381 ), references = 1, size of lhs = 11:
% 3.91/4.09 P_a-{F}(V0), P_b-{F}(V1), P_equivalent-{F}(V0,V1,V2), P_c-{F}(V3), P_equivalent-{F}(V2,V3,V4), P_equivalent-{F}(V3,V0,V5), P_equivalent-{F}(V1,V5,V6), P_equivalent-{F}(V7,V8,V4), P_equivalent-{F}(V8,V9,V10), P_equivalent-{F}(V11,V10,V6), P_equivalent-{F}(V9,V11,V7) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #387: exists( #3, #383 ), references = 1, size of lhs = 11:
% 3.91/4.09 P_a-{F}(V0), P_b-{F}(V1), P_equivalent-{F}(V0,V1,V2), P_c-{F}(V3), P_equivalent-{F}(V2,V3,V4), P_equivalent-{F}(V3,V0,V5), P_equivalent-{F}(V1,V5,V6), P_equivalent-{F}(V7,V8,V4), P_equivalent-{F}(V8,V9,V10), P_equivalent-{F}(V11,V10,V6), P_equivalent-{F}(V9,V11,V7) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #390: exists( #3, #384 ), references = 1, size of lhs = 9:
% 3.91/4.09 P_a-{F}(V0), P_b-{F}(V1), P_equivalent-{F}(V0,V1,V2), P_c-{F}(V3), P_equivalent-{F}(V3,V0,V4), P_equivalent-{F}(V1,V4,V5), P_equivalent-{F}(V3,V6,V7), P_equivalent-{F}(V8,V7,V5), P_equivalent-{F}(V6,V8,V2) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #391: exists( #3, #385 ), references = 1, size of lhs = 9:
% 3.91/4.09 P_a-{F}(V0), P_b-{F}(V1), P_equivalent-{F}(V0,V1,V2), P_c-{F}(V3), P_equivalent-{F}(V3,V0,V4), P_equivalent-{F}(V1,V4,V5), P_equivalent-{F}(V3,V6,V7), P_equivalent-{F}(V8,V7,V5), P_equivalent-{F}(V6,V8,V2) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #394: exists( #3, #388 ), references = 2, size of lhs = 7:
% 3.91/4.09 P_a-{F}(V0), P_b-{F}(V1), P_equivalent-{F}(V0,V1,V2), P_c-{F}(V3), P_equivalent-{F}(V3,V0,V4), P_equivalent-{F}(V3,V5,V4), P_equivalent-{F}(V5,V1,V2) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #397: exists( #3, #392 ), references = 1, size of lhs = 3:
% 3.91/4.09 P_a-{F}(V0), P_b-{F}(V0), P_c-{F}(V0) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #399: exists( #3, #394 ), references = 1, size of lhs = 4:
% 3.91/4.09 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_equivalent-{F}(V0,V1,V3) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #401: exists( #3, #398 ), references = 1, size of lhs = 3:
% 3.91/4.09 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #403: exists( #6, #400 ), references = 1, size of lhs = 2:
% 3.91/4.09 P_a-{F}(V0), P_b-{F}(V1) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #405: exists( #5, #402 ), references = 1, size of lhs = 1:
% 3.91/4.09 P_a-{F}(V0) | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 #407: exists( #4, #404 ), references = 1, size of lhs = 0:
% 3.91/4.09 FALSE | FALSE
% 3.91/4.09 (used 0 times, uses = {})
% 3.91/4.09
% 3.91/4.09 number of learnt formulas = 86
% 3.91/4.09
% 3.91/4.09
% 3.91/4.09 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.91/4.09
% 3.91/4.09 randbase = 1
%------------------------------------------------------------------------------