TSTP Solution File: REL002+1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : REL002+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n024.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 06:14:37 EDT 2022
% Result : Theorem 14.23s 14.38s
% Output : Refutation 14.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL002+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n024.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 : Sat Jul 23 00:36:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 14.23/14.38 GeoParameters:
% 14.23/14.38
% 14.23/14.38 tptp_input = 1
% 14.23/14.38 tptp_output = 0
% 14.23/14.38 nonempty = 1
% 14.23/14.38 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.23/14.38 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 14.23/14.38
% 14.23/14.38
% 14.23/14.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.23/14.38 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.23/14.38
% 14.23/14.38 RuleSystem INPUT:
% 14.23/14.38
% 14.23/14.38 Initial Rules:
% 14.23/14.38 #0: input, references = 7, size of lhs = 3:
% 14.23/14.38 P_join-{F}(V0,V1,V2), P_join-{F}(V1,V0,V3), V2 == V3 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #1: input, references = 8, size of lhs = 5:
% 14.23/14.38 P_join-{F}(V1,V2,V3), P_join-{F}(V0,V3,V4), P_join-{F}(V0,V1,V5), P_join-{F}(V5,V2,V6), V4 == V6 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #2: input, references = 10, size of lhs = 8:
% 14.23/14.38 P_complement-{F}(V0,V2), P_complement-{F}(V1,V3), P_join-{F}(V2,V3,V4), P_complement-{F}(V4,V5), P_join-{F}(V2,V1,V6), P_complement-{F}(V6,V7), P_join-{F}(V5,V7,V8), V0 == V8 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #3: input, references = 9, size of lhs = 6:
% 14.23/14.38 P_meet-{F}(V0,V1,V2), P_complement-{F}(V0,V3), P_complement-{F}(V1,V4), P_join-{F}(V3,V4,V5), P_complement-{F}(V5,V6), V2 == V6 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #4: input, references = 3, size of lhs = 5:
% 14.23/14.38 P_composition-{F}(V1,V2,V3), P_composition-{F}(V0,V3,V4), P_composition-{F}(V0,V1,V5), P_composition-{F}(V5,V2,V6), V4 == V6 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #5: input, references = 4, size of lhs = 3:
% 14.23/14.38 P_one-{F}(V0), P_composition-{F}(V1,V0,V2), V2 == V1 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #6: input, references = 8, size of lhs = 7:
% 14.23/14.38 P_one-{F}(V0), P_join-{F}(V1,V2,V4), P_composition-{F}(V4,V3,V5), P_composition-{F}(V1,V3,V6), P_composition-{F}(V2,V3,V7), P_join-{F}(V6,V7,V8), V5 == V8 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #7: input, references = 4, size of lhs = 4:
% 14.23/14.38 P_one-{F}(V0), P_converse-{F}(V1,V2), P_converse-{F}(V2,V3), V3 == V1 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #8: input, references = 5, size of lhs = 7:
% 14.23/14.38 P_one-{F}(V0), P_join-{F}(V1,V2,V3), P_converse-{F}(V3,V4), P_converse-{F}(V1,V5), P_converse-{F}(V2,V6), P_join-{F}(V5,V6,V7), V4 == V7 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #9: input, references = 5, size of lhs = 7:
% 14.23/14.38 P_one-{F}(V0), P_composition-{F}(V1,V2,V3), P_converse-{F}(V3,V4), P_converse-{F}(V2,V5), P_converse-{F}(V1,V6), P_composition-{F}(V5,V6,V7), V4 == V7 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #10: input, references = 5, size of lhs = 8:
% 14.23/14.38 P_one-{F}(V0), P_converse-{F}(V1,V3), P_composition-{F}(V1,V2,V4), P_complement-{F}(V4,V5), P_composition-{F}(V3,V5,V6), P_complement-{F}(V2,V7), P_join-{F}(V6,V7,V8), V8 == V7 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #11: input, references = 5, size of lhs = 5:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V2,V3), P_join-{F}(V2,V3,V4), V1 == V4 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #12: input, references = 4, size of lhs = 6:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_zero-{F}(V2), P_complement-{F}(V3,V4), P_meet-{F}(V3,V4,V5), V2 == V5 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #13: input, references = 4, size of lhs = 3:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_zero-{F}(V2) | EXISTS V3: pppp0-{T}(V1,V3)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #14: input, references = 4, size of lhs = 2:
% 14.23/14.38 pppp0-{F}(V0,V1), P_join-{F}(V1,V0,V0) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #15: input, references = 16, size of lhs = 2:
% 14.23/14.38 #-{F} V0, #-{F} V1 | EXISTS V2: P_join-{T}(V0,V1,V2)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #16: input, references = 15, size of lhs = 1:
% 14.23/14.38 #-{F} V0 | EXISTS V1: P_complement-{T}(V0,V1)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #17: input, references = 10, size of lhs = 2:
% 14.23/14.38 #-{F} V0, #-{F} V1 | EXISTS V2: P_meet-{T}(V0,V1,V2)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #18: input, references = 12, size of lhs = 2:
% 14.23/14.38 #-{F} V0, #-{F} V1 | EXISTS V2: P_composition-{T}(V0,V1,V2)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #19: input, references = 4, size of lhs = 0:
% 14.23/14.38 FALSE | EXISTS V0: P_one-{T}(V0)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #20: input, references = 17, size of lhs = 1:
% 14.23/14.38 #-{F} V0 | EXISTS V1: P_converse-{T}(V0,V1)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #21: input, references = 4, size of lhs = 0:
% 14.23/14.38 FALSE | EXISTS V0: P_top-{T}(V0)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #22: input, references = 5, size of lhs = 0:
% 14.23/14.38 FALSE | EXISTS V0: P_zero-{T}(V0)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 number of initial rules = 23
% 14.23/14.38
% 14.23/14.38 Simplifiers:
% 14.23/14.38 #23: unsound, references = 3, size of lhs = 3:
% 14.23/14.38 P_join-{F}(V0,V1,V2), P_join-{F}(V0,V1,V5), V2 == V5 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #24: unsound, references = 3, size of lhs = 3:
% 14.23/14.38 P_complement-{F}(V0,V1), P_complement-{F}(V0,V3), V1 == V3 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #25: unsound, references = 3, size of lhs = 3:
% 14.23/14.38 P_meet-{F}(V0,V1,V2), P_meet-{F}(V0,V1,V5), V2 == V5 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #26: unsound, references = 3, size of lhs = 3:
% 14.23/14.38 P_composition-{F}(V0,V1,V2), P_composition-{F}(V0,V1,V5), V2 == V5 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #27: unsound, references = 3, size of lhs = 3:
% 14.23/14.38 P_one-{F}(V0), P_one-{F}(V1), V0 == V1 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #28: unsound, references = 3, size of lhs = 3:
% 14.23/14.38 P_converse-{F}(V0,V1), P_converse-{F}(V0,V3), V1 == V3 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #29: unsound, references = 3, size of lhs = 3:
% 14.23/14.38 P_top-{F}(V0), P_top-{F}(V1), V0 == V1 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #30: unsound, references = 3, size of lhs = 3:
% 14.23/14.38 P_zero-{F}(V0), P_zero-{F}(V1), V0 == V1 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #31: unsound, references = 3, size of lhs = 3:
% 14.23/14.38 pppp0-{F}(V0,V1), pppp0-{F}(V0,V3), V1 == V3 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #32: unsound, references = 3, size of lhs = 3:
% 14.23/14.38 pppp0-{F}(V0,V1), pppp0-{F}(V2,V3), V0 == V2 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 number of simplifiers = 10
% 14.23/14.38
% 14.23/14.38 Learnt:
% 14.23/14.38 #34: exists( #17, #12 ), references = 5, size of lhs = 4:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_zero-{F}(V2), P_complement-{F}(V3,V4) | P_meet-{T}(V3,V4,V2)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #36: exists( #20, #7 ), references = 20, size of lhs = 2:
% 14.23/14.38 P_one-{F}(V0), P_converse-{F}(V1,V2) | P_converse-{T}(V2,V1)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #38: exists( #15, #8 ), references = 10, size of lhs = 5:
% 14.23/14.38 P_one-{F}(V0), P_converse-{F}(V1,V2), P_join-{F}(V1,V3,V4), P_converse-{F}(V4,V5), P_converse-{F}(V3,V6) | P_join-{T}(V2,V6,V5)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #40: exists( #15, #11 ), references = 22, size of lhs = 3:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V2,V3) | P_join-{T}(V2,V3,V1)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #44: exists( #16, #42 ), references = 2, size of lhs = 4:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V2,V1), P_meet-{F}(V2,V1,V3) | P_complement-{T}(V1,V3)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #49: exists( #15, #1 ), references = 14, size of lhs = 3:
% 14.23/14.38 P_join-{F}(V0,V1,V2), P_join-{F}(V3,V0,V4), P_join-{F}(V4,V1,V5) | P_join-{T}(V3,V2,V5)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #51: exists( #18, #5 ), references = 22, size of lhs = 2:
% 14.23/14.38 P_one-{F}(V0), #-{F} V1 | P_composition-{T}(V1,V0,V1)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #54: exists( #15, #0 ), references = 20, size of lhs = 1:
% 14.23/14.38 P_join-{F}(V0,V1,V2) | P_join-{T}(V1,V0,V2)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #77: exists( #18, #9 ), references = 18, size of lhs = 5:
% 14.23/14.38 P_one-{F}(V0), P_converse-{F}(V1,V2), P_composition-{F}(V3,V1,V4), P_converse-{F}(V4,V5), P_converse-{F}(V3,V6) | P_composition-{T}(V2,V6,V5)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #102: exists( #16, #100 ), references = 2, size of lhs = 4:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), pppp0-{F}(V1,V2), P_join-{F}(V2,V3,V3) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #121: mergings( V2 == V4, V5 == V6; #116 ), references = 1, size of lhs = 6:
% 14.23/14.38 P_top-{F}(V0), P_one-{F}(V1), P_converse-{F}(V0,V2), V0 == V2, P_converse-{F}(V2,V0), P_join-{F}(V2,V3,V3) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #125: mergings( V2 == V4, V5 == V6, V7 == V9; #117 ), references = 1, size of lhs = 7:
% 14.23/14.38 P_top-{F}(V0), P_one-{F}(V1), P_converse-{F}(V0,V2), P_converse-{F}(V3,V0), V0 == V3, P_join-{F}(V3,V4,V4), P_join-{F}(V2,V5,V3) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #130: mergings( V9 == V11, V2 == V4, V4 == V5, V6 == V7; #118 ), references = 1, size of lhs = 8:
% 14.23/14.38 P_top-{F}(V0), P_one-{F}(V1), P_converse-{F}(V0,V2), P_converse-{F}(V3,V4), V4 == V2, P_join-{F}(V3,V5,V5), P_composition-{F}(V3,V6,V2), P_composition-{F}(V0,V6,V4) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #144: mergings( V2 == V3, V3 == V4, V4 == V5; #138 ), references = 2, size of lhs = 3:
% 14.23/14.38 P_top-{F}(V0), P_join-{F}(V0,V0,V0), P_one-{F}(V1) | P_converse-{T}(V0,V0)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #152: mergings( V2 == V0, V0 == V3; #149 ), references = 1, size of lhs = 1:
% 14.23/14.38 P_one-{F}(V0) | P_converse-{T}(V0,V0)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #154: exists( #15, #10 ), references = 15, size of lhs = 6:
% 14.23/14.38 P_one-{F}(V0), P_converse-{F}(V1,V2), P_composition-{F}(V1,V3,V4), P_complement-{F}(V4,V5), P_composition-{F}(V2,V5,V6), P_complement-{F}(V3,V7) | P_join-{T}(V6,V7,V7)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #178: mergings( V2 == V3, V3 == V4, V4 == V5; #172 ), references = 1, size of lhs = 4:
% 14.23/14.38 P_one-{F}(V0), P_complement-{F}(V1,V0), P_complement-{F}(V2,V3), P_composition-{F}(V3,V2,V1) | P_converse-{T}(V3,V3)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #181: exists( #17, #3 ), references = 3, size of lhs = 4:
% 14.23/14.38 P_complement-{F}(V0,V1), P_complement-{F}(V2,V3), P_join-{F}(V1,V3,V4), P_complement-{F}(V4,V5) | P_meet-{T}(V0,V2,V5)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #190: exists( #15, #6 ), references = 6, size of lhs = 5:
% 14.23/14.38 P_one-{F}(V0), P_join-{F}(V1,V2,V3), P_composition-{F}(V3,V4,V5), P_composition-{F}(V1,V4,V6), P_composition-{F}(V2,V4,V7) | P_join-{T}(V6,V7,V5)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #200: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6; #195 ), references = 1, size of lhs = 5:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), pppp0-{F}(V1,V2), P_converse-{F}(V0,V3), P_join-{F}(V3,V3,V3) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #207: mergings( V0 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8; #201 ), references = 3, size of lhs = 5:
% 14.23/14.38 P_zero-{F}(V0), P_one-{F}(V1), P_top-{F}(V2), P_converse-{F}(V1,V3), P_join-{F}(V3,V3,V3) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #233: mergings( V2 == V3, V3 == V4, V4 == V5; #227 ), references = 1, size of lhs = 10:
% 14.23/14.38 P_one-{F}(V0), P_converse-{F}(V0,V1), P_converse-{F}(V2,V1), P_composition-{F}(V2,V3,V4), P_complement-{F}(V4,V5), P_complement-{F}(V3,V6), P_join-{F}(V7,V6,V8), P_join-{F}(V7,V5,V9), P_join-{F}(V9,V6,V10), V8 == V10 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #240: mergings( V3 == V4, V4 == V5, V5 == V6; #236 ), references = 5, size of lhs = 10:
% 14.23/14.38 P_one-{F}(V0), P_converse-{F}(V0,V1), P_converse-{F}(V2,V1), P_composition-{F}(V2,V3,V4), P_complement-{F}(V4,V5), P_complement-{F}(V3,V6), P_join-{F}(V6,V7,V8), P_join-{F}(V7,V9,V10), P_join-{F}(V11,V5,V10), P_join-{F}(V11,V6,V12) | P_join-{T}(V8,V9,V12)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #244: exists( #16, #3 ), references = 17, size of lhs = 4:
% 14.23/14.38 P_complement-{F}(V0,V1), P_meet-{F}(V0,V2,V3), P_complement-{F}(V2,V4), P_join-{F}(V1,V4,V5) | P_complement-{T}(V5,V3)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #256: exists( #15, #254 ), references = 6, size of lhs = 11:
% 14.23/14.38 P_complement-{F}(V0,V1), P_complement-{F}(V2,V1), P_join-{F}(V1,V3,V4), P_join-{F}(V3,V5,V6), P_complement-{F}(V7,V6), P_meet-{F}(V0,V7,V8), P_complement-{F}(V9,V6), P_join-{F}(V1,V9,V10), P_complement-{F}(V10,V11), P_join-{F}(V8,V11,V12), V2 == V12 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #259: exists( #16, #257 ), references = 2, size of lhs = 11:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V2,V3), P_complement-{F}(V4,V3), V4 == V1, P_join-{F}(V3,V5,V6), P_join-{F}(V5,V7,V8), P_complement-{F}(V9,V8), P_meet-{F}(V2,V9,V10), P_complement-{F}(V11,V8), P_join-{F}(V3,V11,V10) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #269: exists( #15, #267 ), references = 1, size of lhs = 12:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_zero-{F}(V2), P_complement-{F}(V3,V4), P_join-{F}(V4,V5,V6), P_join-{F}(V5,V7,V8), P_complement-{F}(V9,V8), P_meet-{F}(V3,V9,V10), P_complement-{F}(V10,V11), P_join-{F}(V10,V11,V12), P_complement-{F}(V12,V13), V2 == V13 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #271: exists( #16, #268 ), references = 1, size of lhs = 10:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_zero-{F}(V2), P_complement-{F}(V3,V4), P_join-{F}(V4,V5,V6), P_join-{F}(V5,V7,V8), P_complement-{F}(V9,V8), P_meet-{F}(V3,V9,V10), P_complement-{F}(V10,V11), P_join-{F}(V10,V11,V12) | P_complement-{T}(V12,V2)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #309: exists( #15, #305 ), references = 1, size of lhs = 8:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V2,V3), P_join-{F}(V3,V4,V5), P_join-{F}(V6,V5,V5), P_meet-{F}(V2,V7,V6), P_complement-{F}(V7,V8), P_join-{F}(V4,V9,V8) | P_join-{T}(V9,V5,V1)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #310: exists( #15, #306 ), references = 1, size of lhs = 8:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V2,V3), P_join-{F}(V3,V4,V5), P_join-{F}(V5,V6,V5), P_meet-{F}(V2,V7,V6), P_complement-{F}(V7,V8), P_join-{F}(V4,V9,V8) | P_join-{T}(V9,V5,V1)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #342: exists( #20, #8 ), references = 1, size of lhs = 5:
% 14.23/14.38 P_one-{F}(V0), P_converse-{F}(V1,V2), P_join-{F}(V1,V3,V4), P_converse-{F}(V3,V5), P_join-{F}(V2,V5,V6) | P_converse-{T}(V4,V6)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #360: mergings( V3 == V5, V4 == V6; #355 ), references = 1, size of lhs = 9:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V2,V3), P_complement-{F}(V4,V5), P_join-{F}(V3,V5,V6), P_complement-{F}(V7,V6), P_meet-{F}(V7,V6,V8), P_join-{F}(V1,V8,V9), V1 == V9 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #361: exists( #17, #353 ), references = 1, size of lhs = 12:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_join-{F}(V2,V1,V1), P_complement-{F}(V3,V2), P_join-{F}(V2,V4,V1), P_join-{F}(V4,V4,V5), V3 == V5, P_complement-{F}(V6,V7), P_complement-{F}(V8,V9), P_join-{F}(V7,V9,V10), P_complement-{F}(V11,V10), P_meet-{F}(V11,V10,V4) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #363: mergings( V3 == V5; #357 ), references = 1, size of lhs = 12:
% 14.23/14.38 P_top-{F}(V0), P_one-{F}(V1), P_composition-{F}(V2,V0,V0), P_converse-{F}(V2,V3), P_complement-{F}(V4,V5), P_complement-{F}(V6,V7), P_join-{F}(V5,V7,V8), P_complement-{F}(V9,V8), P_meet-{F}(V9,V8,V10), P_composition-{F}(V3,V10,V11), P_join-{F}(V11,V10,V12), V12 == V10 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #392: exists( #16, #389 ), references = 1, size of lhs = 6:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V1,V2), P_complement-{F}(V3,V4), P_meet-{F}(V3,V4,V5), V5 == V2 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #394: exists( #16, #391 ), references = 2, size of lhs = 4:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V2,V3), P_meet-{F}(V2,V3,V4) | P_complement-{T}(V1,V4)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #411: mergings( V12 == V13, V16 == V18, V2 == V3, V3 == V4, V4 == V5, V5 == V8, V6 == V10, V10 == V11; #402 ), references = 2, size of lhs = 11:
% 14.23/14.38 P_zero-{F}(V0), P_one-{F}(V1), P_top-{F}(V2), P_converse-{F}(V1,V3), P_converse-{F}(V3,V3), P_complement-{F}(V4,V5), P_join-{F}(V5,V6,V3), P_join-{F}(V6,V7,V8), P_join-{F}(V9,V5,V8), P_join-{F}(V7,V10,V3), P_join-{F}(V8,V10,V3) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #431: mergings( V2 == V3, V3 == V5, V5 == V6, V6 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V14, V12 == V7, V7 == V16, V4 == V16, V16 == V15, V0 == V13; #417 ), references = 1, size of lhs = 5:
% 14.23/14.38 P_zero-{F}(V0), P_one-{F}(V1), P_top-{F}(V2), P_converse-{F}(V1,V2), P_converse-{F}(V2,V2) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #445: mergings( V1 == V2, V2 == V4, V4 == V5, V5 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V12, V11 == V6, V6 == V14, V3 == V14, V14 == V13; #432 ), references = 1, size of lhs = 4:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_converse-{F}(V0,V1), P_converse-{F}(V1,V1) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #465: mergings( V9 == V12, V2 == V3, V3 == V4, V4 == V5, V5 == V7, V12 == V10; #457 ), references = 1, size of lhs = 7:
% 14.23/14.38 P_zero-{F}(V0), P_one-{F}(V1), P_top-{F}(V2), P_converse-{F}(V1,V3), P_converse-{F}(V3,V4), P_composition-{F}(V4,V3,V3), P_complement-{F}(V5,V3) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #492: exists( #18, #6 ), references = 1, size of lhs = 5:
% 14.23/14.38 P_one-{F}(V0), P_join-{F}(V1,V2,V3), P_composition-{F}(V1,V4,V5), P_composition-{F}(V2,V4,V6), P_join-{F}(V5,V6,V7) | P_composition-{T}(V3,V4,V7)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #503: mergings( V3 == V4; #501 ), references = 1, size of lhs = 7:
% 14.23/14.38 P_one-{F}(V0), P_converse-{F}(V1,V2), P_join-{F}(V2,V3,V2), P_composition-{F}(V1,V4,V5), P_complement-{F}(V5,V6), P_complement-{F}(V4,V7), P_composition-{F}(V3,V6,V7) | P_composition-{T}(V2,V6,V7)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #543: exists( #18, #541 ), references = 1, size of lhs = 14:
% 14.23/14.38 P_one-{F}(V0), P_converse-{F}(V1,V2), P_composition-{F}(V1,V3,V4), P_complement-{F}(V4,V5), P_complement-{F}(V3,V6), P_complement-{F}(V7,V6), P_complement-{F}(V8,V6), P_complement-{F}(V9,V6), P_meet-{F}(V7,V9,V10), P_complement-{F}(V11,V6), P_join-{F}(V6,V11,V12), P_complement-{F}(V12,V13), P_join-{F}(V10,V13,V14), V8 == V14 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #557: exists( #18, #554 ), references = 1, size of lhs = 10:
% 14.23/14.38 P_one-{F}(V0), P_complement-{F}(V1,V2), P_complement-{F}(V3,V4), P_join-{F}(V2,V4,V5), P_complement-{F}(V5,V6), P_join-{F}(V2,V3,V7), P_complement-{F}(V7,V8), P_composition-{F}(V9,V10,V6), P_composition-{F}(V11,V10,V8), P_join-{F}(V9,V11,V12) | P_composition-{T}(V12,V10,V1)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #571: mergings( V6 == V7, V11 == V16, V13 == V17, V3 == V4; #564 ), references = 1, size of lhs = 15:
% 14.23/14.38 P_one-{F}(V0), P_complement-{F}(V1,V2), P_complement-{F}(V3,V4), P_join-{F}(V2,V4,V5), P_complement-{F}(V5,V6), P_join-{F}(V2,V3,V7), P_complement-{F}(V7,V8), P_complement-{F}(V9,V6), P_complement-{F}(V10,V8), P_join-{F}(V6,V10,V11), P_complement-{F}(V11,V12), P_join-{F}(V2,V12,V13), V9 == V13, P_composition-{F}(V14,V15,V6), P_composition-{F}(V16,V15,V8) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #576: mergings( V6 == V7, V11 == V16, V13 == V18, V3 == V4; #565 ), references = 1, size of lhs = 18:
% 14.23/14.38 P_one-{F}(V0), P_complement-{F}(V1,V2), P_complement-{F}(V3,V4), P_join-{F}(V2,V4,V5), P_complement-{F}(V5,V6), P_join-{F}(V2,V3,V7), P_complement-{F}(V7,V8), P_complement-{F}(V9,V6), P_complement-{F}(V10,V6), P_complement-{F}(V8,V11), P_complement-{F}(V12,V11), P_meet-{F}(V9,V12,V13), P_join-{F}(V13,V2,V14), V10 == V14, P_composition-{F}(V15,V16,V6), P_composition-{F}(V17,V16,V8), P_join-{F}(V6,V18,V19), P_join-{F}(V18,V20,V11) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #581: mergings( V10 == V13, V17 == V18, V3 == V4, V4 == V5; #566 ), references = 1, size of lhs = 18:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V2,V3), P_complement-{F}(V4,V5), P_complement-{F}(V6,V5), V6 == V1, P_complement-{F}(V7,V5), P_join-{F}(V8,V3,V7), P_join-{F}(V8,V2,V9), P_complement-{F}(V9,V10), P_complement-{F}(V10,V11), P_complement-{F}(V12,V11), P_meet-{F}(V4,V12,V13), P_complement-{F}(V13,V8), P_composition-{F}(V14,V15,V5), P_composition-{F}(V16,V15,V10), P_join-{F}(V5,V17,V18), P_join-{F}(V17,V19,V11) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #589: mergings( V6 == V7, V11 == V17, V13 == V19, V3 == V4; #582 ), references = 1, size of lhs = 15:
% 14.23/14.38 P_one-{F}(V0), P_complement-{F}(V1,V2), P_complement-{F}(V3,V4), P_join-{F}(V2,V4,V5), P_complement-{F}(V5,V6), P_join-{F}(V2,V3,V7), P_complement-{F}(V7,V8), P_complement-{F}(V9,V6), P_complement-{F}(V10,V8), P_join-{F}(V6,V10,V11), P_complement-{F}(V11,V12), P_join-{F}(V2,V12,V13), V9 == V13, P_composition-{F}(V14,V15,V6), P_composition-{F}(V16,V15,V8) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #594: mergings( V6 == V7, V11 == V17, V13 == V20, V3 == V4; #583 ), references = 1, size of lhs = 18:
% 14.23/14.38 P_one-{F}(V0), P_complement-{F}(V1,V2), P_complement-{F}(V3,V4), P_join-{F}(V2,V4,V5), P_complement-{F}(V5,V6), P_join-{F}(V2,V3,V7), P_complement-{F}(V7,V8), P_complement-{F}(V9,V6), P_complement-{F}(V10,V6), P_complement-{F}(V8,V11), P_complement-{F}(V12,V11), P_meet-{F}(V9,V12,V13), P_join-{F}(V13,V2,V14), V10 == V14, P_composition-{F}(V15,V16,V6), P_composition-{F}(V17,V16,V8), P_join-{F}(V6,V18,V19), P_join-{F}(V18,V20,V11) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #599: mergings( V10 == V14, V18 == V20, V3 == V4, V4 == V5; #584 ), references = 1, size of lhs = 18:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V2,V3), P_complement-{F}(V4,V5), P_complement-{F}(V6,V5), V6 == V1, P_complement-{F}(V7,V5), P_join-{F}(V8,V3,V7), P_join-{F}(V8,V2,V9), P_complement-{F}(V9,V10), P_complement-{F}(V10,V11), P_complement-{F}(V12,V11), P_meet-{F}(V4,V12,V13), P_complement-{F}(V13,V8), P_composition-{F}(V14,V15,V5), P_composition-{F}(V16,V15,V10), P_join-{F}(V5,V17,V18), P_join-{F}(V17,V19,V11) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #624: mergings( V11 == V13, V20 == V21, V15 == V17, V3 == V4, V4 == V6, V6 == V7; #615 ), references = 2, size of lhs = 17:
% 14.23/14.38 P_top-{F}(V0), P_one-{F}(V1), P_complement-{F}(V0,V2), P_complement-{F}(V3,V4), P_complement-{F}(V5,V6), P_join-{F}(V4,V6,V7), P_complement-{F}(V8,V7), P_join-{F}(V7,V9,V7), P_complement-{F}(V10,V7), P_composition-{F}(V11,V1,V10), P_complement-{F}(V12,V10), P_complement-{F}(V13,V14), P_join-{F}(V2,V14,V15), V7 == V15, P_join-{F}(V14,V16,V12), P_complement-{F}(V16,V17), P_join-{F}(V14,V17,V7) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #632: mergings( V14 == V16, V18 == V20, V3 == V4, V4 == V6, V6 == V7, V7 == V8, V5 == V9; #616 ), references = 2, size of lhs = 16:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V1,V2), P_complement-{F}(V2,V3), P_complement-{F}(V4,V5), P_complement-{F}(V6,V7), P_join-{F}(V5,V7,V8), V8 == V1, P_complement-{F}(V9,V8), P_join-{F}(V8,V10,V8), P_join-{F}(V3,V11,V8), P_complement-{F}(V12,V11), P_join-{F}(V3,V12,V13), P_complement-{F}(V13,V14), P_complement-{F}(V14,V8), P_composition-{F}(V15,V0,V14) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #639: mergings( V27 == V28, V19 == V24, V3 == V4, V4 == V6, V6 == V9, V9 == V10; #617 ), references = 2, size of lhs = 23:
% 14.23/14.38 P_top-{F}(V0), P_one-{F}(V1), P_converse-{F}(V1,V2), P_converse-{F}(V3,V2), P_complement-{F}(V4,V5), P_complement-{F}(V6,V7), P_join-{F}(V5,V7,V8), P_composition-{F}(V3,V9,V10), P_complement-{F}(V10,V11), P_complement-{F}(V9,V12), P_join-{F}(V12,V8,V13), P_complement-{F}(V13,V14), P_join-{F}(V15,V11,V0), P_join-{F}(V15,V12,V16), P_complement-{F}(V16,V17), P_composition-{F}(V18,V1,V14), P_complement-{F}(V19,V14), P_complement-{F}(V20,V21), P_join-{F}(V21,V17,V22), V8 == V22, P_join-{F}(V21,V23,V19), P_complement-{F}(V23,V24), P_join-{F}(V21,V24,V8) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #743: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6; #736 ), references = 1, size of lhs = 18:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V1,V2), P_complement-{F}(V2,V3), V3 == V1, P_complement-{F}(V4,V3), P_complement-{F}(V5,V3), P_complement-{F}(V6,V3), P_complement-{F}(V7,V3), P_complement-{F}(V8,V3), P_join-{F}(V3,V8,V9), P_complement-{F}(V9,V10), P_complement-{F}(V10,V3), P_composition-{F}(V11,V0,V10), P_converse-{F}(V0,V12), P_converse-{F}(V13,V12), P_composition-{F}(V13,V4,V14), P_complement-{F}(V14,V3) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #748: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V7; #737 ), references = 1, size of lhs = 19:
% 14.23/14.38 P_top-{F}(V0), P_one-{F}(V1), P_complement-{F}(V0,V2), P_converse-{F}(V1,V3), P_converse-{F}(V4,V3), P_complement-{F}(V5,V6), P_composition-{F}(V4,V5,V7), P_complement-{F}(V7,V6), P_complement-{F}(V8,V6), P_complement-{F}(V9,V6), P_complement-{F}(V10,V6), P_complement-{F}(V11,V6), P_join-{F}(V2,V6,V12), V6 == V12, P_complement-{F}(V13,V6), P_join-{F}(V6,V13,V14), P_complement-{F}(V14,V15), P_complement-{F}(V15,V6), P_composition-{F}(V16,V1,V15) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #754: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V7, V8 == V10; #738 ), references = 1, size of lhs = 25:
% 14.23/14.38 P_top-{F}(V0), P_one-{F}(V1), P_converse-{F}(V1,V2), P_converse-{F}(V3,V2), P_converse-{F}(V4,V2), P_complement-{F}(V5,V6), P_complement-{F}(V7,V6), P_complement-{F}(V8,V6), P_composition-{F}(V4,V9,V8), P_complement-{F}(V9,V10), P_complement-{F}(V11,V10), P_complement-{F}(V12,V10), P_join-{F}(V6,V12,V13), P_complement-{F}(V13,V14), P_composition-{F}(V15,V1,V14), P_complement-{F}(V16,V14), P_join-{F}(V17,V10,V16), P_complement-{F}(V18,V17), P_composition-{F}(V3,V18,V19), P_complement-{F}(V19,V20), P_join-{F}(V21,V20,V0), P_join-{F}(V21,V17,V22), P_complement-{F}(V22,V23), P_join-{F}(V6,V23,V24), V10 == V24 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #778: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V20 == V21; #767 ), references = 1, size of lhs = 16:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V1,V2), P_complement-{F}(V2,V3), V3 == V1, P_complement-{F}(V4,V3), P_complement-{F}(V5,V3), P_complement-{F}(V6,V3), P_complement-{F}(V7,V3), P_join-{F}(V3,V7,V8), P_complement-{F}(V8,V9), P_complement-{F}(V9,V3), P_composition-{F}(V10,V0,V9), P_converse-{F}(V0,V11), P_converse-{F}(V11,V11), P_complement-{F}(V12,V3) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #787: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V10, V12 == V13; #768 ), references = 1, size of lhs = 17:
% 14.23/14.38 P_top-{F}(V0), P_one-{F}(V1), P_complement-{F}(V0,V2), P_converse-{F}(V1,V3), P_converse-{F}(V3,V3), P_complement-{F}(V4,V5), P_complement-{F}(V6,V5), P_complement-{F}(V7,V5), P_complement-{F}(V8,V5), P_complement-{F}(V9,V5), P_join-{F}(V2,V5,V10), V5 == V10, P_complement-{F}(V11,V5), P_join-{F}(V5,V11,V12), P_complement-{F}(V12,V13), P_complement-{F}(V13,V5), P_composition-{F}(V14,V1,V13) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #809: mergings( V20 == V21, V14 == V23, V26 == V27, V29 == V7, V27 == V31, V31 == V35, V2 == V3, V3 == V4, V4 == V5, V5 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V15, V6 == V16, V16 == V17, V17 == V25, V7 == V23, V21 == V24; #769 ), references = 1, size of lhs = 24:
% 14.23/14.38 P_top-{F}(V0), P_one-{F}(V1), P_composition-{F}(V0,V2,V0), P_converse-{F}(V2,V3), P_converse-{F}(V3,V4), P_converse-{F}(V1,V4), P_converse-{F}(V4,V4), P_complement-{F}(V0,V5), P_join-{F}(V6,V5,V0), P_join-{F}(V7,V0,V0), P_join-{F}(V8,V7,V0), P_join-{F}(V9,V8,V0), P_complement-{F}(V10,V8), P_complement-{F}(V11,V8), P_join-{F}(V8,V5,V12), V8 == V12, P_complement-{F}(V13,V8), P_complement-{F}(V14,V8), P_complement-{F}(V15,V8), P_join-{F}(V8,V15,V16), P_complement-{F}(V16,V17), P_composition-{F}(V18,V1,V17), P_join-{F}(V5,V8,V19), P_complement-{F}(V19,V17) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #839: mergings( V2 == V3, V3 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V15 == V16, V4 == V14; #824 ), references = 2, size of lhs = 6:
% 14.23/14.38 P_zero-{F}(V0), P_one-{F}(V1), P_top-{F}(V2), P_converse-{F}(V1,V3), P_converse-{F}(V3,V3), P_composition-{F}(V4,V1,V0) | P_complement-{T}(V0,V2)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #899: mergings( V3 == V4; #897 ), references = 3, size of lhs = 6:
% 14.23/14.38 P_one-{F}(V0), P_join-{F}(V1,V2,V1), P_join-{F}(V1,V3,V4), P_composition-{F}(V4,V5,V6), P_composition-{F}(V3,V5,V7), P_composition-{F}(V2,V5,V7) | P_composition-{T}(V1,V5,V6)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #933: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7; #926 ), references = 1, size of lhs = 24:
% 14.23/14.38 P_one-{F}(V0), P_join-{F}(V1,V2,V2), P_complement-{F}(V2,V3), P_converse-{F}(V1,V4), P_complement-{F}(V5,V3), P_join-{F}(V2,V6,V7), P_converse-{F}(V7,V8), P_converse-{F}(V6,V9), P_join-{F}(V9,V10,V11), P_join-{F}(V8,V10,V12), P_composition-{F}(V12,V13,V14), P_composition-{F}(V11,V13,V15), P_composition-{F}(V4,V13,V15), P_converse-{F}(V13,V16), P_converse-{F}(V16,V17), P_converse-{F}(V14,V18), P_complement-{F}(V18,V19), P_composition-{F}(V17,V19,V20), P_complement-{F}(V21,V20), P_complement-{F}(V22,V23), V22 == V3, P_join-{F}(V23,V24,V5), P_complement-{F}(V24,V25), P_join-{F}(V23,V25,V21) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #939: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7; #927 ), references = 1, size of lhs = 27:
% 14.23/14.38 P_one-{F}(V0), P_join-{F}(V1,V2,V2), P_complement-{F}(V2,V3), P_converse-{F}(V1,V4), P_complement-{F}(V5,V3), P_join-{F}(V2,V6,V7), P_converse-{F}(V7,V8), P_converse-{F}(V6,V9), P_join-{F}(V9,V10,V11), P_join-{F}(V8,V10,V12), P_composition-{F}(V12,V13,V14), P_composition-{F}(V11,V13,V15), P_composition-{F}(V4,V13,V15), P_converse-{F}(V13,V16), P_converse-{F}(V16,V17), P_converse-{F}(V14,V18), P_complement-{F}(V18,V19), P_composition-{F}(V17,V19,V20), P_complement-{F}(V21,V22), P_complement-{F}(V23,V22), V23 == V3, P_meet-{F}(V21,V24,V20), P_complement-{F}(V24,V25), P_complement-{F}(V26,V25), P_join-{F}(V22,V26,V5), P_join-{F}(V22,V27,V28), P_join-{F}(V27,V29,V25) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #949: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8; #942 ), references = 1, size of lhs = 24:
% 14.23/14.38 P_one-{F}(V0), P_complement-{F}(V1,V2), P_complement-{F}(V3,V4), P_join-{F}(V2,V4,V5), P_join-{F}(V6,V5,V5), P_converse-{F}(V6,V7), P_join-{F}(V5,V8,V9), P_converse-{F}(V9,V10), P_converse-{F}(V8,V11), P_join-{F}(V11,V12,V13), P_join-{F}(V10,V12,V14), P_composition-{F}(V14,V15,V16), P_composition-{F}(V13,V15,V17), P_composition-{F}(V7,V15,V17), P_converse-{F}(V15,V18), P_converse-{F}(V18,V19), P_converse-{F}(V16,V20), P_complement-{F}(V20,V21), P_composition-{F}(V19,V21,V22), P_complement-{F}(V23,V22), P_complement-{F}(V24,V25), P_join-{F}(V25,V26,V5), P_complement-{F}(V26,V27), P_join-{F}(V25,V27,V23) | P_meet-{T}(V1,V3,V24)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #955: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8; #943 ), references = 1, size of lhs = 27:
% 14.23/14.38 P_one-{F}(V0), P_complement-{F}(V1,V2), P_complement-{F}(V3,V4), P_join-{F}(V2,V4,V5), P_join-{F}(V6,V5,V5), P_converse-{F}(V6,V7), P_join-{F}(V5,V8,V9), P_converse-{F}(V9,V10), P_converse-{F}(V8,V11), P_join-{F}(V11,V12,V13), P_join-{F}(V10,V12,V14), P_composition-{F}(V14,V15,V16), P_composition-{F}(V13,V15,V17), P_composition-{F}(V7,V15,V17), P_converse-{F}(V15,V18), P_converse-{F}(V18,V19), P_converse-{F}(V16,V20), P_complement-{F}(V20,V21), P_composition-{F}(V19,V21,V22), P_complement-{F}(V23,V24), P_complement-{F}(V25,V24), P_meet-{F}(V23,V26,V22), P_complement-{F}(V26,V27), P_complement-{F}(V28,V27), P_join-{F}(V24,V28,V5), P_join-{F}(V24,V29,V30), P_join-{F}(V29,V31,V27) | P_meet-{T}(V1,V3,V25)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #1040: mergings( V12 == V15, V2 == V3, V3 == V4, V4 == V5; #1033 ), references = 2, size of lhs = 12:
% 14.23/14.38 P_one-{F}(V0), P_converse-{F}(V0,V1), P_converse-{F}(V2,V1), P_complement-{F}(V3,V4), P_complement-{F}(V5,V4), P_composition-{F}(V2,V6,V5), P_complement-{F}(V6,V7), P_complement-{F}(V7,V8), P_join-{F}(V4,V8,V9), P_complement-{F}(V9,V10), P_join-{F}(V10,V8,V11), V3 == V11 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #1045: mergings( V13 == V16, V2 == V3, V3 == V4, V4 == V5; #1034 ), references = 1, size of lhs = 15:
% 14.23/14.38 P_one-{F}(V0), P_converse-{F}(V0,V1), P_converse-{F}(V2,V1), P_complement-{F}(V3,V4), P_complement-{F}(V5,V4), P_complement-{F}(V6,V4), P_composition-{F}(V2,V7,V6), P_complement-{F}(V7,V8), P_complement-{F}(V8,V9), P_complement-{F}(V10,V9), P_meet-{F}(V3,V10,V11), P_join-{F}(V11,V9,V12), V5 == V12, P_join-{F}(V4,V13,V14), P_join-{F}(V13,V15,V9) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #1049: mergings( V2 == V3, V3 == V4, V4 == V5; #1035 ), references = 1, size of lhs = 11:
% 14.23/14.38 P_one-{F}(V0), P_converse-{F}(V0,V1), P_converse-{F}(V2,V1), P_complement-{F}(V3,V4), P_complement-{F}(V5,V4), P_composition-{F}(V2,V6,V5), P_complement-{F}(V6,V7), P_complement-{F}(V8,V7), P_meet-{F}(V3,V8,V9), P_complement-{F}(V7,V10), V9 == V10 | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #1056: mergings( V2 == V3, V3 == V4, V4 == V5; #1052 ), references = 2, size of lhs = 9:
% 14.23/14.38 P_one-{F}(V0), P_converse-{F}(V0,V1), P_converse-{F}(V2,V1), P_complement-{F}(V3,V4), P_complement-{F}(V5,V4), P_composition-{F}(V2,V6,V5), P_complement-{F}(V6,V7), P_complement-{F}(V8,V7), P_meet-{F}(V3,V8,V9) | P_complement-{T}(V7,V9)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #1065: exists( #15, #2 ), references = 1, size of lhs = 6:
% 14.23/14.38 P_complement-{F}(V0,V1), P_complement-{F}(V2,V3), P_join-{F}(V1,V3,V4), P_complement-{F}(V4,V5), P_join-{F}(V1,V2,V6), P_complement-{F}(V6,V7) | P_join-{T}(V5,V7,V0)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #1066: exists( #15, #1040 ), references = 3, size of lhs = 10:
% 14.23/14.38 P_one-{F}(V0), P_converse-{F}(V0,V1), P_converse-{F}(V2,V1), P_complement-{F}(V3,V4), P_complement-{F}(V5,V4), P_composition-{F}(V2,V6,V5), P_complement-{F}(V6,V7), P_complement-{F}(V7,V8), P_join-{F}(V4,V8,V9), P_complement-{F}(V9,V10) | P_join-{T}(V10,V8,V3)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #1076: mergings( V3 == V4, V4 == V7; #1073 ), references = 1, size of lhs = 19:
% 14.23/14.38 P_one-{F}(V0), P_converse-{F}(V0,V1), P_converse-{F}(V2,V1), P_top-{F}(V3), P_complement-{F}(V3,V4), P_join-{F}(V5,V4,V4), P_converse-{F}(V6,V7), P_composition-{F}(V6,V8,V9), P_complement-{F}(V9,V10), P_complement-{F}(V8,V11), P_complement-{F}(V12,V11), P_composition-{F}(V2,V12,V13), P_complement-{F}(V13,V11), P_complement-{F}(V14,V11), P_join-{F}(V5,V14,V15), V15 == V14, P_complement-{F}(V16,V11), P_complement-{F}(V17,V11), P_meet-{F}(V16,V17,V18) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #1080: mergings( V3 == V4, V4 == V7; #1077 ), references = 1, size of lhs = 18:
% 14.23/14.38 P_one-{F}(V0), P_converse-{F}(V0,V1), P_converse-{F}(V2,V1), P_top-{F}(V3), P_complement-{F}(V3,V4), P_join-{F}(V5,V4,V4), P_converse-{F}(V6,V7), P_composition-{F}(V6,V8,V9), P_complement-{F}(V9,V10), P_complement-{F}(V8,V11), P_complement-{F}(V12,V11), P_composition-{F}(V2,V12,V13), P_complement-{F}(V13,V11), P_complement-{F}(V14,V11), P_join-{F}(V5,V14,V15), V15 == V14, P_complement-{F}(V16,V11), P_complement-{F}(V17,V11) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #1084: mergings( V3 == V4, V4 == V7; #1081 ), references = 1, size of lhs = 16:
% 14.23/14.38 P_one-{F}(V0), P_converse-{F}(V0,V1), P_converse-{F}(V2,V1), P_top-{F}(V3), P_complement-{F}(V3,V4), P_join-{F}(V5,V4,V4), P_converse-{F}(V6,V7), P_composition-{F}(V6,V8,V9), P_complement-{F}(V9,V10), P_complement-{F}(V8,V11), P_complement-{F}(V12,V11), P_composition-{F}(V2,V12,V13), P_complement-{F}(V13,V11), P_complement-{F}(V14,V11), P_complement-{F}(V15,V11), P_complement-{F}(V16,V11) | P_join-{T}(V5,V14,V14)
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #1122: mergings( V3 == V6, V6 == V8, V8 == V12, V4 == V9, V9 == V14, V7 == V13; #1115 ), references = 1, size of lhs = 18:
% 14.23/14.38 P_zero-{F}(V0), P_one-{F}(V1), P_top-{F}(V2), P_converse-{F}(V1,V3), P_converse-{F}(V3,V3), P_converse-{F}(V4,V3), P_converse-{F}(V5,V3), P_complement-{F}(V3,V6), P_complement-{F}(V7,V6), P_composition-{F}(V4,V7,V8), P_complement-{F}(V8,V9), P_complement-{F}(V10,V9), P_complement-{F}(V11,V6), P_complement-{F}(V2,V12), P_join-{F}(V3,V12,V3), P_complement-{F}(V13,V6), P_composition-{F}(V5,V13,V14), P_complement-{F}(V14,V6) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #1138: mergings( V2 == V3, V3 == V6, V6 == V9, V9 == V12, V12 == V14, V14 == V18, V4 == V10, V10 == V15, V15 == V0, V7 == V13, V8 == V20, V13 == V19; #1125 ), references = 2, size of lhs = 15:
% 14.23/14.38 P_zero-{F}(V0), P_one-{F}(V1), P_top-{F}(V2), P_converse-{F}(V1,V3), P_converse-{F}(V3,V3), P_converse-{F}(V4,V3), P_composition-{F}(V4,V3,V3), P_converse-{F}(V5,V3), P_composition-{F}(V5,V3,V3), P_converse-{F}(V6,V3), P_composition-{F}(V6,V3,V3), P_complement-{F}(V2,V7), P_join-{F}(V7,V7,V7), P_composition-{F}(V8,V3,V3), P_converse-{F}(V8,V9) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #1159: mergings( V15 == V20, V2 == V3, V3 == V4, V4 == V5, V5 == V8, V6 == V10, V10 == V19; #1151 ), references = 2, size of lhs = 19:
% 14.23/14.38 P_zero-{F}(V0), P_one-{F}(V1), P_top-{F}(V2), P_complement-{F}(V2,V3), P_complement-{F}(V3,V4), P_complement-{F}(V4,V3), P_join-{F}(V4,V3,V5), P_complement-{F}(V5,V3), P_converse-{F}(V1,V6), P_converse-{F}(V6,V6), P_converse-{F}(V7,V6), P_composition-{F}(V7,V6,V6), P_converse-{F}(V8,V6), P_composition-{F}(V8,V6,V6), P_converse-{F}(V9,V6), P_composition-{F}(V9,V6,V6), P_composition-{F}(V10,V6,V6), P_converse-{F}(V10,V11), P_complement-{F}(V12,V4) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #1178: mergings( V1 == V3, V3 == V4, V4 == V6, V6 == V7, V2 == V9, V5 == V8; #1171 ), references = 1, size of lhs = 12:
% 14.23/14.38 P_one-{F}(V0), P_top-{F}(V1), P_converse-{F}(V0,V2), P_converse-{F}(V2,V2), P_converse-{F}(V3,V2), P_composition-{F}(V3,V2,V2), P_converse-{F}(V4,V2), P_composition-{F}(V4,V2,V2), P_converse-{F}(V5,V2), P_composition-{F}(V5,V2,V2), P_composition-{F}(V6,V2,V2), P_converse-{F}(V6,V7) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #1185: mergings( V1 == V3, V3 == V4, V4 == V5, V5 == V6, V2 == V7; #1179 ), references = 1, size of lhs = 11:
% 14.23/14.38 P_one-{F}(V0), P_converse-{F}(V0,V1), P_converse-{F}(V1,V1), P_converse-{F}(V2,V1), P_composition-{F}(V2,V1,V1), P_converse-{F}(V3,V1), P_composition-{F}(V3,V1,V1), P_converse-{F}(V4,V1), P_composition-{F}(V4,V1,V1), P_composition-{F}(V5,V1,V1), P_converse-{F}(V5,V6) | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 #1189: exists( #19, #1187 ), references = 1, size of lhs = 0:
% 14.23/14.38 FALSE | FALSE
% 14.23/14.38 (used 0 times, uses = {})
% 14.23/14.38
% 14.23/14.38 number of learnt formulas = 80
% 14.23/14.38
% 14.23/14.38
% 14.23/14.38 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.23/14.38
% 14.23/14.38 randbase = 1
%------------------------------------------------------------------------------