%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : CAT002-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n014.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 05:58:47 EDT 2022
% Result : Unsatisfiable 2.08s 2.24s
% Output : Refutation 2.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT002-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jul 22 07:23:12 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.08/2.24 GeoParameters:
% 2.08/2.24
% 2.08/2.24 tptp_input = 1
% 2.08/2.24 tptp_output = 0
% 2.08/2.24 nonempty = 1
% 2.08/2.24 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.08/2.24 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 2.08/2.24
% 2.08/2.24
% 2.08/2.24 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.08/2.24 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.08/2.24
% 2.08/2.24 RuleSystem INPUT:
% 2.08/2.24
% 2.08/2.24 Initial Rules:
% 2.08/2.24 #0: input, references = 3, size of lhs = 1:
% 2.08/2.24 equivalent-{F}(V0,V1) | there_exists-{T}(V0)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #1: input, references = 3, size of lhs = 2:
% 2.08/2.24 equivalent-{F}(V0,V1), V0 == V1 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #2: input, references = 3, size of lhs = 1:
% 2.08/2.24 there_exists-{F}(V1) | equivalent-{T}(V1,V1)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #3: input, references = 9, size of lhs = 2:
% 2.08/2.24 P_domain-{F}(V0,V1), there_exists-{F}(V1) | there_exists-{T}(V0)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #4: input, references = 7, size of lhs = 2:
% 2.08/2.24 P_codomain-{F}(V0,V1), there_exists-{F}(V1) | there_exists-{T}(V0)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #5: input, references = 8, size of lhs = 3:
% 2.08/2.24 P_domain-{F}(V0,V1), P_compose-{F}(V0,V2,V3), there_exists-{F}(V3) | there_exists-{T}(V1)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #6: input, references = 15, size of lhs = 5:
% 2.08/2.24 P_compose-{F}(V0,V1,V2), P_domain-{F}(V0,V3), P_codomain-{F}(V1,V4), there_exists-{F}(V2), V3 == V4 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #7: input, references = 4, size of lhs = 4:
% 2.08/2.24 P_domain-{F}(V0,V3), there_exists-{F}(V3), P_codomain-{F}(V2,V3), P_compose-{F}(V0,V2,V4) | there_exists-{T}(V4)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #8: input, references = 5, size of lhs = 5:
% 2.08/2.24 P_compose-{F}(V1,V2,V3), P_compose-{F}(V0,V3,V4), P_compose-{F}(V0,V1,V5), P_compose-{F}(V5,V2,V6), V4 == V6 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #9: input, references = 4, size of lhs = 3:
% 2.08/2.24 P_domain-{F}(V0,V1), P_compose-{F}(V0,V1,V2), V2 == V0 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #10: input, references = 4, size of lhs = 3:
% 2.08/2.24 P_codomain-{F}(V0,V1), P_compose-{F}(V1,V0,V2), V2 == V0 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #11: input, references = 9, size of lhs = 3:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_compose-{F}(V0,V1,V2) | there_exists-{T}(V2)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #12: input, references = 6, size of lhs = 6:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_compose-{F}(V0,V1,V2), P_compose-{F}(V0,V4,V3), P_compose-{F}(V0,V6,V3), V6 == V4 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #13: input, references = 5, size of lhs = 6:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_compose-{F}(V0,V1,V2), P_compose-{F}(V1,V4,V3), P_compose-{F}(V1,V6,V3), V6 == V4 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #14: input, references = 7, size of lhs = 4:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_compose-{F}(V0,V1,V2), P_h-{F}(V3) | there_exists-{T}(V3)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #15: input, references = 6, size of lhs = 8:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_compose-{F}(V0,V1,V2), P_h-{F}(V3), P_compose-{F}(V2,V3,V4), P_g-{F}(V5), P_compose-{F}(V2,V5,V6), V4 == V6 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #16: input, references = 4, size of lhs = 7:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_compose-{F}(V0,V1,V2), P_h-{F}(V3), P_compose-{F}(V2,V3,V4), P_g-{F}(V3), P_compose-{F}(V2,V3,V6) | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #17: input, references = 9, size of lhs = 1:
% 2.08/2.24 #-{F} V0 | EXISTS V1: P_domain-{T}(V0,V1)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #18: input, references = 9, size of lhs = 1:
% 2.08/2.24 #-{F} V0 | EXISTS V1: P_codomain-{T}(V0,V1)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #19: input, references = 32, size of lhs = 2:
% 2.08/2.24 #-{F} V0, #-{F} V1 | EXISTS V2: P_compose-{T}(V0,V1,V2)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #20: input, references = 4, size of lhs = 0:
% 2.08/2.24 FALSE | EXISTS V0: P_a-{T}(V0)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #21: input, references = 4, size of lhs = 0:
% 2.08/2.24 FALSE | EXISTS V0: P_b-{T}(V0)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #22: input, references = 5, size of lhs = 0:
% 2.08/2.24 FALSE | EXISTS V0: P_h-{T}(V0)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #23: input, references = 6, size of lhs = 0:
% 2.08/2.24 FALSE | EXISTS V0: P_g-{T}(V0)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 number of initial rules = 24
% 2.08/2.24
% 2.08/2.24 Simplifiers:
% 2.08/2.24 #24: unsound, references = 3, size of lhs = 2:
% 2.08/2.24 equivalent-{F}(V0,V1), V1 == V0 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #25: unsound, references = 3, size of lhs = 3:
% 2.08/2.24 P_domain-{F}(V0,V1), P_domain-{F}(V0,V3), V1 == V3 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #26: unsound, references = 3, size of lhs = 3:
% 2.08/2.24 P_codomain-{F}(V0,V1), P_codomain-{F}(V0,V3), V1 == V3 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #27: unsound, references = 3, size of lhs = 3:
% 2.08/2.24 P_compose-{F}(V0,V1,V2), P_compose-{F}(V0,V1,V5), V2 == V5 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #28: unsound, references = 3, size of lhs = 3:
% 2.08/2.24 P_a-{F}(V0), P_a-{F}(V1), V0 == V1 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #29: unsound, references = 3, size of lhs = 3:
% 2.08/2.24 P_b-{F}(V0), P_b-{F}(V1), V0 == V1 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #30: unsound, references = 3, size of lhs = 3:
% 2.08/2.24 P_h-{F}(V0), P_h-{F}(V1), V0 == V1 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #31: unsound, references = 3, size of lhs = 3:
% 2.08/2.24 P_g-{F}(V0), P_g-{F}(V1), V0 == V1 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 number of simplifiers = 8
% 2.08/2.24
% 2.08/2.24 Learnt:
% 2.08/2.24 #33: exists( #19, #9 ), references = 3, size of lhs = 1:
% 2.08/2.24 P_domain-{F}(V0,V1) | P_compose-{T}(V0,V1,V0)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #35: exists( #19, #8 ), references = 11, size of lhs = 3:
% 2.08/2.24 P_compose-{F}(V0,V1,V2), P_compose-{F}(V3,V0,V4), P_compose-{F}(V4,V1,V5) | P_compose-{T}(V3,V2,V5)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #39: exists( #18, #6 ), references = 3, size of lhs = 3:
% 2.08/2.24 there_exists-{F}(V0), P_compose-{F}(V1,V2,V0), P_domain-{F}(V1,V3) | P_codomain-{T}(V2,V3)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #43: exists( #19, #16 ), references = 1, size of lhs = 5:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_compose-{F}(V0,V1,V2), P_h-{F}(V3), P_g-{F}(V3) | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #45: exists( #19, #42 ), references = 3, size of lhs = 4:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_h-{F}(V2), P_g-{F}(V2) | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #47: exists( #19, #10 ), references = 4, size of lhs = 1:
% 2.08/2.24 P_codomain-{F}(V0,V1) | P_compose-{T}(V1,V0,V0)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #52: exists( #19, #48 ), references = 1, size of lhs = 5:
% 2.08/2.24 P_a-{F}(V0), P_compose-{F}(V0,V0,V0), P_b-{F}(V1), P_compose-{F}(V0,V1,V2), #-{F} V3 | P_compose-{T}(V0,V3,V3)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #53: exists( #19, #49 ), references = 1, size of lhs = 5:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_compose-{F}(V1,V1,V1), P_compose-{F}(V0,V1,V2), #-{F} V3 | P_compose-{T}(V1,V3,V3)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #58: exists( #19, #12 ), references = 3, size of lhs = 5:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_compose-{F}(V0,V2,V3), P_compose-{F}(V0,V4,V3), V4 == V2 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #59: exists( #19, #13 ), references = 3, size of lhs = 5:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_compose-{F}(V1,V2,V3), P_compose-{F}(V1,V4,V3), V4 == V2 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #69: exists( #19, #67 ), references = 2, size of lhs = 7:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_h-{F}(V2), P_compose-{F}(V3,V4,V2), P_domain-{F}(V3,V5), P_codomain-{F}(V4,V6), V5 == V6 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #78: exists( #19, #76 ), references = 4, size of lhs = 8:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_domain-{F}(V0,V2), P_domain-{F}(V3,V2), P_compose-{F}(V4,V5,V3), P_domain-{F}(V4,V6), P_codomain-{F}(V5,V7), V6 == V7 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #81: exists( #17, #69 ), references = 1, size of lhs = 5:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_h-{F}(V2), P_compose-{F}(V3,V4,V2), P_codomain-{F}(V4,V5) | P_domain-{T}(V3,V5)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #82: exists( #17, #78 ), references = 3, size of lhs = 6:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_domain-{F}(V0,V2), P_domain-{F}(V3,V2), P_compose-{F}(V4,V5,V3), P_codomain-{F}(V5,V6) | P_domain-{T}(V4,V6)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #90: exists( #19, #8 ), references = 8, size of lhs = 3:
% 2.08/2.24 P_compose-{F}(V0,V1,V2), P_compose-{F}(V3,V2,V4), P_compose-{F}(V3,V0,V5) | P_compose-{T}(V5,V1,V4)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #100: exists( #19, #94 ), references = 4, size of lhs = 5:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_compose-{F}(V0,V2,V3), P_compose-{F}(V3,V4,V5), P_compose-{F}(V0,V6,V5) | P_compose-{T}(V2,V4,V6)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #101: exists( #19, #95 ), references = 1, size of lhs = 5:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_compose-{F}(V1,V2,V3), P_compose-{F}(V3,V4,V5), P_compose-{F}(V1,V6,V5) | P_compose-{T}(V2,V4,V6)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #108: mergings( V9 == V11, V0 == V4, V3 == V5; #104 ), references = 1, size of lhs = 9:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_compose-{F}(V0,V1,V2), P_compose-{F}(V0,V2,V0), P_h-{F}(V3), P_compose-{F}(V2,V3,V4), P_g-{F}(V5), V4 == V5, P_compose-{F}(V6,V7,V5) | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #110: exists( #18, #78 ), references = 2, size of lhs = 6:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_domain-{F}(V0,V2), P_domain-{F}(V3,V2), P_compose-{F}(V4,V5,V3), P_domain-{F}(V4,V6) | P_codomain-{T}(V5,V6)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #114: exists( #17, #6 ), references = 3, size of lhs = 3:
% 2.08/2.24 there_exists-{F}(V0), P_compose-{F}(V1,V2,V0), P_codomain-{F}(V2,V3) | P_domain-{T}(V1,V3)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #126: exists( #19, #15 ), references = 4, size of lhs = 6:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_compose-{F}(V0,V1,V2), P_h-{F}(V3), P_compose-{F}(V2,V3,V4), P_g-{F}(V5) | P_compose-{T}(V2,V5,V4)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #137: exists( #19, #135 ), references = 1, size of lhs = 13:
% 2.08/2.24 there_exists-{F}(V0), P_domain-{F}(V1,V0), P_a-{F}(V2), P_b-{F}(V3), P_compose-{F}(V2,V3,V4), P_h-{F}(V5), P_g-{F}(V6), P_domain-{F}(V4,V7), P_codomain-{F}(V6,V8), V7 == V8, P_compose-{F}(V1,V9,V4), P_compose-{F}(V9,V5,V10), P_codomain-{F}(V10,V0) | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #139: exists( #18, #136 ), references = 2, size of lhs = 11:
% 2.08/2.24 there_exists-{F}(V0), P_domain-{F}(V1,V0), P_a-{F}(V2), P_b-{F}(V3), P_compose-{F}(V2,V3,V4), P_h-{F}(V5), P_g-{F}(V6), P_domain-{F}(V4,V7), P_compose-{F}(V1,V8,V4), P_compose-{F}(V8,V5,V9), P_codomain-{F}(V9,V0) | P_codomain-{T}(V6,V7)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #151: mergings( V3 == V4; #149 ), references = 2, size of lhs = 14:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_h-{F}(V2), P_g-{F}(V3), P_compose-{F}(V1,V4,V1), P_compose-{F}(V5,V4,V2), P_domain-{F}(V5,V6), P_domain-{F}(V0,V6), P_compose-{F}(V4,V2,V7), P_codomain-{F}(V7,V6), P_domain-{F}(V8,V3), P_compose-{F}(V9,V3,V8), P_domain-{F}(V9,V10), V10 == V6 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #156: exists( #19, #154 ), references = 1, size of lhs = 5:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_domain-{F}(V0,V2), P_codomain-{F}(V1,V3), V2 == V3 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #158: exists( #18, #155 ), references = 3, size of lhs = 3:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_domain-{F}(V0,V2) | P_codomain-{T}(V1,V2)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #163: exists( #17, #161 ), references = 1, size of lhs = 7:
% 2.08/2.24 P_h-{F}(V0), P_b-{F}(V0), P_a-{F}(V0), P_g-{F}(V1), P_domain-{F}(V2,V1), P_compose-{F}(V3,V1,V2), P_domain-{F}(V3,V4) | P_domain-{T}(V0,V4)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #173: mergings( V0 == V4, V3 == V5; #170 ), references = 1, size of lhs = 8:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_domain-{F}(V0,V2), P_domain-{F}(V3,V2), P_compose-{F}(V0,V4,V0), P_domain-{F}(V4,V5), P_codomain-{F}(V3,V6), V5 == V6 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #177: mergings( V2 == V4, V3 == V5; #174 ), references = 1, size of lhs = 6:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_domain-{F}(V0,V2), P_domain-{F}(V3,V2), P_compose-{F}(V0,V4,V0), P_domain-{F}(V4,V5) | P_codomain-{T}(V3,V5)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #180: exists( #19, #178 ), references = 3, size of lhs = 8:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_compose-{F}(V0,V1,V2), P_h-{F}(V3), P_g-{F}(V4), P_compose-{F}(V2,V4,V5), P_compose-{F}(V6,V3,V7), P_compose-{F}(V8,V6,V2) | P_compose-{T}(V8,V7,V5)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #190: exists( #19, #186 ), references = 1, size of lhs = 5:
% 2.08/2.24 P_h-{F}(V0), P_a-{F}(V0), P_b-{F}(V0), P_g-{F}(V1), P_compose-{F}(V0,V1,V0) | P_compose-{T}(V0,V0,V0)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #213: exists( #19, #210 ), references = 2, size of lhs = 8:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_h-{F}(V2), P_domain-{F}(V3,V2), P_compose-{F}(V4,V5,V3), P_domain-{F}(V4,V6), P_codomain-{F}(V5,V7), V6 == V7 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #216: exists( #18, #213 ), references = 1, size of lhs = 6:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_h-{F}(V2), P_domain-{F}(V3,V2), P_compose-{F}(V4,V5,V3), P_domain-{F}(V4,V6) | P_codomain-{T}(V5,V6)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #239: exists( #19, #237 ), references = 1, size of lhs = 8:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_h-{F}(V2), P_codomain-{F}(V3,V2), P_compose-{F}(V4,V5,V3), P_domain-{F}(V4,V6), P_codomain-{F}(V5,V7), V6 == V7 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #250: mergings( V6 == V8, V5 == V9, V0 == V3, V3 == V2, V2 == V4; #244 ), references = 1, size of lhs = 5:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V0), P_h-{F}(V1), P_codomain-{F}(V2,V1), P_compose-{F}(V0,V3,V2) | P_domain-{T}(V0,V1)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #284: exists( #19, #282 ), references = 1, size of lhs = 13:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_h-{F}(V2), P_g-{F}(V3), P_compose-{F}(V1,V4,V1), P_codomain-{F}(V4,V5), P_domain-{F}(V0,V5), P_compose-{F}(V4,V2,V6), P_codomain-{F}(V6,V5), P_compose-{F}(V7,V8,V3), P_domain-{F}(V7,V9), P_codomain-{F}(V8,V10), V9 == V10 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #308: mergings( V3 == V6, V6 == V10, V4 == V9, V9 == V11, V7 == V11, V10 == V11, V12 == V5; #299 ), references = 2, size of lhs = 7:
% 2.08/2.24 P_h-{F}(V0), P_g-{F}(V1), V0 == V1, P_a-{F}(V2), P_b-{F}(V2), P_compose-{F}(V2,V2,V3), P_compose-{F}(V2,V0,V4) | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #315: mergings( V3 == V6, V6 == V10, V4 == V9, V9 == V11, V11 == V7, V12 == V5; #300 ), references = 2, size of lhs = 7:
% 2.08/2.24 P_h-{F}(V0), P_g-{F}(V1), V0 == V1, P_a-{F}(V2), P_b-{F}(V3), P_compose-{F}(V2,V3,V4), P_compose-{F}(V3,V0,V5) | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #320: mergings( V0 == V3, V3 == V4; #316 ), references = 1, size of lhs = 5:
% 2.08/2.24 P_h-{F}(V0), P_a-{F}(V0), P_b-{F}(V0), P_g-{F}(V1), V0 == V1 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #325: mergings( V1 == V2, V2 == V3; #321 ), references = 1, size of lhs = 3:
% 2.08/2.24 P_h-{F}(V0), P_a-{F}(V0), P_b-{F}(V0) | P_g-{T}(V0)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #347: exists( #19, #345 ), references = 1, size of lhs = 11:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_domain-{F}(V0,V2), P_compose-{F}(V3,V0,V0), P_domain-{F}(V3,V4), P_domain-{F}(V5,V2), P_domain-{F}(V6,V5), P_compose-{F}(V7,V1,V6), P_compose-{F}(V8,V0,V7), P_domain-{F}(V8,V9), V9 == V4 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #354: mergings( V0 == V2, V2 == V3; #351 ), references = 1, size of lhs = 6:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V0), P_domain-{F}(V1,V0), P_compose-{F}(V2,V0,V1), P_compose-{F}(V3,V0,V2), P_domain-{F}(V3,V4) | P_domain-{T}(V0,V4)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #370: exists( #19, #308 ), references = 3, size of lhs = 6:
% 2.08/2.24 P_h-{F}(V0), P_g-{F}(V1), V0 == V1, P_a-{F}(V2), P_b-{F}(V2), P_compose-{F}(V2,V0,V3) | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #371: exists( #19, #315 ), references = 3, size of lhs = 6:
% 2.08/2.24 P_h-{F}(V0), P_g-{F}(V1), V0 == V1, P_a-{F}(V2), P_b-{F}(V3), P_compose-{F}(V3,V0,V4) | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #388: exists( #19, #386 ), references = 1, size of lhs = 11:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1), P_domain-{F}(V0,V2), P_compose-{F}(V1,V3,V1), P_codomain-{F}(V3,V4), P_domain-{F}(V5,V2), P_codomain-{F}(V6,V5), P_compose-{F}(V0,V7,V6), P_compose-{F}(V1,V8,V7), P_codomain-{F}(V8,V9), V4 == V9 | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #393: mergings( V2 == V0; #391 ), references = 1, size of lhs = 6:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V0), P_codomain-{F}(V1,V0), P_compose-{F}(V0,V2,V1), P_compose-{F}(V0,V3,V2), P_codomain-{F}(V3,V4) | P_domain-{T}(V0,V4)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #425: mergings( V3 == V8, V4 == V8, V1 == V6, V5 == V7, V9 == V8; #417 ), references = 1, size of lhs = 7:
% 2.08/2.24 P_h-{F}(V0), P_g-{F}(V1), V0 == V1, P_a-{F}(V2), P_b-{F}(V2), P_compose-{F}(V2,V1,V0), P_compose-{F}(V2,V2,V3) | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #430: mergings( V3 == V8, V4 == V9, V1 == V6, V5 == V7; #418 ), references = 1, size of lhs = 8:
% 2.08/2.24 P_h-{F}(V0), P_g-{F}(V1), V0 == V1, P_a-{F}(V2), P_b-{F}(V3), P_compose-{F}(V2,V3,V4), P_compose-{F}(V5,V1,V0), P_compose-{F}(V3,V5,V4) | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #440: exists( #19, #370 ), references = 1, size of lhs = 5:
% 2.08/2.24 P_h-{F}(V0), P_g-{F}(V1), V0 == V1, P_a-{F}(V2), P_b-{F}(V2) | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #441: exists( #19, #371 ), references = 2, size of lhs = 5:
% 2.08/2.24 P_h-{F}(V0), P_g-{F}(V1), V0 == V1, P_a-{F}(V2), P_b-{F}(V3) | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #444: exists( #23, #438 ), references = 1, size of lhs = 3:
% 2.08/2.24 P_h-{F}(V0), P_a-{F}(V1), P_b-{F}(V1) | P_g-{T}(V0)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #445: exists( #23, #439 ), references = 1, size of lhs = 3:
% 2.08/2.24 P_h-{F}(V0), P_a-{F}(V1), P_b-{F}(V2) | P_g-{T}(V0)
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #450: mergings( V1 == V2, V2 == V3; #447 ), references = 1, size of lhs = 2:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V0) | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #456: mergings( V1 == V3, V2 == V4; #453 ), references = 1, size of lhs = 2:
% 2.08/2.24 P_a-{F}(V0), P_b-{F}(V1) | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #459: mergings( V1 == V2; #457 ), references = 1, size of lhs = 1:
% 2.08/2.24 P_a-{F}(V0) | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 #461: exists( #20, #457 ), references = 1, size of lhs = 0:
% 2.08/2.24 FALSE | FALSE
% 2.08/2.24 (used 0 times, uses = {})
% 2.08/2.24
% 2.08/2.24 number of learnt formulas = 56
% 2.08/2.24
% 2.08/2.24
% 2.08/2.24 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.08/2.24
% 2.08/2.24 randbase = 1
%------------------------------------------------------------------------------