TSTP Solution File: CAT004-1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : CAT004-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n008.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 3.38s 3.59s
% Output : Refutation 3.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT004-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jul 22 07:21:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.38/3.59 GeoParameters:
% 3.38/3.59
% 3.38/3.59 tptp_input = 1
% 3.38/3.59 tptp_output = 0
% 3.38/3.59 nonempty = 1
% 3.38/3.59 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.38/3.59 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 3.38/3.59
% 3.38/3.59
% 3.38/3.59 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.38/3.59 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.38/3.59
% 3.38/3.59 RuleSystem INPUT:
% 3.38/3.59
% 3.38/3.59 Initial Rules:
% 3.38/3.59 #0: input, references = 32, size of lhs = 2:
% 3.38/3.59 P_compose-{F}(V0,V1,V2), defined-{F}(V0,V1) | product-{T}(V0,V1,V2)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #1: input, references = 21, size of lhs = 1:
% 3.38/3.59 product-{F}(V0,V1,V2) | defined-{T}(V0,V1)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #2: input, references = 18, size of lhs = 2:
% 3.38/3.59 defined-{F}(V1,V0), product-{F}(V3,V2,V1) | defined-{T}(V2,V0)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #3: input, references = 9, size of lhs = 3:
% 3.38/3.59 defined-{F}(V1,V0), product-{F}(V3,V0,V2), product-{F}(V4,V3,V1) | defined-{T}(V4,V2)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #4: input, references = 9, size of lhs = 3:
% 3.38/3.59 product-{F}(V1,V0,V2), product-{F}(V4,V0,V3), product-{F}(V5,V4,V1) | product-{T}(V5,V3,V2)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #5: input, references = 28, size of lhs = 2:
% 3.38/3.59 product-{F}(V0,V2,V1), defined-{F}(V3,V1) | defined-{T}(V3,V0)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #6: input, references = 7, size of lhs = 3:
% 3.38/3.59 product-{F}(V3,V0,V2), product-{F}(V4,V3,V1), defined-{F}(V4,V2) | defined-{T}(V1,V0)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #7: input, references = 17, size of lhs = 3:
% 3.38/3.59 product-{F}(V4,V0,V3), product-{F}(V5,V3,V2), product-{F}(V5,V4,V1) | product-{T}(V1,V0,V2)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #8: input, references = 3, size of lhs = 3:
% 3.38/3.59 identity_map-{F}(V0), defined-{F}(V0,V1), defined-{F}(V2,V0) | defined-{T}(V2,V1)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #9: input, references = 13, size of lhs = 1:
% 3.38/3.59 P_domain-{F}(V0,V1) | identity_map-{T}(V1)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #10: input, references = 5, size of lhs = 1:
% 3.38/3.59 P_codomain-{F}(V0,V1) | identity_map-{T}(V1)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #11: input, references = 5, size of lhs = 1:
% 3.38/3.59 P_domain-{F}(V0,V1) | defined-{T}(V0,V1)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #12: input, references = 7, size of lhs = 1:
% 3.38/3.59 P_codomain-{F}(V0,V1) | defined-{T}(V1,V0)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #13: input, references = 15, size of lhs = 1:
% 3.38/3.59 P_domain-{F}(V0,V1) | product-{T}(V0,V1,V0)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #14: input, references = 7, size of lhs = 1:
% 3.38/3.59 P_codomain-{F}(V0,V1) | product-{T}(V1,V0,V0)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #15: input, references = 22, size of lhs = 2:
% 3.38/3.59 identity_map-{F}(V0), defined-{F}(V0,V1) | product-{T}(V0,V1,V1)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #16: input, references = 10, size of lhs = 2:
% 3.38/3.59 identity_map-{F}(V0), defined-{F}(V1,V0) | product-{T}(V1,V0,V1)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #17: input, references = 6, size of lhs = 3:
% 3.38/3.59 product-{F}(V3,V2,V0), product-{F}(V3,V2,V1), V0 == V1 | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #18: input, references = 13, size of lhs = 4:
% 3.38/3.59 P_a-{F}(V0), product-{F}(V1,V0,V2), product-{F}(V3,V0,V2), V3 == V1 | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #19: input, references = 11, size of lhs = 5:
% 3.38/3.59 P_a-{F}(V0), P_b-{F}(V1), product-{F}(V2,V1,V3), product-{F}(V4,V1,V3), V4 == V2 | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #20: input, references = 5, size of lhs = 3:
% 3.38/3.59 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2) | product-{T}(V0,V1,V2)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #21: input, references = 9, size of lhs = 5:
% 3.38/3.59 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_h-{F}(V3), P_d-{F}(V4) | product-{T}(V3,V2,V4)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #22: input, references = 21, size of lhs = 6:
% 3.38/3.59 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_h-{F}(V3), P_d-{F}(V4), P_g-{F}(V5) | product-{T}(V5,V2,V4)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #23: input, references = 8, size of lhs = 6:
% 3.38/3.59 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_h-{F}(V5), P_d-{F}(V4), P_g-{F}(V5) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #24: input, references = 10, size of lhs = 2:
% 3.38/3.59 #-{F} V0, #-{F} V1 | EXISTS V2: P_compose-{T}(V0,V1,V2)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #25: input, references = 8, size of lhs = 1:
% 3.38/3.59 #-{F} V0 | EXISTS V1: P_domain-{T}(V0,V1)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #26: input, references = 6, size of lhs = 1:
% 3.38/3.59 #-{F} V0 | EXISTS V1: P_codomain-{T}(V0,V1)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #27: input, references = 4, size of lhs = 0:
% 3.38/3.59 FALSE | EXISTS V0: P_a-{T}(V0)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #28: input, references = 4, size of lhs = 0:
% 3.38/3.59 FALSE | EXISTS V0: P_b-{T}(V0)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #29: input, references = 5, size of lhs = 0:
% 3.38/3.59 FALSE | EXISTS V0: P_c-{T}(V0)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #30: input, references = 6, size of lhs = 0:
% 3.38/3.59 FALSE | EXISTS V0: P_h-{T}(V0)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #31: input, references = 9, size of lhs = 0:
% 3.38/3.59 FALSE | EXISTS V0: P_d-{T}(V0)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #32: input, references = 12, size of lhs = 0:
% 3.38/3.59 FALSE | EXISTS V0: P_g-{T}(V0)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 number of initial rules = 33
% 3.38/3.59
% 3.38/3.59 Simplifiers:
% 3.38/3.59 #33: unsound, references = 3, size of lhs = 3:
% 3.38/3.59 P_compose-{F}(V0,V1,V2), P_compose-{F}(V0,V1,V5), V2 == V5 | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #34: unsound, references = 3, size of lhs = 3:
% 3.38/3.59 P_domain-{F}(V0,V1), P_domain-{F}(V0,V3), V1 == V3 | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #35: unsound, references = 3, size of lhs = 3:
% 3.38/3.59 P_codomain-{F}(V0,V1), P_codomain-{F}(V0,V3), V1 == V3 | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #36: unsound, references = 3, size of lhs = 3:
% 3.38/3.59 P_a-{F}(V0), P_a-{F}(V1), V0 == V1 | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #37: unsound, references = 3, size of lhs = 3:
% 3.38/3.59 P_b-{F}(V0), P_b-{F}(V1), V0 == V1 | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #38: unsound, references = 3, size of lhs = 3:
% 3.38/3.59 P_c-{F}(V0), P_c-{F}(V1), V0 == V1 | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #39: unsound, references = 3, size of lhs = 3:
% 3.38/3.59 P_h-{F}(V0), P_h-{F}(V1), V0 == V1 | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #40: unsound, references = 3, size of lhs = 3:
% 3.38/3.59 P_d-{F}(V0), P_d-{F}(V1), V0 == V1 | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #41: unsound, references = 3, size of lhs = 3:
% 3.38/3.59 P_g-{F}(V0), P_g-{F}(V1), V0 == V1 | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 number of simplifiers = 9
% 3.38/3.59
% 3.38/3.59 Learnt:
% 3.38/3.59 #44: exists( #31, #42 ), references = 1, size of lhs = 5:
% 3.38/3.59 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_h-{F}(V3), product-{F}(V3,V2,V4) | P_d-{T}(V4)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #50: mergings( V1 == V3; #47 ), references = 2, size of lhs = 6:
% 3.38/3.59 P_b-{F}(V0), P_c-{F}(V1), P_a-{F}(V1), P_h-{F}(V2), P_d-{F}(V3), product-{F}(V4,V1,V3) | P_g-{T}(V4)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #53: mergings( V1 == V6, V2 == V3; #48 ), references = 1, size of lhs = 6:
% 3.38/3.59 P_c-{F}(V0), P_b-{F}(V0), P_h-{F}(V1), P_d-{F}(V2), P_a-{F}(V3), product-{F}(V4,V0,V2) | P_g-{T}(V4)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #65: mergings( V1 == V4, V4 == V6, V2 == V3, V3 == V7, V6 == V8, V5 == V9; #58 ), references = 1, size of lhs = 4:
% 3.38/3.59 P_a-{F}(V0), P_c-{F}(V0), P_b-{F}(V1), P_h-{F}(V2) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #72: mergings( V1 == V4, V4 == V5, V2 == V3, V3 == V6, V5 == V7; #66 ), references = 1, size of lhs = 3:
% 3.38/3.59 P_a-{F}(V0), P_c-{F}(V0), P_b-{F}(V1) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #77: exists( #24, #75 ), references = 1, size of lhs = 2:
% 3.38/3.59 defined-{F}(V0,V1), product-{F}(V0,V1,V2) | P_compose-{T}(V0,V1,V2)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #87: exists( #26, #83 ), references = 1, size of lhs = 2:
% 3.38/3.59 P_a-{F}(V0), product-{F}(V1,V0,V0) | P_codomain-{T}(V0,V1)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #88: exists( #26, #84 ), references = 1, size of lhs = 3:
% 3.38/3.59 P_a-{F}(V0), P_b-{F}(V1), product-{F}(V2,V1,V1) | P_codomain-{T}(V1,V2)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #101: exists( #24, #97 ), references = 9, size of lhs = 5:
% 3.38/3.59 P_a-{F}(V0), defined-{F}(V1,V2), product-{F}(V2,V0,V3), product-{F}(V1,V3,V4), product-{F}(V5,V0,V4) | P_compose-{T}(V1,V2,V5)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #102: exists( #24, #98 ), references = 8, size of lhs = 6:
% 3.38/3.59 P_a-{F}(V0), P_b-{F}(V1), defined-{F}(V2,V3), product-{F}(V3,V1,V4), product-{F}(V2,V4,V5), product-{F}(V6,V1,V5) | P_compose-{T}(V2,V3,V6)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #122: mergings( V2 == V3; #119 ), references = 2, size of lhs = 9:
% 3.38/3.59 P_a-{F}(V0), defined-{F}(V1,V0), product-{F}(V0,V0,V2), defined-{F}(V3,V0), product-{F}(V3,V2,V0), product-{F}(V0,V0,V4), defined-{F}(V5,V0), V3 == V5, product-{F}(V5,V4,V0) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #124: mergings( V2 == V3; #120 ), references = 2, size of lhs = 10:
% 3.38/3.59 P_a-{F}(V0), defined-{F}(V1,V0), P_b-{F}(V2), product-{F}(V2,V0,V3), defined-{F}(V4,V2), product-{F}(V4,V3,V0), product-{F}(V2,V0,V5), defined-{F}(V6,V2), V4 == V6, product-{F}(V6,V5,V0) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #132: mergings( V1 == V5; #129 ), references = 1, size of lhs = 11:
% 3.38/3.59 P_b-{F}(V0), P_c-{F}(V1), P_h-{F}(V2), P_d-{F}(V3), P_a-{F}(V3), product-{F}(V3,V3,V1), product-{F}(V3,V3,V4), defined-{F}(V5,V3), product-{F}(V5,V4,V3), defined-{F}(V3,V6), product-{F}(V1,V6,V3) | P_g-{T}(V5)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #136: mergings( V1 == V5, V5 == V6, V2 == V6; #130 ), references = 1, size of lhs = 11:
% 3.38/3.59 P_c-{F}(V0), P_h-{F}(V1), P_d-{F}(V2), P_b-{F}(V2), product-{F}(V2,V2,V0), P_a-{F}(V2), product-{F}(V2,V2,V3), defined-{F}(V4,V2), product-{F}(V4,V3,V2), defined-{F}(V2,V5), product-{F}(V0,V5,V2) | P_g-{T}(V4)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #200: exists( #24, #198 ), references = 5, size of lhs = 16:
% 3.38/3.59 P_a-{F}(V0), product-{F}(V1,V0,V2), product-{F}(V3,V1,V4), product-{F}(V3,V5,V6), product-{F}(V5,V7,V8), defined-{F}(V8,V9), defined-{F}(V8,V10), product-{F}(V7,V9,V11), product-{F}(V6,V11,V12), product-{F}(V9,V13,V10), product-{F}(V8,V14,V2), product-{F}(V9,V15,V14), product-{F}(V16,V0,V15), product-{F}(V16,V17,V13), product-{F}(V12,V16,V18), V18 == V4 | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #242: exists( #26, #238 ), references = 1, size of lhs = 3:
% 3.38/3.59 P_a-{F}(V0), product-{F}(V1,V0,V0), product-{F}(V0,V2,V3) | P_codomain-{T}(V3,V1)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #243: exists( #26, #239 ), references = 1, size of lhs = 4:
% 3.38/3.59 P_b-{F}(V0), P_a-{F}(V1), product-{F}(V2,V0,V0), product-{F}(V0,V3,V4) | P_codomain-{T}(V4,V2)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #265: exists( #25, #261 ), references = 3, size of lhs = 3:
% 3.38/3.59 P_a-{F}(V0), defined-{F}(V1,V0), product-{F}(V2,V0,V0) | P_domain-{T}(V1,V2)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #266: exists( #25, #262 ), references = 1, size of lhs = 4:
% 3.38/3.59 P_b-{F}(V0), defined-{F}(V1,V0), P_a-{F}(V2), product-{F}(V3,V0,V0) | P_domain-{T}(V1,V3)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #301: mergings( V3 == V4; #297 ), references = 3, size of lhs = 10:
% 3.38/3.59 P_a-{F}(V0), product-{F}(V0,V0,V1), defined-{F}(V2,V0), product-{F}(V2,V1,V3), product-{F}(V0,V0,V4), product-{F}(V5,V4,V3), V5 == V2, defined-{F}(V6,V7), product-{F}(V8,V0,V7), product-{F}(V6,V8,V5) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #303: mergings( V3 == V4; #298 ), references = 3, size of lhs = 11:
% 3.38/3.59 P_a-{F}(V0), P_b-{F}(V1), product-{F}(V1,V0,V2), defined-{F}(V3,V1), product-{F}(V3,V2,V4), product-{F}(V1,V0,V5), product-{F}(V6,V5,V4), V6 == V3, defined-{F}(V7,V8), product-{F}(V9,V1,V8), product-{F}(V7,V9,V6) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #305: mergings( V4 == V5; #299 ), references = 1, size of lhs = 24:
% 3.38/3.59 identity_map-{F}(V0), P_a-{F}(V1), product-{F}(V1,V1,V2), defined-{F}(V3,V1), product-{F}(V3,V2,V4), defined-{F}(V0,V5), defined-{F}(V0,V6), product-{F}(V5,V7,V4), product-{F}(V8,V1,V7), product-{F}(V9,V1,V8), product-{F}(V5,V10,V6), product-{F}(V9,V11,V10), defined-{F}(V12,V13), product-{F}(V0,V12,V14), defined-{F}(V14,V13), product-{F}(V15,V8,V13), product-{F}(V12,V15,V5), product-{F}(V16,V3,V17), product-{F}(V16,V18,V19), product-{F}(V18,V20,V0), product-{F}(V20,V5,V21), product-{F}(V19,V21,V22), product-{F}(V22,V9,V23), V23 == V17 | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #313: mergings( V3 == V4; #309 ), references = 1, size of lhs = 11:
% 3.38/3.59 P_a-{F}(V0), product-{F}(V0,V0,V1), defined-{F}(V2,V0), product-{F}(V2,V1,V3), product-{F}(V0,V0,V4), product-{F}(V5,V4,V3), V5 == V2, defined-{F}(V6,V7), P_compose-{F}(V6,V7,V5), defined-{F}(V6,V8), product-{F}(V7,V0,V8) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #315: mergings( V3 == V4; #310 ), references = 1, size of lhs = 12:
% 3.38/3.59 P_a-{F}(V0), P_b-{F}(V1), product-{F}(V1,V0,V2), defined-{F}(V3,V1), product-{F}(V3,V2,V4), product-{F}(V1,V0,V5), product-{F}(V6,V5,V4), V6 == V3, defined-{F}(V7,V8), P_compose-{F}(V7,V8,V6), defined-{F}(V7,V9), product-{F}(V8,V1,V9) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #326: mergings( V1 == V6, V6 == V7; #322 ), references = 1, size of lhs = 13:
% 3.38/3.59 P_b-{F}(V0), P_c-{F}(V1), P_h-{F}(V2), P_d-{F}(V3), P_a-{F}(V4), product-{F}(V4,V4,V1), product-{F}(V4,V4,V5), product-{F}(V4,V6,V1), product-{F}(V7,V5,V3), defined-{F}(V8,V9), P_compose-{F}(V8,V9,V7), defined-{F}(V8,V10), product-{F}(V9,V4,V10) | P_g-{T}(V7)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #330: mergings( V1 == V6, V6 == V7, V2 == V8; #323 ), references = 1, size of lhs = 13:
% 3.38/3.59 P_c-{F}(V0), P_h-{F}(V1), P_d-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), product-{F}(V4,V3,V0), product-{F}(V4,V3,V5), product-{F}(V4,V6,V0), product-{F}(V7,V5,V2), defined-{F}(V8,V9), P_compose-{F}(V8,V9,V7), defined-{F}(V8,V10), product-{F}(V9,V4,V10) | P_g-{T}(V7)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #345: mergings( V1 == V4, V4 == V8, V8 == V9, V9 == V11, V2 == V5, V5 == V12, V3 == V6, V6 == V13, V7 == V14; #335 ), references = 1, size of lhs = 10:
% 3.38/3.59 P_a-{F}(V0), product-{F}(V0,V0,V1), P_c-{F}(V1), product-{F}(V0,V2,V1), P_b-{F}(V3), P_h-{F}(V4), product-{F}(V5,V0,V1), defined-{F}(V6,V5), P_compose-{F}(V6,V5,V4), product-{F}(V7,V6,V4) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #363: mergings( V1 == V6, V6 == V7; #359 ), references = 1, size of lhs = 9:
% 3.38/3.59 P_b-{F}(V0), P_c-{F}(V1), P_h-{F}(V2), P_d-{F}(V3), P_a-{F}(V4), product-{F}(V4,V4,V1), product-{F}(V4,V5,V1), product-{F}(V6,V4,V3), product-{F}(V7,V4,V6) | P_g-{T}(V7)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #367: mergings( V1 == V6, V6 == V7, V2 == V8; #360 ), references = 1, size of lhs = 9:
% 3.38/3.59 P_c-{F}(V0), P_h-{F}(V1), P_d-{F}(V2), P_a-{F}(V3), P_b-{F}(V4), product-{F}(V4,V3,V0), product-{F}(V4,V5,V0), product-{F}(V6,V3,V2), product-{F}(V7,V4,V6) | P_g-{T}(V7)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #382: mergings( V1 == V5, V5 == V9, V9 == V10, V10 == V12, V2 == V6, V6 == V13, V3 == V7, V7 == V14, V4 == V8, V8 == V15; #371 ), references = 1, size of lhs = 9:
% 3.38/3.59 P_a-{F}(V0), product-{F}(V0,V0,V1), P_c-{F}(V1), product-{F}(V0,V2,V1), P_b-{F}(V3), P_h-{F}(V4), product-{F}(V4,V0,V5), product-{F}(V6,V0,V1), product-{F}(V4,V6,V5) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #460: exists( #25, #456 ), references = 2, size of lhs = 13:
% 3.38/3.59 P_a-{F}(V0), product-{F}(V0,V0,V1), defined-{F}(V2,V0), product-{F}(V2,V1,V3), product-{F}(V0,V0,V4), defined-{F}(V5,V0), defined-{F}(V6,V5), product-{F}(V6,V5,V7), product-{F}(V8,V4,V3), V8 == V2, product-{F}(V9,V7,V8), product-{F}(V9,V7,V10), defined-{F}(V10,V0) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #461: exists( #25, #457 ), references = 1, size of lhs = 14:
% 3.38/3.59 P_b-{F}(V0), P_a-{F}(V1), product-{F}(V0,V1,V2), defined-{F}(V3,V0), product-{F}(V3,V2,V4), product-{F}(V0,V1,V5), defined-{F}(V6,V0), defined-{F}(V7,V6), product-{F}(V7,V6,V8), product-{F}(V9,V5,V4), V9 == V3, product-{F}(V10,V8,V9), product-{F}(V10,V8,V11), defined-{F}(V11,V0) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #471: mergings( V1 == V6; #468 ), references = 1, size of lhs = 13:
% 3.38/3.59 P_b-{F}(V0), P_c-{F}(V1), P_h-{F}(V2), P_d-{F}(V3), P_a-{F}(V4), product-{F}(V4,V4,V1), defined-{F}(V3,V4), product-{F}(V4,V4,V5), product-{F}(V3,V5,V3), product-{F}(V4,V6,V1), defined-{F}(V7,V4), defined-{F}(V8,V7), product-{F}(V8,V7,V1) | P_g-{T}(V3)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #474: mergings( V1 == V7, V2 == V6; #469 ), references = 1, size of lhs = 13:
% 3.38/3.59 P_c-{F}(V0), P_h-{F}(V1), P_d-{F}(V2), P_b-{F}(V3), defined-{F}(V2,V3), P_a-{F}(V4), product-{F}(V3,V4,V0), product-{F}(V3,V4,V5), product-{F}(V2,V5,V2), product-{F}(V3,V6,V0), defined-{F}(V7,V3), defined-{F}(V8,V7), product-{F}(V8,V7,V0) | P_g-{T}(V2)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #496: mergings( V1 == V5; #493 ), references = 1, size of lhs = 11:
% 3.38/3.59 P_b-{F}(V0), P_c-{F}(V1), P_h-{F}(V2), P_d-{F}(V3), P_a-{F}(V3), product-{F}(V3,V3,V1), defined-{F}(V4,V3), product-{F}(V3,V3,V5), defined-{F}(V6,V3), product-{F}(V6,V5,V3), product-{F}(V3,V7,V1) | P_g-{T}(V6)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #499: mergings( V1 == V5, V2 == V7; #494 ), references = 1, size of lhs = 11:
% 3.38/3.59 P_c-{F}(V0), P_h-{F}(V1), P_d-{F}(V2), P_a-{F}(V2), defined-{F}(V3,V2), P_b-{F}(V4), product-{F}(V4,V2,V0), product-{F}(V4,V2,V5), defined-{F}(V6,V4), product-{F}(V6,V5,V2), product-{F}(V4,V7,V0) | P_g-{T}(V6)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #651: exists( #25, #645 ), references = 1, size of lhs = 12:
% 3.38/3.59 P_a-{F}(V0), defined-{F}(V1,V0), product-{F}(V0,V0,V2), defined-{F}(V3,V0), product-{F}(V3,V2,V4), product-{F}(V0,V0,V5), product-{F}(V6,V5,V4), V6 == V3, defined-{F}(V6,V0), defined-{F}(V6,V7), defined-{F}(V0,V8), product-{F}(V0,V8,V7) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #652: exists( #25, #647 ), references = 1, size of lhs = 12:
% 3.38/3.59 P_a-{F}(V0), defined-{F}(V1,V0), defined-{F}(V2,V0), defined-{F}(V2,V3), product-{F}(V0,V0,V4), defined-{F}(V5,V0), V2 == V5, product-{F}(V5,V4,V6), product-{F}(V0,V0,V7), product-{F}(V2,V7,V6), defined-{F}(V0,V8), product-{F}(V0,V8,V3) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #653: exists( #25, #646 ), references = 1, size of lhs = 13:
% 3.38/3.59 P_b-{F}(V0), defined-{F}(V1,V0), P_a-{F}(V2), product-{F}(V0,V2,V3), defined-{F}(V4,V0), product-{F}(V4,V3,V5), product-{F}(V0,V2,V6), product-{F}(V7,V6,V5), V7 == V4, defined-{F}(V7,V0), defined-{F}(V7,V8), defined-{F}(V0,V9), product-{F}(V0,V9,V8) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #667: mergings( V1 == V6; #663 ), references = 1, size of lhs = 13:
% 3.38/3.59 P_b-{F}(V0), P_c-{F}(V1), P_h-{F}(V2), P_d-{F}(V3), P_a-{F}(V4), product-{F}(V4,V4,V1), defined-{F}(V5,V4), product-{F}(V4,V4,V6), defined-{F}(V7,V4), product-{F}(V7,V6,V3), defined-{F}(V4,V8), product-{F}(V4,V8,V1), product-{F}(V4,V9,V1) | P_g-{T}(V7)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #669: mergings( V1 == V6; #664 ), references = 1, size of lhs = 14:
% 3.38/3.59 P_b-{F}(V0), P_c-{F}(V1), P_h-{F}(V2), P_d-{F}(V3), P_a-{F}(V4), product-{F}(V4,V4,V1), defined-{F}(V5,V4), defined-{F}(V6,V4), defined-{F}(V6,V7), product-{F}(V4,V4,V8), product-{F}(V6,V8,V3), defined-{F}(V4,V9), product-{F}(V4,V9,V7), product-{F}(V4,V10,V1) | P_g-{T}(V6)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #672: mergings( V1 == V8, V2 == V6; #665 ), references = 1, size of lhs = 13:
% 3.38/3.59 P_c-{F}(V0), P_h-{F}(V1), P_d-{F}(V2), P_b-{F}(V3), defined-{F}(V4,V3), P_a-{F}(V5), product-{F}(V3,V5,V0), product-{F}(V3,V5,V6), defined-{F}(V7,V3), product-{F}(V7,V6,V2), defined-{F}(V3,V8), product-{F}(V3,V8,V0), product-{F}(V3,V9,V0) | P_g-{T}(V7)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #686: mergings( V1 == V4, V4 == V8, V8 == V12, V2 == V5, V5 == V13, V3 == V6, V6 == V14, V7 == V15; #677 ), references = 1, size of lhs = 10:
% 3.38/3.59 P_a-{F}(V0), product-{F}(V0,V0,V1), P_c-{F}(V1), defined-{F}(V2,V0), defined-{F}(V0,V3), product-{F}(V0,V3,V1), product-{F}(V0,V4,V1), P_b-{F}(V5), P_h-{F}(V6), product-{F}(V0,V7,V1) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #695: mergings( V1 == V4, V4 == V7, V7 == V11, V2 == V5, V5 == V12, V3 == V6, V6 == V13; #687 ), references = 1, size of lhs = 9:
% 3.38/3.59 P_a-{F}(V0), product-{F}(V0,V0,V1), P_c-{F}(V1), defined-{F}(V2,V0), defined-{F}(V0,V3), product-{F}(V0,V3,V1), product-{F}(V0,V4,V1), P_b-{F}(V5), product-{F}(V0,V6,V1) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #705: mergings( V1 == V2, V2 == V4, V4 == V6, V6 == V3, V3 == V5, V5 == V7; #698 ), references = 1, size of lhs = 2:
% 3.38/3.59 P_a-{F}(V0), P_b-{F}(V0) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #787: mergings( V2 == V4, V4 == V5, V5 == V7, V3 == V6; #781 ), references = 1, size of lhs = 14:
% 3.38/3.59 P_b-{F}(V0), P_a-{F}(V1), product-{F}(V1,V0,V2), defined-{F}(V3,V1), product-{F}(V3,V2,V4), product-{F}(V1,V0,V5), defined-{F}(V6,V1), V3 == V6, product-{F}(V6,V5,V4), product-{F}(V7,V8,V0), product-{F}(V9,V8,V4), product-{F}(V9,V0,V10), product-{F}(V7,V0,V10), product-{F}(V7,V11,V10) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #792: mergings( V2 == V4, V4 == V5, V5 == V7, V3 == V6; #782 ), references = 1, size of lhs = 14:
% 3.38/3.59 P_b-{F}(V0), P_a-{F}(V1), defined-{F}(V1,V1), product-{F}(V1,V0,V2), defined-{F}(V1,V2), defined-{F}(V3,V1), V1 == V3, product-{F}(V1,V0,V4), product-{F}(V3,V4,V5), product-{F}(V1,V0,V6), product-{F}(V1,V6,V5), product-{F}(V1,V7,V0), product-{F}(V1,V7,V5), product-{F}(V1,V8,V2) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #807: mergings( V1 == V6, V6 == V8, V8 == V9, V9 == V11, V2 == V7, V7 == V10; #799 ), references = 1, size of lhs = 15:
% 3.38/3.59 P_c-{F}(V0), P_h-{F}(V1), P_d-{F}(V2), P_b-{F}(V3), P_a-{F}(V4), product-{F}(V4,V3,V0), product-{F}(V4,V3,V5), defined-{F}(V6,V4), product-{F}(V6,V5,V2), product-{F}(V4,V7,V0), product-{F}(V8,V9,V3), product-{F}(V10,V9,V2), product-{F}(V10,V3,V11), product-{F}(V8,V3,V11), product-{F}(V8,V12,V11) | P_g-{T}(V6)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #814: mergings( V1 == V6, V6 == V8, V8 == V9, V9 == V11, V2 == V7, V7 == V10; #800 ), references = 1, size of lhs = 15:
% 3.38/3.59 P_c-{F}(V0), P_h-{F}(V1), P_d-{F}(V2), P_b-{F}(V3), P_a-{F}(V4), defined-{F}(V4,V4), product-{F}(V4,V3,V0), product-{F}(V4,V3,V5), defined-{F}(V4,V5), product-{F}(V4,V3,V6), product-{F}(V4,V6,V2), product-{F}(V4,V7,V3), product-{F}(V4,V7,V2), product-{F}(V4,V8,V5), product-{F}(V4,V9,V0) | P_g-{T}(V4)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #847: exists( #24, #845 ), references = 1, size of lhs = 15:
% 3.38/3.59 P_a-{F}(V0), product-{F}(V0,V1,V2), defined-{F}(V2,V3), product-{F}(V1,V3,V0), product-{F}(V4,V0,V5), product-{F}(V6,V4,V7), product-{F}(V6,V8,V9), product-{F}(V9,V10,V0), product-{F}(V8,V11,V12), defined-{F}(V12,V13), product-{F}(V11,V13,V10), product-{F}(V13,V2,V14), product-{F}(V14,V3,V15), defined-{F}(V12,V15), product-{F}(V12,V15,V5) | P_compose-{T}(V2,V3,V7)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #864: exists( #25, #862 ), references = 1, size of lhs = 14:
% 3.38/3.59 P_a-{F}(V0), defined-{F}(V1,V0), defined-{F}(V2,V1), product-{F}(V2,V1,V3), defined-{F}(V1,V4), product-{F}(V5,V1,V0), product-{F}(V0,V5,V6), defined-{F}(V6,V1), product-{F}(V0,V6,V7), product-{F}(V7,V1,V0), product-{F}(V8,V1,V3), product-{F}(V9,V6,V8), V3 == V9, product-{F}(V10,V9,V1) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #930: mergings( V3 == V1; #927 ), references = 1, size of lhs = 9:
% 3.38/3.59 P_b-{F}(V0), P_a-{F}(V1), defined-{F}(V2,V1), product-{F}(V1,V0,V3), defined-{F}(V4,V1), V2 == V4, product-{F}(V4,V3,V5), product-{F}(V1,V0,V6), product-{F}(V2,V6,V5) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #938: mergings( V1 == V6, V6 == V8, V2 == V7; #934 ), references = 1, size of lhs = 10:
% 3.38/3.59 P_c-{F}(V0), P_h-{F}(V1), P_d-{F}(V2), P_b-{F}(V3), P_a-{F}(V4), product-{F}(V4,V3,V0), defined-{F}(V5,V4), product-{F}(V4,V3,V6), product-{F}(V5,V6,V2), product-{F}(V4,V7,V0) | P_g-{T}(V5)
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #954: mergings( V1 == V4, V4 == V8, V8 == V10, V10 == V12, V2 == V5, V5 == V9, V9 == V13, V3 == V6, V6 == V14, V7 == V15; #943 ), references = 1, size of lhs = 7:
% 3.38/3.59 P_a-{F}(V0), P_b-{F}(V1), product-{F}(V0,V1,V2), P_c-{F}(V2), product-{F}(V0,V3,V2), P_h-{F}(V4), product-{F}(V0,V5,V2) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #965: mergings( V1 == V4, V4 == V7, V7 == V9, V9 == V11, V2 == V5, V5 == V8, V8 == V12, V3 == V6, V6 == V13; #955 ), references = 1, size of lhs = 6:
% 3.38/3.59 P_a-{F}(V0), P_b-{F}(V1), product-{F}(V0,V1,V2), P_c-{F}(V2), product-{F}(V0,V3,V2), product-{F}(V0,V4,V2) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #975: mergings( V1 == V3, V3 == V5, V5 == V7, V7 == V8, V2 == V4, V4 == V6, V6 == V9; #967 ), references = 1, size of lhs = 2:
% 3.38/3.59 P_a-{F}(V0), P_b-{F}(V1) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #981: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5; #976 ), references = 1, size of lhs = 1:
% 3.38/3.59 P_a-{F}(V0) | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 #983: exists( #27, #976 ), references = 1, size of lhs = 0:
% 3.38/3.59 FALSE | FALSE
% 3.38/3.59 (used 0 times, uses = {})
% 3.38/3.59
% 3.38/3.59 number of learnt formulas = 58
% 3.38/3.59
% 3.38/3.59
% 3.38/3.59 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.38/3.59
% 3.38/3.59 randbase = 1
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