TSTP Solution File: GRP114-1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : GRP114-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n005.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 06:03:10 EDT 2022
% Result : Unsatisfiable 232.04s 232.19s
% Output : Refutation 232.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP114-1 : TPTP v8.1.0. Released v1.2.0.
% 0.00/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jul 22 14:16:51 EDT 2022
% 0.11/0.32 % CPUTime :
% 232.04/232.19 GeoParameters:
% 232.04/232.19
% 232.04/232.19 tptp_input = 1
% 232.04/232.19 tptp_output = 0
% 232.04/232.19 nonempty = 1
% 232.04/232.19 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 232.04/232.19 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 232.04/232.19
% 232.04/232.19
% 232.04/232.19 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 232.04/232.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 232.04/232.19
% 232.04/232.19 RuleSystem INPUT:
% 232.04/232.19
% 232.04/232.19 Initial Rules:
% 232.04/232.19 #0: input, references = 4, size of lhs = 3:
% 232.04/232.19 P_identity-{F}(V0), P_multiply-{F}(V0,V1,V2), V2 == V1 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #1: input, references = 4, size of lhs = 4:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V1,V2), P_multiply-{F}(V2,V1,V3), V3 == V0 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #2: input, references = 8, size of lhs = 6:
% 232.04/232.19 P_identity-{F}(V0), P_multiply-{F}(V1,V2,V4), P_multiply-{F}(V4,V3,V5), P_multiply-{F}(V2,V3,V6), P_multiply-{F}(V1,V6,V7), V5 == V7 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #3: input, references = 4, size of lhs = 3:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), V1 == V0 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #4: input, references = 4, size of lhs = 5:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_inverse-{F}(V2,V3), P_inverse-{F}(V3,V4), V4 == V2 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #5: input, references = 4, size of lhs = 8:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_multiply-{F}(V2,V3,V4), P_inverse-{F}(V4,V5), P_inverse-{F}(V3,V6), P_inverse-{F}(V2,V7), P_multiply-{F}(V6,V7,V8), V5 == V8 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #6: input, references = 4, size of lhs = 4:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_intersection-{F}(V2,V2,V3), V3 == V2 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #7: input, references = 4, size of lhs = 4:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_union-{F}(V2,V2,V3), V3 == V2 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #8: input, references = 4, size of lhs = 5:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_intersection-{F}(V2,V3,V4), P_intersection-{F}(V3,V2,V5), V4 == V5 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #9: input, references = 4, size of lhs = 5:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_union-{F}(V2,V3,V4), P_union-{F}(V3,V2,V5), V4 == V5 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #10: input, references = 5, size of lhs = 7:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_intersection-{F}(V3,V4,V5), P_intersection-{F}(V2,V5,V6), P_intersection-{F}(V2,V3,V7), P_intersection-{F}(V7,V4,V8), V6 == V8 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #11: input, references = 5, size of lhs = 7:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_union-{F}(V3,V4,V5), P_union-{F}(V2,V5,V6), P_union-{F}(V2,V3,V7), P_union-{F}(V7,V4,V8), V6 == V8 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #12: input, references = 4, size of lhs = 5:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_intersection-{F}(V2,V3,V4), P_union-{F}(V4,V3,V5), V5 == V3 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #13: input, references = 4, size of lhs = 5:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_union-{F}(V2,V3,V4), P_intersection-{F}(V4,V3,V5), V5 == V3 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #14: input, references = 6, size of lhs = 8:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_union-{F}(V3,V4,V5), P_multiply-{F}(V2,V5,V6), P_multiply-{F}(V2,V3,V7), P_multiply-{F}(V2,V4,V8), P_union-{F}(V7,V8,V9), V6 == V9 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #15: input, references = 4, size of lhs = 8:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_intersection-{F}(V3,V4,V5), P_multiply-{F}(V2,V5,V6), P_multiply-{F}(V2,V3,V7), P_multiply-{F}(V2,V4,V8), P_intersection-{F}(V7,V8,V9), V6 == V9 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #16: input, references = 6, size of lhs = 8:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_union-{F}(V3,V4,V5), P_multiply-{F}(V5,V2,V6), P_multiply-{F}(V3,V2,V7), P_multiply-{F}(V4,V2,V8), P_union-{F}(V7,V8,V9), V6 == V9 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #17: input, references = 4, size of lhs = 8:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_intersection-{F}(V3,V4,V5), P_multiply-{F}(V5,V2,V6), P_multiply-{F}(V3,V2,V7), P_multiply-{F}(V4,V2,V8), P_intersection-{F}(V7,V8,V9), V6 == V9 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #18: input, references = 5, size of lhs = 5:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_positive_part-{F}(V2,V3), P_union-{F}(V2,V0,V4), V3 == V4 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #19: input, references = 5, size of lhs = 5:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_negative_part-{F}(V2,V3), P_intersection-{F}(V2,V0,V4), V3 == V4 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #20: input, references = 4, size of lhs = 6:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_a-{F}(V2), P_positive_part-{F}(V2,V3), P_negative_part-{F}(V2,V4), P_multiply-{F}(V3,V4,V2) | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #21: input, references = 12, size of lhs = 2:
% 232.04/232.19 #-{F} V0, #-{F} V1 | EXISTS V2: P_multiply-{T}(V0,V1,V2)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #22: input, references = 4, size of lhs = 0:
% 232.04/232.19 FALSE | EXISTS V0: P_identity-{T}(V0)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #23: input, references = 10, size of lhs = 1:
% 232.04/232.19 #-{F} V0 | EXISTS V1: P_inverse-{T}(V0,V1)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #24: input, references = 8, size of lhs = 2:
% 232.04/232.19 #-{F} V0, #-{F} V1 | EXISTS V2: P_intersection-{T}(V0,V1,V2)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #25: input, references = 10, size of lhs = 2:
% 232.04/232.19 #-{F} V0, #-{F} V1 | EXISTS V2: P_union-{T}(V0,V1,V2)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #26: input, references = 7, size of lhs = 1:
% 232.04/232.19 #-{F} V0 | EXISTS V1: P_positive_part-{T}(V0,V1)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #27: input, references = 6, size of lhs = 1:
% 232.04/232.19 #-{F} V0 | EXISTS V1: P_negative_part-{T}(V0,V1)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #28: input, references = 4, size of lhs = 0:
% 232.04/232.19 FALSE | EXISTS V0: P_a-{T}(V0)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 number of initial rules = 29
% 232.04/232.19
% 232.04/232.19 Simplifiers:
% 232.04/232.19 #29: unsound, references = 3, size of lhs = 3:
% 232.04/232.19 P_multiply-{F}(V0,V1,V2), P_multiply-{F}(V0,V1,V5), V2 == V5 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #30: unsound, references = 3, size of lhs = 3:
% 232.04/232.19 P_identity-{F}(V0), P_identity-{F}(V1), V0 == V1 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #31: unsound, references = 3, size of lhs = 3:
% 232.04/232.19 P_inverse-{F}(V0,V1), P_inverse-{F}(V0,V3), V1 == V3 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #32: unsound, references = 3, size of lhs = 3:
% 232.04/232.19 P_intersection-{F}(V0,V1,V2), P_intersection-{F}(V0,V1,V5), V2 == V5 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #33: unsound, references = 3, size of lhs = 3:
% 232.04/232.19 P_union-{F}(V0,V1,V2), P_union-{F}(V0,V1,V5), V2 == V5 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #34: unsound, references = 3, size of lhs = 3:
% 232.04/232.19 P_positive_part-{F}(V0,V1), P_positive_part-{F}(V0,V3), V1 == V3 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #35: unsound, references = 3, size of lhs = 3:
% 232.04/232.19 P_negative_part-{F}(V0,V1), P_negative_part-{F}(V0,V3), V1 == V3 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #36: unsound, references = 3, size of lhs = 3:
% 232.04/232.19 P_a-{F}(V0), P_a-{F}(V1), V0 == V1 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 number of simplifiers = 8
% 232.04/232.19
% 232.04/232.19 Learnt:
% 232.04/232.19 #38: exists( #23, #3 ), references = 1, size of lhs = 1:
% 232.04/232.19 P_identity-{F}(V0) | P_inverse-{T}(V0,V0)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #41: exists( #25, #7 ), references = 1, size of lhs = 3:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), #-{F} V2 | P_union-{T}(V2,V2,V2)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #42: exists( #25, #12 ), references = 7, size of lhs = 3:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_intersection-{F}(V2,V3,V4) | P_union-{T}(V4,V3,V3)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #45: exists( #24, #6 ), references = 1, size of lhs = 3:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), #-{F} V2 | P_intersection-{T}(V2,V2,V2)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #46: exists( #24, #13 ), references = 7, size of lhs = 3:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_union-{F}(V2,V3,V4) | P_intersection-{T}(V4,V3,V3)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #48: exists( #21, #1 ), references = 10, size of lhs = 2:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V1,V2) | P_multiply-{T}(V2,V1,V0)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #50: exists( #26, #18 ), references = 1, size of lhs = 3:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_union-{F}(V2,V0,V3) | P_positive_part-{T}(V2,V3)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #52: exists( #27, #19 ), references = 1, size of lhs = 3:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_intersection-{F}(V2,V0,V3) | P_negative_part-{T}(V2,V3)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #54: exists( #24, #19 ), references = 3, size of lhs = 3:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_negative_part-{F}(V2,V3) | P_intersection-{T}(V2,V0,V3)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #57: exists( #21, #0 ), references = 9, size of lhs = 2:
% 232.04/232.19 P_identity-{F}(V0), #-{F} V1 | P_multiply-{T}(V0,V1,V1)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #58: exists( #21, #2 ), references = 9, size of lhs = 4:
% 232.04/232.19 P_identity-{F}(V0), P_multiply-{F}(V1,V2,V3), P_multiply-{F}(V2,V4,V5), P_multiply-{F}(V1,V5,V6) | P_multiply-{T}(V3,V4,V6)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #60: exists( #24, #8 ), references = 7, size of lhs = 3:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_intersection-{F}(V2,V3,V4) | P_intersection-{T}(V3,V2,V4)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #62: exists( #25, #18 ), references = 5, size of lhs = 3:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_positive_part-{F}(V2,V3) | P_union-{T}(V2,V0,V3)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #64: exists( #25, #16 ), references = 6, size of lhs = 6:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_union-{F}(V2,V3,V4), P_multiply-{F}(V4,V5,V6), P_multiply-{F}(V2,V5,V7), P_multiply-{F}(V3,V5,V8) | P_union-{T}(V7,V8,V6)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #69: exists( #25, #9 ), references = 12, size of lhs = 3:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_union-{F}(V2,V3,V4) | P_union-{T}(V3,V2,V4)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #79: exists( #23, #4 ), references = 5, size of lhs = 3:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_inverse-{F}(V2,V3) | P_inverse-{T}(V3,V2)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #81: exists( #24, #17 ), references = 3, size of lhs = 6:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_intersection-{F}(V2,V3,V4), P_multiply-{F}(V4,V5,V6), P_multiply-{F}(V2,V5,V7), P_multiply-{F}(V3,V5,V8) | P_intersection-{T}(V7,V8,V6)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #85: exists( #21, #2 ), references = 6, size of lhs = 4:
% 232.04/232.19 P_identity-{F}(V0), P_multiply-{F}(V1,V2,V3), P_multiply-{F}(V3,V4,V5), P_multiply-{F}(V2,V4,V6) | P_multiply-{T}(V1,V6,V5)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #86: exists( #21, #5 ), references = 2, size of lhs = 6:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_inverse-{F}(V2,V3), P_multiply-{F}(V4,V2,V5), P_inverse-{F}(V5,V6), P_inverse-{F}(V4,V7) | P_multiply-{T}(V3,V7,V6)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #120: mergings( V3 == V4, V4 == V6, V6 == V7, V7 == V9, V5 == V8, V8 == V10; #113 ), references = 3, size of lhs = 11:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_union-{F}(V0,V2,V2), P_multiply-{F}(V2,V3,V4), P_multiply-{F}(V4,V5,V6), P_union-{F}(V7,V3,V8), P_multiply-{F}(V8,V5,V9), P_multiply-{F}(V7,V5,V10), P_union-{F}(V10,V6,V11), P_union-{F}(V9,V6,V12), V11 == V12 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #141: mergings( V3 == V5, V5 == V7, V7 == V9, V9 == V11, V4 == V6, V6 == V8, V8 == V10, V10 == V12; #132 ), references = 1, size of lhs = 10:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_union-{F}(V2,V3,V3), P_multiply-{F}(V2,V4,V5), P_intersection-{F}(V6,V3,V7), P_multiply-{F}(V7,V4,V8), P_multiply-{F}(V6,V4,V9), P_intersection-{F}(V9,V5,V10), P_intersection-{F}(V8,V5,V11), V10 == V11 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #160: exists( #21, #14 ), references = 5, size of lhs = 6:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_union-{F}(V2,V3,V4), P_multiply-{F}(V5,V2,V6), P_multiply-{F}(V5,V3,V7), P_union-{F}(V6,V7,V8) | P_multiply-{T}(V5,V4,V8)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #184: exists( #21, #16 ), references = 10, size of lhs = 6:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_union-{F}(V2,V3,V4), P_multiply-{F}(V2,V5,V6), P_multiply-{F}(V3,V5,V7), P_union-{F}(V6,V7,V8) | P_multiply-{T}(V4,V5,V8)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #205: mergings( V2 == V3; #203 ), references = 2, size of lhs = 4:
% 232.04/232.19 P_identity-{F}(V0), P_multiply-{F}(V0,V1,V2), V2 == V0, P_multiply-{F}(V3,V1,V3) | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #237: exists( #25, #11 ), references = 4, size of lhs = 5:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_union-{F}(V2,V3,V4), P_union-{F}(V5,V2,V6), P_union-{F}(V6,V3,V7) | P_union-{T}(V5,V4,V7)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #238: exists( #25, #120 ), references = 2, size of lhs = 9:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_union-{F}(V0,V2,V2), P_multiply-{F}(V2,V3,V4), P_multiply-{F}(V4,V5,V6), P_union-{F}(V7,V3,V8), P_multiply-{F}(V8,V5,V9), P_multiply-{F}(V7,V5,V10), P_union-{F}(V9,V6,V11) | P_union-{T}(V10,V6,V11)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #280: mergings( V2 == V3, V3 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V11, V4 == V9, V9 == V12; #271 ), references = 1, size of lhs = 15:
% 232.04/232.19 P_identity-{F}(V0), P_union-{F}(V0,V1,V1), P_inverse-{F}(V0,V2), P_union-{F}(V0,V3,V3), P_multiply-{F}(V1,V4,V5), P_multiply-{F}(V3,V6,V5), P_union-{F}(V0,V4,V7), P_multiply-{F}(V8,V7,V5), P_multiply-{F}(V8,V0,V9), P_union-{F}(V0,V9,V10), P_union-{F}(V0,V6,V11), P_multiply-{F}(V12,V7,V11), P_multiply-{F}(V12,V0,V13), P_union-{F}(V13,V9,V14), V10 == V14 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #311: mergings( V3 == V4, V4 == V6, V6 == V8, V8 == V10, V10 == V12, V12 == V13, V13 == V15, V15 == V16, V16 == V17, V17 == V19, V19 == V20, V20 == V21, V21 == V22, V22 == V24, V5 == V7, V7 == V9, V9 == V11, V11 == V14, V14 == V18, V18 == V23, V23 == V25; #289 ), references = 1, size of lhs = 25:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_union-{F}(V0,V2,V2), P_union-{F}(V0,V3,V3), P_union-{F}(V4,V5,V2), P_multiply-{F}(V4,V6,V7), P_multiply-{F}(V5,V6,V8), P_union-{F}(V0,V6,V9), P_multiply-{F}(V10,V0,V7), P_union-{F}(V0,V7,V11), P_multiply-{F}(V10,V12,V0), P_multiply-{F}(V12,V7,V13), P_multiply-{F}(V12,V8,V14), P_union-{F}(V13,V14,V9), P_multiply-{F}(V15,V0,V8), P_multiply-{F}(V15,V9,V16), P_union-{F}(V0,V17,V16), P_multiply-{F}(V18,V17,V19), P_multiply-{F}(V20,V19,V7), P_multiply-{F}(V21,V19,V8), P_union-{F}(V20,V21,V22), P_union-{F}(V23,V24,V22), P_multiply-{F}(V23,V18,V25), P_multiply-{F}(V24,V18,V26), P_union-{F}(V25,V26,V3) | P_union-{T}(V7,V8,V11)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #371: mergings( V2 == V4, V4 == V6, V6 == V8, V8 == V10, V10 == V12, V12 == V14, V14 == V16, V16 == V17, V17 == V19, V19 == V21, V21 == V23, V23 == V25, V25 == V26, V26 == V28, V28 == V29, V29 == V31, V31 == V32, V32 == V33, V33 == V34, V34 == V36, V36 == V39, V3 == V5, V5 == V7, V7 == V9, V9 == V11, V11 == V13, V13 == V15, V15 == V18, V18 == V20, V20 == V22, V22 == V24, V24 == V27, V27 == V30, V30 == V35, V35 == V37, V37 == V38, V38 == V40; #332 ), references = 1, size of lhs = 27:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_multiply-{F}(V0,V2,V0), P_multiply-{F}(V3,V2,V3), P_union-{F}(V0,V4,V4), P_union-{F}(V3,V5,V5), P_multiply-{F}(V5,V2,V5), P_multiply-{F}(V2,V5,V6), P_multiply-{F}(V5,V6,V7), P_union-{F}(V0,V7,V8), P_union-{F}(V0,V9,V8), P_multiply-{F}(V10,V9,V7), P_union-{F}(V10,V11,V4), P_multiply-{F}(V11,V9,V12), P_multiply-{F}(V0,V6,V12), P_multiply-{F}(V13,V0,V7), P_multiply-{F}(V13,V14,V0), P_multiply-{F}(V14,V7,V15), P_multiply-{F}(V14,V12,V16), P_union-{F}(V15,V16,V8), P_multiply-{F}(V17,V0,V12), P_multiply-{F}(V17,V7,V18), P_multiply-{F}(V17,V12,V19), P_union-{F}(V18,V19,V20), P_multiply-{F}(V17,V21,V0), P_union-{F}(V21,V22,V8), P_multiply-{F}(V17,V22,V5) | P_positive_part-{T}(V5,V20)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #412: mergings( V2 == V4, V4 == V6, V6 == V8, V8 == V10, V10 == V12, V12 == V14, V14 == V16, V16 == V18, V18 == V19, V19 == V20, V20 == V22, V22 == V24, V24 == V26, V26 == V28, V28 == V29, V29 == V31, V31 == V32, V32 == V34, V34 == V35, V35 == V36, V36 == V37, V37 == V39, V39 == V42, V3 == V5, V5 == V7, V7 == V9, V9 == V11, V11 == V13, V13 == V15, V15 == V17, V17 == V21, V21 == V23, V23 == V25, V25 == V27, V27 == V30, V30 == V33, V33 == V38, V38 == V40, V40 == V41, V41 == V43; #333 ), references = 1, size of lhs = 31:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_union-{F}(V0,V2,V2), P_multiply-{F}(V0,V3,V0), P_multiply-{F}(V4,V3,V4), P_union-{F}(V4,V5,V5), P_multiply-{F}(V5,V3,V5), P_multiply-{F}(V3,V5,V6), P_multiply-{F}(V5,V6,V7), P_multiply-{F}(V8,V0,V7), P_union-{F}(V0,V7,V9), P_multiply-{F}(V8,V10,V0), P_multiply-{F}(V10,V7,V11), P_multiply-{F}(V0,V6,V12), P_multiply-{F}(V10,V12,V13), P_union-{F}(V11,V13,V14), P_union-{F}(V0,V15,V14), P_multiply-{F}(V16,V15,V7), P_union-{F}(V16,V17,V2), P_multiply-{F}(V17,V15,V12), P_multiply-{F}(V18,V0,V12), P_multiply-{F}(V18,V19,V0), P_union-{F}(V19,V20,V14), P_multiply-{F}(V18,V20,V5), P_multiply-{F}(V7,V21,V22), P_multiply-{F}(V12,V21,V23), P_union-{F}(V22,V23,V24), P_multiply-{F}(V25,V21,V3), P_multiply-{F}(V0,V25,V26), P_multiply-{F}(V5,V25,V27), P_union-{F}(V26,V27,V9) | P_positive_part-{T}(V5,V24)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #506: exists( #21, #15 ), references = 2, size of lhs = 6:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_intersection-{F}(V2,V3,V4), P_multiply-{F}(V5,V2,V6), P_multiply-{F}(V5,V3,V7), P_intersection-{F}(V6,V7,V8) | P_multiply-{T}(V5,V4,V8)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #531: mergings( V3 == V5, V5 == V7, V4 == V6; #527 ), references = 1, size of lhs = 6:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_multiply-{F}(V0,V2,V3), V3 == V0, P_multiply-{F}(V4,V2,V5), P_multiply-{F}(V5,V2,V4) | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #587: mergings( V2 == V4, V4 == V5; #584 ), references = 1, size of lhs = 5:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_multiply-{F}(V2,V3,V3), P_multiply-{F}(V2,V0,V4), V0 == V4 | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #675: exists( #24, #10 ), references = 2, size of lhs = 5:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_intersection-{F}(V2,V3,V4), P_intersection-{F}(V5,V2,V6), P_intersection-{F}(V6,V3,V7) | P_intersection-{T}(V5,V4,V7)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #760: mergings( V3 == V4, V4 == V6, V6 == V8, V8 == V10, V5 == V7, V7 == V9, V9 == V11; #752 ), references = 2, size of lhs = 11:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_union-{F}(V2,V3,V3), P_multiply-{F}(V4,V3,V5), P_multiply-{F}(V6,V5,V7), P_union-{F}(V6,V8,V9), P_multiply-{F}(V9,V4,V10), P_multiply-{F}(V10,V2,V11), P_multiply-{F}(V8,V5,V12), P_union-{F}(V11,V12,V13), P_union-{F}(V13,V7,V14) | P_multiply-{T}(V9,V5,V14)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #804: mergings( V2 == V3, V3 == V4, V4 == V6, V6 == V7, V7 == V9, V9 == V11, V11 == V13, V13 == V14, V14 == V16, V16 == V18, V18 == V20, V20 == V22, V22 == V24, V24 == V26, V26 == V28, V5 == V8, V8 == V10, V10 == V12, V12 == V15, V15 == V17, V17 == V19, V19 == V21, V21 == V23, V23 == V25, V25 == V27; #778 ), references = 1, size of lhs = 17:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_union-{F}(V0,V2,V2), P_intersection-{F}(V3,V0,V0), P_multiply-{F}(V4,V3,V2), P_multiply-{F}(V4,V0,V5), P_intersection-{F}(V5,V0,V6), P_multiply-{F}(V3,V7,V3), P_multiply-{F}(V7,V6,V8), P_multiply-{F}(V0,V8,V9), P_multiply-{F}(V10,V3,V3), P_inverse-{F}(V10,V11), P_multiply-{F}(V12,V8,V13), P_union-{F}(V12,V14,V3), P_multiply-{F}(V14,V8,V15), P_union-{F}(V0,V15,V16), P_union-{F}(V16,V13,V11) | P_inverse-{T}(V3,V9)
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #855: mergings( V2 == V4, V4 == V6, V6 == V8, V8 == V9, V9 == V10, V10 == V12, V12 == V14, V14 == V16, V16 == V18, V18 == V20, V20 == V21, V21 == V23, V23 == V25, V25 == V27, V27 == V29, V29 == V31, V31 == V33, V33 == V35, V35 == V36, V36 == V38, V38 == V39, V39 == V40, V40 == V41, V3 == V5, V5 == V7, V7 == V11, V11 == V13, V13 == V15, V15 == V17, V17 == V19, V19 == V22, V22 == V24, V24 == V26, V26 == V28, V28 == V30, V30 == V32, V32 == V34, V34 == V37, V37 == V42; #815 ), references = 1, size of lhs = 20:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_a-{F}(V2), P_positive_part-{F}(V2,V3), P_negative_part-{F}(V2,V4), P_union-{F}(V0,V4,V0), P_multiply-{F}(V5,V0,V2), P_multiply-{F}(V5,V6,V3), P_inverse-{F}(V7,V0), P_union-{F}(V0,V8,V8), P_multiply-{F}(V7,V9,V9), P_intersection-{F}(V9,V0,V0), P_multiply-{F}(V9,V0,V9), P_multiply-{F}(V10,V9,V8), P_multiply-{F}(V10,V0,V11), P_multiply-{F}(V6,V12,V9), P_union-{F}(V0,V12,V9), P_multiply-{F}(V12,V11,V13), P_multiply-{F}(V12,V0,V14), P_intersection-{F}(V13,V14,V4) | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #920: mergings( V2 == V4, V4 == V6, V6 == V8, V8 == V10, V10 == V12, V12 == V13, V13 == V15, V15 == V16, V16 == V18, V18 == V20, V20 == V22, V22 == V23, V23 == V25, V25 == V27, V27 == V29, V29 == V31, V31 == V33, V33 == V35, V35 == V36, V36 == V38, V38 == V40, V40 == V42, V42 == V44, V44 == V46, V46 == V48, V48 == V50, V50 == V51, V51 == V53, V53 == V54, V54 == V55, V55 == V56, V3 == V5, V5 == V7, V7 == V9, V9 == V11, V11 == V14, V14 == V17, V17 == V19, V19 == V21, V21 == V24, V24 == V26, V26 == V28, V28 == V30, V30 == V32, V32 == V34, V34 == V37, V37 == V39, V39 == V41, V41 == V43, V43 == V45, V45 == V47, V47 == V49, V49 == V52, V52 == V57; #865 ), references = 1, size of lhs = 26:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_a-{F}(V2), P_positive_part-{F}(V2,V3), P_negative_part-{F}(V2,V4), P_union-{F}(V0,V4,V0), P_multiply-{F}(V5,V0,V2), P_inverse-{F}(V6,V0), P_multiply-{F}(V6,V7,V7), P_intersection-{F}(V7,V0,V0), P_multiply-{F}(V7,V0,V7), P_union-{F}(V0,V8,V7), P_multiply-{F}(V8,V0,V9), P_intersection-{F}(V10,V9,V4), P_multiply-{F}(V8,V11,V10), P_multiply-{F}(V12,V0,V11), P_multiply-{F}(V5,V12,V13), P_multiply-{F}(V13,V7,V3), P_multiply-{F}(V12,V14,V0), P_union-{F}(V14,V15,V7), P_multiply-{F}(V12,V15,V16), P_multiply-{F}(V17,V8,V18), P_multiply-{F}(V19,V17,V0), P_multiply-{F}(V20,V17,V16), P_union-{F}(V19,V20,V21), P_multiply-{F}(V21,V18,V7) | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #987: mergings( V2 == V4, V4 == V6, V6 == V8, V8 == V10, V10 == V12, V12 == V14, V14 == V16, V16 == V18, V18 == V19, V19 == V21, V21 == V22, V22 == V24, V24 == V26, V26 == V28, V28 == V29, V29 == V31, V31 == V33, V33 == V36, V36 == V38, V38 == V40, V40 == V42, V42 == V43, V43 == V45, V45 == V47, V47 == V49, V49 == V51, V51 == V53, V53 == V55, V55 == V57, V57 == V58, V58 == V60, V60 == V61, V61 == V62, V62 == V63, V3 == V5, V5 == V7, V7 == V9, V9 == V11, V11 == V13, V13 == V15, V15 == V17, V17 == V20, V20 == V23, V23 == V25, V25 == V27, V27 == V30, V30 == V32, V32 == V34, V34 == V35, V35 == V37, V37 == V39, V39 == V41, V41 == V44, V44 == V46, V46 == V48, V48 == V50, V50 == V52, V52 == V54, V54 == V56, V56 == V59, V59 == V64; #925 ), references = 1, size of lhs = 23:
% 232.04/232.19 P_identity-{F}(V0), P_inverse-{F}(V0,V1), P_a-{F}(V2), P_positive_part-{F}(V2,V3), P_multiply-{F}(V4,V0,V2), P_inverse-{F}(V5,V0), P_multiply-{F}(V6,V0,V2), P_union-{F}(V0,V6,V7), P_multiply-{F}(V5,V7,V7), P_intersection-{F}(V7,V0,V0), P_multiply-{F}(V7,V0,V7), P_multiply-{F}(V6,V8,V0), P_multiply-{F}(V9,V0,V8), P_multiply-{F}(V4,V9,V10), P_multiply-{F}(V10,V7,V3), P_multiply-{F}(V9,V11,V0), P_union-{F}(V11,V12,V7), P_multiply-{F}(V9,V12,V13), P_multiply-{F}(V14,V6,V15), P_multiply-{F}(V16,V14,V0), P_multiply-{F}(V17,V14,V13), P_union-{F}(V16,V17,V18), P_multiply-{F}(V18,V15,V7) | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #1064: mergings( V2 == V3, V3 == V5, V5 == V7, V7 == V9, V9 == V11, V11 == V13, V13 == V15, V15 == V17, V17 == V19, V19 == V21, V21 == V23, V23 == V25, V25 == V26, V26 == V28, V28 == V29, V29 == V31, V31 == V33, V33 == V35, V35 == V38, V38 == V40, V74 == V76, V40 == V43, V43 == V45, V45 == V47, V47 == V49, V49 == V50, V50 == V52, V52 == V54, V54 == V56, V56 == V58, V58 == V60, V60 == V62, V62 == V64, V64 == V65, V65 == V67, V67 == V68, V68 == V69, V69 == V70, V4 == V6, V6 == V8, V8 == V10, V10 == V12, V12 == V14, V14 == V16, V16 == V18, V18 == V20, V20 == V22, V22 == V24, V24 == V27, V27 == V30, V30 == V32, V32 == V34, V34 == V36, V36 == V37, V37 == V39, V39 == V70, V70 == V41, V41 == V42, V42 == V44, V44 == V46, V46 == V48, V48 == V51, V51 == V53, V53 == V55, V55 == V57, V57 == V59, V59 == V61, V61 == V63, V63 == V66, V66 == V71; #993 ), references = 1, size of lhs = 13:
% 232.04/232.19 P_identity-{F}(V0), P_multiply-{F}(V0,V0,V0), P_inverse-{F}(V0,V0), P_a-{F}(V1), P_multiply-{F}(V1,V0,V1), P_multiply-{F}(V2,V0,V1), P_multiply-{F}(V3,V1,V0), P_multiply-{F}(V1,V3,V0), P_multiply-{F}(V0,V3,V4), P_multiply-{F}(V1,V4,V0), P_multiply-{F}(V5,V1,V0), P_multiply-{F}(V2,V5,V0), P_multiply-{F}(V5,V0,V4) | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #1142: mergings( V2 == V4, V4 == V5, V5 == V6, V6 == V8, V8 == V10, V10 == V12, V12 == V14, V14 == V16, V16 == V18, V18 == V20, V20 == V22, V22 == V24, V24 == V26, V26 == V28, V28 == V29, V29 == V31, V31 == V32, V32 == V34, V34 == V36, V36 == V38, V38 == V40, V40 == V45, V45 == V47, V47 == V49, V49 == V51, V51 == V52, V52 == V54, V54 == V56, V56 == V58, V58 == V60, V60 == V62, V62 == V64, V64 == V66, V66 == V67, V67 == V69, V69 == V70, V70 == V71, V3 == V7, V7 == V9, V9 == V11, V11 == V13, V13 == V15, V15 == V17, V17 == V19, V19 == V21, V21 == V23, V23 == V25, V25 == V27, V27 == V30, V30 == V33, V33 == V35, V35 == V37, V37 == V39, V39 == V71, V71 == V41, V41 == V42, V42 == V43, V43 == V44, V44 == V46, V46 == V48, V48 == V50, V50 == V53, V53 == V55, V55 == V57, V57 == V59, V59 == V61, V61 == V63, V63 == V65, V65 == V68, V68 == V72; #1071 ), references = 2, size of lhs = 5:
% 232.04/232.19 P_identity-{F}(V0), P_multiply-{F}(V0,V0,V0), P_inverse-{F}(V0,V0), P_a-{F}(V1), P_multiply-{F}(V0,V1,V1) | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #1145: exists( #28, #1143 ), references = 1, size of lhs = 3:
% 232.04/232.19 P_identity-{F}(V0), P_multiply-{F}(V0,V0,V0), P_inverse-{F}(V0,V0) | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 #1149: exists( #22, #1147 ), references = 1, size of lhs = 0:
% 232.04/232.19 FALSE | FALSE
% 232.04/232.19 (used 0 times, uses = {})
% 232.04/232.19
% 232.04/232.19 number of learnt formulas = 43
% 232.04/232.19
% 232.04/232.19
% 232.04/232.19 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 232.04/232.19
% 232.04/232.19 randbase = 1
%------------------------------------------------------------------------------