TSTP Solution File: GRP040-3 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : GRP040-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n007.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 06:03:03 EDT 2022
% Result : Unsatisfiable 2.34s 2.51s
% Output : Refutation 2.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP040-3 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jul 22 14:11:42 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.34/2.51 GeoParameters:
% 2.34/2.51
% 2.34/2.51 tptp_input = 1
% 2.34/2.51 tptp_output = 0
% 2.34/2.51 nonempty = 1
% 2.34/2.51 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.34/2.51 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 2.34/2.51
% 2.34/2.51
% 2.34/2.51 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.34/2.51 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.34/2.51
% 2.34/2.51 RuleSystem INPUT:
% 2.34/2.51
% 2.34/2.51 Initial Rules:
% 2.34/2.51 #0: input, references = 10, size of lhs = 2:
% 2.34/2.51 P_identity-{F}(V0), #-{F} V1 | product-{T}(V0,V1,V1)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #1: input, references = 7, size of lhs = 2:
% 2.34/2.51 P_identity-{F}(V0), #-{F} V1 | product-{T}(V1,V0,V1)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #2: input, references = 13, size of lhs = 2:
% 2.34/2.51 P_identity-{F}(V0), P_inverse-{F}(V1,V2) | product-{T}(V2,V1,V0)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #3: input, references = 8, size of lhs = 2:
% 2.34/2.51 P_identity-{F}(V0), P_inverse-{F}(V1,V2) | product-{T}(V1,V2,V0)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #4: input, references = 5, size of lhs = 2:
% 2.34/2.51 P_identity-{F}(V0), P_multiply-{F}(V1,V2,V3) | product-{T}(V1,V2,V3)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #5: input, references = 15, size of lhs = 4:
% 2.34/2.51 P_identity-{F}(V0), product-{F}(V4,V3,V1), product-{F}(V4,V3,V2), V1 == V2 | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #6: input, references = 12, size of lhs = 4:
% 2.34/2.51 P_identity-{F}(V0), product-{F}(V3,V1,V2), product-{F}(V5,V1,V4), product-{F}(V6,V5,V3) | product-{T}(V6,V4,V2)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #7: input, references = 10, size of lhs = 4:
% 2.34/2.51 P_identity-{F}(V0), product-{F}(V5,V1,V4), product-{F}(V6,V5,V3), product-{F}(V6,V4,V2) | product-{T}(V3,V1,V2)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #8: input, references = 11, size of lhs = 5:
% 2.34/2.51 P_identity-{F}(V0), P_inverse-{F}(V2,V3), subgroup_member-{F}(V2), subgroup_member-{F}(V4), product-{F}(V4,V3,V1) | subgroup_member-{T}(V1)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #9: input, references = 6, size of lhs = 2:
% 2.34/2.51 P_identity-{F}(V0), P_element_in_O2-{F}(V2,V1,V3) | subgroup_member-{T}(V1), subgroup_member-{T}(V3), subgroup_member-{T}(V2)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #10: input, references = 5, size of lhs = 2:
% 2.34/2.51 P_identity-{F}(V0), P_element_in_O2-{F}(V2,V1,V3) | subgroup_member-{T}(V1), product-{T}(V2,V3,V1), subgroup_member-{T}(V2)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #11: input, references = 6, size of lhs = 3:
% 2.34/2.51 P_identity-{F}(V0), P_a-{F}(V1), subgroup_member-{F}(V1) | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #12: input, references = 5, size of lhs = 3:
% 2.34/2.51 P_identity-{F}(V0), P_a-{F}(V1), P_b-{F}(V2) | subgroup_member-{T}(V2)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #13: input, references = 4, size of lhs = 5:
% 2.34/2.51 P_identity-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_d-{F}(V3), subgroup_member-{F}(V3) | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #14: input, references = 10, size of lhs = 6:
% 2.34/2.51 P_identity-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_d-{F}(V3), P_inverse-{F}(V1,V4), P_c-{F}(V5) | product-{T}(V2,V4,V5)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #15: input, references = 8, size of lhs = 6:
% 2.34/2.51 P_identity-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_d-{F}(V3), P_inverse-{F}(V1,V4), P_c-{F}(V5) | product-{T}(V1,V5,V3)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #16: input, references = 3, size of lhs = 9:
% 2.34/2.51 P_identity-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_d-{F}(V3), P_inverse-{F}(V1,V4), P_c-{F}(V5), P_inverse-{F}(V6,V7), P_inverse-{F}(V7,V8), V8 == V6 | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #17: input, references = 4, size of lhs = 0:
% 2.34/2.51 FALSE | EXISTS V0: P_identity-{T}(V0)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #18: input, references = 17, size of lhs = 1:
% 2.34/2.51 #-{F} V0 | EXISTS V1: P_inverse-{T}(V0,V1)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #19: input, references = 5, size of lhs = 2:
% 2.34/2.51 #-{F} V0, #-{F} V1 | EXISTS V2: P_multiply-{T}(V0,V1,V2)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #20: input, references = 5, size of lhs = 2:
% 2.34/2.51 #-{F} V0, #-{F} V1 | EXISTS V2: P_element_in_O2-{T}(V0,V1,V2)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #21: input, references = 4, size of lhs = 0:
% 2.34/2.51 FALSE | EXISTS V0: P_a-{T}(V0)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #22: input, references = 5, size of lhs = 0:
% 2.34/2.51 FALSE | EXISTS V0: P_b-{T}(V0)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #23: input, references = 5, size of lhs = 0:
% 2.34/2.51 FALSE | EXISTS V0: P_d-{T}(V0)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #24: input, references = 5, size of lhs = 0:
% 2.34/2.51 FALSE | EXISTS V0: P_c-{T}(V0)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 number of initial rules = 25
% 2.34/2.51
% 2.34/2.51 Simplifiers:
% 2.34/2.51 #25: unsound, references = 3, size of lhs = 3:
% 2.34/2.51 P_identity-{F}(V0), P_identity-{F}(V1), V0 == V1 | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #26: unsound, references = 3, size of lhs = 3:
% 2.34/2.51 P_inverse-{F}(V0,V1), P_inverse-{F}(V0,V3), V1 == V3 | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #27: unsound, references = 3, size of lhs = 3:
% 2.34/2.51 P_multiply-{F}(V0,V1,V2), P_multiply-{F}(V0,V1,V5), V2 == V5 | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #28: unsound, references = 3, size of lhs = 3:
% 2.34/2.51 P_element_in_O2-{F}(V0,V1,V2), P_element_in_O2-{F}(V0,V1,V5), V2 == V5 | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #29: unsound, references = 3, size of lhs = 3:
% 2.34/2.51 P_a-{F}(V0), P_a-{F}(V1), V0 == V1 | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #30: unsound, references = 3, size of lhs = 3:
% 2.34/2.51 P_b-{F}(V0), P_b-{F}(V1), V0 == V1 | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #31: unsound, references = 3, size of lhs = 3:
% 2.34/2.51 P_d-{F}(V0), P_d-{F}(V1), V0 == V1 | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #32: unsound, references = 3, size of lhs = 3:
% 2.34/2.51 P_c-{F}(V0), P_c-{F}(V1), V0 == V1 | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 number of simplifiers = 8
% 2.34/2.51
% 2.34/2.51 Learnt:
% 2.34/2.51 #41: mergings( V2 == V3, V3 == V4; #38 ), references = 1, size of lhs = 3:
% 2.34/2.51 P_a-{F}(V0), P_identity-{F}(V0), subgroup_member-{F}(V1) | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #48: mergings( V1 == V3, V3 == V4, V4 == V5, V2 == V5; #43 ), references = 1, size of lhs = 2:
% 2.34/2.51 P_a-{F}(V0), P_identity-{F}(V0) | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #58: mergings( V2 == V3, V3 == V6; #55 ), references = 2, size of lhs = 5:
% 2.34/2.51 P_b-{F}(V0), P_identity-{F}(V0), P_a-{F}(V1), P_d-{F}(V2), P_c-{F}(V3) | P_inverse-{T}(V1,V3)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #73: mergings( V1 == V3, V3 == V4, V4 == V8, V8 == V6, V2 == V7; #67 ), references = 1, size of lhs = 5:
% 2.34/2.51 P_a-{F}(V0), P_b-{F}(V1), P_identity-{F}(V1), P_d-{F}(V2), V1 == V2 | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #79: mergings( V1 == V2, V2 == V3, V3 == V6, V6 == V5; #74 ), references = 1, size of lhs = 3:
% 2.34/2.51 P_a-{F}(V0), P_b-{F}(V1), P_identity-{F}(V1) | P_d-{T}(V1)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #86: mergings( V3 == V4; #84 ), references = 1, size of lhs = 2:
% 2.34/2.51 P_identity-{F}(V0), product-{F}(V1,V2,V3) | P_multiply-{T}(V1,V2,V3)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #107: mergings( V2 == V3, V3 == V6, V6 == V7, V7 == V11, V11 == V12, V4 == V8, V5 == V9; #99 ), references = 1, size of lhs = 8:
% 2.34/2.51 P_a-{F}(V0), P_b-{F}(V1), P_d-{F}(V2), P_c-{F}(V3), P_identity-{F}(V4), product-{F}(V1,V4,V3), product-{F}(V2,V0,V5), V2 == V5 | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #125: mergings( V2 == V3, V3 == V6, V6 == V7, V7 == V10, V4 == V8, V5 == V9; #118 ), references = 1, size of lhs = 7:
% 2.34/2.51 P_a-{F}(V0), P_c-{F}(V0), P_b-{F}(V1), P_d-{F}(V2), P_identity-{F}(V3), product-{F}(V1,V3,V4), V4 == V2 | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #132: mergings( V0 == V2, V2 == V3; #129 ), references = 1, size of lhs = 1:
% 2.34/2.51 P_identity-{F}(V0) | P_inverse-{T}(V0,V0)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #140: mergings( V2 == V3, V3 == V4; #137 ), references = 1, size of lhs = 5:
% 2.34/2.51 P_d-{F}(V0), P_identity-{F}(V0), subgroup_member-{F}(V1), P_a-{F}(V2), P_b-{F}(V3) | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #157: mergings( V2 == V3, V3 == V7, V7 == V8; #153 ), references = 1, size of lhs = 8:
% 2.34/2.51 P_a-{F}(V0), P_b-{F}(V1), P_d-{F}(V2), P_c-{F}(V3), P_identity-{F}(V4), product-{F}(V3,V0,V5), product-{F}(V1,V4,V6), V6 == V5 | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #176: mergings( V2 == V3, V3 == V7, V7 == V8, V8 == V9; #171 ), references = 1, size of lhs = 10:
% 2.34/2.51 P_a-{F}(V0), P_b-{F}(V1), P_d-{F}(V2), P_c-{F}(V3), P_identity-{F}(V4), product-{F}(V1,V4,V5), product-{F}(V6,V3,V7), product-{F}(V7,V0,V8), product-{F}(V6,V5,V9), V9 == V8 | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #184: mergings( V2 == V3, V3 == V4, V4 == V8, V8 == V9, V9 == V10; #178 ), references = 1, size of lhs = 8:
% 2.34/2.51 P_a-{F}(V0), P_b-{F}(V1), P_d-{F}(V2), P_c-{F}(V3), P_identity-{F}(V4), product-{F}(V1,V4,V3), product-{F}(V4,V0,V5), V4 == V5 | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #211: mergings( V2 == V3, V3 == V6, V6 == V7, V7 == V10, V10 == V11, V11 == V12, V4 == V8, V5 == V9; #202 ), references = 2, size of lhs = 10:
% 2.34/2.51 P_a-{F}(V0), P_b-{F}(V1), P_d-{F}(V2), P_c-{F}(V2), P_identity-{F}(V3), product-{F}(V1,V3,V4), product-{F}(V4,V5,V6), product-{F}(V0,V6,V7), product-{F}(V4,V5,V8), V8 == V7 | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #216: mergings( V2 == V6; #214 ), references = 1, size of lhs = 8:
% 2.34/2.51 P_a-{F}(V0), P_b-{F}(V1), P_d-{F}(V2), P_c-{F}(V2), P_identity-{F}(V3), product-{F}(V1,V3,V4), product-{F}(V0,V3,V5), V3 == V5 | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #247: mergings( V2 == V3, V3 == V4, V4 == V5; #243 ), references = 3, size of lhs = 3:
% 2.34/2.51 P_identity-{F}(V0), product-{F}(V1,V2,V0), product-{F}(V0,V2,V3) | P_inverse-{T}(V1,V3)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #252: mergings( V0 == V4, V4 == V5, V2 == V1; #248 ), references = 1, size of lhs = 3:
% 2.34/2.51 P_identity-{F}(V0), P_a-{F}(V1), P_element_in_O2-{F}(V1,V1,V2) | subgroup_member-{T}(V2)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #261: mergings( V0 == V4, V4 == V7, V5 == V8, V6 == V9, V2 == V1; #255 ), references = 2, size of lhs = 5:
% 2.34/2.51 P_identity-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_d-{F}(V3), P_element_in_O2-{F}(V3,V3,V4) | product-{T}(V3,V4,V3)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #271: mergings( V2 == V3, V3 == V6, V6 == V7; #267 ), references = 1, size of lhs = 6:
% 2.34/2.51 P_a-{F}(V0), P_b-{F}(V1), P_d-{F}(V2), P_identity-{F}(V3), product-{F}(V4,V2,V3), product-{F}(V4,V2,V5) | P_element_in_O2-{T}(V2,V2,V5)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #291: mergings( V0 == V4, V4 == V8, V8 == V12, V12 == V13, V13 == V17, V17 == V21, V11 == V20; #283 ), references = 1, size of lhs = 15:
% 2.34/2.51 subgroup_member-{F}(V0), P_inverse-{F}(V0,V1), subgroup_member-{F}(V2), subgroup_member-{F}(V3), subgroup_member-{F}(V4), P_a-{F}(V5), P_identity-{F}(V6), product-{F}(V2,V7,V5), P_inverse-{F}(V8,V7), product-{F}(V9,V1,V8), product-{F}(V4,V10,V5), P_inverse-{F}(V11,V10), product-{F}(V3,V12,V11), P_inverse-{F}(V13,V12), P_element_in_O2-{F}(V14,V9,V13) | subgroup_member-{T}(V14)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #297: mergings( V0 == V4, V4 == V7, V5 == V1; #293 ), references = 2, size of lhs = 5:
% 2.34/2.51 P_b-{F}(V0), P_d-{F}(V1), P_identity-{F}(V2), P_a-{F}(V3), P_element_in_O2-{F}(V3,V1,V4) | product-{T}(V3,V4,V1)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #306: mergings( V3 == V5, V5 == V6, V6 == V7; #302 ), references = 1, size of lhs = 6:
% 2.34/2.51 P_b-{F}(V0), P_d-{F}(V1), P_a-{F}(V2), P_identity-{F}(V3), product-{F}(V4,V2,V3), product-{F}(V4,V1,V5) | P_element_in_O2-{T}(V2,V1,V5)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #342: mergings( V0 == V4, V4 == V7, V5 == V1; #338 ), references = 1, size of lhs = 5:
% 2.34/2.51 P_b-{F}(V0), P_d-{F}(V1), P_identity-{F}(V2), P_a-{F}(V3), P_element_in_O2-{F}(V3,V1,V4) | subgroup_member-{T}(V4)
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #403: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V9, V9 == V13; #395 ), references = 1, size of lhs = 10:
% 2.34/2.51 subgroup_member-{F}(V0), P_identity-{F}(V0), subgroup_member-{F}(V1), subgroup_member-{F}(V2), P_inverse-{F}(V2,V3), P_a-{F}(V4), product-{F}(V5,V3,V6), product-{F}(V7,V6,V4), product-{F}(V1,V7,V8), product-{F}(V8,V5,V0) | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #436: mergings( V2 == V6, V6 == V7, V7 == V10, V10 == V11, V11 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V21, V21 == V22, V22 == V23, V23 == V24, V24 == V25, V25 == V26, V26 == V27, V27 == V31, V18 == V0, V0 == V30, V3 == V8, V8 == V12, V12 == V19, V4 == V20, V5 == V9; #411 ), references = 2, size of lhs = 13:
% 2.34/2.51 P_c-{F}(V0), P_b-{F}(V1), P_d-{F}(V2), subgroup_member-{F}(V3), product-{F}(V3,V0,V0), P_identity-{F}(V3), subgroup_member-{F}(V4), P_inverse-{F}(V4,V5), P_a-{F}(V6), product-{F}(V1,V3,V7), product-{F}(V7,V8,V3), product-{F}(V8,V5,V9), product-{F}(V6,V9,V6) | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #451: mergings( V2 == V3, V3 == V4, V4 == V5; #447 ), references = 1, size of lhs = 10:
% 2.34/2.51 P_identity-{F}(V0), subgroup_member-{F}(V1), product-{F}(V0,V1,V1), P_c-{F}(V2), product-{F}(V0,V2,V2), P_b-{F}(V3), product-{F}(V3,V0,V1), P_d-{F}(V4), P_a-{F}(V5), product-{F}(V5,V0,V5) | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #457: mergings( V1 == V2, V2 == V3, V3 == V4; #453 ), references = 1, size of lhs = 8:
% 2.34/2.51 P_identity-{F}(V0), subgroup_member-{F}(V1), product-{F}(V0,V1,V1), P_b-{F}(V2), product-{F}(V2,V0,V1), P_d-{F}(V3), P_a-{F}(V4), product-{F}(V4,V0,V4) | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #462: mergings( V1 == V2, V2 == V3, V3 == V4; #458 ), references = 2, size of lhs = 7:
% 2.34/2.51 P_identity-{F}(V0), subgroup_member-{F}(V1), product-{F}(V0,V1,V1), P_b-{F}(V2), product-{F}(V2,V0,V1), P_a-{F}(V3), product-{F}(V3,V0,V3) | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #470: mergings( V1 == V3, V2 == V4; #467 ), references = 1, size of lhs = 3:
% 2.34/2.51 P_identity-{F}(V0), P_a-{F}(V1), product-{F}(V1,V0,V1) | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #474: mergings( V1 == V2; #472 ), references = 1, size of lhs = 1:
% 2.34/2.51 P_identity-{F}(V0) | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 #476: exists( #17, #472 ), references = 1, size of lhs = 0:
% 2.34/2.51 FALSE | FALSE
% 2.34/2.51 (used 0 times, uses = {})
% 2.34/2.51
% 2.34/2.51 number of learnt formulas = 31
% 2.34/2.51
% 2.34/2.51
% 2.34/2.51 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.34/2.51
% 2.34/2.51 randbase = 1
%------------------------------------------------------------------------------