TSTP Solution File: GRP040-4 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : GRP040-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n011.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 1.94s 2.14s
% Output : Refutation 1.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP040-4 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n011.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 14:07:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.94/2.14 GeoParameters:
% 1.94/2.14
% 1.94/2.14 tptp_input = 1
% 1.94/2.14 tptp_output = 0
% 1.94/2.14 nonempty = 1
% 1.94/2.14 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.94/2.14 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 1.94/2.14
% 1.94/2.14
% 1.94/2.14 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.94/2.14 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.94/2.14
% 1.94/2.14 RuleSystem INPUT:
% 1.94/2.14
% 1.94/2.14 Initial Rules:
% 1.94/2.14 #0: input, references = 5, size of lhs = 2:
% 1.94/2.14 P_identity-{F}(V0), #-{F} V1 | product-{T}(V0,V1,V1)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #1: input, references = 5, size of lhs = 2:
% 1.94/2.14 P_identity-{F}(V0), #-{F} V1 | product-{T}(V1,V0,V1)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #2: input, references = 9, size of lhs = 2:
% 1.94/2.14 P_identity-{F}(V0), P_inverse-{F}(V1,V2) | product-{T}(V2,V1,V0)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #3: input, references = 7, size of lhs = 2:
% 1.94/2.14 P_identity-{F}(V0), P_inverse-{F}(V1,V2) | product-{T}(V1,V2,V0)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #4: input, references = 7, size of lhs = 2:
% 1.94/2.14 P_identity-{F}(V0), P_multiply-{F}(V1,V2,V3) | product-{T}(V1,V2,V3)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #5: input, references = 6, size of lhs = 4:
% 1.94/2.14 P_identity-{F}(V0), product-{F}(V4,V3,V1), product-{F}(V4,V3,V2), V1 == V2 | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #6: input, references = 6, size of lhs = 4:
% 1.94/2.14 P_identity-{F}(V0), product-{F}(V3,V1,V2), product-{F}(V5,V1,V4), product-{F}(V6,V5,V3) | product-{T}(V6,V4,V2)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #7: input, references = 7, size of lhs = 4:
% 1.94/2.14 P_identity-{F}(V0), product-{F}(V5,V1,V4), product-{F}(V6,V5,V3), product-{F}(V6,V4,V2) | product-{T}(V3,V1,V2)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #8: input, references = 4, size of lhs = 5:
% 1.94/2.14 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)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #9: input, references = 3, size of lhs = 1:
% 1.94/2.14 P_identity-{F}(V0) | subgroup_member-{T}(V0)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #10: input, references = 5, size of lhs = 3:
% 1.94/2.14 P_identity-{F}(V0), P_inverse-{F}(V1,V2), subgroup_member-{F}(V1) | subgroup_member-{T}(V2)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #11: input, references = 9, size of lhs = 4:
% 1.94/2.14 P_identity-{F}(V0), product-{F}(V4,V1,V3), product-{F}(V4,V2,V3), V2 == V1 | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #12: input, references = 4, size of lhs = 4:
% 1.94/2.14 P_identity-{F}(V0), product-{F}(V3,V1,V2), product-{F}(V4,V1,V2), V3 == V4 | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #13: input, references = 5, size of lhs = 2:
% 1.94/2.14 P_identity-{F}(V0), P_element_in_O2-{F}(V2,V1,V3) | subgroup_member-{T}(V1), subgroup_member-{T}(V3), subgroup_member-{T}(V2)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #14: input, references = 6, size of lhs = 2:
% 1.94/2.14 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)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #15: input, references = 4, size of lhs = 3:
% 1.94/2.14 P_identity-{F}(V0), P_a-{F}(V1), subgroup_member-{F}(V1) | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #16: input, references = 4, size of lhs = 3:
% 1.94/2.14 P_identity-{F}(V0), P_a-{F}(V1), P_b-{F}(V2) | subgroup_member-{T}(V2)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #17: input, references = 4, size of lhs = 5:
% 1.94/2.14 P_identity-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_d-{F}(V3), subgroup_member-{F}(V3) | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #18: input, references = 7, size of lhs = 6:
% 1.94/2.14 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)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #19: input, references = 7, size of lhs = 6:
% 1.94/2.14 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)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #20: input, references = 4, size of lhs = 9:
% 1.94/2.14 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
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #21: input, references = 4, size of lhs = 0:
% 1.94/2.14 FALSE | EXISTS V0: P_identity-{T}(V0)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #22: input, references = 12, size of lhs = 1:
% 1.94/2.14 #-{F} V0 | EXISTS V1: P_inverse-{T}(V0,V1)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #23: input, references = 7, size of lhs = 2:
% 1.94/2.14 #-{F} V0, #-{F} V1 | EXISTS V2: P_multiply-{T}(V0,V1,V2)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #24: input, references = 6, size of lhs = 2:
% 1.94/2.14 #-{F} V0, #-{F} V1 | EXISTS V2: P_element_in_O2-{T}(V0,V1,V2)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #25: input, references = 4, size of lhs = 0:
% 1.94/2.14 FALSE | EXISTS V0: P_a-{T}(V0)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #26: input, references = 4, size of lhs = 0:
% 1.94/2.14 FALSE | EXISTS V0: P_b-{T}(V0)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #27: input, references = 5, size of lhs = 0:
% 1.94/2.14 FALSE | EXISTS V0: P_d-{T}(V0)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #28: input, references = 6, size of lhs = 0:
% 1.94/2.14 FALSE | EXISTS V0: P_c-{T}(V0)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 number of initial rules = 29
% 1.94/2.14
% 1.94/2.14 Simplifiers:
% 1.94/2.14 #29: unsound, references = 3, size of lhs = 3:
% 1.94/2.14 P_identity-{F}(V0), P_identity-{F}(V1), V0 == V1 | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #30: unsound, references = 3, size of lhs = 3:
% 1.94/2.14 P_inverse-{F}(V0,V1), P_inverse-{F}(V0,V3), V1 == V3 | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #31: unsound, references = 3, size of lhs = 3:
% 1.94/2.14 P_multiply-{F}(V0,V1,V2), P_multiply-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #32: unsound, references = 3, size of lhs = 3:
% 1.94/2.14 P_element_in_O2-{F}(V0,V1,V2), P_element_in_O2-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #33: unsound, references = 3, size of lhs = 3:
% 1.94/2.14 P_a-{F}(V0), P_a-{F}(V1), V0 == V1 | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #34: unsound, references = 3, size of lhs = 3:
% 1.94/2.14 P_b-{F}(V0), P_b-{F}(V1), V0 == V1 | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #35: unsound, references = 3, size of lhs = 3:
% 1.94/2.14 P_d-{F}(V0), P_d-{F}(V1), V0 == V1 | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #36: unsound, references = 3, size of lhs = 3:
% 1.94/2.14 P_c-{F}(V0), P_c-{F}(V1), V0 == V1 | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 number of simplifiers = 8
% 1.94/2.14
% 1.94/2.14 Learnt:
% 1.94/2.14 #41: mergings( V3 == V4; #39 ), references = 1, size of lhs = 2:
% 1.94/2.14 P_identity-{F}(V0), product-{F}(V1,V2,V3) | P_multiply-{T}(V1,V2,V3)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #51: mergings( V2 == V6; #49 ), references = 3, size of lhs = 6:
% 1.94/2.14 P_a-{F}(V0), P_b-{F}(V1), P_d-{F}(V2), P_c-{F}(V3), P_identity-{F}(V4), product-{F}(V1,V5,V3) | P_inverse-{T}(V0,V5)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #68: mergings( V1 == V3, V3 == V4, V4 == V5, V5 == V9, V9 == V7, V2 == V8; #61 ), references = 1, size of lhs = 5:
% 1.94/2.14 P_a-{F}(V0), P_b-{F}(V1), P_identity-{F}(V1), P_d-{F}(V2), V1 == V2 | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #75: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V7, V7 == V6; #69 ), references = 1, size of lhs = 3:
% 1.94/2.14 P_a-{F}(V0), P_b-{F}(V1), P_identity-{F}(V1) | P_d-{T}(V1)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #96: mergings( V2 == V6; #94 ), references = 1, size of lhs = 7:
% 1.94/2.14 P_a-{F}(V0), P_b-{F}(V1), P_d-{F}(V2), P_c-{F}(V3), P_identity-{F}(V4), product-{F}(V5,V3,V2), V5 == V0 | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #105: mergings( V2 == V3; #103 ), references = 5, size of lhs = 2:
% 1.94/2.14 P_identity-{F}(V0), product-{F}(V1,V2,V0) | P_inverse-{T}(V1,V2)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #124: mergings( V2 == V3, V3 == V5, V5 == V6, V0 == V8, V4 == V9, V6 == V10; #117 ), references = 1, size of lhs = 6:
% 1.94/2.14 P_identity-{F}(V0), P_c-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), V2 == V1, P_d-{F}(V3) | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #133: mergings( V2 == V6; #131 ), references = 1, size of lhs = 7:
% 1.94/2.14 P_a-{F}(V0), P_b-{F}(V1), P_d-{F}(V2), P_c-{F}(V3), P_identity-{F}(V4), product-{F}(V0,V5,V2), V3 == V5 | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #136: mergings( V1 == V5; #134 ), references = 1, size of lhs = 5:
% 1.94/2.14 P_a-{F}(V0), P_b-{F}(V1), P_d-{F}(V2), P_identity-{F}(V3), product-{F}(V0,V4,V2) | P_c-{T}(V4)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #154: mergings( V2 == V3, V3 == V6, V6 == V9, V9 == V10, V4 == V7, V5 == V8; #147 ), references = 1, size of lhs = 7:
% 1.94/2.14 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), V2 == V4 | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #170: mergings( V0 == V4, V4 == V5, V2 == V1; #166 ), references = 1, size of lhs = 3:
% 1.94/2.14 P_identity-{F}(V0), P_a-{F}(V1), P_element_in_O2-{F}(V1,V1,V2) | product-{T}(V1,V2,V1)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #179: mergings( V3 == V4, V4 == V5, V5 == V6, V1 == V0; #174 ), references = 1, size of lhs = 3:
% 1.94/2.14 P_a-{F}(V0), P_identity-{F}(V1), product-{F}(V0,V2,V0) | P_element_in_O2-{T}(V0,V0,V2)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #195: mergings( V0 == V4, V4 == V7, V5 == V8, V6 == V9, V2 == V1; #189 ), references = 1, size of lhs = 5:
% 1.94/2.14 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)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #206: mergings( V3 == V4, V4 == V7, V7 == V10, V5 == V8, V6 == V9, V1 == V0; #199 ), references = 1, size of lhs = 5:
% 1.94/2.14 P_a-{F}(V0), P_b-{F}(V1), P_d-{F}(V2), P_identity-{F}(V3), product-{F}(V2,V4,V2) | P_element_in_O2-{T}(V2,V2,V4)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #216: mergings( V0 == V4, V4 == V5, V3 == V1; #212 ), references = 1, size of lhs = 3:
% 1.94/2.14 P_identity-{F}(V0), P_a-{F}(V1), P_element_in_O2-{F}(V1,V2,V1) | subgroup_member-{T}(V2)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #223: mergings( V0 == V4, V4 == V6; #218 ), references = 1, size of lhs = 5:
% 1.94/2.14 P_identity-{F}(V0), P_a-{F}(V1), P_element_in_O2-{F}(V1,V2,V3), product-{F}(V1,V3,V4), V4 == V2 | subgroup_member-{T}(V2)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #226: mergings( V0 == V4, V4 == V6; #219 ), references = 1, size of lhs = 5:
% 1.94/2.14 P_identity-{F}(V0), P_a-{F}(V1), P_element_in_O2-{F}(V1,V2,V3), product-{F}(V4,V3,V2), V4 == V1 | subgroup_member-{T}(V2)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #229: mergings( V0 == V6, V6 == V7; #220 ), references = 2, size of lhs = 7:
% 1.94/2.14 P_b-{F}(V0), P_d-{F}(V1), P_c-{F}(V2), P_identity-{F}(V3), P_a-{F}(V4), P_element_in_O2-{F}(V4,V1,V5), V2 == V5 | subgroup_member-{T}(V1)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #235: mergings( V0 == V4, V4 == V7, V5 == V1; #231 ), references = 2, size of lhs = 5:
% 1.94/2.14 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)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #244: mergings( V5 == V6, V0 == V7, V3 == V8; #240 ), references = 1, size of lhs = 5:
% 1.94/2.14 P_c-{F}(V0), P_identity-{F}(V1), P_a-{F}(V2), P_b-{F}(V3), P_d-{F}(V4) | P_element_in_O2-{T}(V2,V4,V0)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #258: mergings( V2 == V3, V3 == V7, V7 == V8; #254 ), references = 1, size of lhs = 8:
% 1.94/2.14 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}(V3,V6,V5), V0 == V6 | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #267: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V11, V11 == V12; #261 ), references = 1, size of lhs = 8:
% 1.94/2.14 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}(V3,V6,V7), product-{F}(V7,V8,V5) | P_multiply-{T}(V6,V8,V0)
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #293: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V8, V8 == V9, V9 == V12; #286 ), references = 2, size of lhs = 7:
% 1.94/2.14 subgroup_member-{F}(V0), subgroup_member-{F}(V1), product-{F}(V1,V0,V2), P_a-{F}(V2), P_identity-{F}(V3), product-{F}(V0,V4,V5), product-{F}(V5,V6,V3) | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #329: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V11; #323 ), references = 1, size of lhs = 10:
% 1.94/2.14 subgroup_member-{F}(V0), subgroup_member-{F}(V1), P_a-{F}(V2), P_identity-{F}(V3), product-{F}(V4,V1,V5), product-{F}(V6,V5,V2), product-{F}(V0,V6,V7), product-{F}(V7,V4,V3), product-{F}(V1,V8,V9), product-{F}(V9,V10,V3) | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #343: mergings( V2 == V3, V3 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V15, V0 == V14; #333 ), references = 2, size of lhs = 13:
% 1.94/2.14 P_b-{F}(V0), P_d-{F}(V1), P_c-{F}(V2), subgroup_member-{F}(V2), subgroup_member-{F}(V3), P_a-{F}(V4), P_identity-{F}(V5), product-{F}(V0,V5,V6), product-{F}(V6,V7,V5), product-{F}(V7,V3,V8), product-{F}(V4,V8,V4), product-{F}(V3,V9,V10), product-{F}(V10,V11,V5) | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #349: mergings( V2 == V7; #347 ), references = 1, size of lhs = 10:
% 1.94/2.14 P_b-{F}(V0), P_d-{F}(V1), P_c-{F}(V2), subgroup_member-{F}(V2), subgroup_member-{F}(V3), P_a-{F}(V4), P_identity-{F}(V5), product-{F}(V4,V5,V4), product-{F}(V0,V5,V3), product-{F}(V5,V6,V5) | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #363: mergings( V2 == V3, V3 == V8, V8 == V10, V10 == V15, V4 == V9, V9 == V14, V1 == V5, V5 == V6, V6 == V11, V7 == V12; #352 ), references = 1, size of lhs = 8:
% 1.94/2.14 P_b-{F}(V0), P_d-{F}(V1), subgroup_member-{F}(V2), P_a-{F}(V3), P_identity-{F}(V4), product-{F}(V3,V4,V3), product-{F}(V0,V4,V2), product-{F}(V4,V5,V4) | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #374: mergings( V2 == V3, V3 == V7, V7 == V9, V9 == V13, V4 == V8, V8 == V12, V1 == V5, V5 == V6, V6 == V10; #364 ), references = 2, size of lhs = 7:
% 1.94/2.14 P_b-{F}(V0), subgroup_member-{F}(V1), P_a-{F}(V2), P_identity-{F}(V3), product-{F}(V2,V3,V2), product-{F}(V0,V3,V1), product-{F}(V3,V4,V3) | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #381: mergings( V1 == V4, V2 == V3; #378 ), references = 1, size of lhs = 4:
% 1.94/2.14 P_a-{F}(V0), P_identity-{F}(V1), product-{F}(V0,V1,V0), product-{F}(V1,V2,V1) | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #385: mergings( V1 == V2; #383 ), references = 1, size of lhs = 2:
% 1.94/2.14 P_identity-{F}(V0), product-{F}(V0,V1,V0) | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 #388: exists( #21, #386 ), references = 1, size of lhs = 0:
% 1.94/2.14 FALSE | FALSE
% 1.94/2.14 (used 0 times, uses = {})
% 1.94/2.14
% 1.94/2.14 number of learnt formulas = 31
% 1.94/2.14
% 1.94/2.14
% 1.94/2.14 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.94/2.14
% 1.94/2.14 randbase = 1
%------------------------------------------------------------------------------