%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : GRP002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n003.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 06:02:56 EDT 2022
% Result : Unsatisfiable 61.96s 62.11s
% Output : Refutation 61.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Jul 22 14:25:38 EDT 2022
% 0.14/0.34 % CPUTime :
% 61.96/62.11 GeoParameters:
% 61.96/62.11
% 61.96/62.11 tptp_input = 1
% 61.96/62.11 tptp_output = 0
% 61.96/62.11 nonempty = 1
% 61.96/62.11 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 61.96/62.11 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 61.96/62.11
% 61.96/62.11
% 61.96/62.11 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 61.96/62.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 61.96/62.11
% 61.96/62.11 RuleSystem INPUT:
% 61.96/62.11
% 61.96/62.11 Initial Rules:
% 61.96/62.11 #0: input, references = 15, size of lhs = 2:
% 61.96/62.11 P_identity-{F}(V0), #-{F} V1 | product-{T}(V0,V1,V1)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #1: input, references = 12, size of lhs = 2:
% 61.96/62.11 P_identity-{F}(V0), #-{F} V1 | product-{T}(V1,V0,V1)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #2: input, references = 17, size of lhs = 2:
% 61.96/62.11 P_identity-{F}(V0), P_inverse-{F}(V1,V2) | product-{T}(V2,V1,V0)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #3: input, references = 16, size of lhs = 2:
% 61.96/62.11 P_identity-{F}(V0), P_inverse-{F}(V1,V2) | product-{T}(V1,V2,V0)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #4: input, references = 22, size of lhs = 2:
% 61.96/62.11 P_identity-{F}(V0), P_multiply-{F}(V1,V2,V3) | product-{T}(V1,V2,V3)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #5: input, references = 21, size of lhs = 4:
% 61.96/62.11 P_identity-{F}(V0), product-{F}(V4,V3,V1), product-{F}(V4,V3,V2), V1 == V2 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #6: input, references = 26, size of lhs = 4:
% 61.96/62.11 P_identity-{F}(V0), product-{F}(V3,V1,V2), product-{F}(V5,V1,V4), product-{F}(V6,V5,V3) | product-{T}(V6,V4,V2)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #7: input, references = 18, size of lhs = 4:
% 61.96/62.11 P_identity-{F}(V0), product-{F}(V5,V1,V4), product-{F}(V6,V5,V3), product-{F}(V6,V4,V2) | product-{T}(V3,V1,V2)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #8: input, references = 3, size of lhs = 2:
% 61.96/62.11 P_identity-{F}(V0), product-{F}(V1,V1,V2) | product-{T}(V1,V2,V0)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #9: input, references = 4, size of lhs = 2:
% 61.96/62.11 P_identity-{F}(V0), product-{F}(V1,V1,V2) | product-{T}(V2,V1,V0)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #10: input, references = 5, size of lhs = 4:
% 61.96/62.11 P_identity-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_c-{F}(V3) | product-{T}(V1,V2,V3)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #11: input, references = 9, size of lhs = 6:
% 61.96/62.11 P_identity-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_c-{F}(V3), P_inverse-{F}(V1,V4), P_d-{F}(V5) | product-{T}(V3,V4,V5)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #12: input, references = 12, size of lhs = 8:
% 61.96/62.11 P_identity-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_c-{F}(V3), P_inverse-{F}(V1,V4), P_d-{F}(V5), P_inverse-{F}(V2,V6), P_h-{F}(V7) | product-{T}(V5,V6,V7)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #13: input, references = 7, size of lhs = 9:
% 61.96/62.11 P_identity-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_c-{F}(V3), P_inverse-{F}(V1,V4), P_d-{F}(V5), P_inverse-{F}(V2,V6), P_h-{F}(V7), P_j-{F}(V8) | product-{T}(V7,V2,V8)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #14: input, references = 8, size of lhs = 11:
% 61.96/62.11 P_identity-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_c-{F}(V3), P_inverse-{F}(V1,V4), P_d-{F}(V5), P_inverse-{F}(V2,V6), P_h-{F}(V7), P_j-{F}(V8), P_inverse-{F}(V7,V9), P_k-{F}(V10) | product-{T}(V8,V9,V10)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #15: input, references = 5, size of lhs = 12:
% 61.96/62.11 P_identity-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_c-{F}(V3), P_inverse-{F}(V1,V4), P_d-{F}(V5), P_inverse-{F}(V2,V6), P_h-{F}(V7), P_j-{F}(V8), P_inverse-{F}(V7,V9), P_k-{F}(V10), product-{F}(V10,V6,V0) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #16: input, references = 4, size of lhs = 0:
% 61.96/62.11 FALSE | EXISTS V0: P_identity-{T}(V0)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #17: input, references = 34, size of lhs = 1:
% 61.96/62.11 #-{F} V0 | EXISTS V1: P_inverse-{T}(V0,V1)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #18: input, references = 10, size of lhs = 2:
% 61.96/62.11 #-{F} V0, #-{F} V1 | EXISTS V2: P_multiply-{T}(V0,V1,V2)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #19: input, references = 4, size of lhs = 0:
% 61.96/62.11 FALSE | EXISTS V0: P_a-{T}(V0)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #20: input, references = 4, size of lhs = 0:
% 61.96/62.11 FALSE | EXISTS V0: P_b-{T}(V0)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #21: input, references = 5, size of lhs = 0:
% 61.96/62.11 FALSE | EXISTS V0: P_c-{T}(V0)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #22: input, references = 6, size of lhs = 0:
% 61.96/62.11 FALSE | EXISTS V0: P_d-{T}(V0)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #23: input, references = 8, size of lhs = 0:
% 61.96/62.11 FALSE | EXISTS V0: P_h-{T}(V0)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #24: input, references = 8, size of lhs = 0:
% 61.96/62.11 FALSE | EXISTS V0: P_j-{T}(V0)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #25: input, references = 9, size of lhs = 0:
% 61.96/62.11 FALSE | EXISTS V0: P_k-{T}(V0)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 number of initial rules = 26
% 61.96/62.11
% 61.96/62.11 Simplifiers:
% 61.96/62.11 #26: unsound, references = 3, size of lhs = 3:
% 61.96/62.11 P_identity-{F}(V0), P_identity-{F}(V1), V0 == V1 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #27: unsound, references = 3, size of lhs = 3:
% 61.96/62.11 P_inverse-{F}(V0,V1), P_inverse-{F}(V0,V3), V1 == V3 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #28: unsound, references = 3, size of lhs = 3:
% 61.96/62.11 P_multiply-{F}(V0,V1,V2), P_multiply-{F}(V0,V1,V5), V2 == V5 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #29: unsound, references = 3, size of lhs = 3:
% 61.96/62.11 P_a-{F}(V0), P_a-{F}(V1), V0 == V1 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #30: unsound, references = 3, size of lhs = 3:
% 61.96/62.11 P_b-{F}(V0), P_b-{F}(V1), V0 == V1 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #31: unsound, references = 3, size of lhs = 3:
% 61.96/62.11 P_c-{F}(V0), P_c-{F}(V1), V0 == V1 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #32: unsound, references = 3, size of lhs = 3:
% 61.96/62.11 P_d-{F}(V0), P_d-{F}(V1), V0 == V1 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #33: unsound, references = 3, size of lhs = 3:
% 61.96/62.11 P_h-{F}(V0), P_h-{F}(V1), V0 == V1 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #34: unsound, references = 3, size of lhs = 3:
% 61.96/62.11 P_j-{F}(V0), P_j-{F}(V1), V0 == V1 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #35: unsound, references = 3, size of lhs = 3:
% 61.96/62.11 P_k-{F}(V0), P_k-{F}(V1), V0 == V1 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 number of simplifiers = 10
% 61.96/62.11
% 61.96/62.11 Learnt:
% 61.96/62.11 #42: mergings( V2 == V8; #40 ), references = 8, size of lhs = 9:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_inverse-{F}(V1,V4), P_h-{F}(V5), P_identity-{F}(V6), product-{F}(V3,V4,V7), V7 == V5 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #47: mergings( V2 == V3, V3 == V7; #44 ), references = 2, size of lhs = 7:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_d-{F}(V1), P_c-{F}(V2), P_h-{F}(V3), P_identity-{F}(V4), V4 == V3 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #51: mergings( V1 == V2, V2 == V6; #48 ), references = 1, size of lhs = 5:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_d-{F}(V1), P_c-{F}(V2), P_identity-{F}(V3) | P_h-{T}(V3)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #65: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6; #60 ), references = 9, size of lhs = 3:
% 61.96/62.11 P_identity-{F}(V0), product-{F}(V1,V2,V0), product-{F}(V0,V2,V3) | P_multiply-{T}(V1,V1,V3)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #77: mergings( V2 == V10, V0 == V7, V3 == V8, V4 == V5, V7 == V9; #71 ), references = 1, size of lhs = 9:
% 61.96/62.11 P_b-{F}(V0), P_a-{F}(V0), P_h-{F}(V0), P_j-{F}(V1), P_d-{F}(V1), P_k-{F}(V2), V2 == V0, P_c-{F}(V3), P_identity-{F}(V4) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #84: mergings( V1 == V9, V2 == V6, V3 == V7, V4 == V5, V6 == V8; #78 ), references = 1, size of lhs = 7:
% 61.96/62.11 P_b-{F}(V0), P_a-{F}(V0), P_h-{F}(V0), P_j-{F}(V1), P_d-{F}(V1), P_c-{F}(V2), P_identity-{F}(V3) | P_k-{T}(V0)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #94: mergings( V0 == V2, V2 == V3; #90 ), references = 1, size of lhs = 1:
% 61.96/62.11 P_identity-{F}(V0) | P_inverse-{T}(V0,V0)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #96: mergings( V2 == V6; #91 ), references = 2, size of lhs = 6:
% 61.96/62.11 P_d-{F}(V0), P_identity-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_c-{F}(V3), P_h-{F}(V4) | P_inverse-{T}(V2,V4)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #103: mergings( V1 == V9; #100 ), references = 2, size of lhs = 9:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_inverse-{F}(V0,V3), P_d-{F}(V4), P_inverse-{F}(V1,V5), P_h-{F}(V6), P_identity-{F}(V7), product-{F}(V6,V1,V8) | P_j-{T}(V8)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #111: mergings( V1 == V13, V2 == V9, V3 == V10, V7 == V10, V4 == V11, V6 == V8, V8 == V12; #101 ), references = 3, size of lhs = 8:
% 61.96/62.11 P_d-{F}(V0), P_h-{F}(V0), P_a-{F}(V1), P_inverse-{F}(V1,V2), P_b-{F}(V3), P_inverse-{F}(V3,V3), P_c-{F}(V4), P_identity-{F}(V5) | P_j-{T}(V0)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #116: exists( #23, #42 ), references = 2, size of lhs = 7:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_inverse-{F}(V1,V4), P_identity-{F}(V5), product-{F}(V3,V4,V6) | P_h-{T}(V6)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #123: mergings( V1 == V6; #121 ), references = 3, size of lhs = 6:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_inverse-{F}(V0,V3), P_identity-{F}(V4), product-{F}(V2,V3,V5) | P_d-{T}(V5)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #131: mergings( V1 == V4; #129 ), references = 1, size of lhs = 4:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_identity-{F}(V2), product-{F}(V0,V1,V3) | P_c-{T}(V3)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #142: mergings( V3 == V4; #140 ), references = 1, size of lhs = 2:
% 61.96/62.11 P_identity-{F}(V0), product-{F}(V1,V2,V3) | P_multiply-{T}(V1,V2,V3)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #152: mergings( V2 == V11; #149 ), references = 3, size of lhs = 12:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_inverse-{F}(V1,V4), P_h-{F}(V5), P_j-{F}(V6), P_inverse-{F}(V5,V7), P_k-{F}(V8), P_identity-{F}(V9), product-{F}(V6,V7,V10), V10 == V8 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #160: mergings( V2 == V15, V0 == V11, V3 == V12, V6 == V9, V4 == V13, V5 == V8, V7 == V14; #150 ), references = 3, size of lhs = 11:
% 61.96/62.11 P_j-{F}(V0), P_d-{F}(V0), P_k-{F}(V1), P_a-{F}(V2), P_b-{F}(V3), P_inverse-{F}(V3,V4), P_c-{F}(V5), P_h-{F}(V6), V1 == V6, P_inverse-{F}(V6,V4), P_identity-{F}(V7) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #164: mergings( V1 == V10; #161 ), references = 3, size of lhs = 10:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_inverse-{F}(V1,V4), P_h-{F}(V5), P_j-{F}(V6), P_inverse-{F}(V5,V7), P_identity-{F}(V8), product-{F}(V6,V7,V9) | P_k-{T}(V9)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #172: mergings( V1 == V14, V2 == V10, V3 == V11, V6 == V9, V4 == V12, V5 == V8, V7 == V13; #162 ), references = 1, size of lhs = 9:
% 61.96/62.11 P_j-{F}(V0), P_d-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_inverse-{F}(V2,V3), P_c-{F}(V4), P_h-{F}(V5), P_inverse-{F}(V5,V3), P_identity-{F}(V6) | P_k-{T}(V5)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #174: exists( #17, #15 ), references = 3, size of lhs = 11:
% 61.96/62.11 P_identity-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_c-{F}(V3), P_d-{F}(V4), P_inverse-{F}(V2,V5), P_h-{F}(V6), P_j-{F}(V7), P_inverse-{F}(V6,V8), P_k-{F}(V9), product-{F}(V9,V5,V0) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #186: mergings( V5 == V12, V0 == V7, V3 == V8, V8 == V9, V4 == V10, V2 == V11; #178 ), references = 1, size of lhs = 10:
% 61.96/62.11 P_d-{F}(V0), P_h-{F}(V0), P_k-{F}(V1), V1 == V0, P_a-{F}(V2), P_b-{F}(V3), P_inverse-{F}(V3,V3), P_inverse-{F}(V0,V3), P_c-{F}(V4), P_identity-{F}(V5) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #194: mergings( V5 == V14, V0 == V6, V3 == V7, V7 == V10, V4 == V8, V2 == V9, V9 == V11; #179 ), references = 1, size of lhs = 11:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_inverse-{F}(V1,V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V3), P_inverse-{F}(V3,V4), P_k-{F}(V5), P_identity-{F}(V6), product-{F}(V3,V4,V7), V7 == V5 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #216: mergings( V1 == V8, V8 == V13, V13 == V19, V2 == V10, V10 == V14, V3 == V11, V6 == V11, V11 == V15, V15 == V16, V4 == V12, V12 == V17, V5 == V9, V7 == V9, V9 == V18, V19 == V16; #199 ), references = 1, size of lhs = 8:
% 61.96/62.11 P_d-{F}(V0), P_h-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_inverse-{F}(V2,V2), P_inverse-{F}(V0,V2), P_identity-{F}(V2), P_c-{F}(V3) | P_j-{T}(V0)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #233: mergings( V1 == V8, V8 == V13, V13 == V21, V2 == V10, V10 == V14, V3 == V11, V6 == V11, V11 == V15, V15 == V18, V4 == V12, V12 == V16, V5 == V9, V9 == V17, V7 == V17, V17 == V19, V21 == V20; #200 ), references = 1, size of lhs = 9:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_inverse-{F}(V1,V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V3), P_inverse-{F}(V3,V4), P_identity-{F}(V4), product-{F}(V3,V4,V5) | P_j-{T}(V5)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #238: exists( #23, #42 ), references = 1, size of lhs = 7:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_inverse-{F}(V1,V4), P_identity-{F}(V5), product-{F}(V3,V4,V6) | P_h-{T}(V6)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #258: mergings( V2 == V3, V3 == V6; #253 ), references = 1, size of lhs = 6:
% 61.96/62.11 P_a-{F}(V0), P_c-{F}(V0), P_b-{F}(V1), P_d-{F}(V2), P_identity-{F}(V3), V3 == V2 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #264: mergings( V2 == V4, V4 == V8, V0 == V5, V8 == V3, V5 == V6; #254 ), references = 1, size of lhs = 6:
% 61.96/62.11 P_b-{F}(V0), P_identity-{F}(V0), P_a-{F}(V1), P_c-{F}(V1), P_h-{F}(V2), V0 == V2 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #270: mergings( V2 == V4, V4 == V10, V0 == V5, V3 == V6, V5 == V7; #255 ), references = 1, size of lhs = 8:
% 61.96/62.11 P_a-{F}(V0), P_c-{F}(V0), P_b-{F}(V1), P_inverse-{F}(V1,V2), P_h-{F}(V3), P_identity-{F}(V4), product-{F}(V4,V2,V5), V5 == V3 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #280: mergings( V1 == V2, V2 == V5; #275 ), references = 1, size of lhs = 4:
% 61.96/62.11 P_a-{F}(V0), P_c-{F}(V0), P_b-{F}(V1), P_identity-{F}(V2) | P_d-{T}(V2)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #292: mergings( V1 == V5, V5 == V6, V6 == V9, V9 == V14, V2 == V7, V7 == V10, V3 == V8, V8 == V11, V14 == V13, V4 == V10, V10 == V12; #277 ), references = 1, size of lhs = 6:
% 61.96/62.11 P_a-{F}(V0), P_c-{F}(V0), P_b-{F}(V1), P_inverse-{F}(V1,V2), P_identity-{F}(V2), product-{F}(V2,V2,V3) | P_d-{T}(V3)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #313: mergings( V2 == V3, V3 == V4; #310 ), references = 4, size of lhs = 4:
% 61.96/62.11 P_identity-{F}(V0), product-{F}(V1,V2,V1), product-{F}(V0,V2,V3), V0 == V3 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #326: mergings( V1 == V5, V5 == V6, V6 == V7; #322 ), references = 1, size of lhs = 8:
% 61.96/62.11 P_d-{F}(V0), P_identity-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_c-{F}(V3), product-{F}(V4,V2,V2), product-{F}(V4,V0,V5), V5 == V0 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #349: mergings( V2 == V3, V3 == V4, V4 == V8, V8 == V9; #344 ), references = 2, size of lhs = 10:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_identity-{F}(V4), product-{F}(V3,V5,V2), product-{F}(V0,V6,V5), product-{F}(V4,V6,V7), product-{F}(V4,V7,V8), V4 == V8 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #359: exists( #17, #152 ), references = 3, size of lhs = 11:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V4), P_j-{F}(V5), P_inverse-{F}(V4,V6), P_k-{F}(V7), P_identity-{F}(V8), product-{F}(V5,V6,V9), V9 == V7 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #361: exists( #25, #358 ), references = 1, size of lhs = 9:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V4), P_j-{F}(V5), P_inverse-{F}(V4,V6), P_identity-{F}(V7), product-{F}(V5,V6,V8) | P_k-{T}(V8)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #379: mergings( V2 == V7, V3 == V8, V4 == V9, V6 == V10, V7 == V11; #372 ), references = 1, size of lhs = 10:
% 61.96/62.11 P_k-{F}(V0), P_d-{F}(V0), P_identity-{F}(V1), P_h-{F}(V1), P_a-{F}(V2), P_inverse-{F}(V2,V3), P_b-{F}(V4), P_c-{F}(V5), P_j-{F}(V6), P_inverse-{F}(V1,V7) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #386: mergings( V2 == V7, V3 == V8, V5 == V10, V4 == V9, V6 == V11, V7 == V12; #373 ), references = 1, size of lhs = 10:
% 61.96/62.11 P_k-{F}(V0), P_d-{F}(V0), P_identity-{F}(V1), P_h-{F}(V1), P_a-{F}(V2), P_b-{F}(V3), P_c-{F}(V4), P_inverse-{F}(V2,V5), P_j-{F}(V6), P_inverse-{F}(V1,V7) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #393: mergings( V2 == V5, V3 == V7, V4 == V8, V5 == V9; #388 ), references = 1, size of lhs = 9:
% 61.96/62.11 P_k-{F}(V0), P_d-{F}(V0), P_identity-{F}(V1), P_h-{F}(V1), P_a-{F}(V2), P_b-{F}(V3), P_c-{F}(V4), P_j-{F}(V5), P_inverse-{F}(V1,V6) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #399: mergings( V2 == V5, V0 == V6, V3 == V8, V4 == V9, V5 == V10; #387 ), references = 1, size of lhs = 9:
% 61.96/62.11 P_k-{F}(V0), P_d-{F}(V0), P_identity-{F}(V1), P_h-{F}(V1), P_a-{F}(V2), P_b-{F}(V3), P_c-{F}(V4), P_j-{F}(V5), P_inverse-{F}(V1,V6) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #416: exists( #17, #411 ), references = 2, size of lhs = 9:
% 61.96/62.11 P_identity-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_k-{F}(V2), P_c-{F}(V3), P_d-{F}(V4), P_h-{F}(V5), P_j-{F}(V6), P_inverse-{F}(V5,V7) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #430: mergings( V2 == V3, V3 == V4; #427 ), references = 1, size of lhs = 4:
% 61.96/62.11 P_identity-{F}(V0), product-{F}(V1,V2,V2), product-{F}(V1,V0,V3), V3 == V0 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #434: exists( #25, #359 ), references = 1, size of lhs = 9:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V4), P_j-{F}(V5), P_inverse-{F}(V4,V6), P_identity-{F}(V7), product-{F}(V5,V6,V8) | P_k-{T}(V8)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #468: mergings( V2 == V9; #464 ), references = 1, size of lhs = 10:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_inverse-{F}(V0,V3), P_d-{F}(V4), P_h-{F}(V5), P_j-{F}(V6), P_identity-{F}(V7), product-{F}(V5,V1,V8), V8 == V6 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #470: mergings( V2 == V8; #465 ), references = 1, size of lhs = 10:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_inverse-{F}(V0,V3), P_d-{F}(V4), P_h-{F}(V5), P_j-{F}(V5), P_identity-{F}(V6), product-{F}(V6,V1,V7), V6 == V7 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #477: mergings( V7 == V16, V2 == V9, V0 == V10, V3 == V11, V5 == V12, V6 == V13; #466 ), references = 1, size of lhs = 12:
% 61.96/62.11 P_a-{F}(V0), P_inverse-{F}(V0,V1), P_b-{F}(V2), P_c-{F}(V3), P_d-{F}(V4), P_h-{F}(V5), product-{F}(V5,V2,V6), P_inverse-{F}(V5,V7), P_k-{F}(V8), P_identity-{F}(V9), product-{F}(V6,V7,V10), V10 == V8 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #482: mergings( V2 == V8; #478 ), references = 3, size of lhs = 9:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V4), P_j-{F}(V5), P_identity-{F}(V6), product-{F}(V4,V1,V7), V7 == V5 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #484: mergings( V2 == V7; #479 ), references = 1, size of lhs = 9:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V4), P_j-{F}(V4), P_identity-{F}(V5), product-{F}(V5,V1,V6), V5 == V6 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #491: mergings( V6 == V15, V0 == V8, V2 == V9, V3 == V10, V4 == V11, V5 == V12; #480 ), references = 1, size of lhs = 11:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V4), product-{F}(V4,V1,V5), P_inverse-{F}(V4,V6), P_k-{F}(V7), P_identity-{F}(V8), product-{F}(V5,V6,V9), V9 == V7 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #495: mergings( V1 == V7; #493 ), references = 1, size of lhs = 7:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V4), P_identity-{F}(V5), product-{F}(V4,V1,V6) | P_j-{T}(V6)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #522: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V8, V8 == V9; #516 ), references = 1, size of lhs = 6:
% 61.96/62.11 P_a-{F}(V0), P_d-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_identity-{F}(V3), product-{F}(V2,V3,V4) | P_inverse-{T}(V0,V4)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #528: exists( #24, #482 ), references = 1, size of lhs = 7:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V4), P_identity-{F}(V5), product-{F}(V4,V1,V6) | P_j-{T}(V6)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #530: exists( #17, #416 ), references = 2, size of lhs = 8:
% 61.96/62.11 P_identity-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_k-{F}(V2), P_c-{F}(V3), P_d-{F}(V4), P_h-{F}(V5), P_j-{F}(V6) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #575: mergings( V2 == V3, V3 == V9, V9 == V10; #569 ), references = 1, size of lhs = 10:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_inverse-{F}(V0,V3), P_d-{F}(V4), P_h-{F}(V5), P_identity-{F}(V6), product-{F}(V4,V6,V7), product-{F}(V5,V1,V8), V8 == V7 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #582: mergings( V2 == V3, V3 == V8, V8 == V14, V4 == V9, V5 == V10, V7 == V11; #570 ), references = 1, size of lhs = 10:
% 61.96/62.11 P_a-{F}(V0), P_inverse-{F}(V0,V1), P_b-{F}(V2), P_c-{F}(V3), P_d-{F}(V4), P_h-{F}(V5), P_j-{F}(V6), P_identity-{F}(V7), product-{F}(V4,V7,V8), V8 == V6 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #589: mergings( V2 == V3, V3 == V8, V8 == V13, V4 == V9, V0 == V10, V5 == V11; #571 ), references = 1, size of lhs = 12:
% 61.96/62.11 P_h-{F}(V0), P_a-{F}(V1), P_inverse-{F}(V1,V2), P_b-{F}(V3), P_c-{F}(V4), product-{F}(V0,V3,V4), P_d-{F}(V5), P_identity-{F}(V6), product-{F}(V1,V7,V6), product-{F}(V6,V7,V8), product-{F}(V6,V8,V9), V6 == V9 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #598: mergings( V2 == V3, V3 == V8, V8 == V9; #592 ), references = 1, size of lhs = 9:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V4), P_identity-{F}(V5), product-{F}(V3,V5,V6), product-{F}(V4,V1,V7), V7 == V6 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #605: mergings( V2 == V3, V3 == V6, V6 == V13, V0 == V7, V4 == V9, V5 == V10; #593 ), references = 2, size of lhs = 9:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V4), P_j-{F}(V5), P_identity-{F}(V6), product-{F}(V3,V6,V7), V7 == V5 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #608: exists( #24, #605 ), references = 2, size of lhs = 7:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V4), P_identity-{F}(V5), product-{F}(V3,V5,V6) | P_j-{T}(V6)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #618: exists( #17, #160 ), references = 1, size of lhs = 9:
% 61.96/62.11 P_j-{F}(V0), P_d-{F}(V0), P_k-{F}(V1), P_a-{F}(V2), P_b-{F}(V3), V1 == V3, P_h-{F}(V3), P_c-{F}(V4), P_identity-{F}(V5) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #620: exists( #25, #617 ), references = 1, size of lhs = 7:
% 61.96/62.11 P_j-{F}(V0), P_d-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_h-{F}(V2), P_c-{F}(V3), P_identity-{F}(V4) | P_k-{T}(V2)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #789: mergings( V2 == V3, V3 == V4, V4 == V13, V13 == V14; #783 ), references = 1, size of lhs = 15:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_inverse-{F}(V0,V3), P_d-{F}(V4), P_inverse-{F}(V1,V5), P_h-{F}(V6), P_j-{F}(V7), P_k-{F}(V8), P_identity-{F}(V9), product-{F}(V8,V10,V7), product-{F}(V6,V11,V10), product-{F}(V9,V11,V12), product-{F}(V9,V12,V13), V9 == V13 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #794: mergings( V2 == V3, V3 == V4, V4 == V13, V13 == V14; #784 ), references = 2, size of lhs = 15:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_inverse-{F}(V0,V3), P_d-{F}(V4), P_inverse-{F}(V1,V5), P_h-{F}(V6), P_j-{F}(V7), P_k-{F}(V8), P_identity-{F}(V9), product-{F}(V9,V10,V11), product-{F}(V6,V10,V12), product-{F}(V8,V12,V13), product-{F}(V7,V11,V14), V14 == V13 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #804: mergings( V2 == V3, V3 == V4, V4 == V12, V12 == V13; #798 ), references = 2, size of lhs = 14:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_inverse-{F}(V0,V3), P_d-{F}(V4), P_h-{F}(V5), P_j-{F}(V6), P_k-{F}(V7), P_identity-{F}(V8), product-{F}(V8,V9,V10), product-{F}(V5,V9,V11), product-{F}(V7,V11,V12), product-{F}(V6,V10,V13), V13 == V12 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #816: mergings( V2 == V3, V3 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V19, V19 == V20, V4 == V12, V6 == V14, V5 == V13, V7 == V15; #799 ), references = 1, size of lhs = 14:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_inverse-{F}(V0,V3), P_d-{F}(V4), P_h-{F}(V5), P_j-{F}(V6), P_k-{F}(V7), P_identity-{F}(V8), product-{F}(V4,V8,V9), product-{F}(V7,V9,V6), product-{F}(V8,V1,V10), product-{F}(V8,V10,V11), V8 == V11 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #823: mergings( V2 == V3, V3 == V4, V4 == V11, V11 == V12; #817 ), references = 2, size of lhs = 13:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V4), P_j-{F}(V5), P_k-{F}(V6), P_identity-{F}(V7), product-{F}(V7,V8,V9), product-{F}(V4,V8,V10), product-{F}(V6,V10,V11), product-{F}(V5,V9,V12), V12 == V11 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #833: mergings( V2 == V3, V3 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V16, V16 == V17, V4 == V11, V5 == V12; #818 ), references = 1, size of lhs = 13:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V4), P_j-{F}(V5), P_k-{F}(V6), P_identity-{F}(V7), product-{F}(V3,V7,V8), product-{F}(V6,V8,V5), product-{F}(V7,V1,V9), product-{F}(V7,V9,V10), V7 == V10 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #992: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V15; #984 ), references = 1, size of lhs = 15:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V4), P_j-{F}(V5), P_k-{F}(V6), P_identity-{F}(V7), product-{F}(V5,V8,V9), product-{F}(V8,V9,V10), product-{F}(V7,V11,V10), product-{F}(V4,V11,V12), product-{F}(V6,V12,V13), product-{F}(V9,V14,V15), product-{F}(V15,V16,V7) | P_multiply-{T}(V14,V16,V13)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #998: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V16; #985 ), references = 1, size of lhs = 16:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_inverse-{F}(V0,V3), P_d-{F}(V4), P_h-{F}(V5), P_j-{F}(V6), P_k-{F}(V7), P_identity-{F}(V8), product-{F}(V6,V9,V10), product-{F}(V9,V10,V11), product-{F}(V8,V12,V11), product-{F}(V5,V12,V13), product-{F}(V7,V13,V14), product-{F}(V10,V15,V16), product-{F}(V16,V17,V8) | P_multiply-{T}(V15,V17,V14)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #1004: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V17; #986 ), references = 1, size of lhs = 17:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_inverse-{F}(V0,V3), P_d-{F}(V4), P_inverse-{F}(V1,V5), P_h-{F}(V6), P_j-{F}(V7), P_k-{F}(V8), P_identity-{F}(V9), product-{F}(V7,V10,V11), product-{F}(V10,V11,V12), product-{F}(V9,V13,V12), product-{F}(V6,V13,V14), product-{F}(V8,V14,V15), product-{F}(V11,V16,V17), product-{F}(V17,V18,V9) | P_multiply-{T}(V16,V18,V15)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #1029: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V20, V20 == V21, V21 == V22, V22 == V23, V23 == V24; #1014 ), references = 1, size of lhs = 26:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V4), P_j-{F}(V5), P_k-{F}(V6), P_identity-{F}(V7), product-{F}(V5,V8,V9), product-{F}(V8,V10,V11), product-{F}(V11,V12,V13), product-{F}(V12,V14,V9), product-{F}(V14,V10,V15), product-{F}(V13,V15,V16), product-{F}(V7,V17,V16), product-{F}(V4,V17,V18), product-{F}(V6,V18,V19), product-{F}(V10,V20,V21), product-{F}(V9,V21,V22), product-{F}(V22,V23,V7), product-{F}(V24,V25,V23), product-{F}(V20,V24,V26), product-{F}(V25,V27,V28), product-{F}(V26,V28,V29), product-{F}(V19,V27,V30), V30 == V29 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #1049: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V21, V21 == V22, V22 == V23, V23 == V24, V24 == V25; #1032 ), references = 1, size of lhs = 26:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V4), P_j-{F}(V5), P_k-{F}(V6), P_identity-{F}(V7), product-{F}(V5,V8,V9), product-{F}(V8,V10,V11), product-{F}(V11,V12,V13), product-{F}(V12,V14,V9), product-{F}(V14,V10,V15), product-{F}(V13,V15,V16), product-{F}(V7,V17,V16), product-{F}(V4,V17,V18), product-{F}(V18,V19,V20), product-{F}(V6,V20,V21), product-{F}(V10,V22,V23), product-{F}(V9,V23,V24), product-{F}(V24,V25,V7), product-{F}(V26,V27,V25), product-{F}(V22,V26,V28), product-{F}(V27,V19,V29), product-{F}(V28,V29,V30), V21 == V30 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #1072: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V22, V22 == V23, V23 == V24, V24 == V25, V25 == V26; #1054 ), references = 2, size of lhs = 24:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V4), P_j-{F}(V5), P_k-{F}(V6), P_identity-{F}(V7), product-{F}(V5,V8,V9), product-{F}(V8,V10,V11), product-{F}(V10,V12,V13), product-{F}(V9,V13,V14), product-{F}(V12,V14,V15), product-{F}(V11,V16,V17), product-{F}(V16,V18,V9), product-{F}(V18,V10,V19), product-{F}(V17,V19,V20), product-{F}(V7,V21,V20), product-{F}(V4,V21,V22), product-{F}(V22,V23,V24), product-{F}(V6,V24,V25), product-{F}(V14,V23,V26), product-{F}(V15,V26,V27), V25 == V27 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #1096: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V25, V25 == V26, V26 == V27, V27 == V28, V28 == V29; #1076 ), references = 1, size of lhs = 21:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V4), P_j-{F}(V5), P_k-{F}(V6), P_identity-{F}(V7), product-{F}(V5,V8,V9), product-{F}(V8,V10,V11), product-{F}(V10,V12,V13), product-{F}(V9,V13,V14), product-{F}(V12,V14,V15), product-{F}(V4,V15,V16), product-{F}(V11,V17,V15), product-{F}(V17,V18,V9), product-{F}(V18,V10,V19), product-{F}(V16,V19,V20), product-{F}(V14,V21,V19), product-{F}(V20,V21,V22), product-{F}(V6,V22,V23) | P_multiply-{T}(V15,V19,V23)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #1137: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V20, V20 == V21, V21 == V22, V22 == V23, V23 == V24, V24 == V25, V25 == V33, V33 == V34, V34 == V35, V35 == V36, V36 == V37, V37 == V38, V38 == V39, V39 == V40, V6 == V26, V0 == V27, V7 == V28, V9 == V29; #1105 ), references = 1, size of lhs = 26:
% 61.96/62.11 P_a-{F}(V0), P_inverse-{F}(V0,V1), P_b-{F}(V2), P_c-{F}(V3), P_d-{F}(V4), P_h-{F}(V5), P_j-{F}(V6), P_k-{F}(V7), P_identity-{F}(V8), product-{F}(V4,V8,V9), product-{F}(V6,V10,V11), product-{F}(V10,V12,V13), product-{F}(V13,V14,V2), product-{F}(V14,V15,V11), product-{F}(V15,V12,V16), product-{F}(V9,V16,V17), product-{F}(V18,V17,V2), product-{F}(V12,V18,V19), product-{F}(V11,V19,V17), product-{F}(V7,V16,V20), product-{F}(V21,V2,V17), product-{F}(V21,V8,V16), product-{F}(V16,V22,V23), product-{F}(V2,V23,V24), product-{F}(V20,V22,V25), V25 == V24 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #1190: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V19, V19 == V20, V20 == V21, V21 == V22, V22 == V23, V23 == V24, V24 == V25, V25 == V26, V26 == V27, V27 == V28, V28 == V29, V29 == V30, V30 == V31, V31 == V32, V32 == V33, V33 == V34, V34 == V41, V41 == V42, V42 == V43, V43 == V44, V44 == V45, V45 == V46, V46 == V47, V47 == V48, V0 == V35, V8 == V16, V16 == V36, V9 == V17, V17 == V37, V10 == V18, V18 == V38; #1148 ), references = 1, size of lhs = 20:
% 61.96/62.11 P_j-{F}(V0), P_d-{F}(V0), P_k-{F}(V1), P_a-{F}(V1), P_b-{F}(V2), P_c-{F}(V3), P_h-{F}(V4), P_identity-{F}(V5), product-{F}(V0,V5,V0), product-{F}(V5,V1,V6), product-{F}(V7,V5,V1), product-{F}(V7,V2,V8), product-{F}(V8,V5,V8), product-{F}(V3,V5,V8), product-{F}(V8,V9,V8), product-{F}(V9,V1,V1), product-{F}(V2,V5,V10), V6 == V10, product-{F}(V1,V11,V8), product-{F}(V5,V11,V2) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #1253: mergings( V2 == V10; #1251 ), references = 1, size of lhs = 22:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V4), P_j-{F}(V5), P_k-{F}(V6), P_identity-{F}(V7), product-{F}(V6,V7,V8), product-{F}(V5,V9,V10), product-{F}(V9,V11,V12), product-{F}(V11,V13,V14), product-{F}(V10,V14,V15), product-{F}(V13,V15,V16), product-{F}(V4,V17,V15), product-{F}(V7,V17,V18), product-{F}(V16,V7,V19), V8 == V19, product-{F}(V12,V20,V21), product-{F}(V20,V22,V10), product-{F}(V22,V11,V23), product-{F}(V21,V23,V18) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #1261: mergings( V3 == V4, V4 == V5, V5 == V13; #1257 ), references = 1, size of lhs = 21:
% 61.96/62.11 P_a-{F}(V0), P_b-{F}(V1), P_c-{F}(V2), P_d-{F}(V3), P_h-{F}(V4), P_j-{F}(V5), P_k-{F}(V6), P_identity-{F}(V7), product-{F}(V6,V7,V8), product-{F}(V5,V9,V10), product-{F}(V9,V11,V12), product-{F}(V11,V13,V14), product-{F}(V10,V14,V15), product-{F}(V13,V15,V16), product-{F}(V16,V7,V17), V8 == V17, product-{F}(V12,V18,V19), product-{F}(V4,V19,V20), product-{F}(V18,V21,V10), product-{F}(V21,V11,V22), product-{F}(V20,V22,V15) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #1276: mergings( V2 == V3, V3 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V19, V4 == V12, V0 == V13, V5 == V14, V7 == V15; #1265 ), references = 1, size of lhs = 22:
% 61.96/62.11 P_a-{F}(V0), P_inverse-{F}(V0,V1), P_b-{F}(V2), P_c-{F}(V3), P_d-{F}(V4), P_h-{F}(V5), P_j-{F}(V6), P_k-{F}(V7), P_identity-{F}(V8), product-{F}(V7,V8,V9), product-{F}(V4,V8,V10), product-{F}(V6,V11,V12), product-{F}(V11,V13,V14), product-{F}(V14,V15,V2), product-{F}(V15,V16,V12), product-{F}(V16,V13,V17), product-{F}(V10,V17,V18), product-{F}(V12,V19,V18), product-{F}(V13,V20,V19), product-{F}(V20,V18,V21), product-{F}(V21,V8,V22), V9 == V22 | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #1305: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V10, V10 == V11, V11 == V12, V12 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V26, V0 == V20, V7 == V13, V13 == V21, V8 == V14, V14 == V22, V9 == V15, V15 == V23; #1285 ), references = 2, size of lhs = 18:
% 61.96/62.11 P_j-{F}(V0), P_d-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_c-{F}(V3), P_h-{F}(V4), P_k-{F}(V5), P_identity-{F}(V6), product-{F}(V0,V6,V0), product-{F}(V5,V6,V7), product-{F}(V2,V6,V8), V7 == V8, product-{F}(V3,V6,V9), product-{F}(V9,V6,V9), product-{F}(V9,V10,V9), product-{F}(V10,V1,V1), product-{F}(V1,V11,V9), product-{F}(V6,V11,V2) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #1308: exists( #25, #1306 ), references = 1, size of lhs = 15:
% 61.96/62.11 P_j-{F}(V0), P_d-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_c-{F}(V3), P_h-{F}(V4), P_identity-{F}(V5), product-{F}(V0,V5,V0), product-{F}(V2,V5,V6), product-{F}(V3,V5,V7), product-{F}(V7,V5,V7), product-{F}(V7,V8,V7), product-{F}(V8,V1,V1), product-{F}(V1,V9,V7), product-{F}(V5,V9,V2) | P_k-{T}(V6)
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #1322: mergings( V5 == V10, V10 == V15, V1 == V7, V7 == V16, V2 == V8, V8 == V11, V3 == V9, V9 == V17, V4 == V6, V6 == V18; #1311 ), references = 1, size of lhs = 13:
% 61.96/62.11 P_b-{F}(V0), P_identity-{F}(V1), product-{F}(V0,V1,V0), product-{F}(V1,V2,V0), P_a-{F}(V3), product-{F}(V4,V3,V3), product-{F}(V3,V2,V5), product-{F}(V5,V1,V5), product-{F}(V5,V4,V5), P_c-{F}(V6), product-{F}(V6,V1,V5), P_d-{F}(V7), product-{F}(V7,V1,V7) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #1332: mergings( V7 == V12, V1 == V4, V4 == V13, V2 == V5, V5 == V8, V3 == V6, V6 == V14; #1324 ), references = 1, size of lhs = 11:
% 61.96/62.11 P_b-{F}(V0), P_identity-{F}(V1), product-{F}(V0,V1,V0), product-{F}(V1,V2,V0), P_a-{F}(V3), product-{F}(V4,V3,V3), product-{F}(V3,V2,V5), product-{F}(V5,V1,V5), product-{F}(V5,V4,V5), P_c-{F}(V6), product-{F}(V6,V1,V5) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #1343: mergings( V1 == V7, V7 == V9, V3 == V5, V5 == V10, V2 == V4, V4 == V6, V6 == V8; #1335 ), references = 1, size of lhs = 6:
% 61.96/62.11 P_b-{F}(V0), P_identity-{F}(V1), product-{F}(V1,V0,V0), product-{F}(V0,V1,V0), P_a-{F}(V2), product-{F}(V1,V2,V2) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #1351: mergings( V1 == V4, V4 == V5, V2 == V3, V3 == V6; #1346 ), references = 2, size of lhs = 3:
% 61.96/62.11 P_identity-{F}(V0), P_a-{F}(V1), product-{F}(V0,V1,V1) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #1354: exists( #19, #1352 ), references = 1, size of lhs = 1:
% 61.96/62.11 P_identity-{F}(V0) | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 #1356: exists( #16, #1353 ), references = 1, size of lhs = 0:
% 61.96/62.11 FALSE | FALSE
% 61.96/62.11 (used 0 times, uses = {})
% 61.96/62.11
% 61.96/62.11 number of learnt formulas = 85
% 61.96/62.11
% 61.96/62.11
% 61.96/62.11 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 61.96/62.11
% 61.96/62.11 randbase = 1
%------------------------------------------------------------------------------