TSTP Solution File: GRP124-9.004 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : GRP124-9.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n013.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 06:03:14 EDT 2022
% Result : Unsatisfiable 0.47s 0.67s
% Output : Refutation 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP124-9.004 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jul 22 13:43:45 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.47/0.67 GeoParameters:
% 0.47/0.67
% 0.47/0.67 tptp_input = 1
% 0.47/0.67 tptp_output = 0
% 0.47/0.67 nonempty = 1
% 0.47/0.67 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.67 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 0.47/0.67
% 0.47/0.67
% 0.47/0.67 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.67 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.67
% 0.47/0.67 RuleSystem INPUT:
% 0.47/0.67
% 0.47/0.67 Initial Rules:
% 0.47/0.67 #0: input, references = 3, size of lhs = 6:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), group_element-{F}(V4), group_element-{F}(V5) | product-{T}(V0,V5,V4), product-{T}(V1,V5,V4), product-{T}(V2,V5,V4), product-{T}(V3,V5,V4)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #1: input, references = 3, size of lhs = 6:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), group_element-{F}(V4), group_element-{F}(V5) | product-{T}(V5,V0,V4), product-{T}(V5,V1,V4), product-{T}(V5,V2,V4), product-{T}(V5,V3,V4)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #2: input, references = 4, size of lhs = 4:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3) | group_element-{T}(V0)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #3: input, references = 4, size of lhs = 4:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3) | group_element-{T}(V1)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #4: input, references = 4, size of lhs = 4:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3) | group_element-{T}(V2)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #5: input, references = 4, size of lhs = 4:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3) | group_element-{T}(V3)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #6: input, references = 12, size of lhs = 5:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), equalish-{F}(V0,V1) | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #7: input, references = 5, size of lhs = 5:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), equalish-{F}(V0,V2) | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #8: input, references = 4, size of lhs = 5:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), equalish-{F}(V0,V3) | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #9: input, references = 7, size of lhs = 5:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), equalish-{F}(V1,V0) | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #10: input, references = 5, size of lhs = 5:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), equalish-{F}(V1,V2) | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #11: input, references = 4, size of lhs = 5:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), equalish-{F}(V1,V3) | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #12: input, references = 4, size of lhs = 5:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), equalish-{F}(V2,V0) | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #13: input, references = 5, size of lhs = 5:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), equalish-{F}(V2,V1) | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #14: input, references = 3, size of lhs = 5:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), equalish-{F}(V2,V3) | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #15: input, references = 4, size of lhs = 5:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), equalish-{F}(V3,V0) | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #16: input, references = 6, size of lhs = 5:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), equalish-{F}(V3,V1) | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #17: input, references = 4, size of lhs = 5:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), equalish-{F}(V3,V2) | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #18: input, references = 11, size of lhs = 6:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), group_element-{F}(V4), group_element-{F}(V5) | product1-{T}(V5,V4,V0), product1-{T}(V5,V4,V1), product1-{T}(V5,V4,V2), product1-{T}(V5,V4,V3)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #19: input, references = 6, size of lhs = 6:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), product1-{F}(V7,V6,V4), product1-{F}(V7,V6,V5) | equalish-{T}(V4,V5)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #20: input, references = 13, size of lhs = 6:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), product1-{F}(V7,V4,V6), product1-{F}(V7,V5,V6) | equalish-{T}(V4,V5)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #21: input, references = 14, size of lhs = 6:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), product1-{F}(V4,V6,V7), product1-{F}(V5,V6,V7) | equalish-{T}(V4,V5)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #22: input, references = 10, size of lhs = 5:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), #-{F} V4 | product1-{T}(V4,V4,V4)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #23: input, references = 3, size of lhs = 6:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), group_element-{F}(V4), group_element-{F}(V5) | product2-{T}(V5,V4,V0), product2-{T}(V5,V4,V1), product2-{T}(V5,V4,V2), product2-{T}(V5,V4,V3)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #24: input, references = 6, size of lhs = 6:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), product2-{F}(V7,V6,V4), product2-{F}(V7,V6,V5) | equalish-{T}(V4,V5)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #25: input, references = 3, size of lhs = 6:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), product2-{F}(V7,V4,V6), product2-{F}(V7,V5,V6) | equalish-{T}(V4,V5)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #26: input, references = 3, size of lhs = 6:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), product2-{F}(V4,V6,V7), product2-{F}(V5,V6,V7) | equalish-{T}(V4,V5)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #27: input, references = 4, size of lhs = 5:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), #-{F} V4 | product2-{T}(V4,V4,V4)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #28: input, references = 6, size of lhs = 6:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), product1-{F}(V5,V4,V6), product1-{F}(V4,V7,V5) | product2-{T}(V6,V7,V4)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #29: input, references = 4, size of lhs = 0:
% 0.47/0.67 FALSE | EXISTS V0: P_e_1-{T}(V0)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #30: input, references = 4, size of lhs = 0:
% 0.47/0.67 FALSE | EXISTS V0: P_e_2-{T}(V0)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #31: input, references = 5, size of lhs = 0:
% 0.47/0.67 FALSE | EXISTS V0: P_e_3-{T}(V0)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #32: input, references = 6, size of lhs = 0:
% 0.47/0.67 FALSE | EXISTS V0: P_e_4-{T}(V0)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 number of initial rules = 33
% 0.47/0.67
% 0.47/0.67 Simplifiers:
% 0.47/0.67 #33: unsound, references = 3, size of lhs = 3:
% 0.47/0.67 P_e_1-{F}(V0), P_e_1-{F}(V1), V0 == V1 | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #34: unsound, references = 3, size of lhs = 3:
% 0.47/0.67 P_e_2-{F}(V0), P_e_2-{F}(V1), V0 == V1 | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #35: unsound, references = 3, size of lhs = 3:
% 0.47/0.67 P_e_3-{F}(V0), P_e_3-{F}(V1), V0 == V1 | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #36: unsound, references = 3, size of lhs = 3:
% 0.47/0.67 P_e_4-{F}(V0), P_e_4-{F}(V1), V0 == V1 | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 number of simplifiers = 4
% 0.47/0.67
% 0.47/0.67 Learnt:
% 0.47/0.67 #51: mergings( V1 == V4, V4 == V7, V2 == V5, V5 == V7, V3 == V6, V6 == V8; #43 ), references = 1, size of lhs = 3:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V0), P_e_3-{F}(V1) | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #58: mergings( V1 == V4, V4 == V7, V2 == V5, V5 == V8, V3 == V6, V6 == V7; #44 ), references = 1, size of lhs = 3:
% 0.47/0.67 P_e_1-{F}(V0), P_e_3-{F}(V0), P_e_2-{F}(V1) | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #64: mergings( V1 == V3, V3 == V5, V2 == V4, V4 == V5; #59 ), references = 1, size of lhs = 2:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V0) | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #77: mergings( V1 == V4, V4 == V7, V2 == V5, V5 == V8, V3 == V6, V6 == V8; #69 ), references = 1, size of lhs = 3:
% 0.47/0.67 P_e_1-{F}(V0), P_e_2-{F}(V1), P_e_3-{F}(V1) | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #104: mergings( V0 == V6, V6 == V10, V10 == V14, V14 == V18, V18 == V22, V1 == V4, V4 == V7, V7 == V11, V11 == V19, V2 == V8, V8 == V12, V12 == V15, V15 == V20, V20 == V23, V3 == V9, V9 == V13, V13 == V16, V16 == V21, V21 == V24; #83 ), references = 1, size of lhs = 9:
% 0.47/0.67 group_element-{F}(V0), P_e_2-{F}(V0), group_element-{F}(V1), product1-{F}(V0,V2,V1), P_e_1-{F}(V3), product2-{F}(V3,V2,V3), P_e_3-{F}(V4), P_e_4-{F}(V5), product1-{F}(V1,V5,V5) | product1-{T}(V1,V0,V0), product1-{T}(V1,V0,V4)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #134: mergings( V0 == V6, V6 == V10, V10 == V14, V14 == V18, V18 == V22, V22 == V25, V25 == V29, V1 == V4, V4 == V7, V7 == V11, V11 == V19, V19 == V26, V26 == V30, V2 == V8, V8 == V12, V12 == V15, V15 == V20, V20 == V23, V23 == V27, V27 == V31, V3 == V5, V5 == V9, V9 == V13, V13 == V16, V16 == V21, V21 == V24, V24 == V28; #106 ), references = 1, size of lhs = 10:
% 0.47/0.67 group_element-{F}(V0), P_e_2-{F}(V0), product1-{F}(V0,V0,V0), group_element-{F}(V1), product1-{F}(V1,V1,V1), P_e_4-{F}(V1), product1-{F}(V0,V2,V1), P_e_1-{F}(V3), product2-{F}(V3,V2,V3), P_e_3-{F}(V4) | product1-{T}(V1,V0,V4)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #182: mergings( V0 == V6, V6 == V10, V10 == V13, V13 == V17, V17 == V21, V21 == V25, V25 == V28, V28 == V32, V32 == V35, V35 == V39, V39 == V42, V42 == V46, V1 == V7, V7 == V14, V14 == V5, V5 == V18, V18 == V22, V22 == V29, V29 == V36, V36 == V40, V40 == V43, V2 == V8, V8 == V11, V11 == V15, V15 == V19, V19 == V23, V23 == V26, V26 == V30, V30 == V33, V33 == V37, V37 == V41, V41 == V44, V44 == V47, V9 == V12, V12 == V16, V16 == V3, V3 == V20, V20 == V24, V24 == V27, V27 == V31, V31 == V34, V34 == V38, V38 == V45, V45 == V48; #137 ), references = 1, size of lhs = 12:
% 0.47/0.67 group_element-{F}(V0), group_element-{F}(V1), product1-{F}(V1,V1,V1), P_e_2-{F}(V1), group_element-{F}(V2), product1-{F}(V2,V2,V2), P_e_4-{F}(V2), P_e_1-{F}(V3), product1-{F}(V3,V0,V3), product2-{F}(V3,V0,V3), product1-{F}(V2,V3,V4), P_e_3-{F}(V4) | product1-{T}(V1,V0,V1), product1-{T}(V1,V0,V4)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #236: mergings( V0 == V4, V4 == V8, V8 == V11, V11 == V17, V17 == V21, V21 == V25, V25 == V28, V28 == V32, V32 == V35, V35 == V39, V39 == V42, V42 == V46, V46 == V49, V49 == V53, V1 == V5, V5 == V12, V12 == V15, V15 == V18, V18 == V22, V22 == V29, V29 == V36, V36 == V40, V40 == V43, V43 == V50, V2 == V6, V6 == V9, V9 == V13, V13 == V19, V19 == V23, V23 == V26, V26 == V30, V30 == V33, V33 == V37, V37 == V41, V41 == V44, V44 == V47, V47 == V51, V51 == V54, V7 == V10, V10 == V14, V14 == V16, V16 == V20, V20 == V24, V24 == V27, V27 == V31, V31 == V34, V34 == V38, V38 == V45, V45 == V48, V48 == V52, V52 == V55; #184 ), references = 2, size of lhs = 13:
% 0.47/0.67 group_element-{F}(V0), group_element-{F}(V1), product1-{F}(V1,V1,V1), P_e_2-{F}(V1), group_element-{F}(V2), product1-{F}(V2,V2,V2), P_e_4-{F}(V2), P_e_1-{F}(V3), product1-{F}(V3,V0,V3), product2-{F}(V3,V0,V3), product1-{F}(V2,V3,V4), P_e_3-{F}(V4), product1-{F}(V2,V0,V4) | product1-{T}(V1,V0,V1)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #257: mergings( V0 == V6, V6 == V10, V10 == V13, V13 == V17, V1 == V7, V7 == V11, V11 == V14, V14 == V18, V2 == V5, V5 == V8, V8 == V15, V3 == V9, V9 == V12, V12 == V16, V16 == V19; #241 ), references = 1, size of lhs = 8:
% 0.47/0.67 group_element-{F}(V0), group_element-{F}(V1), P_e_3-{F}(V1), P_e_1-{F}(V2), product1-{F}(V2,V0,V2), P_e_2-{F}(V3), P_e_4-{F}(V4), product1-{F}(V4,V0,V3) | product1-{T}(V1,V0,V1), product1-{T}(V1,V0,V4)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #283: mergings( V0 == V4, V4 == V6, V6 == V10, V10 == V13, V13 == V17, V17 == V20, V1 == V7, V7 == V11, V11 == V14, V14 == V18, V18 == V21, V21 == V24, V2 == V5, V5 == V8, V8 == V15, V15 == V22, V22 == V25, V3 == V9, V9 == V12, V12 == V16, V16 == V19, V19 == V23, V23 == V26; #259 ), references = 2, size of lhs = 9:
% 0.47/0.67 group_element-{F}(V0), product1-{F}(V0,V0,V0), P_e_1-{F}(V0), group_element-{F}(V1), P_e_3-{F}(V1), product1-{F}(V1,V1,V1), P_e_2-{F}(V2), P_e_4-{F}(V3), product1-{F}(V3,V0,V2) | product1-{T}(V1,V0,V3)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #303: mergings( V0 == V5, V5 == V6, V6 == V10, V10 == V13, V1 == V4, V4 == V7, V7 == V14, V14 == V17, V2 == V8, V8 == V11, V11 == V15, V15 == V18, V3 == V9, V9 == V12, V12 == V16, V16 == V19; #286 ), references = 1, size of lhs = 8:
% 0.47/0.67 group_element-{F}(V0), P_e_2-{F}(V0), product1-{F}(V0,V0,V0), group_element-{F}(V1), product1-{F}(V1,V1,V1), P_e_1-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3) | product1-{T}(V1,V0,V2), product1-{T}(V1,V0,V3)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #325: mergings( V0 == V4, V4 == V7, V7 == V14, V1 == V6, V6 == V8, V8 == V11, V11 == V15, V15 == V18, V2 == V9, V9 == V12, V12 == V16, V16 == V19, V3 == V5, V5 == V10, V10 == V13, V13 == V17, V17 == V20; #307 ), references = 1, size of lhs = 11:
% 0.47/0.67 group_element-{F}(V0), product1-{F}(V0,V0,V0), product2-{F}(V0,V0,V0), P_e_1-{F}(V0), group_element-{F}(V1), product1-{F}(V1,V1,V1), P_e_2-{F}(V1), group_element-{F}(V2), P_e_4-{F}(V2), product1-{F}(V2,V2,V2), P_e_3-{F}(V3) | product1-{T}(V2,V0,V0), product1-{T}(V2,V0,V1)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #352: mergings( V0 == V3, V3 == V7, V7 == V14, V14 == V21, V21 == V25, V1 == V4, V4 == V8, V8 == V11, V11 == V15, V15 == V18, V18 == V22, V22 == V26, V6 == V9, V9 == V12, V12 == V16, V16 == V19, V19 == V23, V23 == V27, V2 == V5, V5 == V10, V10 == V13, V13 == V17, V17 == V20, V20 == V24; #327 ), references = 1, size of lhs = 11:
% 0.47/0.67 group_element-{F}(V0), product2-{F}(V0,V0,V0), P_e_1-{F}(V0), product1-{F}(V0,V0,V0), group_element-{F}(V1), product1-{F}(V1,V1,V1), P_e_2-{F}(V1), group_element-{F}(V2), product1-{F}(V2,V2,V2), P_e_4-{F}(V2), P_e_3-{F}(V3) | product1-{T}(V2,V0,V1)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #373: mergings( V0 == V6, V6 == V10, V10 == V13, V13 == V17, V1 == V5, V5 == V7, V7 == V14, V2 == V8, V8 == V11, V11 == V15, V15 == V18, V3 == V9, V9 == V12, V12 == V16, V16 == V19; #357 ), references = 1, size of lhs = 8:
% 0.47/0.67 group_element-{F}(V0), group_element-{F}(V1), P_e_2-{F}(V1), P_e_1-{F}(V2), product1-{F}(V2,V0,V2), P_e_3-{F}(V3), P_e_4-{F}(V4), product1-{F}(V4,V0,V1) | product1-{T}(V1,V0,V3), product1-{T}(V1,V0,V4)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #390: mergings( V0 == V4, V4 == V6, V6 == V10, V10 == V13, V1 == V5, V5 == V7, V7 == V14, V14 == V17, V2 == V8, V8 == V11, V11 == V15, V15 == V18, V3 == V9, V9 == V12, V12 == V16, V16 == V19; #356 ), references = 1, size of lhs = 8:
% 0.47/0.67 group_element-{F}(V0), product1-{F}(V0,V0,V0), P_e_1-{F}(V0), group_element-{F}(V1), P_e_2-{F}(V1), product1-{F}(V1,V1,V1), P_e_3-{F}(V2), P_e_4-{F}(V3) | product1-{T}(V1,V0,V2), product1-{T}(V1,V0,V3)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #415: mergings( V0 == V6, V6 == V10, V10 == V13, V13 == V17, V17 == V20, V20 == V24, V1 == V5, V5 == V7, V7 == V14, V14 == V21, V2 == V8, V8 == V11, V11 == V15, V15 == V18, V18 == V22, V22 == V25, V3 == V9, V9 == V12, V12 == V16, V16 == V19, V19 == V23, V23 == V26; #392 ), references = 1, size of lhs = 9:
% 0.47/0.67 group_element-{F}(V0), group_element-{F}(V1), P_e_2-{F}(V1), P_e_1-{F}(V2), product1-{F}(V2,V0,V2), P_e_3-{F}(V3), product1-{F}(V3,V0,V4), product1-{F}(V4,V0,V1), P_e_4-{F}(V4) | product1-{T}(V1,V0,V3)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #440: mergings( V0 == V5, V5 == V6, V6 == V10, V10 == V13, V13 == V17, V1 == V4, V4 == V7, V7 == V14, V14 == V18, V18 == V21, V2 == V8, V8 == V11, V11 == V15, V15 == V19, V19 == V22, V3 == V9, V9 == V12, V12 == V16, V16 == V20, V20 == V23; #419 ), references = 1, size of lhs = 9:
% 0.47/0.67 group_element-{F}(V0), P_e_2-{F}(V0), group_element-{F}(V1), product1-{F}(V1,V1,V1), P_e_1-{F}(V1), P_e_3-{F}(V2), P_e_4-{F}(V3), product1-{F}(V3,V1,V4), product2-{F}(V4,V0,V0) | product1-{T}(V1,V0,V0), product1-{T}(V1,V0,V2)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #463: mergings( V0 == V6, V6 == V10, V10 == V13, V13 == V17, V1 == V4, V4 == V7, V7 == V14, V2 == V8, V8 == V11, V11 == V15, V15 == V18, V3 == V9, V9 == V12, V12 == V16, V16 == V19; #446 ), references = 1, size of lhs = 8:
% 0.47/0.67 group_element-{F}(V0), P_e_2-{F}(V0), group_element-{F}(V1), P_e_1-{F}(V2), product1-{F}(V1,V2,V3), P_e_4-{F}(V3), P_e_3-{F}(V4), product1-{F}(V1,V4,V4) | product1-{T}(V1,V0,V2), product1-{T}(V1,V0,V0)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #493: mergings( V0 == V6, V6 == V10, V10 == V13, V13 == V17, V17 == V20, V20 == V24, V24 == V28, V1 == V4, V4 == V7, V7 == V14, V14 == V21, V21 == V25, V2 == V8, V8 == V11, V11 == V15, V15 == V18, V18 == V22, V22 == V26, V26 == V29, V3 == V9, V9 == V12, V12 == V16, V16 == V19, V19 == V23, V23 == V27, V27 == V30; #466 ), references = 1, size of lhs = 10:
% 0.47/0.67 group_element-{F}(V0), P_e_2-{F}(V0), group_element-{F}(V1), P_e_1-{F}(V2), product1-{F}(V1,V2,V3), P_e_4-{F}(V3), P_e_3-{F}(V4), product1-{F}(V1,V4,V4), product1-{F}(V0,V5,V1), product2-{F}(V2,V5,V2) | product1-{T}(V1,V0,V0)
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #581: mergings( V3 == V5, V5 == V7, V7 == V10, V10 == V13, V13 == V16, V16 == V19, V19 == V22, V22 == V26, V26 == V30, V30 == V35, V35 == V41, V41 == V42, V42 == V46, V46 == V49, V49 == V51, V51 == V54, V54 == V57, V57 == V60, V60 == V61, V61 == V65, V65 == V68, V68 == V72, V72 == V75, V1 == V6, V6 == V8, V8 == V11, V11 == V14, V14 == V17, V17 == V20, V20 == V23, V23 == V27, V27 == V31, V31 == V33, V33 == V36, V36 == V38, V38 == V40, V40 == V43, V43 == V47, V47 == V52, V52 == V55, V55 == V58, V58 == V62, V62 == V66, V66 == V69, V69 == V73, V2 == V4, V4 == V9, V9 == V12, V12 == V15, V15 == V18, V18 == V21, V21 == V24, V24 == V25, V25 == V28, V28 == V29, V29 == V32, V32 == V34, V34 == V37, V37 == V39, V39 == V44, V44 == V45, V45 == V48, V48 == V50, V50 == V53, V53 == V56, V56 == V59, V59 == V63, V63 == V64, V64 == V67, V67 == V70, V70 == V71, V71 == V74; #508 ), references = 1, size of lhs = 3:
% 0.47/0.67 P_e_2-{F}(V0), P_e_3-{F}(V1), P_e_1-{F}(V2) | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #628: mergings( V2 == V3, V3 == V5, V5 == V7, V7 == V9, V9 == V11, V11 == V13, V13 == V15, V15 == V17, V17 == V19, V19 == V22, V22 == V26, V26 == V27, V27 == V29, V29 == V31, V31 == V32, V32 == V34, V34 == V36, V36 == V38, V38 == V39, V39 == V41, V41 == V43, V43 == V45, V45 == V47, V1 == V4, V4 == V6, V6 == V8, V8 == V10, V10 == V12, V12 == V14, V14 == V16, V16 == V18, V18 == V20, V20 == V21, V21 == V23, V23 == V24, V24 == V25, V25 == V28, V28 == V30, V30 == V33, V33 == V35, V35 == V37, V37 == V40, V40 == V42, V42 == V44, V44 == V46; #582 ), references = 1, size of lhs = 2:
% 0.47/0.67 P_e_2-{F}(V0), P_e_1-{F}(V1) | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #653: mergings( V1 == V2, 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 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V20, V20 == V21, V21 == V22, V22 == V23, V23 == V24; #629 ), references = 1, size of lhs = 1:
% 0.47/0.67 P_e_1-{F}(V0) | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 #655: exists( #29, #629 ), references = 1, size of lhs = 0:
% 0.47/0.67 FALSE | FALSE
% 0.47/0.67 (used 0 times, uses = {})
% 0.47/0.67
% 0.47/0.67 number of learnt formulas = 23
% 0.47/0.67
% 0.47/0.67
% 0.47/0.67 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.67
% 0.47/0.67 randbase = 1
%------------------------------------------------------------------------------