TSTP Solution File: BOO024-1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : BOO024-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n024.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 05:58:40 EDT 2022
% Result : Unsatisfiable 27.11s 27.31s
% Output : Refutation 27.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO024-1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n024.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 08:43:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 27.11/27.31 GeoParameters:
% 27.11/27.31
% 27.11/27.31 tptp_input = 1
% 27.11/27.31 tptp_output = 0
% 27.11/27.31 nonempty = 1
% 27.11/27.31 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.11/27.31 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 27.11/27.31
% 27.11/27.31
% 27.11/27.31 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.11/27.31 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.11/27.31
% 27.11/27.31 RuleSystem INPUT:
% 27.11/27.31
% 27.11/27.31 Initial Rules:
% 27.11/27.31 #0: input, references = 6, size of lhs = 3:
% 27.11/27.31 P_add-{F}(V0,V1,V2), P_multiply-{F}(V2,V1,V3), V3 == V1 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #1: input, references = 12, size of lhs = 6:
% 27.11/27.31 P_add-{F}(V1,V2,V3), P_multiply-{F}(V0,V3,V4), P_multiply-{F}(V1,V0,V5), P_multiply-{F}(V2,V0,V6), P_add-{F}(V5,V6,V7), V4 == V7 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #2: input, references = 4, size of lhs = 4:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_add-{F}(V1,V2,V3), V3 == V0 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #3: input, references = 10, size of lhs = 9:
% 27.11/27.31 P_n1-{F}(V0), P_pixley-{F}(V1,V2,V3,V4), P_inverse-{F}(V2,V5), P_multiply-{F}(V1,V5,V6), P_multiply-{F}(V1,V3,V7), P_multiply-{F}(V5,V3,V8), P_add-{F}(V7,V8,V9), P_add-{F}(V6,V9,V10), V4 == V10 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #4: input, references = 4, size of lhs = 3:
% 27.11/27.31 P_n1-{F}(V0), P_pixley-{F}(V1,V1,V2,V3), V3 == V2 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #5: input, references = 4, size of lhs = 3:
% 27.11/27.31 P_n1-{F}(V0), P_pixley-{F}(V1,V2,V2,V3), V3 == V1 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #6: input, references = 4, size of lhs = 3:
% 27.11/27.31 P_n1-{F}(V0), P_pixley-{F}(V1,V2,V1,V3), V3 == V1 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #7: input, references = 5, size of lhs = 5:
% 27.11/27.31 P_n1-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_multiply-{F}(V1,V2,V3), P_add-{F}(V3,V2,V2) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #8: input, references = 25, size of lhs = 2:
% 27.11/27.31 #-{F} V0, #-{F} V1 | EXISTS V2: P_multiply-{T}(V0,V1,V2)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #9: input, references = 20, size of lhs = 2:
% 27.11/27.31 #-{F} V0, #-{F} V1 | EXISTS V2: P_add-{T}(V0,V1,V2)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #10: input, references = 5, size of lhs = 1:
% 27.11/27.31 #-{F} V0 | EXISTS V1: P_inverse-{T}(V0,V1)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #11: input, references = 4, size of lhs = 0:
% 27.11/27.31 FALSE | EXISTS V0: P_n1-{T}(V0)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #12: input, references = 6, size of lhs = 3:
% 27.11/27.31 #-{F} V0, #-{F} V1, #-{F} V2 | EXISTS V3: P_pixley-{T}(V0,V1,V2,V3)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #13: input, references = 4, size of lhs = 0:
% 27.11/27.31 FALSE | EXISTS V0: P_a-{T}(V0)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #14: input, references = 4, size of lhs = 0:
% 27.11/27.31 FALSE | EXISTS V0: P_b-{T}(V0)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 number of initial rules = 15
% 27.11/27.31
% 27.11/27.31 Simplifiers:
% 27.11/27.31 #15: unsound, references = 3, size of lhs = 3:
% 27.11/27.31 P_multiply-{F}(V0,V1,V2), P_multiply-{F}(V0,V1,V5), V2 == V5 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #16: unsound, references = 3, size of lhs = 3:
% 27.11/27.31 P_add-{F}(V0,V1,V2), P_add-{F}(V0,V1,V5), V2 == V5 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #17: unsound, references = 3, size of lhs = 3:
% 27.11/27.31 P_inverse-{F}(V0,V1), P_inverse-{F}(V0,V3), V1 == V3 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #18: unsound, references = 3, size of lhs = 3:
% 27.11/27.31 P_n1-{F}(V0), P_n1-{F}(V1), V0 == V1 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #19: unsound, references = 3, size of lhs = 3:
% 27.11/27.31 P_pixley-{F}(V0,V1,V2,V3), P_pixley-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #20: unsound, references = 3, size of lhs = 3:
% 27.11/27.31 P_a-{F}(V0), P_a-{F}(V1), V0 == V1 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #21: unsound, references = 3, size of lhs = 3:
% 27.11/27.31 P_b-{F}(V0), P_b-{F}(V1), V0 == V1 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 number of simplifiers = 7
% 27.11/27.31
% 27.11/27.31 Learnt:
% 27.11/27.31 #24: exists( #12, #4 ), references = 18, size of lhs = 3:
% 27.11/27.31 P_n1-{F}(V0), #-{F} V1, #-{F} V2 | P_pixley-{T}(V1,V1,V2,V2)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #25: exists( #12, #3 ), references = 1, size of lhs = 7:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_multiply-{F}(V3,V2,V4), P_multiply-{F}(V3,V5,V6), P_multiply-{F}(V2,V5,V7), P_add-{F}(V6,V7,V8), P_add-{F}(V4,V8,V9) | P_pixley-{T}(V3,V1,V5,V9)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #28: exists( #9, #2 ), references = 3, size of lhs = 2:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2) | P_add-{T}(V1,V2,V0)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #29: exists( #9, #1 ), references = 35, size of lhs = 4:
% 27.11/27.31 P_add-{F}(V0,V1,V2), P_multiply-{F}(V3,V2,V4), P_multiply-{F}(V0,V3,V5), P_multiply-{F}(V1,V3,V6) | P_add-{T}(V5,V6,V4)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #34: exists( #8, #0 ), references = 42, size of lhs = 1:
% 27.11/27.31 P_add-{F}(V0,V1,V2) | P_multiply-{T}(V2,V1,V1)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #39: exists( #12, #5 ), references = 4, size of lhs = 3:
% 27.11/27.31 P_n1-{F}(V0), #-{F} V1, #-{F} V2 | P_pixley-{T}(V1,V2,V2,V1)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #43: exists( #12, #6 ), references = 2, size of lhs = 3:
% 27.11/27.31 P_n1-{F}(V0), #-{F} V1, #-{F} V2 | P_pixley-{T}(V2,V1,V2,V2)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #47: exists( #9, #3 ), references = 13, size of lhs = 7:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_multiply-{F}(V3,V2,V4), P_pixley-{F}(V3,V1,V5,V6), P_multiply-{F}(V3,V5,V7), P_multiply-{F}(V2,V5,V8), P_add-{F}(V7,V8,V9) | P_add-{T}(V4,V9,V6)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #52: mergings( V3 == V4; #50 ), references = 5, size of lhs = 15:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_multiply-{F}(V3,V2,V4), P_pixley-{F}(V3,V1,V5,V6), P_multiply-{F}(V3,V5,V7), P_multiply-{F}(V2,V5,V8), P_multiply-{F}(V9,V10,V7), P_multiply-{F}(V11,V10,V8), P_add-{F}(V9,V11,V12), P_inverse-{F}(V13,V14), P_multiply-{F}(V15,V14,V4), P_multiply-{F}(V15,V16,V7), P_multiply-{F}(V14,V16,V8), P_pixley-{F}(V15,V13,V16,V17), V17 == V6 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #67: exists( #8, #62 ), references = 1, size of lhs = 12:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_multiply-{F}(V3,V2,V4), P_pixley-{F}(V3,V1,V5,V6), P_multiply-{F}(V3,V5,V7), P_multiply-{F}(V2,V5,V8), P_multiply-{F}(V7,V6,V9), P_multiply-{F}(V8,V6,V10), P_add-{F}(V9,V10,V11), P_multiply-{F}(V12,V13,V7), P_multiply-{F}(V14,V13,V8), P_add-{F}(V12,V14,V15) | P_multiply-{T}(V13,V15,V11)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #70: mergings( V3 == V4, V4 == V5; #66 ), references = 2, size of lhs = 15:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V1), P_multiply-{F}(V1,V1,V2), P_multiply-{F}(V3,V3,V2), P_inverse-{F}(V4,V3), P_add-{F}(V3,V3,V5), P_inverse-{F}(V6,V7), P_multiply-{F}(V8,V7,V9), P_pixley-{F}(V8,V6,V10,V1), P_multiply-{F}(V8,V10,V11), P_multiply-{F}(V7,V10,V12), P_multiply-{F}(V13,V3,V11), P_multiply-{F}(V14,V3,V12), P_add-{F}(V13,V14,V15), P_pixley-{F}(V3,V4,V15,V16) | P_multiply-{T}(V3,V15,V16)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #96: exists( #8, #52 ), references = 1, size of lhs = 8:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_add-{F}(V2,V2,V3), P_inverse-{F}(V4,V2), P_multiply-{F}(V2,V2,V5), P_pixley-{F}(V2,V1,V6,V7), P_pixley-{F}(V2,V4,V6,V8), V8 == V7 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #103: mergings( V3 == V4; #101 ), references = 1, size of lhs = 10:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V1), P_multiply-{F}(V1,V1,V2), P_multiply-{F}(V1,V3,V2), P_multiply-{F}(V4,V3,V1), P_inverse-{F}(V5,V6), P_multiply-{F}(V7,V6,V1), P_multiply-{F}(V7,V8,V1), P_multiply-{F}(V6,V8,V2), P_pixley-{F}(V7,V5,V8,V9) | P_add-{T}(V4,V1,V9)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #121: mergings( V0 == V12, V12 == V21, V9 == V11, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7; #112 ), references = 1, size of lhs = 19:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V1), P_inverse-{F}(V2,V1), P_inverse-{F}(V3,V1), P_inverse-{F}(V4,V1), P_pixley-{F}(V1,V4,V1,V1), P_inverse-{F}(V5,V1), P_pixley-{F}(V1,V5,V1,V6), P_add-{F}(V1,V1,V7), P_pixley-{F}(V1,V2,V7,V7), P_multiply-{F}(V7,V1,V1), P_pixley-{F}(V1,V3,V7,V8), V8 == V6, P_inverse-{F}(V9,V1), P_multiply-{F}(V10,V1,V1), P_pixley-{F}(V10,V9,V1,V7), P_inverse-{F}(V11,V1), P_pixley-{F}(V12,V11,V1,V7), P_multiply-{F}(V12,V1,V1) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #125: exists( #8, #1 ), references = 34, size of lhs = 4:
% 27.11/27.31 P_add-{F}(V0,V1,V2), P_multiply-{F}(V0,V3,V4), P_multiply-{F}(V1,V3,V5), P_add-{F}(V4,V5,V6) | P_multiply-{T}(V3,V2,V6)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #127: exists( #9, #3 ), references = 1, size of lhs = 7:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_multiply-{F}(V3,V2,V4), P_pixley-{F}(V3,V1,V5,V6), P_multiply-{F}(V3,V5,V7), P_multiply-{F}(V2,V5,V8), P_add-{F}(V7,V8,V9) | P_add-{T}(V4,V9,V6)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #140: mergings( V5 == V6; #138 ), references = 7, size of lhs = 6:
% 27.11/27.31 P_add-{F}(V0,V0,V1), P_multiply-{F}(V1,V0,V2), P_add-{F}(V2,V2,V1), P_multiply-{F}(V3,V4,V1), P_multiply-{F}(V5,V4,V1), P_add-{F}(V3,V5,V6) | P_multiply-{T}(V4,V6,V1)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #144: exists( #8, #52 ), references = 2, size of lhs = 12:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_inverse-{F}(V3,V2), P_multiply-{F}(V4,V2,V5), P_multiply-{F}(V6,V2,V5), P_pixley-{F}(V4,V1,V7,V8), P_multiply-{F}(V4,V7,V9), P_multiply-{F}(V6,V7,V9), P_multiply-{F}(V10,V7,V9), P_add-{F}(V10,V2,V11), P_pixley-{F}(V6,V3,V7,V12), V12 == V8 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #156: exists( #8, #154 ), references = 4, size of lhs = 10:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_multiply-{F}(V3,V2,V4), P_pixley-{F}(V3,V1,V5,V6), P_multiply-{F}(V3,V5,V7), P_multiply-{F}(V8,V5,V7), P_add-{F}(V8,V2,V9), P_multiply-{F}(V5,V9,V10), P_add-{F}(V4,V10,V11), V6 == V11 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #168: mergings( V3 == V4; #165 ), references = 3, size of lhs = 16:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_multiply-{F}(V3,V2,V4), P_pixley-{F}(V3,V1,V5,V6), P_multiply-{F}(V3,V5,V7), P_multiply-{F}(V8,V5,V7), P_add-{F}(V8,V2,V9), P_multiply-{F}(V5,V9,V10), P_inverse-{F}(V11,V12), P_multiply-{F}(V13,V12,V4), P_pixley-{F}(V13,V11,V14,V15), V15 == V6, P_multiply-{F}(V13,V14,V16), P_multiply-{F}(V17,V14,V16), P_add-{F}(V17,V12,V18), P_multiply-{F}(V14,V18,V10) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #169: exists( #8, #164 ), references = 2, size of lhs = 13:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_multiply-{F}(V3,V2,V4), P_pixley-{F}(V3,V1,V5,V6), P_multiply-{F}(V3,V5,V7), P_multiply-{F}(V8,V5,V7), P_add-{F}(V8,V2,V9), P_multiply-{F}(V5,V9,V10), P_multiply-{F}(V11,V6,V12), P_multiply-{F}(V4,V11,V13), P_multiply-{F}(V10,V11,V14), P_add-{F}(V13,V14,V15), V12 == V15 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #172: mergings( V3 == V4; #170 ), references = 2, size of lhs = 16:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_multiply-{F}(V3,V2,V4), P_pixley-{F}(V3,V1,V5,V6), P_multiply-{F}(V3,V5,V7), P_multiply-{F}(V8,V5,V7), P_add-{F}(V8,V2,V9), P_multiply-{F}(V5,V9,V10), P_inverse-{F}(V11,V12), P_multiply-{F}(V13,V12,V4), P_pixley-{F}(V13,V11,V14,V15), V15 == V6, P_multiply-{F}(V13,V14,V16), P_multiply-{F}(V17,V14,V16), P_add-{F}(V17,V12,V18), P_multiply-{F}(V14,V18,V10) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #178: mergings( V2 == V3, V3 == V4; #175 ), references = 2, size of lhs = 10:
% 27.11/27.31 P_n1-{F}(V0), P_multiply-{F}(V0,V1,V2), P_multiply-{F}(V3,V1,V2), P_pixley-{F}(V0,V3,V1,V4), P_multiply-{F}(V1,V0,V5), P_multiply-{F}(V6,V0,V5), P_pixley-{F}(V0,V3,V6,V7), V7 == V4, P_multiply-{F}(V0,V6,V8), P_multiply-{F}(V3,V6,V8) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #185: exists( #8, #144 ), references = 2, size of lhs = 8:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_inverse-{F}(V3,V2), P_multiply-{F}(V4,V2,V5), P_add-{F}(V4,V2,V6), P_pixley-{F}(V4,V1,V7,V8), P_pixley-{F}(V4,V3,V7,V9), V9 == V8 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #190: exists( #8, #178 ), references = 4, size of lhs = 7:
% 27.11/27.31 P_n1-{F}(V0), P_pixley-{F}(V0,V0,V1,V2), P_multiply-{F}(V1,V0,V3), P_multiply-{F}(V4,V0,V3), P_pixley-{F}(V0,V0,V4,V5), V5 == V2, P_multiply-{F}(V0,V4,V6) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #191: exists( #8, #168 ), references = 5, size of lhs = 14:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_multiply-{F}(V3,V2,V4), P_add-{F}(V3,V2,V5), P_pixley-{F}(V3,V1,V6,V7), P_multiply-{F}(V6,V5,V8), P_inverse-{F}(V9,V10), P_multiply-{F}(V11,V10,V4), P_pixley-{F}(V11,V9,V12,V13), V13 == V7, P_multiply-{F}(V11,V12,V14), P_multiply-{F}(V15,V12,V14), P_add-{F}(V15,V10,V16), P_multiply-{F}(V12,V16,V8) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #192: exists( #8, #172 ), references = 5, size of lhs = 14:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_multiply-{F}(V3,V2,V4), P_add-{F}(V3,V2,V5), P_pixley-{F}(V3,V1,V6,V7), P_multiply-{F}(V6,V5,V8), P_inverse-{F}(V9,V10), P_multiply-{F}(V11,V10,V4), P_pixley-{F}(V11,V9,V12,V13), V13 == V7, P_multiply-{F}(V11,V12,V14), P_multiply-{F}(V15,V12,V14), P_add-{F}(V15,V10,V16), P_multiply-{F}(V12,V16,V8) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #213: exists( #8, #208 ), references = 2, size of lhs = 10:
% 27.11/27.31 P_n1-{F}(V0), P_add-{F}(V0,V0,V1), P_multiply-{F}(V2,V0,V3), P_multiply-{F}(V2,V1,V3), P_pixley-{F}(V0,V0,V2,V4), P_multiply-{F}(V5,V6,V3), P_multiply-{F}(V7,V6,V3), P_add-{F}(V5,V7,V0), P_pixley-{F}(V0,V0,V6,V8), V4 == V8 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #215: mergings( V3 == V4; #212 ), references = 2, size of lhs = 16:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_multiply-{F}(V2,V2,V3), P_add-{F}(V2,V2,V4), P_pixley-{F}(V2,V1,V5,V6), P_multiply-{F}(V5,V4,V7), P_multiply-{F}(V8,V9,V7), P_multiply-{F}(V10,V9,V7), P_add-{F}(V8,V10,V11), P_inverse-{F}(V12,V13), P_add-{F}(V14,V13,V11), P_multiply-{F}(V14,V9,V15), P_multiply-{F}(V16,V9,V15), P_multiply-{F}(V16,V13,V3), P_pixley-{F}(V16,V12,V9,V17), V17 == V6 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #231: exists( #8, #227 ), references = 1, size of lhs = 13:
% 27.11/27.31 P_n1-{F}(V0), P_add-{F}(V0,V0,V1), P_add-{F}(V2,V2,V0), P_multiply-{F}(V3,V2,V4), P_multiply-{F}(V5,V2,V4), P_add-{F}(V3,V5,V6), P_multiply-{F}(V7,V0,V4), P_multiply-{F}(V7,V1,V4), P_pixley-{F}(V0,V0,V7,V8), P_pixley-{F}(V0,V0,V6,V9), V8 == V9, P_add-{F}(V10,V10,V11), P_multiply-{F}(V12,V11,V4) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #232: exists( #8, #228 ), references = 1, size of lhs = 17:
% 27.11/27.31 P_n1-{F}(V0), P_add-{F}(V1,V1,V2), P_add-{F}(V1,V3,V2), P_inverse-{F}(V4,V3), P_multiply-{F}(V1,V3,V5), P_multiply-{F}(V6,V6,V5), P_inverse-{F}(V7,V6), P_add-{F}(V6,V6,V8), P_multiply-{F}(V9,V1,V10), P_multiply-{F}(V11,V1,V10), P_add-{F}(V9,V11,V12), P_pixley-{F}(V1,V4,V12,V13), P_multiply-{F}(V14,V8,V10), P_pixley-{F}(V6,V7,V14,V15), V13 == V15, P_add-{F}(V16,V16,V17), P_multiply-{F}(V18,V17,V10) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #235: exists( #8, #229 ), references = 2, size of lhs = 7:
% 27.11/27.31 P_n1-{F}(V0), P_add-{F}(V0,V0,V0), P_add-{F}(V1,V1,V0), P_add-{F}(V2,V2,V3), P_pixley-{F}(V0,V0,V2,V4), P_pixley-{F}(V0,V0,V3,V5), V4 == V5 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #236: exists( #8, #230 ), references = 1, size of lhs = 13:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_inverse-{F}(V3,V4), P_multiply-{F}(V4,V4,V5), P_add-{F}(V4,V4,V6), P_multiply-{F}(V6,V2,V5), P_add-{F}(V6,V6,V7), P_add-{F}(V6,V2,V7), P_add-{F}(V8,V8,V6), P_add-{F}(V9,V9,V10), P_pixley-{F}(V6,V1,V10,V11), P_pixley-{F}(V4,V3,V9,V12), V11 == V12 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #256: exists( #8, #185 ), references = 1, size of lhs = 7:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_inverse-{F}(V3,V2), P_add-{F}(V4,V2,V5), P_pixley-{F}(V4,V1,V6,V7), P_pixley-{F}(V4,V3,V6,V8), V8 == V7 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #268: exists( #9, #265 ), references = 7, size of lhs = 8:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_multiply-{F}(V3,V2,V4), P_pixley-{F}(V3,V1,V5,V6), P_multiply-{F}(V3,V5,V7), P_multiply-{F}(V2,V5,V8), P_multiply-{F}(V4,V8,V7), P_multiply-{F}(V8,V6,V9) | P_add-{T}(V7,V8,V9)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #320: exists( #9, #316 ), references = 1, size of lhs = 10:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_multiply-{F}(V3,V2,V4), P_multiply-{F}(V3,V5,V4), P_multiply-{F}(V2,V5,V4), P_pixley-{F}(V3,V1,V5,V6), P_multiply-{F}(V6,V6,V4), P_multiply-{F}(V7,V6,V6), P_multiply-{F}(V8,V6,V6), P_add-{F}(V7,V8,V9) | P_add-{T}(V6,V6,V6)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #322: mergings( V8 == V9; #319 ), references = 1, size of lhs = 8:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_multiply-{F}(V3,V2,V2), P_multiply-{F}(V4,V2,V2), P_add-{F}(V3,V4,V5), P_pixley-{F}(V6,V1,V2,V2), P_multiply-{F}(V6,V2,V7), P_multiply-{F}(V2,V2,V7) | P_add-{T}(V2,V2,V2)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #325: exists( #8, #323 ), references = 10, size of lhs = 6:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_pixley-{F}(V2,V1,V2,V2), P_multiply-{F}(V3,V2,V2), P_multiply-{F}(V4,V2,V2), P_add-{F}(V3,V4,V5) | P_multiply-{T}(V2,V2,V2)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #348: mergings( V3 == V4, V4 == V5; #343 ), references = 2, size of lhs = 24:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_pixley-{F}(V2,V1,V2,V2), P_multiply-{F}(V3,V2,V2), P_multiply-{F}(V4,V2,V2), P_inverse-{F}(V5,V2), P_pixley-{F}(V2,V5,V2,V2), P_inverse-{F}(V6,V2), P_multiply-{F}(V7,V2,V2), P_add-{F}(V7,V2,V8), P_inverse-{F}(V9,V10), P_multiply-{F}(V11,V10,V12), P_add-{F}(V11,V10,V13), P_multiply-{F}(V14,V2,V12), P_pixley-{F}(V11,V9,V15,V16), P_multiply-{F}(V15,V13,V17), P_pixley-{F}(V14,V6,V18,V19), V19 == V16, P_multiply-{F}(V14,V18,V20), P_multiply-{F}(V18,V21,V17), P_multiply-{F}(V22,V18,V20), P_multiply-{F}(V23,V8,V22), P_add-{F}(V23,V2,V24), P_multiply-{F}(V8,V24,V21) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #351: mergings( V3 == V4, V4 == V5; #344 ), references = 2, size of lhs = 24:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_pixley-{F}(V2,V1,V2,V2), P_multiply-{F}(V3,V2,V2), P_multiply-{F}(V4,V2,V2), P_inverse-{F}(V5,V2), P_pixley-{F}(V2,V5,V2,V2), P_inverse-{F}(V6,V2), P_multiply-{F}(V7,V2,V2), P_add-{F}(V7,V2,V8), P_inverse-{F}(V9,V10), P_multiply-{F}(V11,V10,V12), P_add-{F}(V11,V10,V13), P_multiply-{F}(V14,V2,V12), P_pixley-{F}(V11,V9,V15,V16), P_multiply-{F}(V15,V13,V17), P_pixley-{F}(V14,V6,V18,V19), V19 == V16, P_multiply-{F}(V14,V18,V20), P_multiply-{F}(V18,V21,V17), P_multiply-{F}(V22,V18,V20), P_multiply-{F}(V23,V8,V22), P_add-{F}(V23,V2,V24), P_multiply-{F}(V8,V24,V21) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #354: mergings( V3 == V4, V4 == V5; #345 ), references = 2, size of lhs = 26:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_pixley-{F}(V2,V1,V2,V2), P_multiply-{F}(V3,V2,V2), P_multiply-{F}(V4,V2,V2), P_inverse-{F}(V5,V2), P_pixley-{F}(V2,V5,V2,V2), P_inverse-{F}(V6,V2), P_multiply-{F}(V7,V2,V2), P_add-{F}(V7,V2,V8), P_inverse-{F}(V9,V10), P_multiply-{F}(V11,V10,V12), P_multiply-{F}(V13,V2,V12), P_pixley-{F}(V11,V9,V14,V15), P_multiply-{F}(V11,V14,V16), P_multiply-{F}(V17,V14,V16), P_add-{F}(V17,V10,V18), P_multiply-{F}(V14,V18,V19), P_pixley-{F}(V13,V6,V20,V21), V21 == V15, P_multiply-{F}(V13,V20,V22), P_multiply-{F}(V20,V23,V19), P_multiply-{F}(V24,V20,V22), P_multiply-{F}(V25,V8,V24), P_add-{F}(V25,V2,V26), P_multiply-{F}(V8,V26,V23) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #380: mergings( V3 == V1; #376 ), references = 1, size of lhs = 12:
% 27.11/27.31 P_n1-{F}(V0), P_add-{F}(V1,V1,V2), P_add-{F}(V3,V3,V2), P_multiply-{F}(V0,V3,V4), P_multiply-{F}(V0,V1,V5), P_add-{F}(V6,V5,V0), P_multiply-{F}(V7,V1,V6), P_multiply-{F}(V7,V3,V8), P_add-{F}(V8,V4,V9), P_add-{F}(V9,V9,V10), P_pixley-{F}(V0,V0,V10,V11), P_multiply-{F}(V0,V10,V12) | P_add-{T}(V7,V0,V11)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #382: mergings( V3 == V4; #377 ), references = 1, size of lhs = 19:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_multiply-{F}(V1,V2,V3), P_add-{F}(V1,V2,V4), P_add-{F}(V5,V5,V6), P_add-{F}(V7,V7,V6), P_multiply-{F}(V4,V7,V8), P_multiply-{F}(V4,V5,V9), P_add-{F}(V10,V9,V4), P_multiply-{F}(V11,V5,V10), P_multiply-{F}(V11,V7,V12), P_add-{F}(V12,V8,V13), P_add-{F}(V13,V13,V14), P_inverse-{F}(V15,V16), P_multiply-{F}(V17,V16,V3), P_pixley-{F}(V17,V15,V14,V18), P_multiply-{F}(V17,V14,V19), P_multiply-{F}(V20,V14,V19), P_add-{F}(V20,V16,V4) | P_add-{T}(V11,V4,V18)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #384: mergings( V3 == V4; #378 ), references = 1, size of lhs = 19:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_multiply-{F}(V1,V2,V3), P_add-{F}(V1,V2,V4), P_add-{F}(V5,V5,V6), P_add-{F}(V7,V7,V6), P_multiply-{F}(V4,V7,V8), P_multiply-{F}(V4,V5,V9), P_add-{F}(V10,V9,V4), P_multiply-{F}(V11,V5,V10), P_multiply-{F}(V11,V7,V12), P_add-{F}(V12,V8,V13), P_add-{F}(V13,V13,V14), P_inverse-{F}(V15,V16), P_multiply-{F}(V17,V16,V3), P_pixley-{F}(V17,V15,V14,V18), P_multiply-{F}(V17,V14,V19), P_multiply-{F}(V20,V14,V19), P_add-{F}(V20,V16,V4) | P_add-{T}(V11,V4,V18)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #393: mergings( V3 == V4; #389 ), references = 1, size of lhs = 26:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_pixley-{F}(V2,V1,V2,V2), P_multiply-{F}(V3,V2,V2), P_multiply-{F}(V4,V2,V2), P_multiply-{F}(V5,V2,V2), P_inverse-{F}(V6,V7), P_pixley-{F}(V7,V6,V7,V7), P_multiply-{F}(V8,V7,V7), P_multiply-{F}(V9,V7,V7), P_inverse-{F}(V10,V7), P_pixley-{F}(V7,V10,V7,V7), P_inverse-{F}(V11,V7), P_multiply-{F}(V12,V7,V7), P_add-{F}(V12,V7,V13), P_multiply-{F}(V5,V7,V14), P_pixley-{F}(V5,V11,V2,V15), P_multiply-{F}(V16,V13,V2), P_add-{F}(V16,V7,V17), P_multiply-{F}(V13,V17,V2), P_inverse-{F}(V18,V19), P_multiply-{F}(V20,V19,V14), P_add-{F}(V20,V19,V21), P_multiply-{F}(V22,V21,V2), P_pixley-{F}(V20,V18,V22,V23), V15 == V23 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #395: mergings( V3 == V4; #390 ), references = 1, size of lhs = 26:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_pixley-{F}(V2,V1,V2,V2), P_multiply-{F}(V3,V2,V2), P_multiply-{F}(V4,V2,V2), P_multiply-{F}(V5,V2,V2), P_inverse-{F}(V6,V7), P_pixley-{F}(V7,V6,V7,V7), P_multiply-{F}(V8,V7,V7), P_multiply-{F}(V9,V7,V7), P_inverse-{F}(V10,V7), P_pixley-{F}(V7,V10,V7,V7), P_inverse-{F}(V11,V7), P_multiply-{F}(V12,V7,V7), P_add-{F}(V12,V7,V13), P_multiply-{F}(V5,V7,V14), P_pixley-{F}(V5,V11,V2,V15), P_multiply-{F}(V16,V13,V2), P_add-{F}(V16,V7,V17), P_multiply-{F}(V13,V17,V2), P_inverse-{F}(V18,V19), P_multiply-{F}(V20,V19,V14), P_add-{F}(V20,V19,V21), P_multiply-{F}(V22,V21,V2), P_pixley-{F}(V20,V18,V22,V23), V15 == V23 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #397: mergings( V3 == V4; #391 ), references = 1, size of lhs = 28:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_pixley-{F}(V2,V1,V2,V2), P_multiply-{F}(V3,V2,V2), P_multiply-{F}(V4,V2,V2), P_multiply-{F}(V5,V2,V2), P_inverse-{F}(V6,V7), P_pixley-{F}(V7,V6,V7,V7), P_multiply-{F}(V8,V7,V7), P_multiply-{F}(V9,V7,V7), P_inverse-{F}(V10,V7), P_pixley-{F}(V7,V10,V7,V7), P_inverse-{F}(V11,V7), P_multiply-{F}(V12,V7,V7), P_add-{F}(V12,V7,V13), P_multiply-{F}(V5,V7,V14), P_pixley-{F}(V5,V11,V2,V15), P_multiply-{F}(V16,V13,V2), P_add-{F}(V16,V7,V17), P_multiply-{F}(V13,V17,V2), P_inverse-{F}(V18,V19), P_multiply-{F}(V20,V19,V14), P_pixley-{F}(V20,V18,V21,V22), V15 == V22, P_multiply-{F}(V20,V21,V23), P_multiply-{F}(V24,V21,V23), P_add-{F}(V24,V19,V25), P_multiply-{F}(V21,V25,V2) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #413: exists( #9, #411 ), references = 1, size of lhs = 8:
% 27.11/27.31 P_add-{F}(V0,V0,V1), P_multiply-{F}(V2,V0,V2), P_multiply-{F}(V3,V0,V3), P_add-{F}(V4,V4,V1), P_multiply-{F}(V2,V4,V5), P_multiply-{F}(V3,V4,V6), P_add-{F}(V5,V6,V7), P_add-{F}(V7,V7,V4) | P_add-{T}(V2,V3,V7)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #477: mergings( V3 == V4, V4 == V5, V5 == V6; #471 ), references = 1, size of lhs = 20:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_pixley-{F}(V2,V1,V2,V2), P_multiply-{F}(V3,V2,V2), P_multiply-{F}(V4,V2,V2), P_inverse-{F}(V5,V2), P_pixley-{F}(V2,V5,V2,V2), P_inverse-{F}(V6,V2), P_inverse-{F}(V7,V2), P_multiply-{F}(V8,V2,V2), P_add-{F}(V8,V2,V9), P_multiply-{F}(V10,V2,V11), P_pixley-{F}(V10,V7,V9,V12), P_multiply-{F}(V12,V2,V11), P_multiply-{F}(V10,V9,V13), P_pixley-{F}(V12,V6,V13,V14), V14 == V12, P_multiply-{F}(V15,V9,V13), P_add-{F}(V15,V2,V16), P_multiply-{F}(V9,V16,V13) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #481: mergings( V3 == V4, V4 == V5, V5 == V6; #472 ), references = 1, size of lhs = 26:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_pixley-{F}(V2,V1,V2,V2), P_multiply-{F}(V3,V2,V2), P_multiply-{F}(V4,V2,V2), P_inverse-{F}(V5,V2), P_pixley-{F}(V2,V5,V2,V2), P_inverse-{F}(V6,V2), P_inverse-{F}(V7,V2), P_multiply-{F}(V8,V2,V2), P_add-{F}(V8,V2,V9), P_multiply-{F}(V10,V2,V11), P_pixley-{F}(V10,V7,V9,V12), P_multiply-{F}(V10,V9,V13), P_pixley-{F}(V13,V6,V12,V14), P_multiply-{F}(V15,V9,V13), P_add-{F}(V15,V2,V16), P_multiply-{F}(V9,V16,V13), P_inverse-{F}(V17,V18), P_multiply-{F}(V19,V18,V2), P_pixley-{F}(V19,V17,V20,V21), V21 == V14, P_multiply-{F}(V19,V20,V22), P_multiply-{F}(V23,V20,V22), P_add-{F}(V23,V18,V24), P_multiply-{F}(V20,V24,V13) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #485: mergings( V3 == V4, V4 == V5, V5 == V6; #473 ), references = 1, size of lhs = 26:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_pixley-{F}(V2,V1,V2,V2), P_multiply-{F}(V3,V2,V2), P_multiply-{F}(V4,V2,V2), P_inverse-{F}(V5,V2), P_pixley-{F}(V2,V5,V2,V2), P_inverse-{F}(V6,V2), P_inverse-{F}(V7,V2), P_multiply-{F}(V8,V2,V2), P_add-{F}(V8,V2,V9), P_multiply-{F}(V10,V2,V11), P_pixley-{F}(V10,V7,V9,V12), P_multiply-{F}(V10,V9,V13), P_pixley-{F}(V13,V6,V12,V14), P_multiply-{F}(V15,V9,V13), P_add-{F}(V15,V2,V16), P_multiply-{F}(V9,V16,V13), P_inverse-{F}(V17,V18), P_multiply-{F}(V19,V18,V2), P_pixley-{F}(V19,V17,V20,V21), V21 == V14, P_multiply-{F}(V19,V20,V22), P_multiply-{F}(V23,V20,V22), P_add-{F}(V23,V18,V24), P_multiply-{F}(V20,V24,V13) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #496: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6; #489 ), references = 1, size of lhs = 15:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_pixley-{F}(V2,V1,V2,V2), P_multiply-{F}(V3,V2,V2), P_multiply-{F}(V4,V2,V2), P_inverse-{F}(V5,V2), P_pixley-{F}(V2,V5,V2,V2), P_inverse-{F}(V6,V2), P_multiply-{F}(V7,V2,V2), P_add-{F}(V7,V2,V8), P_add-{F}(V8,V2,V8), P_pixley-{F}(V8,V6,V8,V9), P_inverse-{F}(V9,V2), P_multiply-{F}(V8,V2,V10), P_multiply-{F}(V9,V2,V10) | P_multiply-{T}(V8,V8,V9)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #501: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6; #490 ), references = 1, size of lhs = 18:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_pixley-{F}(V2,V1,V2,V2), P_multiply-{F}(V3,V2,V2), P_multiply-{F}(V4,V2,V2), P_inverse-{F}(V5,V2), P_pixley-{F}(V2,V5,V2,V2), P_inverse-{F}(V6,V2), P_multiply-{F}(V7,V2,V2), P_add-{F}(V7,V2,V8), P_add-{F}(V8,V2,V8), P_pixley-{F}(V8,V6,V8,V9), P_inverse-{F}(V9,V2), P_multiply-{F}(V8,V2,V10), P_multiply-{F}(V8,V11,V2), P_add-{F}(V8,V11,V8), P_inverse-{F}(V12,V11), P_pixley-{F}(V8,V12,V8,V13) | P_multiply-{T}(V8,V8,V13)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #506: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6; #491 ), references = 1, size of lhs = 18:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_pixley-{F}(V2,V1,V2,V2), P_multiply-{F}(V3,V2,V2), P_multiply-{F}(V4,V2,V2), P_inverse-{F}(V5,V2), P_pixley-{F}(V2,V5,V2,V2), P_inverse-{F}(V6,V2), P_multiply-{F}(V7,V2,V2), P_add-{F}(V7,V2,V8), P_add-{F}(V8,V2,V8), P_pixley-{F}(V8,V6,V8,V9), P_inverse-{F}(V9,V2), P_multiply-{F}(V8,V2,V10), P_multiply-{F}(V8,V11,V2), P_add-{F}(V8,V11,V8), P_inverse-{F}(V12,V11), P_pixley-{F}(V8,V12,V8,V13) | P_multiply-{T}(V8,V8,V13)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #523: mergings( V3 == V1; #519 ), references = 2, size of lhs = 5:
% 27.11/27.31 P_n1-{F}(V0), P_multiply-{F}(V1,V0,V0), P_pixley-{F}(V0,V0,V1,V2), P_multiply-{F}(V0,V1,V3), #-{F} V4 | P_add-{T}(V4,V0,V2)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #525: mergings( V3 == V4; #520 ), references = 1, size of lhs = 12:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_multiply-{F}(V1,V2,V3), P_add-{F}(V1,V2,V4), P_inverse-{F}(V5,V6), P_multiply-{F}(V7,V6,V3), P_pixley-{F}(V7,V5,V8,V9), P_multiply-{F}(V7,V8,V10), P_multiply-{F}(V11,V8,V10), P_add-{F}(V11,V6,V12), P_multiply-{F}(V8,V12,V4), #-{F} V13 | P_add-{T}(V13,V4,V9)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #527: mergings( V3 == V4; #521 ), references = 1, size of lhs = 12:
% 27.11/27.31 P_n1-{F}(V0), P_inverse-{F}(V1,V2), P_multiply-{F}(V1,V2,V3), P_add-{F}(V1,V2,V4), P_inverse-{F}(V5,V6), P_multiply-{F}(V7,V6,V3), P_pixley-{F}(V7,V5,V8,V9), P_multiply-{F}(V7,V8,V10), P_multiply-{F}(V11,V8,V10), P_add-{F}(V11,V6,V12), P_multiply-{F}(V8,V12,V4), #-{F} V13 | P_add-{T}(V13,V4,V9)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #540: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V0; #533 ), references = 1, size of lhs = 6:
% 27.11/27.31 P_n1-{F}(V0), P_pixley-{F}(V0,V0,V0,V0), P_add-{F}(V1,V1,V2), P_pixley-{F}(V0,V0,V1,V3), P_pixley-{F}(V0,V0,V2,V4), V3 == V4 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #550: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9; #542 ), references = 8, size of lhs = 3:
% 27.11/27.31 P_n1-{F}(V0), P_pixley-{F}(V0,V0,V0,V0), P_pixley-{F}(V0,V0,V1,V2) | P_add-{T}(V1,V1,V2)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #556: mergings( V3 == V4, V4 == V5; #553 ), references = 1, size of lhs = 7:
% 27.11/27.31 P_n1-{F}(V0), P_pixley-{F}(V0,V0,V0,V0), P_inverse-{F}(V1,V2), P_add-{F}(V3,V2,V2), P_pixley-{F}(V4,V1,V4,V5), P_multiply-{F}(V4,V4,V6), P_multiply-{F}(V3,V4,V6) | P_multiply-{T}(V4,V2,V5)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #567: exists( #8, #565 ), references = 3, size of lhs = 6:
% 27.11/27.31 P_n1-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_multiply-{F}(V3,V2,V2), P_add-{F}(V1,V3,V4), P_multiply-{F}(V2,V4,V2) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #578: exists( #8, #572 ), references = 1, size of lhs = 10:
% 27.11/27.31 P_add-{F}(V0,V1,V2), P_multiply-{F}(V3,V0,V4), P_add-{F}(V3,V5,V6), P_multiply-{F}(V6,V2,V7), P_multiply-{F}(V1,V6,V8), P_multiply-{F}(V5,V0,V9), P_multiply-{F}(V9,V7,V10), P_multiply-{F}(V8,V9,V11), P_add-{F}(V9,V11,V12), V10 == V12 | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #581: mergings( V3 == V4, V4 == V5; #577 ), references = 2, size of lhs = 8:
% 27.11/27.31 P_n1-{F}(V0), P_pixley-{F}(V0,V0,V0,V0), P_a-{F}(V1), P_b-{F}(V2), P_add-{F}(V1,V1,V3), P_multiply-{F}(V4,V3,V2), P_add-{F}(V2,V4,V5), P_multiply-{F}(V3,V5,V2) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #596: mergings( V3 == V4, V4 == V5; #593 ), references = 1, size of lhs = 10:
% 27.11/27.31 P_n1-{F}(V0), P_pixley-{F}(V0,V0,V0,V0), P_a-{F}(V1), P_b-{F}(V2), P_add-{F}(V1,V1,V3), P_multiply-{F}(V4,V3,V2), P_multiply-{F}(V5,V5,V4), P_add-{F}(V5,V5,V6), P_multiply-{F}(V3,V6,V2), P_multiply-{F}(V7,V5,V2) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #651: mergings( V3 == V4; #649 ), references = 1, size of lhs = 7:
% 27.11/27.31 P_n1-{F}(V0), P_pixley-{F}(V0,V0,V0,V0), P_add-{F}(V1,V1,V2), P_multiply-{F}(V3,V3,V4), P_multiply-{F}(V1,V3,V5), P_add-{F}(V4,V5,V6), P_add-{F}(V6,V2,V7) | P_add-{T}(V3,V1,V7)
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #677: mergings( V3 == V4, V4 == V5; #674 ), references = 1, size of lhs = 9:
% 27.11/27.31 P_n1-{F}(V0), P_pixley-{F}(V0,V0,V0,V0), P_a-{F}(V1), P_b-{F}(V2), P_multiply-{F}(V2,V2,V2), P_add-{F}(V2,V2,V2), P_multiply-{F}(V3,V3,V4), P_multiply-{F}(V2,V3,V5), P_add-{F}(V4,V5,V1) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #694: mergings( V3 == V4, V4 == V5; #691 ), references = 1, size of lhs = 6:
% 27.11/27.31 P_n1-{F}(V0), P_pixley-{F}(V0,V0,V0,V0), P_a-{F}(V1), P_b-{F}(V2), P_add-{F}(V2,V2,V2), P_multiply-{F}(V2,V2,V2) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #703: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5; #698 ), references = 1, size of lhs = 3:
% 27.11/27.31 P_n1-{F}(V0), P_pixley-{F}(V0,V0,V0,V0), P_a-{F}(V1) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #709: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5; #704 ), references = 1, size of lhs = 2:
% 27.11/27.31 P_n1-{F}(V0), P_pixley-{F}(V0,V0,V0,V0) | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 #712: exists( #11, #710 ), references = 1, size of lhs = 0:
% 27.11/27.31 FALSE | FALSE
% 27.11/27.31 (used 0 times, uses = {})
% 27.11/27.31
% 27.11/27.31 number of learnt formulas = 70
% 27.11/27.31
% 27.11/27.31
% 27.11/27.31 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.11/27.31
% 27.11/27.31 randbase = 1
%------------------------------------------------------------------------------