TSTP Solution File: HEN006-2 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : HEN006-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n019.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 06:04:41 EDT 2022
% Result : Unsatisfiable 2.05s 2.25s
% Output : Refutation 2.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : HEN006-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n019.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 21:05:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.05/2.25 GeoParameters:
% 2.05/2.25
% 2.05/2.25 tptp_input = 1
% 2.05/2.25 tptp_output = 0
% 2.05/2.25 nonempty = 1
% 2.05/2.25 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.05/2.25 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 2.05/2.25
% 2.05/2.25
% 2.05/2.25 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.05/2.25 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.05/2.25
% 2.05/2.25 RuleSystem INPUT:
% 2.05/2.25
% 2.05/2.25 Initial Rules:
% 2.05/2.25 #0: input, references = 8, size of lhs = 2:
% 2.05/2.25 P_zero-{F}(V0), less_equal-{F}(V1,V2) | quotient-{T}(V1,V2,V0)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #1: input, references = 7, size of lhs = 2:
% 2.05/2.25 P_zero-{F}(V0), quotient-{F}(V1,V2,V0) | less_equal-{T}(V1,V2)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #2: input, references = 7, size of lhs = 2:
% 2.05/2.25 P_zero-{F}(V0), quotient-{F}(V1,V3,V2) | less_equal-{T}(V2,V1)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #3: input, references = 6, size of lhs = 6:
% 2.05/2.25 P_zero-{F}(V0), quotient-{F}(V3,V4,V1), quotient-{F}(V5,V6,V2), quotient-{F}(V7,V6,V4), quotient-{F}(V8,V7,V5), quotient-{F}(V8,V6,V3) | less_equal-{T}(V1,V2)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #4: input, references = 6, size of lhs = 2:
% 2.05/2.25 P_zero-{F}(V0), #-{F} V1 | less_equal-{T}(V0,V1)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #5: input, references = 9, size of lhs = 4:
% 2.05/2.25 P_zero-{F}(V0), less_equal-{F}(V1,V2), less_equal-{F}(V2,V1), V1 == V2 | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #6: input, references = 6, size of lhs = 3:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), #-{F} V2 | less_equal-{T}(V2,V1)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #7: input, references = 17, size of lhs = 3:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), P_divide-{F}(V2,V3,V4) | quotient-{T}(V2,V3,V4)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #8: input, references = 6, size of lhs = 5:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), quotient-{F}(V5,V4,V2), quotient-{F}(V5,V4,V3), V2 == V3 | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #9: input, references = 3, size of lhs = 3:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), #-{F} V2 | quotient-{T}(V2,V1,V0)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #10: input, references = 4, size of lhs = 3:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), #-{F} V2 | quotient-{T}(V0,V2,V0)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #11: input, references = 4, size of lhs = 3:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), #-{F} V2 | quotient-{T}(V2,V2,V0)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #12: input, references = 3, size of lhs = 3:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), #-{F} V2 | quotient-{T}(V2,V0,V2)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #13: input, references = 5, size of lhs = 4:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), less_equal-{F}(V2,V3), less_equal-{F}(V4,V2) | less_equal-{T}(V4,V3)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #14: input, references = 5, size of lhs = 5:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), P_x-{F}(V2), P_y-{F}(V3), P_xQy-{F}(V4) | quotient-{T}(V2,V3,V4)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #15: input, references = 6, size of lhs = 6:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), P_x-{F}(V2), P_y-{F}(V3), P_xQy-{F}(V4), P_z-{F}(V5) | less_equal-{T}(V4,V5)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #16: input, references = 6, size of lhs = 7:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), P_x-{F}(V2), P_y-{F}(V3), P_xQy-{F}(V4), P_z-{F}(V5), P_xQz-{F}(V6) | quotient-{T}(V2,V5,V6)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #17: input, references = 8, size of lhs = 8:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), P_x-{F}(V2), P_y-{F}(V3), P_xQy-{F}(V4), P_z-{F}(V5), P_xQz-{F}(V6), less_equal-{F}(V6,V3) | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #18: input, references = 4, size of lhs = 0:
% 2.05/2.25 FALSE | EXISTS V0: P_zero-{T}(V0)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #19: input, references = 4, size of lhs = 0:
% 2.05/2.25 FALSE | EXISTS V0: P_identity-{T}(V0)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #20: input, references = 10, size of lhs = 2:
% 2.05/2.25 #-{F} V0, #-{F} V1 | EXISTS V2: P_divide-{T}(V0,V1,V2)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #21: input, references = 4, size of lhs = 0:
% 2.05/2.25 FALSE | EXISTS V0: P_x-{T}(V0)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #22: input, references = 5, size of lhs = 0:
% 2.05/2.25 FALSE | EXISTS V0: P_y-{T}(V0)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #23: input, references = 7, size of lhs = 0:
% 2.05/2.25 FALSE | EXISTS V0: P_xQy-{T}(V0)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #24: input, references = 9, size of lhs = 0:
% 2.05/2.25 FALSE | EXISTS V0: P_z-{T}(V0)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #25: input, references = 7, size of lhs = 0:
% 2.05/2.25 FALSE | EXISTS V0: P_xQz-{T}(V0)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 number of initial rules = 26
% 2.05/2.25
% 2.05/2.25 Simplifiers:
% 2.05/2.25 #26: unsound, references = 3, size of lhs = 3:
% 2.05/2.25 P_zero-{F}(V0), P_zero-{F}(V1), V0 == V1 | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #27: unsound, references = 3, size of lhs = 3:
% 2.05/2.25 P_identity-{F}(V0), P_identity-{F}(V1), V0 == V1 | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #28: unsound, references = 3, size of lhs = 3:
% 2.05/2.25 P_divide-{F}(V0,V1,V2), P_divide-{F}(V0,V1,V5), V2 == V5 | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #29: unsound, references = 3, size of lhs = 3:
% 2.05/2.25 P_x-{F}(V0), P_x-{F}(V1), V0 == V1 | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #30: unsound, references = 3, size of lhs = 3:
% 2.05/2.25 P_y-{F}(V0), P_y-{F}(V1), V0 == V1 | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #31: unsound, references = 3, size of lhs = 3:
% 2.05/2.25 P_xQy-{F}(V0), P_xQy-{F}(V1), V0 == V1 | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #32: unsound, references = 3, size of lhs = 3:
% 2.05/2.25 P_z-{F}(V0), P_z-{F}(V1), V0 == V1 | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #33: unsound, references = 3, size of lhs = 3:
% 2.05/2.25 P_xQz-{F}(V0), P_xQz-{F}(V1), V0 == V1 | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 number of simplifiers = 8
% 2.05/2.25
% 2.05/2.25 Learnt:
% 2.05/2.25 #39: mergings( V1 == V7, V2 == V8; #36 ), references = 3, size of lhs = 7:
% 2.05/2.25 P_x-{F}(V0), P_y-{F}(V1), P_xQy-{F}(V2), P_z-{F}(V3), P_zero-{F}(V4), P_identity-{F}(V5), quotient-{F}(V0,V3,V6) | P_xQz-{T}(V6)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #48: mergings( V1 == V3, V3 == V7, V2 == V4; #44 ), references = 1, size of lhs = 5:
% 2.05/2.25 P_xQy-{F}(V0), P_identity-{F}(V0), P_x-{F}(V1), P_y-{F}(V2), P_zero-{F}(V3) | P_z-{T}(V0)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #62: mergings( V3 == V5, V4 == V6; #59 ), references = 1, size of lhs = 3:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), quotient-{F}(V2,V3,V4) | P_divide-{T}(V2,V3,V4)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #75: mergings( V1 == V2, V2 == V5, V5 == V7, V6 == V8, V7 == V9, V3 == V10, V4 == V11; #67 ), references = 1, size of lhs = 6:
% 2.05/2.25 P_zero-{F}(V0), P_x-{F}(V0), P_identity-{F}(V1), P_y-{F}(V2), less_equal-{F}(V0,V2), P_xQy-{F}(V3) | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #83: mergings( V1 == V2, V2 == V4, V4 == V6, V5 == V7, V6 == V8, V3 == V9; #76 ), references = 2, size of lhs = 5:
% 2.05/2.25 P_zero-{F}(V0), P_x-{F}(V0), P_identity-{F}(V1), P_y-{F}(V2), less_equal-{F}(V0,V2) | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #86: exists( #22, #84 ), references = 1, size of lhs = 3:
% 2.05/2.25 P_zero-{F}(V0), P_x-{F}(V0), P_identity-{F}(V1) | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #92: mergings( V1 == V3, V2 == V4; #89 ), references = 1, size of lhs = 6:
% 2.05/2.25 P_y-{F}(V0), P_identity-{F}(V0), P_zero-{F}(V1), P_x-{F}(V2), P_xQy-{F}(V3), P_z-{F}(V4) | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #96: mergings( V1 == V3, V2 == V4; #93 ), references = 1, size of lhs = 5:
% 2.05/2.25 P_y-{F}(V0), P_identity-{F}(V0), P_zero-{F}(V1), P_x-{F}(V2), P_xQy-{F}(V3) | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #100: mergings( V1 == V3, V2 == V4; #97 ), references = 1, size of lhs = 4:
% 2.05/2.25 P_y-{F}(V0), P_identity-{F}(V0), P_zero-{F}(V1), P_x-{F}(V2) | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #105: mergings( V1 == V5, V2 == V6; #102 ), references = 1, size of lhs = 5:
% 2.05/2.25 P_x-{F}(V0), P_y-{F}(V1), P_zero-{F}(V2), P_identity-{F}(V3), quotient-{F}(V0,V1,V4) | P_xQy-{T}(V4)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #125: mergings( V1 == V6, V6 == V9, V9 == V11, V2 == V10, V10 == V12, V3 == V5, V5 == V13, V4 == V7, V7 == V14, V13 == V8, V8 == V15; #113 ), references = 1, size of lhs = 6:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), P_x-{F}(V2), P_xQy-{F}(V2), P_y-{F}(V3), less_equal-{F}(V0,V3) | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #149: mergings( V1 == V7, V7 == V8, V8 == V10, V2 == V9, V9 == V11, V3 == V12, V4 == V13, V5 == V14, V6 == V15; #139 ), references = 1, size of lhs = 7:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), P_x-{F}(V2), P_y-{F}(V3), less_equal-{F}(V2,V3), P_xQy-{F}(V4), P_z-{F}(V5) | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #159: mergings( V1 == V6, V6 == V7, V7 == V9, V2 == V8, V8 == V10, V3 == V11, V4 == V12, V5 == V13; #150 ), references = 1, size of lhs = 6:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), P_x-{F}(V2), P_y-{F}(V3), less_equal-{F}(V2,V3), P_xQy-{F}(V4) | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #186: mergings( V3 == V4, V4 == V6, V6 == V7; #182 ), references = 6, size of lhs = 6:
% 2.05/2.25 P_identity-{F}(V0), P_zero-{F}(V1), quotient-{F}(V2,V3,V1), quotient-{F}(V4,V3,V5), quotient-{F}(V6,V4,V2), quotient-{F}(V6,V3,V7) | P_divide-{T}(V7,V5,V1)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #206: mergings( V3 == V5, V5 == V6, V6 == V7; #202 ), references = 1, size of lhs = 6:
% 2.05/2.25 P_identity-{F}(V0), P_zero-{F}(V1), quotient-{F}(V2,V3,V4), quotient-{F}(V5,V2,V6), quotient-{F}(V5,V3,V7), quotient-{F}(V7,V4,V6) | P_divide-{T}(V6,V3,V6)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #236: mergings( V3 == V6, V6 == V9, V9 == V10, V10 == V12, V12 == V13, V4 == V5, V5 == V7, V7 == V8, V8 == V11; #226 ), references = 3, size of lhs = 8:
% 2.05/2.25 P_identity-{F}(V0), P_zero-{F}(V1), quotient-{F}(V2,V3,V1), quotient-{F}(V4,V3,V1), quotient-{F}(V5,V6,V2), quotient-{F}(V5,V3,V7), quotient-{F}(V8,V3,V7), quotient-{F}(V6,V8,V4) | P_divide-{T}(V6,V3,V7)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #287: mergings( V3 == V4, V4 == V9, V9 == V12, V12 == V15, V15 == V17, V17 == V18, V0 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V10, V10 == V11, V11 == V13, V13 == V14, V14 == V16; #270 ), references = 1, size of lhs = 7:
% 2.05/2.25 P_identity-{F}(V0), P_zero-{F}(V1), quotient-{F}(V2,V0,V3), quotient-{F}(V3,V4,V1), quotient-{F}(V2,V4,V5), quotient-{F}(V5,V4,V5), quotient-{F}(V4,V5,V1) | P_divide-{T}(V0,V4,V0)
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #345: mergings( V3 == V5, V5 == V6, V6 == V8, V8 == V9, V9 == V11, V11 == V12, V4 == V7, V7 == V10; #336 ), references = 1, size of lhs = 10:
% 2.05/2.25 P_identity-{F}(V0), P_zero-{F}(V1), quotient-{F}(V1,V2,V3), less_equal-{F}(V3,V4), V3 == V4, quotient-{F}(V5,V1,V4), quotient-{F}(V6,V2,V5), quotient-{F}(V7,V8,V6), quotient-{F}(V7,V2,V9), quotient-{F}(V9,V8,V1) | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #384: mergings( V3 == V5, V5 == V7, V7 == V9, V9 == V10, V10 == V12, V4 == V6, V6 == V8, V8 == V11, V11 == V13; #374 ), references = 1, size of lhs = 10:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), P_x-{F}(V2), P_y-{F}(V3), P_xQy-{F}(V4), P_z-{F}(V5), P_xQz-{F}(V6), quotient-{F}(V7,V8,V6), quotient-{F}(V7,V3,V9), quotient-{F}(V9,V8,V0) | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #402: mergings( V1 == V7, V7 == V9, V9 == V11, V11 == V13, V13 == V14, V14 == V16, V2 == V8, V8 == V10, V10 == V12, V12 == V15, V15 == V17, V3 == V18, V4 == V19, V5 == V20, V6 == V21; #386 ), references = 2, size of lhs = 8:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), P_x-{F}(V2), P_y-{F}(V3), P_xQy-{F}(V4), P_z-{F}(V5), quotient-{F}(V2,V3,V6), quotient-{F}(V6,V5,V0) | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #414: mergings( V1 == V6, V2 == V7, V3 == V8, V4 == V9, V5 == V10; #408 ), references = 1, size of lhs = 6:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), P_x-{F}(V2), P_y-{F}(V3), quotient-{F}(V2,V3,V4), P_xQy-{F}(V4) | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #423: mergings( V1 == V3, V3 == V7, V2 == V4, V4 == V8, V5 == V9, V6 == V10; #416 ), references = 1, size of lhs = 4:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), P_x-{F}(V2), P_y-{F}(V3) | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #430: mergings( V1 == V3, V3 == V6, V2 == V4, V4 == V7, V5 == V8; #424 ), references = 1, size of lhs = 3:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1), P_x-{F}(V2) | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #436: mergings( V1 == V3, V3 == V5, V2 == V4, V4 == V6; #431 ), references = 1, size of lhs = 2:
% 2.05/2.25 P_zero-{F}(V0), P_identity-{F}(V1) | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #440: mergings( V1 == V2, V2 == V3; #437 ), references = 1, size of lhs = 1:
% 2.05/2.25 P_zero-{F}(V0) | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 #442: exists( #18, #437 ), references = 1, size of lhs = 0:
% 2.05/2.25 FALSE | FALSE
% 2.05/2.25 (used 0 times, uses = {})
% 2.05/2.25
% 2.05/2.25 number of learnt formulas = 26
% 2.05/2.25
% 2.05/2.25
% 2.05/2.25 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.05/2.25
% 2.05/2.25 randbase = 1
%------------------------------------------------------------------------------