%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : LCL650+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:06:36 PM UTC 2026
% Result : Theorem 0.22s 0.54s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL650+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 5 20:02:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.22/0.54 GeoParameters:
% 0.22/0.54
% 0.22/0.54 tptp_input = 1
% 0.22/0.54 tptp_output = 0
% 0.22/0.54 nonempty = 1
% 0.22/0.54 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.54 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 0.22/0.54
% 0.22/0.54
% 0.22/0.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.54 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.54
% 0.22/0.54 RuleSystem INPUT:
% 0.22/0.54
% 0.22/0.54 Initial Rules:
% 0.22/0.54 #0: input, references = 4, size of lhs = 0:
% 0.22/0.54 FALSE | EXISTS V0: pppp13-{T}(V0)
% 0.22/0.54 (used 0 times, uses = {})
% 0.22/0.54
% 0.22/0.54 #1: input, references = 4, size of lhs = 1:
% 0.22/0.54 pppp13-{F}(V0) | pppp12-{T}(V0)
% 0.22/0.54 (used 0 times, uses = {})
% 0.22/0.54
% 0.22/0.54 #2: input, references = 4, size of lhs = 1:
% 0.22/0.54 pppp12-{F}(V0) | EXISTS V1: pppp11-{T}(V0,V1)
% 0.22/0.54 (used 0 times, uses = {})
% 0.22/0.54
% 0.22/0.54 #3: input, references = 5, size of lhs = 3:
% 0.22/0.54 pppp12-{F}(V0), r1-{F}(V0,V1), r1-{F}(V1,V2) | pppp7-{T}(V2)
% 0.22/0.54 (used 0 times, uses = {})
% 0.22/0.54
% 0.22/0.54 #4: input, references = 3, size of lhs = 2:
% 0.22/0.54 pppp12-{F}(V0), r1-{F}(V0,V1) | EXISTS V2: pppp5-{T}(V2,V1)
% 0.22/0.54 (used 0 times, uses = {})
% 0.22/0.54
% 0.22/0.54 #5: input, references = 3, size of lhs = 7:
% 0.22/0.54 pppp12-{F}(V0), r1-{F}(V0,V1), r1-{F}(V1,V2), r1-{F}(V2,V3), r1-{F}(V3,V4), p1-{F}(V4), p3-{F}(V4) | FALSE
% 0.22/0.54 (used 0 times, uses = {})
% 0.22/0.54
% 0.22/0.54 #6: input, references = 4, size of lhs = 5:
% 0.22/0.54 pppp12-{F}(V0), r1-{F}(V0,V1), r1-{F}(V1,V2), r1-{F}(V2,V3), r1-{F}(V3,V4) | p3-{T}(V4), p1-{T}(V4)
% 0.22/0.54 (used 0 times, uses = {})
% 0.22/0.54
% 0.22/0.54 #7: input, references = 3, size of lhs = 1:
% 0.22/0.54 pppp12-{F}(V0) | EXISTS V1: pppp4-{T}(V0,V1)
% 0.22/0.54 (used 0 times, uses = {})
% 0.22/0.54
% 0.22/0.54 #8: input, references = 3, size of lhs = 1:
% 0.22/0.54 pppp12-{F}(V0) | EXISTS V1: pppp3-{T}(V0,V1)
% 0.22/0.54 (used 0 times, uses = {})
% 0.22/0.54
% 0.22/0.54 #9: input, references = 4, size of lhs = 1:
% 0.22/0.54 pppp11-{F}(V0,V1) | EXISTS V2: pppp10-{T}(V2,V1)
% 0.22/0.54 (used 0 times, uses = {})
% 0.22/0.54
% 0.22/0.54 #10: input, references = 4, size of lhs = 1:
% 0.22/0.54 pppp11-{F}(V0,V1) | r1-{T}(V0,V1)
% 0.22/0.54 (used 0 times, uses = {})
% 0.22/0.54
% 0.22/0.54 #11: input, references = 4, size of lhs = 1:
% 0.22/0.54 pppp10-{F}(V0,V1) | EXISTS V2: pppp9-{T}(V0,V2)
% 0.22/0.54 (used 0 times, uses = {})
% 0.22/0.54
% 0.22/0.54 #12: input, references = 4, size of lhs = 1:
% 0.22/0.54 pppp10-{F}(V0,V1) | r1-{T}(V1,V0)
% 0.22/0.54 (used 0 times, uses = {})
% 0.22/0.54
% 0.22/0.54 #13: input, references = 4, size of lhs = 1:
% 0.22/0.54 pppp9-{F}(V0,V1) | EXISTS V2: pppp8-{T}(V2,V1)
% 0.22/0.54 (used 0 times, uses = {})
% 0.22/0.54
% 0.22/0.54 #14: input, references = 4, size of lhs = 1:
% 0.22/0.54 pppp9-{F}(V0,V1) | r1-{T}(V0,V1)
% 0.22/0.54 (used 0 times, uses = {})
% 0.22/0.54
% 0.22/0.54 #15: input, references = 3, size of lhs = 5:
% 0.22/0.54 pppp8-{F}(V0,V1), p4-{F}(V0), p3-{F}(V0), p2-{F}(V0), p1-{F}(V0) | FALSE
% 0.22/0.54 (used 0 times, uses = {})
% 0.22/0.54
% 0.22/0.54 #16: input, references = 4, size of lhs = 1:
% 0.22/0.54 pppp8-{F}(V0,V1) | r1-{T}(V1,V0)
% 0.22/0.54 (used 0 times, uses = {})
% 0.22/0.54
% 0.22/0.54 #17: input, references = 6, size of lhs = 5:
% 0.22/0.54 pppp7-{F}(V0), r1-{F}(V0,V1), r1-{F}(V1,V2), p2-{F}(V2), p1-{F}(V2) | FALSE
% 0.22/0.54 (used 0 times, uses = {})
% 0.22/0.54
% 0.22/0.54 #18: input, references = 4, size of lhs = 3:
% 0.22/0.54 pppp7-{F}(V0), r1-{F}(V0,V1), r1-{F}(V1,V2) | p1-{T}(V2), p2-{T}(V2)
% 0.22/0.54 (used 0 times, uses = {})
% 0.22/0.54
% 0.22/0.54 #19: input, references = 4, size of lhs = 1:
% 0.22/0.54 pppp7-{F}(V0) | EXISTS V1: pppp6-{T}(V0,V1)
% 0.22/0.54 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #20: input, references = 3, size of lhs = 5:
% 0.22/0.55 pppp7-{F}(V0), r1-{F}(V0,V1), r1-{F}(V1,V2), p3-{F}(V2), p2-{F}(V2) | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #21: input, references = 5, size of lhs = 3:
% 0.22/0.55 pppp7-{F}(V0), r1-{F}(V0,V1), r1-{F}(V1,V2) | p2-{T}(V2), p3-{T}(V2)
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #22: input, references = 3, size of lhs = 2:
% 0.22/0.55 pppp6-{F}(V0,V1), p3-{F}(V1) | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #23: input, references = 4, size of lhs = 1:
% 0.22/0.55 pppp6-{F}(V0,V1) | r1-{T}(V0,V1)
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #24: input, references = 3, size of lhs = 2:
% 0.22/0.55 pppp5-{F}(V0,V1), p4-{F}(V0) | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #25: input, references = 3, size of lhs = 1:
% 0.22/0.55 pppp5-{F}(V0,V1) | r1-{T}(V1,V0)
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #26: input, references = 3, size of lhs = 2:
% 0.22/0.55 pppp4-{F}(V0,V1), p5-{F}(V1) | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #27: input, references = 3, size of lhs = 1:
% 0.22/0.55 pppp4-{F}(V0,V1) | r1-{T}(V0,V1)
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #28: input, references = 4, size of lhs = 1:
% 0.22/0.55 pppp3-{F}(V0,V1) | EXISTS V2: pppp2-{T}(V2,V1)
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #29: input, references = 3, size of lhs = 1:
% 0.22/0.55 pppp3-{F}(V0,V1) | r1-{T}(V0,V1)
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #30: input, references = 3, size of lhs = 1:
% 0.22/0.55 pppp2-{F}(V0,V1) | EXISTS V2: pppp1-{T}(V0,V2)
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #31: input, references = 4, size of lhs = 1:
% 0.22/0.55 pppp2-{F}(V0,V1) | r1-{T}(V1,V0)
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #32: input, references = 3, size of lhs = 1:
% 0.22/0.55 pppp1-{F}(V0,V1) | EXISTS V2: pppp0-{T}(V2,V1)
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #33: input, references = 3, size of lhs = 1:
% 0.22/0.55 pppp1-{F}(V0,V1) | r1-{T}(V0,V1)
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #34: input, references = 3, size of lhs = 1:
% 0.22/0.55 pppp0-{F}(V0,V1) | p8-{T}(V0), p6-{T}(V0), p4-{T}(V0), p2-{T}(V0)
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #35: input, references = 3, size of lhs = 1:
% 0.22/0.55 pppp0-{F}(V0,V1) | r1-{T}(V1,V0)
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 number of initial rules = 36
% 0.22/0.55
% 0.22/0.55 Simplifiers:
% 0.22/0.55 #36: unsound, references = 3, size of lhs = 3:
% 0.22/0.55 pppp0-{F}(V0,V1), pppp0-{F}(V2,V1), V0 == V2 | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #37: unsound, references = 3, size of lhs = 3:
% 0.22/0.55 pppp1-{F}(V0,V1), pppp1-{F}(V0,V3), V1 == V3 | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #38: unsound, references = 3, size of lhs = 3:
% 0.22/0.55 pppp2-{F}(V0,V1), pppp2-{F}(V2,V1), V0 == V2 | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #39: unsound, references = 3, size of lhs = 3:
% 0.22/0.55 pppp3-{F}(V0,V1), pppp3-{F}(V0,V3), V1 == V3 | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #40: unsound, references = 3, size of lhs = 3:
% 0.22/0.55 pppp3-{F}(V0,V1), pppp3-{F}(V2,V3), V0 == V2 | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #41: unsound, references = 3, size of lhs = 3:
% 0.22/0.55 pppp4-{F}(V0,V1), pppp4-{F}(V0,V3), V1 == V3 | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #42: unsound, references = 3, size of lhs = 3:
% 0.22/0.55 pppp4-{F}(V0,V1), pppp4-{F}(V2,V3), V0 == V2 | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #43: unsound, references = 3, size of lhs = 3:
% 0.22/0.55 pppp5-{F}(V0,V1), pppp5-{F}(V2,V1), V0 == V2 | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #44: unsound, references = 3, size of lhs = 3:
% 0.22/0.55 pppp6-{F}(V0,V1), pppp6-{F}(V0,V3), V1 == V3 | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #45: unsound, references = 3, size of lhs = 3:
% 0.22/0.55 pppp8-{F}(V0,V1), pppp8-{F}(V2,V1), V0 == V2 | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #46: unsound, references = 3, size of lhs = 3:
% 0.22/0.55 pppp9-{F}(V0,V1), pppp9-{F}(V0,V3), V1 == V3 | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #47: unsound, references = 3, size of lhs = 3:
% 0.22/0.55 pppp10-{F}(V0,V1), pppp10-{F}(V2,V1), V0 == V2 | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #48: unsound, references = 3, size of lhs = 3:
% 0.22/0.55 pppp11-{F}(V0,V1), pppp11-{F}(V0,V3), V1 == V3 | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #49: unsound, references = 3, size of lhs = 3:
% 0.22/0.55 pppp11-{F}(V0,V1), pppp11-{F}(V2,V3), V0 == V2 | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #50: unsound, references = 3, size of lhs = 3:
% 0.22/0.55 pppp12-{F}(V0), pppp12-{F}(V1), V0 == V1 | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #51: unsound, references = 3, size of lhs = 3:
% 0.22/0.55 pppp13-{F}(V0), pppp13-{F}(V1), V0 == V1 | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 number of simplifiers = 16
% 0.22/0.55
% 0.22/0.55 Learnt:
% 0.22/0.55 #54: disj( #21, input ), references = 2, size of lhs = 4:
% 0.22/0.55 pppp7-{F}(V0), r1-{F}(V0,V1), r1-{F}(V1,V2), pppp6-{F}(V3,V2) | p2-{T}(V2)
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #57: disj( #6, input ), references = 2, size of lhs = 6:
% 0.22/0.55 pppp12-{F}(V0), r1-{F}(V0,V1), r1-{F}(V1,V2), r1-{F}(V2,V3), r1-{F}(V3,V4), pppp6-{F}(V5,V4) | p1-{T}(V4)
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #58: disj( #6, input ), references = 2, size of lhs = 9:
% 0.22/0.55 pppp12-{F}(V0), r1-{F}(V0,V1), r1-{F}(V1,V2), r1-{F}(V2,V3), r1-{F}(V3,V4), p2-{F}(V4), pppp7-{F}(V5), r1-{F}(V5,V6), r1-{F}(V6,V4) | p1-{T}(V4)
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #65: exists( #19, #63 ), references = 2, size of lhs = 9:
% 0.22/0.55 pppp7-{F}(V0), pppp7-{F}(V1), r1-{F}(V1,V0), pppp12-{F}(V2), r1-{F}(V2,V3), r1-{F}(V3,V4), r1-{F}(V4,V0), pppp7-{F}(V5), r1-{F}(V5,V0) | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #78: disj( #18, #58+#17 ), references = 2, size of lhs = 14:
% 0.22/0.55 pppp7-{F}(V0), r1-{F}(V0,V1), r1-{F}(V1,V2), pppp12-{F}(V3), r1-{F}(V3,V4), r1-{F}(V4,V5), r1-{F}(V5,V6), r1-{F}(V6,V2), pppp7-{F}(V7), r1-{F}(V7,V8), r1-{F}(V8,V2), pppp7-{F}(V9), r1-{F}(V9,V10), r1-{F}(V10,V2) | p1-{T}(V2)
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #82: disj( #21, input ), references = 2, size of lhs = 9:
% 0.22/0.55 pppp7-{F}(V0), r1-{F}(V0,V1), r1-{F}(V1,V2), p1-{F}(V2), pppp12-{F}(V3), r1-{F}(V3,V4), r1-{F}(V4,V5), r1-{F}(V5,V6), r1-{F}(V6,V2) | p2-{T}(V2)
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #94: mergings( V3 == V4; #92 ), references = 1, size of lhs = 6:
% 0.22/0.55 pppp7-{F}(V0), pppp3-{F}(V1,V0), pppp12-{F}(V2), r1-{F}(V2,V0), r1-{F}(V2,V3), r1-{F}(V3,V0) | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #134: mergings( V4 == V10; #132 ), references = 1, size of lhs = 18:
% 0.22/0.55 pppp7-{F}(V0), r1-{F}(V0,V1), pppp9-{F}(V2,V1), pppp7-{F}(V3), r1-{F}(V3,V1), pppp7-{F}(V4), r1-{F}(V4,V1), pppp7-{F}(V5), r1-{F}(V5,V1), pppp12-{F}(V6), r1-{F}(V6,V7), r1-{F}(V7,V8), r1-{F}(V8,V1), r1-{F}(V6,V9), r1-{F}(V9,V10), r1-{F}(V10,V1), pppp7-{F}(V11), r1-{F}(V11,V1) | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #138: mergings( V3 == V5; #136 ), references = 1, size of lhs = 7:
% 0.22/0.55 pppp7-{F}(V0), pppp10-{F}(V0,V1), pppp12-{F}(V2), r1-{F}(V2,V3), r1-{F}(V3,V0), r1-{F}(V2,V4), r1-{F}(V4,V0) | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #144: mergings( V3 == V4, V4 == V5; #141 ), references = 1, size of lhs = 3:
% 0.22/0.55 pppp12-{F}(V0), r1-{F}(V0,V1), pppp11-{F}(V2,V1) | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #147: exists( #2, #145 ), references = 1, size of lhs = 1:
% 0.22/0.55 pppp12-{F}(V0) | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 #150: exists( #0, #148 ), references = 1, size of lhs = 0:
% 0.22/0.55 FALSE | FALSE
% 0.22/0.55 (used 0 times, uses = {})
% 0.22/0.55
% 0.22/0.55 number of learnt formulas = 12
% 0.22/0.55
% 0.22/0.55
% 0.22/0.55 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.55
% 0.22/0.55 randbase = 1
%------------------------------------------------------------------------------