%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : LCL688+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n006.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 12:06:55 PM UTC 2026
% Result : Theorem 0.33s 0.59s
% Output : Refutation 0.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL688+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 4 17:57:17 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.33/0.59 GeoParameters:
% 0.33/0.59
% 0.33/0.59 tptp_input = 1
% 0.33/0.59 tptp_output = 0
% 0.33/0.59 nonempty = 1
% 0.33/0.59 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.33/0.59 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 0.33/0.59
% 0.33/0.59
% 0.33/0.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.33/0.59 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.33/0.59
% 0.33/0.59 RuleSystem INPUT:
% 0.33/0.59
% 0.33/0.59 Initial Rules:
% 0.33/0.59 #0: input, references = 7, size of lhs = 1:
% 0.33/0.59 #-{F} V0 | r1-{T}(V0,V0)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #1: input, references = 5, size of lhs = 2:
% 0.33/0.59 r1-{F}(V0,V1), r1-{F}(V2,V0) | r1-{T}(V2,V1)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #2: input, references = 4, size of lhs = 0:
% 0.33/0.59 FALSE | EXISTS V0: pppp13-{T}(V0)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #3: input, references = 4, size of lhs = 1:
% 0.33/0.59 pppp13-{F}(V0) | pppp12-{T}(V0)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #4: input, references = 3, size of lhs = 5:
% 0.33/0.59 pppp12-{F}(V0), r1-{F}(V0,V1), r1-{F}(V1,V2), r1-{F}(V2,V3), p1-{F}(V3) | EXISTS V4: pppp11-{T}(V4,V1)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #5: input, references = 4, size of lhs = 1:
% 0.33/0.59 pppp12-{F}(V0) | EXISTS V1: pppp10-{T}(V0,V1)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #6: input, references = 3, size of lhs = 1:
% 0.33/0.59 pppp12-{F}(V0) | EXISTS V1: pppp8-{T}(V0,V1)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #7: input, references = 3, size of lhs = 2:
% 0.33/0.59 pppp12-{F}(V0), r1-{F}(V0,V1) | p1-{T}(V0), pppp14-{T}(V1), pppp15-{T}(V0)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #8: input, references = 3, size of lhs = 1:
% 0.33/0.59 pppp14-{F}(V0) | EXISTS V1: pppp4-{T}(V1,V0)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #9: input, references = 3, size of lhs = 1:
% 0.33/0.59 pppp15-{F}(V0) | EXISTS V1: pppp5-{T}(V0,V1)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #10: input, references = 4, size of lhs = 6:
% 0.33/0.59 pppp12-{F}(V0), r1-{F}(V0,V1), r1-{F}(V1,V2), r1-{F}(V2,V3), p2-{F}(V2), r1-{F}(V2,V4) | p2-{T}(V3), pppp16-{T}(V4)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #11: input, references = 4, size of lhs = 1:
% 0.33/0.59 pppp16-{F}(V0) | EXISTS V1: pppp3-{T}(V1,V0)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #12: input, references = 3, size of lhs = 6:
% 0.33/0.59 pppp12-{F}(V0), r1-{F}(V0,V1), r1-{F}(V1,V2), r1-{F}(V2,V3), p2-{F}(V2), r1-{F}(V2,V4) | pppp17-{T}(V3), pppp18-{T}(V4)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #13: input, references = 3, size of lhs = 1:
% 0.33/0.59 pppp17-{F}(V0) | EXISTS V1: pppp2-{T}(V1,V0)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #14: input, references = 3, size of lhs = 1:
% 0.33/0.59 pppp18-{F}(V0) | EXISTS V1: pppp3-{T}(V1,V0)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #15: input, references = 6, size of lhs = 3:
% 0.33/0.59 pppp12-{F}(V0), r1-{F}(V0,V1), r1-{F}(V1,V2) | EXISTS V3: pppp1-{T}(V2,V3)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #16: input, references = 3, size of lhs = 3:
% 0.33/0.59 pppp12-{F}(V0), r1-{F}(V0,V1), p4-{F}(V1) | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #17: input, references = 3, size of lhs = 1:
% 0.33/0.59 pppp11-{F}(V0,V1) | p1-{T}(V0)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #18: input, references = 3, size of lhs = 1:
% 0.33/0.59 pppp11-{F}(V0,V1) | r1-{T}(V1,V0)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #19: input, references = 4, size of lhs = 2:
% 0.33/0.59 pppp10-{F}(V0,V1), r1-{F}(V1,V2) | EXISTS V3: pppp9-{T}(V2,V3)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #20: input, references = 4, size of lhs = 1:
% 0.33/0.59 pppp10-{F}(V0,V1) | r1-{T}(V0,V1)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #21: input, references = 3, size of lhs = 2:
% 0.33/0.59 pppp9-{F}(V0,V1), p2-{F}(V1) | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #22: input, references = 4, size of lhs = 1:
% 0.33/0.59 pppp9-{F}(V0,V1) | r1-{T}(V0,V1)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #23: input, references = 3, size of lhs = 1:
% 0.33/0.59 pppp8-{F}(V0,V1) | EXISTS V2: pppp7-{T}(V2,V1)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #24: input, references = 3, size of lhs = 1:
% 0.33/0.59 pppp8-{F}(V0,V1) | EXISTS V2: pppp6-{T}(V2,V1)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #25: input, references = 3, size of lhs = 1:
% 0.33/0.59 pppp8-{F}(V0,V1) | r1-{T}(V0,V1)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #26: input, references = 3, size of lhs = 2:
% 0.33/0.59 pppp7-{F}(V0,V1), p1-{F}(V0) | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #27: input, references = 3, size of lhs = 1:
% 0.33/0.59 pppp7-{F}(V0,V1) | r1-{T}(V1,V0)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #28: input, references = 3, size of lhs = 2:
% 0.33/0.59 pppp6-{F}(V0,V1), r1-{F}(V0,V2) | p1-{T}(V2)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #29: input, references = 3, size of lhs = 1:
% 0.33/0.59 pppp6-{F}(V0,V1) | r1-{T}(V1,V0)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #30: input, references = 3, size of lhs = 4:
% 0.33/0.59 pppp5-{F}(V0,V1), r1-{F}(V1,V2), r1-{F}(V2,V3), p1-{F}(V2) | p1-{T}(V3)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #31: input, references = 3, size of lhs = 2:
% 0.33/0.59 pppp5-{F}(V0,V1), p1-{F}(V1) | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #32: input, references = 3, size of lhs = 1:
% 0.33/0.59 pppp5-{F}(V0,V1) | r1-{T}(V0,V1)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #33: input, references = 3, size of lhs = 2:
% 0.33/0.59 pppp4-{F}(V0,V1), p1-{F}(V0) | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #34: input, references = 3, size of lhs = 1:
% 0.33/0.59 pppp4-{F}(V0,V1) | r1-{T}(V1,V0)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #35: input, references = 4, size of lhs = 3:
% 0.33/0.59 pppp3-{F}(V0,V1), r1-{F}(V0,V2), p2-{F}(V2) | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #36: input, references = 4, size of lhs = 1:
% 0.33/0.59 pppp3-{F}(V0,V1) | r1-{T}(V1,V0)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #37: input, references = 3, size of lhs = 2:
% 0.33/0.59 pppp2-{F}(V0,V1), p3-{F}(V0) | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #38: input, references = 3, size of lhs = 1:
% 0.33/0.59 pppp2-{F}(V0,V1) | r1-{T}(V1,V0)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #39: input, references = 6, size of lhs = 1:
% 0.33/0.59 pppp1-{F}(V0,V1) | p2-{T}(V1)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #40: input, references = 3, size of lhs = 1:
% 0.33/0.59 pppp1-{F}(V0,V1) | EXISTS V2: pppp0-{T}(V2,V1)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #41: input, references = 6, size of lhs = 1:
% 0.33/0.59 pppp1-{F}(V0,V1) | r1-{T}(V0,V1)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #42: input, references = 3, size of lhs = 2:
% 0.33/0.59 pppp0-{F}(V0,V1), p3-{F}(V0) | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #43: input, references = 3, size of lhs = 1:
% 0.33/0.59 pppp0-{F}(V0,V1) | r1-{T}(V1,V0)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 number of initial rules = 44
% 0.33/0.59
% 0.33/0.59 Simplifiers:
% 0.33/0.59 #44: unsound, references = 3, size of lhs = 3:
% 0.33/0.59 pppp0-{F}(V0,V1), pppp0-{F}(V2,V1), V0 == V2 | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #45: unsound, references = 3, size of lhs = 3:
% 0.33/0.59 pppp1-{F}(V0,V1), pppp1-{F}(V0,V3), V1 == V3 | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #46: unsound, references = 3, size of lhs = 3:
% 0.33/0.59 pppp2-{F}(V0,V1), pppp2-{F}(V2,V1), V0 == V2 | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #47: unsound, references = 3, size of lhs = 3:
% 0.33/0.59 pppp3-{F}(V0,V1), pppp3-{F}(V2,V1), V0 == V2 | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #48: unsound, references = 3, size of lhs = 3:
% 0.33/0.59 pppp4-{F}(V0,V1), pppp4-{F}(V2,V1), V0 == V2 | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #49: unsound, references = 3, size of lhs = 3:
% 0.33/0.59 pppp5-{F}(V0,V1), pppp5-{F}(V0,V3), V1 == V3 | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #50: unsound, references = 3, size of lhs = 3:
% 0.33/0.59 pppp5-{F}(V0,V1), pppp5-{F}(V2,V3), V0 == V2 | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #51: unsound, references = 3, size of lhs = 3:
% 0.33/0.59 pppp6-{F}(V0,V1), pppp6-{F}(V2,V1), V0 == V2 | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #52: unsound, references = 3, size of lhs = 3:
% 0.33/0.59 pppp7-{F}(V0,V1), pppp7-{F}(V2,V1), V0 == V2 | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #53: unsound, references = 3, size of lhs = 3:
% 0.33/0.59 pppp8-{F}(V0,V1), pppp8-{F}(V0,V3), V1 == V3 | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #54: unsound, references = 3, size of lhs = 3:
% 0.33/0.59 pppp8-{F}(V0,V1), pppp8-{F}(V2,V3), V0 == V2 | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #55: unsound, references = 3, size of lhs = 3:
% 0.33/0.59 pppp9-{F}(V0,V1), pppp9-{F}(V0,V3), V1 == V3 | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #56: unsound, references = 3, size of lhs = 3:
% 0.33/0.59 pppp10-{F}(V0,V1), pppp10-{F}(V0,V3), V1 == V3 | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #57: unsound, references = 3, size of lhs = 3:
% 0.33/0.59 pppp10-{F}(V0,V1), pppp10-{F}(V2,V3), V0 == V2 | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #58: unsound, references = 3, size of lhs = 3:
% 0.33/0.59 pppp11-{F}(V0,V1), pppp11-{F}(V2,V1), V0 == V2 | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #59: unsound, references = 3, size of lhs = 3:
% 0.33/0.59 pppp12-{F}(V0), pppp12-{F}(V1), V0 == V1 | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #60: unsound, references = 3, size of lhs = 3:
% 0.33/0.59 pppp13-{F}(V0), pppp13-{F}(V1), V0 == V1 | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #61: unsound, references = 3, size of lhs = 3:
% 0.33/0.59 pppp15-{F}(V0), pppp15-{F}(V1), V0 == V1 | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 number of simplifiers = 18
% 0.33/0.59
% 0.33/0.59 Learnt:
% 0.33/0.59 #70: disj( #10, input ), references = 2, size of lhs = 7:
% 0.33/0.59 pppp12-{F}(V0), r1-{F}(V0,V1), r1-{F}(V1,V2), p2-{F}(V2), r1-{F}(V2,V3), r1-{F}(V2,V4), pppp9-{F}(V5,V3) | pppp16-{T}(V4)
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #83: exists( #15, #81 ), references = 1, size of lhs = 4:
% 0.33/0.59 pppp12-{F}(V0), r1-{F}(V0,V1), r1-{F}(V1,V2), pppp3-{F}(V2,V3) | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #88: exists( #11, #86 ), references = 2, size of lhs = 3:
% 0.33/0.59 pppp16-{F}(V0), pppp12-{F}(V1), r1-{F}(V1,V0) | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #96: mergings( V4 == V7; #94 ), references = 3, size of lhs = 8:
% 0.33/0.59 p2-{F}(V0), r1-{F}(V0,V1), pppp12-{F}(V2), r1-{F}(V2,V1), r1-{F}(V2,V3), r1-{F}(V3,V0), r1-{F}(V4,V0), pppp10-{F}(V5,V4) | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #104: mergings( V0 == V2; #102 ), references = 1, size of lhs = 4:
% 0.33/0.59 pppp12-{F}(V0), r1-{F}(V0,V1), r1-{F}(V1,V0), pppp10-{F}(V2,V0) | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #114: mergings( V0 == V4; #112 ), references = 1, size of lhs = 5:
% 0.33/0.59 pppp12-{F}(V0), r1-{F}(V0,V1), r1-{F}(V1,V2), r1-{F}(V0,V2), pppp10-{F}(V3,V2) | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #118: exists( #5, #116 ), references = 1, size of lhs = 1:
% 0.33/0.59 pppp12-{F}(V0) | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 #121: exists( #2, #119 ), references = 1, size of lhs = 0:
% 0.33/0.59 FALSE | FALSE
% 0.33/0.59 (used 0 times, uses = {})
% 0.33/0.59
% 0.33/0.59 number of learnt formulas = 8
% 0.33/0.59
% 0.33/0.59
% 0.33/0.59 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.33/0.59
% 0.33/0.59 randbase = 1
%------------------------------------------------------------------------------