%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : LCL212-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n029.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 12:05:54 PM UTC 2026
% Result : Unsatisfiable 1.00s 1.40s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL212-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.43 % Computer : n029.cluster.edu
% 0.12/0.43 % Model : x86_64 x86_64
% 0.12/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.43 % Memory : 8046.5625MB
% 0.12/0.43 % OS : Linux 6.8.0-71-generic
% 0.12/0.43 % CPULimit : 300
% 0.12/0.44 % WCLimit : 300
% 0.12/0.44 % DateTime : Sat Sep 5 20:17:25 UTC 2026
% 0.12/0.44 % CPUTime :
% 1.00/1.40 GeoParameters:
% 1.00/1.40
% 1.00/1.40 tptp_input = 1
% 1.00/1.40 tptp_output = 0
% 1.00/1.40 nonempty = 1
% 1.00/1.40 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.00/1.40 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 1.00/1.40
% 1.00/1.40
% 1.00/1.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.00/1.40 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.00/1.40
% 1.00/1.40 RuleSystem INPUT:
% 1.00/1.40
% 1.00/1.40 Initial Rules:
% 1.00/1.40 #0: input, references = 3, size of lhs = 2:
% 1.00/1.40 P_or-{F}(V0,V0,V1), P_implies-{F}(V1,V0,V2) | axiom-{T}(V2)
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #1: input, references = 6, size of lhs = 2:
% 1.00/1.40 P_or-{F}(V1,V0,V2), P_implies-{F}(V0,V2,V3) | axiom-{T}(V3)
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #2: input, references = 6, size of lhs = 3:
% 1.00/1.40 P_or-{F}(V0,V1,V2), P_or-{F}(V1,V0,V3), P_implies-{F}(V2,V3,V4) | axiom-{T}(V4)
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #3: input, references = 4, size of lhs = 5:
% 1.00/1.40 P_or-{F}(V1,V2,V3), P_or-{F}(V0,V3,V4), P_or-{F}(V0,V2,V5), P_or-{F}(V1,V5,V6), P_implies-{F}(V4,V6,V7) | axiom-{T}(V7)
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #4: input, references = 5, size of lhs = 5:
% 1.00/1.40 P_implies-{F}(V0,V1,V3), P_or-{F}(V2,V0,V4), P_or-{F}(V2,V1,V5), P_implies-{F}(V4,V5,V6), P_implies-{F}(V3,V6,V7) | axiom-{T}(V7)
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #5: input, references = 5, size of lhs = 4:
% 1.00/1.40 P_implies-{F}(V0,V1,V2), P_not-{F}(V0,V3), P_or-{F}(V3,V1,V4), V2 == V4 | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #6: input, references = 12, size of lhs = 1:
% 1.00/1.40 axiom-{F}(V0) | theorem-{T}(V0)
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #7: input, references = 4, size of lhs = 3:
% 1.00/1.40 theorem-{F}(V0), P_implies-{F}(V0,V1,V2), theorem-{F}(V2) | theorem-{T}(V1)
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #8: input, references = 8, size of lhs = 8:
% 1.00/1.40 P_p-{F}(V0), P_not-{F}(V0,V1), P_q-{F}(V2), P_implies-{F}(V0,V2,V3), P_implies-{F}(V3,V2,V4), P_implies-{F}(V2,V4,V5), P_implies-{F}(V1,V5,V6), theorem-{F}(V6) | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #9: input, references = 20, size of lhs = 2:
% 1.00/1.40 #-{F} V0, #-{F} V1 | EXISTS V2: P_implies-{T}(V0,V1,V2)
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #10: input, references = 5, size of lhs = 2:
% 1.00/1.40 #-{F} V0, #-{F} V1 | EXISTS V2: P_or-{T}(V0,V1,V2)
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #11: input, references = 10, size of lhs = 1:
% 1.00/1.40 #-{F} V0 | EXISTS V1: P_not-{T}(V0,V1)
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #12: input, references = 4, size of lhs = 0:
% 1.00/1.40 FALSE | EXISTS V0: P_p-{T}(V0)
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #13: input, references = 4, size of lhs = 0:
% 1.00/1.40 FALSE | EXISTS V0: P_q-{T}(V0)
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 number of initial rules = 14
% 1.00/1.40
% 1.00/1.40 Simplifiers:
% 1.00/1.40 #14: unsound, references = 3, size of lhs = 3:
% 1.00/1.40 P_implies-{F}(V0,V1,V2), P_implies-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #15: unsound, references = 3, size of lhs = 3:
% 1.00/1.40 P_or-{F}(V0,V1,V2), P_or-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #16: unsound, references = 3, size of lhs = 3:
% 1.00/1.40 P_not-{F}(V0,V1), P_not-{F}(V0,V3), V1 == V3 | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #17: unsound, references = 3, size of lhs = 3:
% 1.00/1.40 P_p-{F}(V0), P_p-{F}(V1), V0 == V1 | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #18: unsound, references = 3, size of lhs = 3:
% 1.00/1.40 P_q-{F}(V0), P_q-{F}(V1), V0 == V1 | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 number of simplifiers = 5
% 1.00/1.40
% 1.00/1.40 Learnt:
% 1.00/1.40 #20: exists( #9, #5 ), references = 12, size of lhs = 2:
% 1.00/1.40 P_not-{F}(V0,V1), P_or-{F}(V1,V2,V3) | P_implies-{T}(V0,V2,V3)
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #24: exists( #10, #5 ), references = 14, size of lhs = 2:
% 1.00/1.40 P_not-{F}(V0,V1), P_implies-{F}(V0,V2,V3) | P_or-{T}(V1,V2,V3)
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #34: exists( #9, #32 ), references = 1, size of lhs = 9:
% 1.00/1.40 P_p-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V1,V2), P_not-{F}(V3,V2), P_q-{F}(V4), P_implies-{F}(V0,V4,V5), P_implies-{F}(V5,V4,V6), P_implies-{F}(V4,V6,V7), P_or-{F}(V8,V1,V7) | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #47: exists( #9, #45 ), references = 1, size of lhs = 10:
% 1.00/1.40 P_p-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V1,V2), P_not-{F}(V3,V2), P_q-{F}(V4), P_implies-{F}(V0,V4,V5), P_implies-{F}(V5,V4,V6), P_implies-{F}(V4,V6,V7), P_or-{F}(V8,V9,V1), P_or-{F}(V9,V8,V7) | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #56: exists( #9, #54 ), references = 2, size of lhs = 12:
% 1.00/1.40 P_p-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V1,V2), P_q-{F}(V3), P_implies-{F}(V0,V3,V4), P_implies-{F}(V4,V3,V5), P_implies-{F}(V3,V5,V6), P_not-{F}(V7,V2), P_implies-{F}(V8,V9,V7), P_or-{F}(V10,V8,V11), P_or-{F}(V10,V9,V12), P_implies-{F}(V11,V12,V6) | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #65: exists( #9, #63 ), references = 1, size of lhs = 10:
% 1.00/1.40 P_p-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V1,V2), P_q-{F}(V3), P_implies-{F}(V0,V3,V4), P_implies-{F}(V4,V3,V5), P_implies-{F}(V3,V5,V6), P_not-{F}(V7,V2), P_or-{F}(V8,V9,V7), P_or-{F}(V9,V8,V6) | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #79: exists( #9, #77 ), references = 1, size of lhs = 11:
% 1.00/1.40 theorem-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V2,V1), P_p-{F}(V3), P_not-{F}(V3,V4), P_q-{F}(V5), P_implies-{F}(V3,V5,V6), P_implies-{F}(V6,V5,V7), P_implies-{F}(V5,V7,V8), P_implies-{F}(V4,V8,V9), P_or-{F}(V10,V0,V9) | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #81: exists( #10, #78 ), references = 1, size of lhs = 11:
% 1.00/1.40 theorem-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V2,V1), P_p-{F}(V3), P_not-{F}(V3,V4), P_q-{F}(V5), P_implies-{F}(V3,V5,V6), P_implies-{F}(V6,V5,V7), P_implies-{F}(V5,V7,V8), P_implies-{F}(V4,V8,V9), P_or-{F}(V10,V0,V9) | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #85: exists( #9, #83 ), references = 1, size of lhs = 11:
% 1.00/1.40 theorem-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V2,V1), P_p-{F}(V3), P_not-{F}(V3,V4), P_not-{F}(V4,V5), P_not-{F}(V6,V5), P_q-{F}(V7), P_implies-{F}(V3,V7,V8), P_implies-{F}(V8,V7,V9), P_implies-{F}(V7,V9,V0) | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #87: exists( #11, #84 ), references = 4, size of lhs = 9:
% 1.00/1.40 theorem-{F}(V0), P_p-{F}(V1), P_not-{F}(V1,V2), P_not-{F}(V2,V3), P_not-{F}(V4,V3), P_q-{F}(V5), P_implies-{F}(V1,V5,V6), P_implies-{F}(V6,V5,V7), P_implies-{F}(V5,V7,V0) | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #93: exists( #9, #91 ), references = 1, size of lhs = 11:
% 1.00/1.40 P_p-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V1,V2), P_not-{F}(V3,V2), P_q-{F}(V4), P_not-{F}(V4,V5), P_implies-{F}(V0,V4,V6), P_implies-{F}(V6,V4,V7), P_not-{F}(V8,V5), P_or-{F}(V9,V10,V8), P_or-{F}(V10,V9,V7) | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #96: exists( #9, #94 ), references = 1, size of lhs = 10:
% 1.00/1.40 P_p-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V1,V2), P_not-{F}(V3,V2), P_q-{F}(V4), P_not-{F}(V4,V5), P_implies-{F}(V0,V4,V6), P_not-{F}(V6,V7), P_or-{F}(V4,V7,V8), P_not-{F}(V8,V5) | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #109: exists( #9, #107 ), references = 1, size of lhs = 13:
% 1.00/1.40 P_p-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V1,V2), P_not-{F}(V3,V2), P_q-{F}(V4), P_not-{F}(V4,V5), P_implies-{F}(V0,V4,V6), P_implies-{F}(V6,V4,V7), P_not-{F}(V8,V5), P_or-{F}(V9,V10,V8), P_or-{F}(V11,V12,V10), P_or-{F}(V9,V12,V13), P_or-{F}(V11,V13,V7) | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #119: exists( #9, #117 ), references = 2, size of lhs = 12:
% 1.00/1.40 P_p-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V1,V2), P_q-{F}(V3), P_not-{F}(V3,V4), P_implies-{F}(V0,V3,V5), P_implies-{F}(V5,V3,V6), P_not-{F}(V7,V4), P_not-{F}(V8,V2), P_implies-{F}(V9,V10,V8), P_or-{F}(V11,V9,V7), P_or-{F}(V11,V10,V6) | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #131: exists( #9, #129 ), references = 1, size of lhs = 13:
% 1.00/1.40 P_p-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V1,V2), P_not-{F}(V3,V2), P_q-{F}(V4), P_not-{F}(V4,V5), P_not-{F}(V6,V5), P_implies-{F}(V0,V4,V7), P_implies-{F}(V7,V4,V8), P_implies-{F}(V9,V10,V4), P_or-{F}(V11,V9,V12), P_or-{F}(V11,V10,V13), P_implies-{F}(V12,V13,V8) | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #133: exists( #9, #130 ), references = 2, size of lhs = 11:
% 1.00/1.40 P_p-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V1,V2), P_not-{F}(V3,V2), P_q-{F}(V4), P_not-{F}(V4,V5), P_not-{F}(V6,V5), P_implies-{F}(V0,V4,V7), P_implies-{F}(V8,V9,V4), P_or-{F}(V10,V8,V7), P_or-{F}(V10,V9,V4) | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #138: mergings( V4 == V5; #136 ), references = 1, size of lhs = 10:
% 1.00/1.40 P_p-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V2,V1), P_not-{F}(V1,V3), P_not-{F}(V4,V3), P_q-{F}(V5), P_not-{F}(V5,V6), P_not-{F}(V7,V6), P_implies-{F}(V5,V8,V5), P_or-{F}(V1,V8,V5) | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #143: exists( #11, #119 ), references = 1, size of lhs = 10:
% 1.00/1.40 P_p-{F}(V0), P_not-{F}(V0,V1), P_q-{F}(V2), P_not-{F}(V2,V3), P_implies-{F}(V0,V2,V4), P_implies-{F}(V4,V2,V5), P_not-{F}(V6,V3), P_implies-{F}(V7,V8,V1), P_or-{F}(V9,V7,V6), P_or-{F}(V9,V8,V5) | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #145: exists( #11, #133 ), references = 1, size of lhs = 9:
% 1.00/1.40 P_p-{F}(V0), P_not-{F}(V0,V1), P_q-{F}(V2), P_not-{F}(V2,V3), P_not-{F}(V4,V3), P_implies-{F}(V0,V2,V5), P_implies-{F}(V6,V7,V2), P_or-{F}(V8,V6,V5), P_or-{F}(V8,V7,V2) | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #161: exists( #9, #159 ), references = 1, size of lhs = 8:
% 1.00/1.40 P_p-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V1,V2), P_not-{F}(V3,V2), P_q-{F}(V4), P_implies-{F}(V0,V4,V5), P_implies-{F}(V5,V4,V6), P_or-{F}(V7,V4,V6) | FALSE
% 1.00/1.40 (used 0 times, uses = {})
% 1.00/1.40
% 1.00/1.40 #164: exists( #9, #162 ), references = 2, size of lhs = 7:
% 1.00/1.40 P_p-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V1,V2), P_not-{F}(V3,V2), P_q-{F}(V4), P_implies-{F}(V0,V4,V5), P_not-{F}(V5,V6) | FALSE
% 0.15/1.40 (used 0 times, uses = {})
% 0.15/1.40
% 0.15/1.40 #166: exists( #11, #163 ), references = 1, size of lhs = 4:
% 0.15/1.40 P_p-{F}(V0), P_not-{F}(V0,V1), P_q-{F}(V2), P_implies-{F}(V0,V2,V1) | FALSE
% 0.15/1.40 (used 0 times, uses = {})
% 0.15/1.40
% 0.15/1.40 #168: exists( #11, #164 ), references = 1, size of lhs = 6:
% 0.15/1.40 P_p-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V1,V2), P_not-{F}(V3,V2), P_q-{F}(V4), P_implies-{F}(V0,V4,V5) | FALSE
% 0.15/1.40 (used 0 times, uses = {})
% 0.15/1.40
% 0.15/1.40 #170: exists( #11, #167 ), references = 1, size of lhs = 4:
% 0.15/1.40 P_p-{F}(V0), P_not-{F}(V0,V1), P_q-{F}(V2), P_implies-{F}(V0,V2,V3) | FALSE
% 0.15/1.40 (used 0 times, uses = {})
% 0.15/1.40
% 0.15/1.40 #172: exists( #9, #169 ), references = 1, size of lhs = 3:
% 0.15/1.40 P_p-{F}(V0), P_not-{F}(V0,V1), P_q-{F}(V2) | FALSE
% 0.15/1.40 (used 0 times, uses = {})
% 0.15/1.40
% 0.15/1.40 #174: exists( #11, #171 ), references = 1, size of lhs = 2:
% 0.15/1.40 P_p-{F}(V0), P_q-{F}(V1) | FALSE
% 0.15/1.40 (used 0 times, uses = {})
% 0.15/1.40
% 0.15/1.40 #176: exists( #13, #173 ), references = 1, size of lhs = 1:
% 0.15/1.40 P_p-{F}(V0) | FALSE
% 0.15/1.40 (used 0 times, uses = {})
% 0.15/1.40
% 0.15/1.40 #178: exists( #12, #175 ), references = 1, size of lhs = 0:
% 0.15/1.40 FALSE | FALSE
% 0.15/1.40 (used 0 times, uses = {})
% 0.15/1.40
% 0.15/1.40 number of learnt formulas = 28
% 0.15/1.40
% 0.15/1.40
% 0.15/1.40 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/1.40
% 0.15/1.40 randbase = 1
%------------------------------------------------------------------------------