%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : LCL190-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n003.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 12:05:51 PM UTC 2026
% Result : Unsatisfiable 1.29s 1.63s
% Output : Refutation 1.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL190-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.10/0.44 % Computer : n003.cluster.edu
% 0.10/0.44 % Model : x86_64 x86_64
% 0.10/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.44 % Memory : 8046.5625MB
% 0.10/0.44 % OS : Linux 6.8.0-71-generic
% 0.10/0.44 % CPULimit : 300
% 0.10/0.44 % WCLimit : 300
% 0.10/0.44 % DateTime : Fri Sep 4 20:37:19 UTC 2026
% 0.10/0.44 % CPUTime :
% 1.29/1.63 GeoParameters:
% 1.29/1.63
% 1.29/1.63 tptp_input = 1
% 1.29/1.63 tptp_output = 0
% 1.29/1.63 nonempty = 1
% 1.29/1.63 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.29/1.63 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 1.29/1.63
% 1.29/1.63
% 1.29/1.63 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.29/1.63 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.29/1.63
% 1.29/1.63 RuleSystem INPUT:
% 1.29/1.63
% 1.29/1.63 Initial Rules:
% 1.29/1.63 #0: input, references = 4, size of lhs = 2:
% 1.29/1.63 P_or-{F}(V0,V0,V1), P_implies-{F}(V1,V0,V2) | axiom-{T}(V2)
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #1: input, references = 4, size of lhs = 2:
% 1.29/1.63 P_or-{F}(V1,V0,V2), P_implies-{F}(V0,V2,V3) | axiom-{T}(V3)
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #2: input, references = 5, size of lhs = 3:
% 1.29/1.63 P_or-{F}(V0,V1,V2), P_or-{F}(V1,V0,V3), P_implies-{F}(V2,V3,V4) | axiom-{T}(V4)
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #3: input, references = 4, size of lhs = 5:
% 1.29/1.63 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)
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #4: input, references = 5, size of lhs = 5:
% 1.29/1.63 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)
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #5: input, references = 5, size of lhs = 4:
% 1.29/1.63 P_implies-{F}(V0,V1,V2), P_not-{F}(V0,V3), P_or-{F}(V3,V1,V4), V2 == V4 | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #6: input, references = 10, size of lhs = 1:
% 1.29/1.63 axiom-{F}(V0) | theorem-{T}(V0)
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #7: input, references = 4, size of lhs = 3:
% 1.29/1.63 theorem-{F}(V0), P_implies-{F}(V0,V1,V2), theorem-{F}(V2) | theorem-{T}(V1)
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #8: input, references = 8, size of lhs = 9:
% 1.29/1.63 P_p-{F}(V0), P_q-{F}(V1), P_r-{F}(V2), P_or-{F}(V1,V2,V3), P_or-{F}(V0,V3,V4), P_or-{F}(V2,V1,V5), P_or-{F}(V0,V5,V6), P_implies-{F}(V4,V6,V7), theorem-{F}(V7) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #9: input, references = 20, size of lhs = 2:
% 1.29/1.63 #-{F} V0, #-{F} V1 | EXISTS V2: P_implies-{T}(V0,V1,V2)
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #10: input, references = 11, size of lhs = 2:
% 1.29/1.63 #-{F} V0, #-{F} V1 | EXISTS V2: P_or-{T}(V0,V1,V2)
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #11: input, references = 5, size of lhs = 1:
% 1.29/1.63 #-{F} V0 | EXISTS V1: P_not-{T}(V0,V1)
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #12: input, references = 4, size of lhs = 0:
% 1.29/1.63 FALSE | EXISTS V0: P_p-{T}(V0)
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #13: input, references = 4, size of lhs = 0:
% 1.29/1.63 FALSE | EXISTS V0: P_q-{T}(V0)
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #14: input, references = 4, size of lhs = 0:
% 1.29/1.63 FALSE | EXISTS V0: P_r-{T}(V0)
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 number of initial rules = 15
% 1.29/1.63
% 1.29/1.63 Simplifiers:
% 1.29/1.63 #15: unsound, references = 3, size of lhs = 3:
% 1.29/1.63 P_implies-{F}(V0,V1,V2), P_implies-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #16: unsound, references = 3, size of lhs = 3:
% 1.29/1.63 P_or-{F}(V0,V1,V2), P_or-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #17: unsound, references = 3, size of lhs = 3:
% 1.29/1.63 P_not-{F}(V0,V1), P_not-{F}(V0,V3), V1 == V3 | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #18: unsound, references = 3, size of lhs = 3:
% 1.29/1.63 P_p-{F}(V0), P_p-{F}(V1), V0 == V1 | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #19: unsound, references = 3, size of lhs = 3:
% 1.29/1.63 P_q-{F}(V0), P_q-{F}(V1), V0 == V1 | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #20: unsound, references = 3, size of lhs = 3:
% 1.29/1.63 P_r-{F}(V0), P_r-{F}(V1), V0 == V1 | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 number of simplifiers = 6
% 1.29/1.63
% 1.29/1.63 Learnt:
% 1.29/1.63 #22: exists( #10, #5 ), references = 12, size of lhs = 2:
% 1.29/1.63 P_not-{F}(V0,V1), P_implies-{F}(V0,V2,V3) | P_or-{T}(V1,V2,V3)
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #26: exists( #9, #24 ), references = 1, size of lhs = 8:
% 1.29/1.63 P_p-{F}(V0), P_q-{F}(V1), P_r-{F}(V2), P_or-{F}(V1,V2,V3), P_or-{F}(V0,V3,V4), P_or-{F}(V2,V1,V5), P_or-{F}(V0,V5,V6), P_or-{F}(V6,V6,V4) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #30: exists( #9, #5 ), references = 5, size of lhs = 2:
% 1.29/1.63 P_not-{F}(V0,V1), P_or-{F}(V1,V2,V3) | P_implies-{T}(V0,V2,V3)
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #43: exists( #9, #41 ), references = 1, size of lhs = 11:
% 1.29/1.63 P_p-{F}(V0), P_q-{F}(V1), P_r-{F}(V2), P_or-{F}(V1,V2,V3), P_or-{F}(V0,V3,V4), P_not-{F}(V4,V5), P_not-{F}(V6,V5), P_or-{F}(V2,V1,V7), P_or-{F}(V0,V7,V8), P_not-{F}(V9,V5), P_or-{F}(V10,V9,V8) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #52: exists( #9, #50 ), references = 1, size of lhs = 13:
% 1.29/1.63 P_p-{F}(V0), P_q-{F}(V1), P_r-{F}(V2), P_or-{F}(V1,V2,V3), P_or-{F}(V0,V3,V4), P_not-{F}(V4,V5), P_or-{F}(V2,V1,V6), P_or-{F}(V0,V6,V7), P_not-{F}(V8,V5), P_implies-{F}(V9,V10,V8), P_or-{F}(V11,V9,V12), P_or-{F}(V11,V10,V13), P_implies-{F}(V12,V13,V7) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #54: exists( #11, #51 ), references = 1, size of lhs = 11:
% 1.29/1.63 P_p-{F}(V0), P_q-{F}(V1), P_r-{F}(V2), P_or-{F}(V1,V2,V3), P_or-{F}(V0,V3,V4), P_or-{F}(V2,V1,V5), P_or-{F}(V0,V5,V6), P_implies-{F}(V7,V8,V4), P_or-{F}(V9,V7,V10), P_or-{F}(V9,V8,V11), P_implies-{F}(V10,V11,V6) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #59: exists( #9, #57 ), references = 2, size of lhs = 11:
% 1.29/1.63 P_p-{F}(V0), P_q-{F}(V1), P_r-{F}(V2), P_or-{F}(V1,V2,V3), P_or-{F}(V0,V3,V4), P_or-{F}(V2,V1,V5), P_or-{F}(V0,V5,V6), P_or-{F}(V7,V8,V4), P_or-{F}(V9,V10,V8), P_or-{F}(V7,V10,V11), P_or-{F}(V9,V11,V6) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #62: exists( #9, #60 ), references = 1, size of lhs = 7:
% 1.29/1.63 P_p-{F}(V0), P_not-{F}(V1,V0), P_q-{F}(V2), P_r-{F}(V3), P_or-{F}(V2,V3,V4), P_or-{F}(V3,V2,V4), P_or-{F}(V0,V5,V4) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #65: exists( #9, #63 ), references = 1, size of lhs = 5:
% 1.29/1.63 P_p-{F}(V0), P_q-{F}(V0), P_r-{F}(V0), P_not-{F}(V1,V0), P_not-{F}(V2,V0) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #68: exists( #10, #59 ), references = 1, size of lhs = 6:
% 1.29/1.63 P_p-{F}(V0), P_q-{F}(V1), P_r-{F}(V2), P_or-{F}(V1,V2,V3), P_or-{F}(V2,V1,V3), P_or-{F}(V0,V4,V3) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #70: exists( #10, #67 ), references = 1, size of lhs = 3:
% 1.29/1.63 P_p-{F}(V0), P_q-{F}(V0), P_r-{F}(V0) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #93: exists( #9, #91 ), references = 1, size of lhs = 15:
% 1.29/1.63 theorem-{F}(V0), P_not-{F}(V0,V1), P_p-{F}(V2), P_q-{F}(V3), P_r-{F}(V4), P_or-{F}(V3,V4,V5), P_or-{F}(V2,V5,V6), P_or-{F}(V4,V3,V7), P_or-{F}(V2,V7,V8), P_implies-{F}(V6,V8,V9), P_not-{F}(V10,V1), P_implies-{F}(V11,V12,V10), P_or-{F}(V13,V11,V14), P_or-{F}(V13,V12,V15), P_implies-{F}(V14,V15,V9) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #95: exists( #9, #92 ), references = 3, size of lhs = 13:
% 1.29/1.63 theorem-{F}(V0), P_not-{F}(V0,V1), P_p-{F}(V2), P_q-{F}(V3), P_r-{F}(V4), P_or-{F}(V3,V4,V5), P_or-{F}(V2,V5,V6), P_or-{F}(V4,V3,V7), P_or-{F}(V2,V7,V8), P_not-{F}(V9,V1), P_implies-{F}(V10,V11,V9), P_or-{F}(V12,V10,V6), P_or-{F}(V12,V11,V8) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #98: exists( #9, #96 ), references = 2, size of lhs = 12:
% 1.29/1.63 theorem-{F}(V0), P_not-{F}(V0,V1), P_p-{F}(V2), P_not-{F}(V3,V2), P_q-{F}(V4), P_r-{F}(V5), P_or-{F}(V4,V5,V6), P_or-{F}(V5,V4,V7), P_or-{F}(V2,V7,V8), P_or-{F}(V2,V9,V8), P_implies-{F}(V6,V9,V10), P_not-{F}(V10,V1) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #103: exists( #11, #98 ), references = 1, size of lhs = 10:
% 1.29/1.63 theorem-{F}(V0), P_p-{F}(V1), P_not-{F}(V2,V1), P_q-{F}(V3), P_r-{F}(V4), P_or-{F}(V3,V4,V5), P_or-{F}(V4,V3,V6), P_or-{F}(V1,V6,V7), P_or-{F}(V1,V8,V7), P_implies-{F}(V5,V8,V0) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #104: exists( #11, #95 ), references = 2, size of lhs = 11:
% 1.29/1.63 theorem-{F}(V0), P_p-{F}(V1), P_q-{F}(V2), P_r-{F}(V3), P_or-{F}(V2,V3,V4), P_or-{F}(V1,V4,V5), P_or-{F}(V3,V2,V6), P_or-{F}(V1,V6,V7), P_implies-{F}(V8,V9,V0), P_or-{F}(V10,V8,V5), P_or-{F}(V10,V9,V7) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #111: exists( #9, #107 ), references = 2, size of lhs = 10:
% 1.29/1.63 P_p-{F}(V0), P_not-{F}(V1,V0), P_q-{F}(V2), P_r-{F}(V3), P_or-{F}(V2,V3,V4), P_or-{F}(V3,V2,V5), P_or-{F}(V0,V5,V6), P_or-{F}(V0,V7,V6), P_or-{F}(V8,V9,V4), P_or-{F}(V9,V8,V7) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #114: exists( #9, #112 ), references = 1, size of lhs = 6:
% 1.29/1.63 P_p-{F}(V0), P_q-{F}(V0), P_not-{F}(V1,V0), P_not-{F}(V2,V0), P_r-{F}(V3), P_or-{F}(V3,V0,V3) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #121: mergings( V6 == V8; #119 ), references = 2, size of lhs = 7:
% 1.29/1.63 P_p-{F}(V0), P_not-{F}(V1,V0), P_q-{F}(V2), P_not-{F}(V3,V2), P_r-{F}(V4), P_or-{F}(V4,V2,V5), P_or-{F}(V0,V5,V6) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #129: exists( #9, #123 ), references = 2, size of lhs = 7:
% 1.29/1.63 P_p-{F}(V0), P_not-{F}(V1,V0), P_not-{F}(V2,V0), P_q-{F}(V3), P_not-{F}(V4,V3), P_r-{F}(V5), P_or-{F}(V5,V3,V6) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #132: exists( #9, #130 ), references = 1, size of lhs = 7:
% 1.29/1.63 P_p-{F}(V0), P_not-{F}(V1,V0), P_not-{F}(V2,V0), P_q-{F}(V3), P_not-{F}(V4,V3), P_r-{F}(V5), P_not-{F}(V6,V5) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #134: exists( #10, #129 ), references = 1, size of lhs = 6:
% 1.29/1.63 P_p-{F}(V0), P_not-{F}(V1,V0), P_not-{F}(V2,V0), P_q-{F}(V3), P_not-{F}(V4,V3), P_r-{F}(V5) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #140: exists( #10, #95 ), references = 1, size of lhs = 11:
% 1.29/1.63 theorem-{F}(V0), P_not-{F}(V0,V1), P_p-{F}(V2), P_q-{F}(V3), P_r-{F}(V4), P_or-{F}(V3,V4,V5), P_or-{F}(V4,V3,V6), P_or-{F}(V2,V6,V7), P_or-{F}(V2,V8,V7), P_implies-{F}(V5,V8,V9), P_not-{F}(V9,V1) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #141: exists( #10, #104 ), references = 2, size of lhs = 9:
% 1.29/1.63 theorem-{F}(V0), P_p-{F}(V1), P_q-{F}(V2), P_r-{F}(V3), P_or-{F}(V2,V3,V4), P_or-{F}(V3,V2,V5), P_or-{F}(V1,V5,V6), P_implies-{F}(V4,V7,V0), P_or-{F}(V1,V7,V6) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #145: exists( #9, #143 ), references = 1, size of lhs = 9:
% 1.29/1.63 P_p-{F}(V0), P_q-{F}(V1), P_r-{F}(V2), P_or-{F}(V1,V2,V3), P_or-{F}(V2,V1,V4), P_or-{F}(V0,V4,V5), P_or-{F}(V0,V6,V5), P_or-{F}(V7,V8,V3), P_or-{F}(V8,V7,V6) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #148: mergings( V4 == V6; #146 ), references = 2, size of lhs = 5:
% 1.29/1.63 P_p-{F}(V0), P_q-{F}(V1), P_r-{F}(V2), P_or-{F}(V2,V1,V3), P_or-{F}(V0,V3,V4) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #152: exists( #10, #148 ), references = 2, size of lhs = 4:
% 1.29/1.63 P_p-{F}(V0), P_q-{F}(V1), P_r-{F}(V2), P_or-{F}(V2,V1,V3) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #156: exists( #9, #153 ), references = 1, size of lhs = 4:
% 1.29/1.63 P_p-{F}(V0), P_q-{F}(V1), P_r-{F}(V2), P_not-{F}(V3,V2) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #158: exists( #10, #152 ), references = 1, size of lhs = 3:
% 1.29/1.63 P_p-{F}(V0), P_q-{F}(V1), P_r-{F}(V2) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #160: exists( #14, #157 ), references = 1, size of lhs = 2:
% 1.29/1.63 P_p-{F}(V0), P_q-{F}(V1) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #162: exists( #13, #159 ), references = 1, size of lhs = 1:
% 1.29/1.63 P_p-{F}(V0) | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 #164: exists( #12, #161 ), references = 1, size of lhs = 0:
% 1.29/1.63 FALSE | FALSE
% 1.29/1.63 (used 0 times, uses = {})
% 1.29/1.63
% 1.29/1.63 number of learnt formulas = 32
% 1.29/1.63
% 1.29/1.63
% 1.29/1.63 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.29/1.63
% 1.29/1.63 randbase = 1
%------------------------------------------------------------------------------