%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : LCL110-2 : TPTP v9.3.1. Released v1.0.0.
% 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 12:05:42 PM UTC 2026
% Result : Unsatisfiable 4.79s 5.12s
% Output : Refutation 4.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL110-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.10/0.35 % Computer : n003.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 4 14:41:49 UTC 2026
% 0.10/0.35 % CPUTime :
% 4.79/5.12 GeoParameters:
% 4.79/5.12
% 4.79/5.12 tptp_input = 1
% 4.79/5.12 tptp_output = 0
% 4.79/5.12 nonempty = 1
% 4.79/5.12 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.79/5.12 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 4.79/5.12
% 4.79/5.12
% 4.79/5.12 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.79/5.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.79/5.12
% 4.79/5.12 RuleSystem INPUT:
% 4.79/5.12
% 4.79/5.12 Initial Rules:
% 4.79/5.12 #0: input, references = 5, size of lhs = 3:
% 4.79/5.12 P_truth-{F}(V0), P_implies-{F}(V0,V1,V2), V2 == V1 | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #1: input, references = 8, size of lhs = 7:
% 4.79/5.12 P_truth-{F}(V0), P_implies-{F}(V1,V2,V4), P_implies-{F}(V2,V3,V5), P_implies-{F}(V1,V3,V6), P_implies-{F}(V5,V6,V7), P_implies-{F}(V4,V7,V8), V8 == V0 | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #2: input, references = 7, size of lhs = 6:
% 4.79/5.12 P_truth-{F}(V0), P_implies-{F}(V1,V2,V3), P_implies-{F}(V3,V2,V4), P_implies-{F}(V2,V1,V5), P_implies-{F}(V5,V1,V6), V4 == V6 | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #3: input, references = 6, size of lhs = 7:
% 4.79/5.12 P_truth-{F}(V0), P_not-{F}(V1,V3), P_not-{F}(V2,V4), P_implies-{F}(V3,V4,V5), P_implies-{F}(V2,V1,V6), P_implies-{F}(V5,V6,V7), V7 == V0 | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #4: input, references = 4, size of lhs = 5:
% 4.79/5.12 P_truth-{F}(V0), P_x-{F}(V1), P_not-{F}(V1,V2), P_not-{F}(V2,V3), P_implies-{F}(V3,V1,V0) | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #5: input, references = 17, size of lhs = 2:
% 4.79/5.12 #-{F} V0, #-{F} V1 | EXISTS V2: P_implies-{T}(V0,V1,V2)
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #6: input, references = 4, size of lhs = 0:
% 4.79/5.12 FALSE | EXISTS V0: P_truth-{T}(V0)
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #7: input, references = 12, size of lhs = 1:
% 4.79/5.12 #-{F} V0 | EXISTS V1: P_not-{T}(V0,V1)
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #8: input, references = 4, size of lhs = 0:
% 4.79/5.12 FALSE | EXISTS V0: P_x-{T}(V0)
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 number of initial rules = 9
% 4.79/5.12
% 4.79/5.12 Simplifiers:
% 4.79/5.12 #9: unsound, references = 3, size of lhs = 3:
% 4.79/5.12 P_implies-{F}(V0,V1,V2), P_implies-{F}(V0,V1,V5), V2 == V5 | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #10: unsound, references = 3, size of lhs = 3:
% 4.79/5.12 P_truth-{F}(V0), P_truth-{F}(V1), V0 == V1 | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #11: unsound, references = 3, size of lhs = 3:
% 4.79/5.12 P_not-{F}(V0,V1), P_not-{F}(V0,V3), V1 == V3 | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #12: unsound, references = 3, size of lhs = 3:
% 4.79/5.12 P_x-{F}(V0), P_x-{F}(V1), V0 == V1 | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 number of simplifiers = 4
% 4.79/5.12
% 4.79/5.12 Learnt:
% 4.79/5.12 #15: exists( #5, #0 ), references = 17, size of lhs = 2:
% 4.79/5.12 P_truth-{F}(V0), #-{F} V1 | P_implies-{T}(V0,V1,V1)
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #16: exists( #5, #1 ), references = 3, size of lhs = 5:
% 4.79/5.12 P_truth-{F}(V0), P_implies-{F}(V1,V2,V3), P_implies-{F}(V2,V4,V5), P_implies-{F}(V1,V4,V6), P_implies-{F}(V5,V6,V7) | P_implies-{T}(V3,V7,V0)
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #23: mergings( V3 == V4; #20 ), references = 11, size of lhs = 4:
% 4.79/5.12 P_truth-{F}(V0), P_implies-{F}(V1,V2,V0), P_implies-{F}(V2,V3,V4), P_implies-{F}(V1,V3,V5) | P_implies-{T}(V4,V5,V0)
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #25: mergings( V3 == V4; #21 ), references = 1, size of lhs = 5:
% 4.79/5.12 P_truth-{F}(V0), P_implies-{F}(V0,V1,V0), P_implies-{F}(V2,V3,V1), P_implies-{F}(V3,V4,V5), P_implies-{F}(V2,V4,V6) | P_implies-{T}(V5,V6,V0)
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #30: mergings( V3 == V4; #28 ), references = 2, size of lhs = 4:
% 4.79/5.12 P_truth-{F}(V0), P_not-{F}(V1,V2), P_implies-{F}(V2,V3,V0), P_not-{F}(V4,V3) | P_implies-{T}(V4,V1,V0)
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #35: exists( #5, #3 ), references = 8, size of lhs = 5:
% 4.79/5.12 P_truth-{F}(V0), P_not-{F}(V1,V2), P_not-{F}(V3,V4), P_implies-{F}(V2,V4,V5), P_implies-{F}(V3,V1,V6) | P_implies-{T}(V5,V6,V0)
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #40: mergings( V3 == V4; #38 ), references = 3, size of lhs = 3:
% 4.79/5.12 P_truth-{F}(V0), P_implies-{F}(V1,V2,V0), P_implies-{F}(V2,V3,V0) | P_implies-{T}(V1,V3,V0)
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #51: exists( #5, #48 ), references = 2, size of lhs = 9:
% 4.79/5.12 P_truth-{F}(V0), P_x-{F}(V1), P_not-{F}(V1,V2), P_not-{F}(V2,V3), P_not-{F}(V4,V5), P_implies-{F}(V5,V6,V0), P_implies-{F}(V7,V4,V1), P_not-{F}(V7,V8), P_implies-{F}(V6,V8,V3) | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #58: mergings( V3 == V4, V4 == V5; #55 ), references = 1, size of lhs = 13:
% 4.79/5.12 P_x-{F}(V0), P_truth-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V1,V2), P_not-{F}(V3,V4), P_implies-{F}(V4,V5,V0), P_not-{F}(V6,V7), P_implies-{F}(V6,V3,V8), P_not-{F}(V8,V9), P_implies-{F}(V9,V10,V0), P_implies-{F}(V5,V7,V11), P_not-{F}(V11,V12), P_implies-{F}(V10,V12,V2) | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #64: mergings( V2 == V3, V3 == V4, V4 == V5; #60 ), references = 1, size of lhs = 10:
% 4.79/5.12 P_x-{F}(V0), P_truth-{F}(V0), P_not-{F}(V0,V1), P_implies-{F}(V2,V0,V0), P_not-{F}(V3,V2), P_not-{F}(V4,V5), P_implies-{F}(V5,V6,V0), P_implies-{F}(V7,V4,V3), P_not-{F}(V7,V8), P_implies-{F}(V6,V8,V1) | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #71: mergings( V2 == V3, V3 == V4, V4 == V0, V0 == V5; #66 ), references = 2, size of lhs = 7:
% 4.79/5.12 P_x-{F}(V0), P_truth-{F}(V0), P_implies-{F}(V1,V0,V0), P_not-{F}(V2,V1), P_implies-{F}(V0,V3,V2), P_not-{F}(V3,V4), P_implies-{F}(V4,V0,V0) | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #73: exists( #5, #2 ), references = 4, size of lhs = 4:
% 4.79/5.12 P_truth-{F}(V0), P_implies-{F}(V1,V2,V3), P_implies-{F}(V3,V2,V4), P_implies-{F}(V2,V1,V5) | P_implies-{T}(V5,V1,V4)
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #77: mergings( V3 == V4; #75 ), references = 6, size of lhs = 5:
% 4.79/5.12 P_truth-{F}(V0), P_implies-{F}(V1,V2,V2), P_implies-{F}(V1,V3,V3), P_implies-{F}(V3,V2,V4), P_implies-{F}(V4,V2,V3) | P_implies-{T}(V2,V3,V0)
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #82: exists( #7, #80 ), references = 1, size of lhs = 4:
% 4.79/5.12 P_x-{F}(V0), P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_implies-{F}(V0,V1,V1) | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #92: mergings( V3 == V4, V4 == V5; #89 ), references = 1, size of lhs = 8:
% 4.79/5.12 P_truth-{F}(V0), P_not-{F}(V1,V2), P_not-{F}(V2,V3), P_not-{F}(V4,V5), P_implies-{F}(V4,V1,V6), P_implies-{F}(V0,V6,V7), P_not-{F}(V5,V8), P_implies-{F}(V8,V3,V6) | P_implies-{T}(V2,V5,V7)
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #96: mergings( V2 == V3; #94 ), references = 2, size of lhs = 6:
% 4.79/5.12 P_truth-{F}(V0), P_x-{F}(V1), P_not-{F}(V1,V2), P_implies-{F}(V2,V3,V1), P_not-{F}(V3,V4), P_implies-{F}(V4,V0,V0) | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #115: mergings( V3 == V4, V4 == V5; #112 ), references = 3, size of lhs = 7:
% 4.79/5.12 P_truth-{F}(V0), P_not-{F}(V1,V2), P_implies-{F}(V2,V3,V0), P_not-{F}(V4,V5), P_implies-{F}(V4,V1,V6), P_implies-{F}(V3,V5,V6), P_implies-{F}(V0,V6,V7) | P_implies-{T}(V2,V5,V7)
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #125: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V11 == V15; #119 ), references = 2, size of lhs = 13:
% 4.79/5.12 P_truth-{F}(V0), P_x-{F}(V1), P_not-{F}(V1,V2), P_not-{F}(V3,V2), P_implies-{F}(V4,V0,V0), P_not-{F}(V5,V4), P_not-{F}(V6,V5), P_implies-{F}(V6,V3,V7), P_implies-{F}(V0,V7,V1), P_implies-{F}(V4,V8,V2), P_not-{F}(V9,V8), P_implies-{F}(V5,V9,V10), P_implies-{F}(V10,V9,V7) | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #143: mergings( V3 == V4; #141 ), references = 1, size of lhs = 7:
% 4.79/5.12 P_truth-{F}(V0), P_implies-{F}(V1,V2,V2), P_implies-{F}(V1,V3,V4), P_implies-{F}(V2,V3,V5), P_implies-{F}(V5,V3,V6), P_implies-{F}(V4,V6,V7), V7 == V0 | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #155: mergings( V3 == V4, V4 == V5; #152 ), references = 3, size of lhs = 6:
% 4.79/5.12 P_truth-{F}(V0), P_implies-{F}(V1,V2,V0), P_implies-{F}(V2,V3,V3), P_implies-{F}(V3,V1,V4), P_implies-{F}(V4,V1,V5), P_implies-{F}(V5,V3,V6) | P_implies-{T}(V1,V3,V6)
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #187: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6; #182 ), references = 1, size of lhs = 14:
% 4.79/5.12 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_implies-{F}(V1,V0,V0), P_not-{F}(V2,V1), P_implies-{F}(V0,V1,V3), P_implies-{F}(V2,V4,V3), P_implies-{F}(V0,V3,V5), P_implies-{F}(V5,V1,V0), P_not-{F}(V6,V1), P_implies-{F}(V4,V6,V7), P_not-{F}(V8,V7), P_implies-{F}(V8,V4,V9), P_implies-{F}(V0,V9,V10), V10 == V0 | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #197: mergings( V2 == V3, V3 == V4, V4 == V5; #193 ), references = 1, size of lhs = 9:
% 4.79/5.12 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_not-{F}(V0,V1), P_implies-{F}(V2,V0,V0), P_implies-{F}(V1,V2,V0), P_not-{F}(V3,V2), P_implies-{F}(V3,V2,V4), P_implies-{F}(V0,V2,V4), P_implies-{F}(V0,V4,V1) | P_not-{T}(V2,V0)
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #201: mergings( V2 == V3; #199 ), references = 1, size of lhs = 9:
% 4.79/5.12 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_x-{F}(V1), P_not-{F}(V2,V0), P_not-{F}(V3,V2), P_implies-{F}(V3,V1,V4), P_implies-{F}(V0,V4,V1), P_implies-{F}(V2,V1,V5), P_implies-{F}(V5,V1,V4) | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #213: mergings( V2 == V0, V0 == V3, V3 == V4, V4 == V5; #208 ), references = 2, size of lhs = 8:
% 4.79/5.12 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_x-{F}(V1), P_implies-{F}(V2,V1,V0), P_not-{F}(V2,V3), P_implies-{F}(V3,V0,V0), P_implies-{F}(V0,V1,V4), P_implies-{F}(V0,V4,V1) | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #218: exists( #7, #216 ), references = 1, size of lhs = 6:
% 4.79/5.12 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_x-{F}(V1), P_implies-{F}(V2,V1,V0), P_implies-{F}(V0,V1,V3), P_implies-{F}(V0,V3,V1) | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #222: exists( #8, #220 ), references = 1, size of lhs = 2:
% 4.79/5.12 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0) | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 #225: exists( #6, #223 ), references = 1, size of lhs = 0:
% 4.79/5.12 FALSE | FALSE
% 4.79/5.12 (used 0 times, uses = {})
% 4.79/5.12
% 4.79/5.12 number of learnt formulas = 27
% 4.79/5.12
% 4.79/5.12
% 4.79/5.12 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.79/5.12
% 4.79/5.12 randbase = 1
%------------------------------------------------------------------------------