%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : LCL903+1 : TPTP v9.3.1. Released v5.5.0.
% 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 12:07:17 PM UTC 2026
% Result : Theorem 16.97s 17.29s
% Output : Refutation 16.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL903+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 13:53:27 UTC 2026
% 0.10/0.37 % CPUTime :
% 16.97/17.29 GeoParameters:
% 16.97/17.29
% 16.97/17.29 tptp_input = 1
% 16.97/17.29 tptp_output = 0
% 16.97/17.29 nonempty = 1
% 16.97/17.29 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.97/17.29 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 16.97/17.29
% 16.97/17.29
% 16.97/17.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.97/17.29 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.97/17.29
% 16.97/17.29 RuleSystem INPUT:
% 16.97/17.29
% 16.97/17.29 Initial Rules:
% 16.97/17.29 #0: input, references = 5, size of lhs = 5:
% 16.97/17.29 P_+-{F}(V0,V1,V3), P_+-{F}(V3,V2,V4), P_+-{F}(V1,V2,V5), P_+-{F}(V0,V5,V6), V4 == V6 | FALSE
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #1: input, references = 6, size of lhs = 3:
% 16.97/17.29 P_+-{F}(V0,V1,V2), P_+-{F}(V1,V0,V3), V2 == V3 | FALSE
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #2: input, references = 6, size of lhs = 3:
% 16.97/17.29 P_0-{F}(V0), P_+-{F}(V1,V0,V2), V2 == V1 | FALSE
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #3: input, references = 18, size of lhs = 2:
% 16.97/17.29 P_0-{F}(V0), #-{F} V1 | >=-{T}(V1,V1)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #4: input, references = 4, size of lhs = 3:
% 16.97/17.29 P_0-{F}(V0), >=-{F}(V1,V2), >=-{F}(V3,V1) | >=-{T}(V3,V2)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #5: input, references = 11, size of lhs = 4:
% 16.97/17.29 P_0-{F}(V0), >=-{F}(V1,V2), >=-{F}(V2,V1), V1 == V2 | FALSE
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #6: input, references = 14, size of lhs = 4:
% 16.97/17.29 P_0-{F}(V0), P_+-{F}(V1,V2,V4), P_==>-{F}(V1,V3,V5), >=-{F}(V4,V3) | >=-{T}(V2,V5)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #7: input, references = 16, size of lhs = 4:
% 16.97/17.29 P_0-{F}(V0), P_+-{F}(V1,V2,V4), P_==>-{F}(V1,V3,V5), >=-{F}(V2,V5) | >=-{T}(V4,V3)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #8: input, references = 6, size of lhs = 2:
% 16.97/17.29 P_0-{F}(V0), #-{F} V1 | >=-{T}(V1,V0)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #9: input, references = 5, size of lhs = 4:
% 16.97/17.29 P_0-{F}(V0), >=-{F}(V1,V2), P_+-{F}(V1,V3,V4), P_+-{F}(V2,V3,V5) | >=-{T}(V4,V5)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #10: input, references = 5, size of lhs = 4:
% 16.97/17.29 P_0-{F}(V0), >=-{F}(V1,V2), P_==>-{F}(V2,V3,V4), P_==>-{F}(V1,V3,V5) | >=-{T}(V4,V5)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #11: input, references = 3, size of lhs = 4:
% 16.97/17.29 P_0-{F}(V0), >=-{F}(V1,V2), P_==>-{F}(V3,V1,V4), P_==>-{F}(V3,V2,V5) | >=-{T}(V4,V5)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #12: input, references = 4, size of lhs = 4:
% 16.97/17.29 P_0-{F}(V0), P_1-{F}(V1), P_+-{F}(V2,V1,V3), V3 == V1 | FALSE
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #13: input, references = 5, size of lhs = 6:
% 16.97/17.29 P_0-{F}(V0), P_1-{F}(V1), P_==>-{F}(V2,V1,V3), P_==>-{F}(V3,V2,V4), P_==>-{F}(V4,V2,V5), V5 == V0 | FALSE
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #14: input, references = 4, size of lhs = 2:
% 16.97/17.29 P_0-{F}(V0), P_1-{F}(V1) | EXISTS V2: pppp0-{T}(V2)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #15: input, references = 4, size of lhs = 2:
% 16.97/17.29 pppp0-{F}(V0), P_+-{F}(V0,V0,V0) | FALSE
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #16: input, references = 11, size of lhs = 2:
% 16.97/17.29 #-{F} V0, #-{F} V1 | EXISTS V2: P_+-{T}(V0,V1,V2)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #17: input, references = 4, size of lhs = 0:
% 16.97/17.29 FALSE | EXISTS V0: P_0-{T}(V0)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #18: input, references = 12, size of lhs = 2:
% 16.97/17.29 #-{F} V0, #-{F} V1 | EXISTS V2: P_==>-{T}(V0,V1,V2)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #19: input, references = 4, size of lhs = 0:
% 16.97/17.29 FALSE | EXISTS V0: P_1-{T}(V0)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 number of initial rules = 20
% 16.97/17.29
% 16.97/17.29 Simplifiers:
% 16.97/17.29 #20: unsound, references = 3, size of lhs = 3:
% 16.97/17.29 P_+-{F}(V0,V1,V2), P_+-{F}(V0,V1,V5), V2 == V5 | FALSE
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #21: unsound, references = 3, size of lhs = 3:
% 16.97/17.29 P_0-{F}(V0), P_0-{F}(V1), V0 == V1 | FALSE
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #22: unsound, references = 3, size of lhs = 3:
% 16.97/17.29 P_==>-{F}(V0,V1,V2), P_==>-{F}(V0,V1,V5), V2 == V5 | FALSE
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #23: unsound, references = 3, size of lhs = 3:
% 16.97/17.29 P_1-{F}(V0), P_1-{F}(V1), V0 == V1 | FALSE
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #24: unsound, references = 3, size of lhs = 3:
% 16.97/17.29 pppp0-{F}(V0), pppp0-{F}(V1), V0 == V1 | FALSE
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 number of simplifiers = 5
% 16.97/17.29
% 16.97/17.29 Learnt:
% 16.97/17.29 #26: exists( #16, #12 ), references = 5, size of lhs = 3:
% 16.97/17.29 P_0-{F}(V0), P_1-{F}(V1), #-{F} V2 | P_+-{T}(V2,V1,V1)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #29: exists( #16, #2 ), references = 14, size of lhs = 2:
% 16.97/17.29 P_0-{F}(V0), #-{F} V1 | P_+-{T}(V1,V0,V1)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #36: mergings( V3 == V4, V4 == V5; #33 ), references = 9, size of lhs = 3:
% 16.97/17.29 P_0-{F}(V0), P_+-{F}(V1,V0,V2), >=-{F}(V2,V3) | P_==>-{T}(V1,V3,V0)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #40: exists( #16, #1 ), references = 11, size of lhs = 1:
% 16.97/17.29 P_+-{F}(V0,V1,V2) | P_+-{T}(V1,V0,V2)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #41: exists( #16, #0 ), references = 4, size of lhs = 3:
% 16.97/17.29 P_+-{F}(V0,V1,V2), P_+-{F}(V1,V3,V4), P_+-{F}(V0,V4,V5) | P_+-{T}(V2,V3,V5)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #54: mergings( V3 == V0, V0 == V4, V4 == V5, V5 == V6; #49 ), references = 4, size of lhs = 3:
% 16.97/17.29 P_0-{F}(V0), P_+-{F}(V0,V1,V2), >=-{F}(V2,V1) | P_==>-{T}(V0,V1,V1)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #68: mergings( V3 == V4, V4 == V6, V6 == V7, V7 == V8; #63 ), references = 6, size of lhs = 5:
% 16.97/17.29 P_1-{F}(V0), >=-{F}(V0,V1), P_0-{F}(V1), >=-{F}(V2,V3), P_==>-{F}(V4,V0,V3) | P_+-{T}(V4,V2,V0)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #90: mergings( V3 == V4, V4 == V5; #87 ), references = 1, size of lhs = 5:
% 16.97/17.29 P_0-{F}(V0), >=-{F}(V1,V2), P_==>-{F}(V1,V3,V4), P_+-{F}(V2,V4,V5), >=-{F}(V5,V3) | P_==>-{T}(V2,V3,V4)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #111: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V1 == V12; #101 ), references = 1, size of lhs = 10:
% 16.97/17.29 P_0-{F}(V0), P_1-{F}(V1), >=-{F}(V1,V0), >=-{F}(V1,V1), >=-{F}(V2,V1), >=-{F}(V3,V1), P_==>-{F}(V4,V1,V5), P_+-{F}(V5,V4,V2), P_+-{F}(V5,V0,V6), P_+-{F}(V5,V6,V3) | P_==>-{T}(V5,V1,V0)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #139: mergings( V3 == V5; #137 ), references = 1, size of lhs = 7:
% 16.97/17.29 P_1-{F}(V0), >=-{F}(V0,V1), P_0-{F}(V1), >=-{F}(V2,V3), P_==>-{F}(V4,V0,V5), P_+-{F}(V4,V6,V6), P_==>-{F}(V6,V5,V3) | P_+-{T}(V6,V2,V0)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #150: mergings( V3 == V4, V4 == V5, V5 == V7, V7 == V8, V8 == V9; #144 ), references = 1, size of lhs = 9:
% 16.97/17.29 P_1-{F}(V0), >=-{F}(V0,V1), P_0-{F}(V1), >=-{F}(V0,V2), P_==>-{F}(V3,V0,V4), P_+-{F}(V3,V5,V5), P_==>-{F}(V5,V2,V6), P_+-{F}(V5,V6,V7), >=-{F}(V7,V4) | P_==>-{T}(V5,V4,V6)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #206: mergings( V3 == V4, V4 == V5; #203 ), references = 5, size of lhs = 5:
% 16.97/17.29 P_0-{F}(V0), >=-{F}(V1,V2), >=-{F}(V2,V3), P_+-{F}(V1,V4,V5), P_==>-{F}(V4,V5,V3) | P_+-{T}(V4,V2,V5)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #239: mergings( V3 == V4, V4 == V5, V5 == V6; #235 ), references = 2, size of lhs = 7:
% 16.97/17.29 P_0-{F}(V0), P_1-{F}(V1), >=-{F}(V2,V3), P_==>-{F}(V2,V1,V4), >=-{F}(V4,V3), P_==>-{F}(V0,V3,V5), V5 == V0 | FALSE
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #253: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9; #246 ), references = 4, size of lhs = 7:
% 16.97/17.29 P_0-{F}(V0), P_1-{F}(V1), P_==>-{F}(V2,V1,V3), P_+-{F}(V4,V3,V5), >=-{F}(V5,V6), P_+-{F}(V4,V2,V7), >=-{F}(V7,V6) | P_==>-{T}(V4,V6,V0)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #290: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V13; #277 ), references = 1, size of lhs = 10:
% 16.97/17.29 P_1-{F}(V0), P_0-{F}(V1), >=-{F}(V2,V1), >=-{F}(V3,V1), >=-{F}(V4,V3), P_+-{F}(V4,V2,V5), P_+-{F}(V4,V5,V6), P_+-{F}(V4,V7,V6), P_==>-{F}(V7,V0,V4), P_+-{F}(V3,V4,V8) | P_+-{T}(V4,V4,V8)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #302: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V13, V13 == V14; #278 ), references = 1, size of lhs = 9:
% 16.97/17.29 P_1-{F}(V0), P_0-{F}(V1), >=-{F}(V1,V1), >=-{F}(V2,V1), >=-{F}(V3,V1), P_+-{F}(V3,V2,V4), P_+-{F}(V3,V4,V5), P_+-{F}(V3,V6,V5), P_==>-{F}(V6,V0,V3) | P_+-{T}(V3,V3,V3)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #315: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V15, V15 == V16; #279 ), references = 1, size of lhs = 11:
% 16.97/17.29 P_1-{F}(V0), P_0-{F}(V1), >=-{F}(V2,V1), >=-{F}(V3,V1), P_+-{F}(V4,V2,V5), P_==>-{F}(V3,V6,V5), >=-{F}(V7,V6), P_+-{F}(V4,V8,V7), P_==>-{F}(V8,V0,V9), P_+-{F}(V9,V3,V10), P_+-{F}(V4,V10,V7) | P_+-{T}(V4,V9,V5)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #336: mergings( V3 == V4, V4 == V5; #333 ), references = 1, size of lhs = 4:
% 16.97/17.29 P_0-{F}(V0), P_1-{F}(V1), >=-{F}(V2,V1), P_+-{F}(V3,V3,V2) | P_==>-{T}(V3,V1,V0)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #368: mergings( V3 == V4, V4 == V5, V5 == V6; #362 ), references = 1, size of lhs = 11:
% 16.97/17.29 P_1-{F}(V0), >=-{F}(V0,V1), P_0-{F}(V1), >=-{F}(V0,V2), >=-{F}(V3,V1), >=-{F}(V4,V3), P_+-{F}(V4,V5,V2), P_+-{F}(V3,V5,V6), V6 == V2, P_+-{F}(V5,V5,V7), >=-{F}(V7,V2) | FALSE
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #373: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7; #363 ), references = 1, size of lhs = 10:
% 16.97/17.29 P_1-{F}(V0), >=-{F}(V0,V1), P_0-{F}(V1), >=-{F}(V1,V1), >=-{F}(V2,V1), >=-{F}(V0,V3), P_+-{F}(V2,V4,V3), V3 == V4, P_+-{F}(V4,V4,V5), >=-{F}(V5,V3) | FALSE
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #378: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7; #364 ), references = 1, size of lhs = 10:
% 16.97/17.29 P_1-{F}(V0), >=-{F}(V0,V1), P_0-{F}(V1), >=-{F}(V2,V1), >=-{F}(V0,V3), >=-{F}(V3,V4), V4 == V3, P_+-{F}(V5,V2,V4), P_+-{F}(V5,V5,V6), >=-{F}(V6,V3) | FALSE
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #405: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V10; #395 ), references = 1, size of lhs = 6:
% 16.97/17.29 P_1-{F}(V0), >=-{F}(V0,V1), P_0-{F}(V1), >=-{F}(V2,V1), >=-{F}(V3,V2), P_+-{F}(V2,V3,V4) | P_+-{T}(V3,V3,V4)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #414: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V10, V10 == V11; #396 ), references = 1, size of lhs = 5:
% 16.97/17.29 P_1-{F}(V0), >=-{F}(V0,V1), P_0-{F}(V1), >=-{F}(V1,V1), >=-{F}(V2,V1) | P_+-{T}(V2,V2,V2)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #424: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V11, V11 == V12; #397 ), references = 1, size of lhs = 7:
% 16.97/17.29 P_1-{F}(V0), >=-{F}(V0,V1), P_0-{F}(V1), >=-{F}(V2,V1), P_+-{F}(V3,V2,V4), P_==>-{F}(V3,V4,V5), >=-{F}(V3,V5) | P_+-{T}(V3,V3,V4)
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #440: mergings( V0 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V12, V1 == V11; #429 ), references = 1, size of lhs = 4:
% 16.97/17.29 P_1-{F}(V0), >=-{F}(V0,V1), >=-{F}(V1,V1), P_0-{F}(V1) | FALSE
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #451: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9; #442 ), references = 1, size of lhs = 2:
% 16.97/17.29 P_0-{F}(V0), >=-{F}(V0,V0) | FALSE
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 #454: exists( #17, #452 ), references = 1, size of lhs = 0:
% 16.97/17.29 FALSE | FALSE
% 16.97/17.29 (used 0 times, uses = {})
% 16.97/17.29
% 16.97/17.29 number of learnt formulas = 27
% 16.97/17.29
% 16.97/17.29
% 16.97/17.29 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.97/17.29
% 16.97/17.29 randbase = 1
%------------------------------------------------------------------------------