%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : LCL109-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n007.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 12:05:41 PM UTC 2026
% Result : Unsatisfiable 88.25s 88.55s
% Output : Refutation 88.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL109-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.10/0.36 % Computer : n007.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 22:07:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 88.25/88.55 GeoParameters:
% 88.25/88.55
% 88.25/88.55 tptp_input = 1
% 88.25/88.55 tptp_output = 0
% 88.25/88.55 nonempty = 1
% 88.25/88.55 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 88.25/88.55 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 88.25/88.55
% 88.25/88.55
% 88.25/88.55 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 88.25/88.55 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 88.25/88.55
% 88.25/88.55 RuleSystem INPUT:
% 88.25/88.55
% 88.25/88.55 Initial Rules:
% 88.25/88.55 #0: input, references = 4, size of lhs = 2:
% 88.25/88.55 P_ifeq-{F}(V0,V0,V1,V2,V3), V3 == V1 | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #1: input, references = 4, size of lhs = 3:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V0,V1,V2), V2 == V1 | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #2: input, references = 3, size of lhs = 7:
% 88.25/88.55 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
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #3: input, references = 5, size of lhs = 6:
% 88.25/88.55 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
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #4: input, references = 3, size of lhs = 7:
% 88.25/88.55 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
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #5: input, references = 4, size of lhs = 3:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V1,V1,V2), V2 == V0 | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #6: input, references = 5, size of lhs = 5:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V1,V2,V3), P_implies-{F}(V2,V1,V4), P_ifeq-{F}(V3,V4,V1,V2,V5), V5 == V2 | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #7: input, references = 4, size of lhs = 3:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V1,V0,V2), V2 == V0 | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #8: input, references = 4, size of lhs = 4:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V2,V1,V3), P_implies-{F}(V1,V3,V4), V4 == V0 | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #9: input, references = 6, size of lhs = 6:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V1,V2,V4), P_implies-{F}(V2,V3,V5), P_implies-{F}(V1,V3,V6), P_ifeq-{F}(V4,V5,V6,V0,V7), V7 == V0 | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #10: input, references = 3, size of lhs = 7:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V1,V2,V4), P_implies-{F}(V3,V1,V5), P_implies-{F}(V3,V2,V6), P_implies-{F}(V5,V6,V7), P_implies-{F}(V4,V7,V8), V8 == V0 | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #11: input, references = 4, size of lhs = 6:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V2,V3,V4), P_implies-{F}(V1,V4,V5), P_implies-{F}(V1,V3,V6), P_implies-{F}(V2,V6,V7), V5 == V7 | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #12: input, references = 5, size of lhs = 5:
% 88.25/88.55 P_truth-{F}(V0), P_not-{F}(V0,V1), P_implies-{F}(V2,V1,V3), P_not-{F}(V2,V4), V3 == V4 | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #13: input, references = 4, size of lhs = 5:
% 88.25/88.55 P_truth-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V2,V3), P_not-{F}(V3,V4), V4 == V2 | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #14: input, references = 5, size of lhs = 7:
% 88.25/88.55 P_truth-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V2,V4), P_not-{F}(V3,V5), P_implies-{F}(V4,V5,V6), P_implies-{F}(V3,V2,V7), V6 == V7 | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #15: input, references = 5, size of lhs = 8:
% 88.25/88.55 P_truth-{F}(V0), P_not-{F}(V0,V1), P_a-{F}(V2), P_b-{F}(V3), P_implies-{F}(V2,V3,V4), P_implies-{F}(V3,V2,V5), P_implies-{F}(V4,V5,V6), P_implies-{F}(V6,V5,V0) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #16: input, references = 6, size of lhs = 4:
% 88.25/88.55 #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3 | EXISTS V4: P_ifeq-{T}(V0,V1,V2,V3,V4)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #17: input, references = 19, size of lhs = 2:
% 88.25/88.55 #-{F} V0, #-{F} V1 | EXISTS V2: P_implies-{T}(V0,V1,V2)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #18: input, references = 4, size of lhs = 0:
% 88.25/88.55 FALSE | EXISTS V0: P_truth-{T}(V0)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #19: input, references = 14, size of lhs = 1:
% 88.25/88.55 #-{F} V0 | EXISTS V1: P_not-{T}(V0,V1)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #20: input, references = 4, size of lhs = 0:
% 88.25/88.55 FALSE | EXISTS V0: P_a-{T}(V0)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #21: input, references = 5, size of lhs = 0:
% 88.25/88.55 FALSE | EXISTS V0: P_b-{T}(V0)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 number of initial rules = 22
% 88.25/88.55
% 88.25/88.55 Simplifiers:
% 88.25/88.55 #22: unsound, references = 3, size of lhs = 3:
% 88.25/88.55 P_ifeq-{F}(V0,V1,V2,V3,V4), P_ifeq-{F}(V0,V1,V2,V3,V9), V4 == V9 | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #23: unsound, references = 3, size of lhs = 3:
% 88.25/88.55 P_implies-{F}(V0,V1,V2), P_implies-{F}(V0,V1,V5), V2 == V5 | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #24: unsound, references = 3, size of lhs = 3:
% 88.25/88.55 P_truth-{F}(V0), P_truth-{F}(V1), V0 == V1 | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #25: unsound, references = 3, size of lhs = 3:
% 88.25/88.55 P_not-{F}(V0,V1), P_not-{F}(V0,V3), V1 == V3 | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #26: unsound, references = 3, size of lhs = 3:
% 88.25/88.55 P_a-{F}(V0), P_a-{F}(V1), V0 == V1 | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #27: unsound, references = 3, size of lhs = 3:
% 88.25/88.55 P_b-{F}(V0), P_b-{F}(V1), V0 == V1 | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 number of simplifiers = 6
% 88.25/88.55
% 88.25/88.55 Learnt:
% 88.25/88.55 #29: exists( #17, #5 ), references = 10, size of lhs = 2:
% 88.25/88.55 P_truth-{F}(V0), #-{F} V1 | P_implies-{T}(V1,V1,V0)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #31: exists( #16, #0 ), references = 3, size of lhs = 3:
% 88.25/88.55 #-{F} V0, #-{F} V1, #-{F} V2 | P_ifeq-{T}(V0,V0,V1,V2,V1)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #33: exists( #19, #13 ), references = 1, size of lhs = 2:
% 88.25/88.55 P_truth-{F}(V0), P_not-{F}(V1,V0) | P_not-{T}(V0,V1)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #36: exists( #17, #7 ), references = 8, size of lhs = 2:
% 88.25/88.55 P_truth-{F}(V0), #-{F} V1 | P_implies-{T}(V1,V0,V0)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #37: exists( #17, #8 ), references = 11, size of lhs = 2:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V1,V2,V3) | P_implies-{T}(V2,V3,V0)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #40: exists( #19, #15 ), references = 5, size of lhs = 7:
% 88.25/88.55 P_truth-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_implies-{F}(V1,V2,V3), P_implies-{F}(V2,V1,V4), P_implies-{F}(V3,V4,V5), P_implies-{F}(V5,V4,V0) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #42: exists( #17, #1 ), references = 15, size of lhs = 2:
% 88.25/88.55 P_truth-{F}(V0), #-{F} V1 | P_implies-{T}(V0,V1,V1)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #47: mergings( V1 == V2; #45 ), references = 1, size of lhs = 3:
% 88.25/88.55 P_a-{F}(V0), P_truth-{F}(V0), P_implies-{F}(V0,V0,V0) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #49: exists( #17, #14 ), references = 7, size of lhs = 5:
% 88.25/88.55 P_truth-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V2,V3), P_not-{F}(V4,V5), P_implies-{F}(V3,V5,V6) | P_implies-{T}(V4,V2,V6)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #65: mergings( V2 == V3, V3 == V4, V4 == V6, V6 == V8, V5 == V7; #58 ), references = 1, size of lhs = 6:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_not-{F}(V0,V1), P_a-{F}(V2), P_b-{F}(V3), P_not-{F}(V3,V0) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #74: exists( #17, #12 ), references = 11, size of lhs = 3:
% 88.25/88.55 P_truth-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V2,V3) | P_implies-{T}(V2,V1,V3)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #75: exists( #17, #14 ), references = 5, size of lhs = 5:
% 88.25/88.55 P_truth-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V2,V3), P_not-{F}(V4,V5), P_implies-{F}(V4,V2,V6) | P_implies-{T}(V3,V5,V6)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #83: mergings( V2 == V0, V0 == V3; #80 ), references = 1, size of lhs = 3:
% 88.25/88.55 P_truth-{F}(V0), P_not-{F}(V1,V2), P_implies-{F}(V0,V1,V2) | P_not-{T}(V0,V0)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #98: exists( #16, #9 ), references = 1, size of lhs = 4:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V1,V2,V3), P_implies-{F}(V2,V4,V5), P_implies-{F}(V1,V4,V6) | P_ifeq-{T}(V3,V5,V6,V0,V0)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #118: mergings( V2 == V3, V3 == V5, V5 == V7, V4 == V6; #112 ), references = 1, size of lhs = 5:
% 88.25/88.55 P_a-{F}(V0), P_not-{F}(V0,V1), P_not-{F}(V1,V0), P_truth-{F}(V1), P_b-{F}(V2) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #129: exists( #16, #6 ), references = 1, size of lhs = 3:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V1,V2,V3), P_implies-{F}(V2,V1,V4) | P_ifeq-{T}(V3,V4,V1,V2,V2)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #131: exists( #19, #12 ), references = 5, size of lhs = 3:
% 88.25/88.55 P_truth-{F}(V0), P_not-{F}(V0,V1), P_implies-{F}(V2,V1,V3) | P_not-{T}(V2,V3)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #136: exists( #17, #3 ), references = 14, size of lhs = 4:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V1,V2,V3), P_implies-{F}(V2,V1,V4), P_implies-{F}(V4,V1,V5) | P_implies-{T}(V3,V2,V5)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #147: mergings( V3 == V4, V4 == V5; #143 ), references = 1, size of lhs = 3:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V1,V2,V0), P_implies-{F}(V3,V2,V1) | P_implies-{T}(V2,V3,V3)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #150: mergings( V3 == V4, V4 == V5; #144 ), references = 1, size of lhs = 4:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V1,V2,V3), P_implies-{F}(V3,V2,V4), P_implies-{F}(V4,V1,V5) | P_implies-{T}(V2,V1,V5)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #168: exists( #17, #11 ), references = 14, size of lhs = 4:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V1,V2,V3), P_implies-{F}(V4,V2,V5), P_implies-{F}(V1,V5,V6) | P_implies-{T}(V4,V3,V6)
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #188: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7; #183 ), references = 1, size of lhs = 12:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V1,V2,V3), P_implies-{F}(V4,V3,V5), P_implies-{F}(V2,V4,V6), P_implies-{F}(V4,V2,V7), P_implies-{F}(V2,V7,V8), P_implies-{F}(V8,V7,V9), P_implies-{F}(V1,V9,V10), P_implies-{F}(V4,V6,V11), P_implies-{F}(V11,V6,V12), P_ifeq-{F}(V12,V5,V10,V0,V13), V13 == V0 | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #217: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9; #209 ), references = 2, size of lhs = 17:
% 88.25/88.55 P_truth-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_implies-{F}(V1,V2,V3), P_implies-{F}(V2,V1,V4), P_implies-{F}(V5,V4,V0), P_implies-{F}(V3,V6,V7), P_implies-{F}(V8,V6,V9), P_implies-{F}(V6,V8,V10), P_implies-{F}(V6,V9,V11), P_implies-{F}(V11,V9,V4), P_implies-{F}(V10,V12,V13), P_implies-{F}(V14,V12,V8), P_implies-{F}(V13,V14,V15), P_implies-{F}(V15,V14,V16), P_implies-{F}(V17,V13,V7), P_implies-{F}(V17,V16,V5) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #224: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9; #210 ), references = 1, size of lhs = 18:
% 88.25/88.55 P_truth-{F}(V0), P_not-{F}(V0,V1), P_a-{F}(V2), P_b-{F}(V3), P_implies-{F}(V2,V3,V4), P_implies-{F}(V3,V2,V5), P_implies-{F}(V6,V5,V0), P_implies-{F}(V4,V7,V8), P_implies-{F}(V9,V7,V10), P_implies-{F}(V7,V9,V11), P_implies-{F}(V7,V10,V12), P_implies-{F}(V12,V10,V5), P_implies-{F}(V11,V13,V14), P_implies-{F}(V15,V13,V9), P_implies-{F}(V14,V15,V16), P_implies-{F}(V16,V15,V17), P_implies-{F}(V18,V14,V8), P_implies-{F}(V18,V17,V6) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #236: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10; #227 ), references = 1, size of lhs = 17:
% 88.25/88.55 P_truth-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_implies-{F}(V1,V2,V3), P_implies-{F}(V2,V1,V4), P_implies-{F}(V5,V4,V0), P_implies-{F}(V3,V6,V7), P_implies-{F}(V8,V6,V9), P_implies-{F}(V8,V10,V5), P_implies-{F}(V7,V11,V12), P_implies-{F}(V12,V11,V10), P_implies-{F}(V11,V13,V14), P_implies-{F}(V14,V9,V15), P_implies-{F}(V9,V14,V16), P_implies-{F}(V16,V13,V7), P_implies-{F}(V9,V15,V17), P_implies-{F}(V17,V15,V4) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #244: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10; #228 ), references = 1, size of lhs = 18:
% 88.25/88.55 P_truth-{F}(V0), P_not-{F}(V0,V1), P_a-{F}(V2), P_b-{F}(V3), P_implies-{F}(V2,V3,V4), P_implies-{F}(V3,V2,V5), P_implies-{F}(V6,V5,V0), P_implies-{F}(V4,V7,V8), P_implies-{F}(V9,V7,V10), P_implies-{F}(V9,V11,V6), P_implies-{F}(V8,V12,V13), P_implies-{F}(V13,V12,V11), P_implies-{F}(V12,V14,V15), P_implies-{F}(V15,V10,V16), P_implies-{F}(V10,V15,V17), P_implies-{F}(V17,V14,V8), P_implies-{F}(V10,V16,V18), P_implies-{F}(V18,V16,V5) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #264: mergings( V2 == V4, V4 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V3 == V5; #251 ), references = 2, size of lhs = 19:
% 88.25/88.55 P_truth-{F}(V0), P_not-{F}(V0,V1), P_a-{F}(V2), P_b-{F}(V3), P_implies-{F}(V2,V3,V4), P_implies-{F}(V3,V2,V5), P_implies-{F}(V6,V5,V0), P_not-{F}(V7,V8), P_implies-{F}(V7,V4,V9), P_implies-{F}(V10,V8,V11), P_implies-{F}(V10,V9,V12), P_implies-{F}(V12,V11,V13), P_implies-{F}(V14,V13,V6), P_implies-{F}(V14,V1,V15), P_implies-{F}(V11,V1,V16), P_implies-{F}(V15,V16,V4), P_implies-{F}(V16,V15,V17), P_implies-{F}(V15,V17,V18), P_implies-{F}(V18,V17,V5) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #277: mergings( V2 == V4, V4 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V3 == V5, V5 == V15; #252 ), references = 2, size of lhs = 19:
% 88.25/88.55 P_truth-{F}(V0), P_not-{F}(V0,V1), P_a-{F}(V2), P_b-{F}(V3), P_implies-{F}(V2,V3,V4), P_implies-{F}(V3,V2,V5), P_implies-{F}(V6,V5,V0), P_not-{F}(V7,V8), P_implies-{F}(V7,V4,V9), P_implies-{F}(V10,V8,V11), P_implies-{F}(V10,V9,V12), P_implies-{F}(V12,V11,V13), P_implies-{F}(V14,V13,V6), P_implies-{F}(V14,V1,V15), P_implies-{F}(V11,V1,V16), P_implies-{F}(V15,V16,V4), P_implies-{F}(V16,V15,V17), P_implies-{F}(V15,V17,V18), P_implies-{F}(V18,V17,V5) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #298: mergings( V3 == V4, V4 == V6, V6 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V5 == V7; #284 ), references = 1, size of lhs = 12:
% 88.25/88.55 P_truth-{F}(V0), P_not-{F}(V0,V1), P_a-{F}(V2), P_b-{F}(V3), P_implies-{F}(V3,V1,V2), P_implies-{F}(V2,V3,V4), P_implies-{F}(V5,V1,V3), P_implies-{F}(V6,V5,V2), P_not-{F}(V7,V8), P_implies-{F}(V7,V4,V9), P_implies-{F}(V10,V8,V5), P_implies-{F}(V10,V9,V6) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #312: mergings( V3 == V4, V4 == V6, V6 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V5 == V7, V7 == V17; #285 ), references = 1, size of lhs = 12:
% 88.25/88.55 P_truth-{F}(V0), P_not-{F}(V0,V1), P_a-{F}(V2), P_b-{F}(V3), P_implies-{F}(V3,V1,V2), P_implies-{F}(V2,V3,V4), P_implies-{F}(V5,V1,V3), P_implies-{F}(V6,V5,V2), P_not-{F}(V7,V8), P_implies-{F}(V7,V4,V9), P_implies-{F}(V10,V8,V5), P_implies-{F}(V10,V9,V6) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #330: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V0; #320 ), references = 1, size of lhs = 11:
% 88.25/88.55 P_truth-{F}(V0), P_a-{F}(V1), P_implies-{F}(V0,V2,V1), P_not-{F}(V2,V3), P_b-{F}(V3), P_implies-{F}(V1,V3,V4), P_implies-{F}(V3,V4,V5), P_not-{F}(V6,V3), P_implies-{F}(V7,V1,V6), P_implies-{F}(V7,V5,V8), P_implies-{F}(V8,V6,V1) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #341: mergings( V2 == V0, V0 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11; #319 ), references = 1, size of lhs = 11:
% 88.25/88.55 P_truth-{F}(V0), P_a-{F}(V1), P_implies-{F}(V0,V2,V1), P_not-{F}(V2,V3), P_b-{F}(V3), P_implies-{F}(V1,V3,V4), P_implies-{F}(V3,V4,V5), P_not-{F}(V6,V3), P_implies-{F}(V7,V1,V6), P_implies-{F}(V7,V5,V8), P_implies-{F}(V8,V6,V1) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #356: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13; #344 ), references = 1, size of lhs = 9:
% 88.25/88.55 P_truth-{F}(V0), P_a-{F}(V1), P_implies-{F}(V0,V2,V1), P_not-{F}(V2,V3), P_b-{F}(V3), P_not-{F}(V4,V3), P_implies-{F}(V5,V1,V4), P_implies-{F}(V5,V0,V6), P_implies-{F}(V6,V4,V1) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #368: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14; #345 ), references = 1, size of lhs = 9:
% 88.25/88.55 P_truth-{F}(V0), P_a-{F}(V1), P_implies-{F}(V0,V2,V1), P_not-{F}(V2,V3), P_b-{F}(V3), P_not-{F}(V4,V3), P_implies-{F}(V5,V1,V4), P_implies-{F}(V5,V0,V6), P_implies-{F}(V6,V4,V1) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #397: exists( #17, #392 ), references = 1, size of lhs = 4:
% 88.25/88.55 P_truth-{F}(V0), P_a-{F}(V1), P_b-{F}(V2), P_implies-{F}(V1,V2,V0) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #415: mergings( V3 == V4, V4 == V5; #411 ), references = 1, size of lhs = 14:
% 88.25/88.55 P_truth-{F}(V0), P_not-{F}(V0,V1), P_a-{F}(V2), P_b-{F}(V3), P_implies-{F}(V4,V1,V2), P_implies-{F}(V2,V3,V5), P_implies-{F}(V4,V6,V2), P_implies-{F}(V3,V6,V7), P_implies-{F}(V8,V1,V3), P_implies-{F}(V9,V8,V7), P_not-{F}(V10,V11), P_implies-{F}(V10,V5,V12), P_implies-{F}(V13,V11,V8), P_implies-{F}(V13,V12,V9) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #418: mergings( V3 == V4, V4 == V5; #412 ), references = 1, size of lhs = 14:
% 88.25/88.55 P_truth-{F}(V0), P_not-{F}(V0,V1), P_a-{F}(V2), P_b-{F}(V3), P_implies-{F}(V4,V1,V2), P_implies-{F}(V2,V3,V5), P_implies-{F}(V4,V6,V2), P_implies-{F}(V3,V6,V7), P_implies-{F}(V8,V1,V3), P_implies-{F}(V9,V8,V7), P_not-{F}(V10,V11), P_implies-{F}(V10,V5,V12), P_implies-{F}(V13,V11,V8), P_implies-{F}(V13,V12,V9) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #426: mergings( V3 == V4, V4 == V5, V5 == V6; #421 ), references = 1, size of lhs = 12:
% 88.25/88.55 P_truth-{F}(V0), P_not-{F}(V0,V1), P_a-{F}(V2), P_b-{F}(V3), P_implies-{F}(V4,V1,V2), P_implies-{F}(V4,V5,V2), P_implies-{F}(V3,V5,V6), P_not-{F}(V3,V7), P_implies-{F}(V8,V1,V3), P_implies-{F}(V9,V7,V8), P_implies-{F}(V9,V0,V10), P_implies-{F}(V10,V8,V6) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #430: mergings( V3 == V4, V4 == V5, V5 == V6; #422 ), references = 1, size of lhs = 12:
% 88.25/88.55 P_truth-{F}(V0), P_not-{F}(V0,V1), P_a-{F}(V2), P_b-{F}(V3), P_implies-{F}(V4,V1,V2), P_implies-{F}(V4,V5,V2), P_implies-{F}(V3,V5,V6), P_not-{F}(V3,V7), P_implies-{F}(V8,V1,V3), P_implies-{F}(V9,V7,V8), P_implies-{F}(V9,V0,V10), P_implies-{F}(V10,V8,V6) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #452: mergings( V2 == V3, V3 == V4, V4 == V6, V6 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V7 == V5; #441 ), references = 1, size of lhs = 8:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_not-{F}(V0,V1), P_not-{F}(V1,V0), P_a-{F}(V2), P_b-{F}(V3), P_implies-{F}(V0,V3,V3), P_implies-{F}(V4,V1,V2) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #462: mergings( V2 == V3, V3 == V4, V4 == V6, V6 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V7 == V5; #442 ), references = 1, size of lhs = 8:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_not-{F}(V0,V1), P_not-{F}(V1,V0), P_a-{F}(V2), P_b-{F}(V3), P_implies-{F}(V0,V3,V3), P_implies-{F}(V4,V1,V2) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #483: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V0, V12 == V13; #473 ), references = 1, size of lhs = 8:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_a-{F}(V1), P_b-{F}(V2), P_implies-{F}(V0,V2,V2), P_not-{F}(V3,V4), P_implies-{F}(V4,V0,V5), P_implies-{F}(V5,V3,V1) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #492: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V0, V12 == V13; #474 ), references = 1, size of lhs = 8:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_a-{F}(V1), P_b-{F}(V2), P_implies-{F}(V0,V2,V2), P_not-{F}(V3,V4), P_implies-{F}(V4,V0,V5), P_implies-{F}(V5,V3,V1) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #504: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9; #495 ), references = 1, size of lhs = 6:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_a-{F}(V1), P_b-{F}(V2), P_implies-{F}(V0,V2,V2), P_implies-{F}(V0,V3,V1) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #520: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8; #511 ), references = 2, size of lhs = 4:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_a-{F}(V1), P_implies-{F}(V0,V2,V1) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #527: exists( #20, #525 ), references = 1, size of lhs = 2:
% 88.25/88.55 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0) | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 #530: exists( #18, #528 ), references = 1, size of lhs = 0:
% 88.25/88.55 FALSE | FALSE
% 88.25/88.55 (used 0 times, uses = {})
% 88.25/88.55
% 88.25/88.55 number of learnt formulas = 47
% 88.25/88.55
% 88.25/88.55
% 88.25/88.55 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 88.25/88.55
% 88.25/88.55 randbase = 1
%------------------------------------------------------------------------------