TSTP Solution File: LCL145-1 by Geo-III---2018C
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : LCL145-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jul 23 06:08:50 EDT 2022
% Result : Unsatisfiable 3.95s 4.13s
% Output : Refutation 3.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL145-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jul 22 22:11:16 EDT 2022
% 0.13/0.33 % CPUTime :
% 3.95/4.13 GeoParameters:
% 3.95/4.13
% 3.95/4.13 tptp_input = 1
% 3.95/4.13 tptp_output = 0
% 3.95/4.13 nonempty = 1
% 3.95/4.13 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.95/4.13 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 3.95/4.13
% 3.95/4.13
% 3.95/4.13 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.95/4.13 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.95/4.13
% 3.95/4.13 RuleSystem INPUT:
% 3.95/4.13
% 3.95/4.13 Initial Rules:
% 3.95/4.13 #0: input, references = 6, size of lhs = 3:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V1,V2), V2 == V1 | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #1: input, references = 8, size of lhs = 7:
% 3.95/4.13 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
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #2: input, references = 10, size of lhs = 6:
% 3.95/4.13 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
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #3: input, references = 5, size of lhs = 7:
% 3.95/4.13 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
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #4: input, references = 5, size of lhs = 5:
% 3.95/4.13 P_truth-{F}(V0), P_big_V-{F}(V1,V2,V3), P_implies-{F}(V1,V2,V4), P_implies-{F}(V4,V2,V5), V3 == V5 | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #5: input, references = 8, size of lhs = 7:
% 3.95/4.13 P_truth-{F}(V0), P_big_hat-{F}(V1,V2,V3), P_not-{F}(V1,V4), P_not-{F}(V2,V5), P_big_V-{F}(V4,V5,V6), P_not-{F}(V6,V7), V3 == V7 | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #6: input, references = 3, size of lhs = 4:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V1,V2,V3), ordered-{F}(V1,V2), V3 == V0 | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #7: input, references = 3, size of lhs = 2:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V1,V2,V0) | ordered-{T}(V1,V2)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #8: input, references = 7, size of lhs = 8:
% 3.95/4.13 P_truth-{F}(V0), P_x-{F}(V1), P_y-{F}(V2), P_big_V-{F}(V1,V2,V3), P_not-{F}(V3,V7), P_not-{F}(V1,V5), P_not-{F}(V2,V6), P_big_hat-{F}(V5,V6,V7) | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #9: input, references = 20, size of lhs = 2:
% 3.95/4.13 #-{F} V0, #-{F} V1 | EXISTS V2: P_implies-{T}(V0,V1,V2)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #10: input, references = 4, size of lhs = 0:
% 3.95/4.13 FALSE | EXISTS V0: P_truth-{T}(V0)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #11: input, references = 17, size of lhs = 1:
% 3.95/4.13 #-{F} V0 | EXISTS V1: P_not-{T}(V0,V1)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #12: input, references = 5, size of lhs = 2:
% 3.95/4.13 #-{F} V0, #-{F} V1 | EXISTS V2: P_big_V-{T}(V0,V1,V2)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #13: input, references = 14, size of lhs = 2:
% 3.95/4.13 #-{F} V0, #-{F} V1 | EXISTS V2: P_big_hat-{T}(V0,V1,V2)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #14: input, references = 4, size of lhs = 0:
% 3.95/4.13 FALSE | EXISTS V0: P_x-{T}(V0)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #15: input, references = 5, size of lhs = 0:
% 3.95/4.13 FALSE | EXISTS V0: P_y-{T}(V0)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 number of initial rules = 16
% 3.95/4.13
% 3.95/4.13 Simplifiers:
% 3.95/4.13 #16: unsound, references = 3, size of lhs = 3:
% 3.95/4.13 P_implies-{F}(V0,V1,V2), P_implies-{F}(V0,V1,V5), V2 == V5 | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #17: unsound, references = 3, size of lhs = 3:
% 3.95/4.13 P_truth-{F}(V0), P_truth-{F}(V1), V0 == V1 | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #18: unsound, references = 3, size of lhs = 3:
% 3.95/4.13 P_not-{F}(V0,V1), P_not-{F}(V0,V3), V1 == V3 | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #19: unsound, references = 3, size of lhs = 3:
% 3.95/4.13 P_big_V-{F}(V0,V1,V2), P_big_V-{F}(V0,V1,V5), V2 == V5 | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #20: unsound, references = 3, size of lhs = 3:
% 3.95/4.13 P_big_hat-{F}(V0,V1,V2), P_big_hat-{F}(V0,V1,V5), V2 == V5 | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #21: unsound, references = 3, size of lhs = 3:
% 3.95/4.13 P_x-{F}(V0), P_x-{F}(V1), V0 == V1 | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #22: unsound, references = 3, size of lhs = 3:
% 3.95/4.13 P_y-{F}(V0), P_y-{F}(V1), V0 == V1 | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 number of simplifiers = 7
% 3.95/4.13
% 3.95/4.13 Learnt:
% 3.95/4.13 #24: exists( #9, #0 ), references = 29, size of lhs = 2:
% 3.95/4.13 P_truth-{F}(V0), #-{F} V1 | P_implies-{T}(V0,V1,V1)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #26: exists( #12, #4 ), references = 21, size of lhs = 3:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V1,V2,V3), P_implies-{F}(V3,V2,V4) | P_big_V-{T}(V1,V2,V4)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #28: exists( #11, #5 ), references = 20, size of lhs = 5:
% 3.95/4.13 P_truth-{F}(V0), P_not-{F}(V1,V2), P_big_hat-{F}(V1,V3,V4), P_not-{F}(V3,V5), P_big_V-{F}(V2,V5,V6) | P_not-{T}(V6,V4)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #32: exists( #9, #1 ), references = 2, size of lhs = 5:
% 3.95/4.13 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)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #33: exists( #9, #3 ), references = 12, size of lhs = 5:
% 3.95/4.13 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)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #42: mergings( V3 == V4; #38 ), references = 3, size of lhs = 4:
% 3.95/4.13 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)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #45: mergings( V3 == V4; #40 ), references = 1, size of lhs = 5:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V1,V0), P_not-{F}(V2,V3), P_implies-{F}(V3,V4,V1), P_not-{F}(V5,V4) | P_implies-{T}(V5,V2,V0)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #53: mergings( V2 == V3, V3 == V4; #50 ), references = 2, size of lhs = 8:
% 3.95/4.13 P_truth-{F}(V0), P_not-{F}(V1,V0), P_implies-{F}(V2,V1,V3), P_implies-{F}(V0,V2,V4), P_not-{F}(V5,V3), P_implies-{F}(V2,V5,V6), P_implies-{F}(V6,V5,V7), V7 == V4 | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #62: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7; #57 ), references = 1, size of lhs = 8:
% 3.95/4.13 P_truth-{F}(V0), P_not-{F}(V1,V0), P_not-{F}(V2,V0), P_implies-{F}(V0,V2,V3), P_implies-{F}(V4,V1,V2), P_not-{F}(V5,V6), P_big_V-{F}(V6,V7,V4), P_not-{F}(V8,V7) | P_big_hat-{T}(V5,V8,V3)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #77: mergings( V3 == V4; #74 ), references = 24, size of lhs = 4:
% 3.95/4.13 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)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #88: exists( #13, #5 ), references = 6, size of lhs = 5:
% 3.95/4.13 P_truth-{F}(V0), P_not-{F}(V1,V2), P_not-{F}(V3,V4), P_big_V-{F}(V2,V4,V5), P_not-{F}(V5,V6) | P_big_hat-{T}(V1,V3,V6)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #105: exists( #9, #2 ), references = 9, size of lhs = 4:
% 3.95/4.13 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)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #106: exists( #9, #4 ), references = 2, size of lhs = 3:
% 3.95/4.13 P_truth-{F}(V0), P_big_V-{F}(V1,V2,V3), P_implies-{F}(V1,V2,V4) | P_implies-{T}(V4,V2,V3)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #110: mergings( V3 == V4; #108 ), references = 11, size of lhs = 5:
% 3.95/4.13 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)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #119: mergings( V3 == V4; #117 ), references = 3, size of lhs = 3:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V1,V2,V0), P_implies-{F}(V2,V3,V0) | P_implies-{T}(V1,V3,V0)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #128: mergings( V3 == V4, V4 == V5, V5 == V6; #124 ), references = 5, size of lhs = 12:
% 3.95/4.13 P_truth-{F}(V0), P_not-{F}(V1,V2), P_not-{F}(V3,V4), P_implies-{F}(V4,V5,V0), P_implies-{F}(V5,V6,V2), P_not-{F}(V7,V6), P_implies-{F}(V7,V3,V8), P_not-{F}(V9,V8), P_implies-{F}(V0,V8,V10), P_not-{F}(V10,V11), P_big_hat-{F}(V1,V9,V12), V12 == V11 | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #133: mergings( V3 == V4, V4 == V5, V5 == V6; #129 ), references = 1, size of lhs = 10:
% 3.95/4.13 P_truth-{F}(V0), P_not-{F}(V1,V2), P_not-{F}(V3,V4), P_implies-{F}(V4,V5,V0), P_implies-{F}(V5,V6,V2), P_not-{F}(V7,V6), P_implies-{F}(V7,V3,V8), P_not-{F}(V9,V8), P_implies-{F}(V0,V8,V10), P_not-{F}(V10,V11) | P_big_hat-{T}(V1,V9,V11)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #148: mergings( V3 == V4, V4 == V5, V5 == V6; #144 ), references = 1, size of lhs = 12:
% 3.95/4.13 P_truth-{F}(V0), P_not-{F}(V1,V2), P_implies-{F}(V3,V2,V2), P_not-{F}(V4,V2), P_implies-{F}(V5,V3,V0), P_not-{F}(V6,V5), P_implies-{F}(V4,V6,V5), P_implies-{F}(V0,V5,V7), P_not-{F}(V7,V8), P_not-{F}(V9,V5), P_big_hat-{F}(V9,V1,V10), V10 == V8 | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #153: mergings( V3 == V4, V4 == V5, V5 == V6; #149 ), references = 1, size of lhs = 10:
% 3.95/4.13 P_truth-{F}(V0), P_not-{F}(V1,V2), P_implies-{F}(V3,V2,V2), P_not-{F}(V4,V2), P_implies-{F}(V5,V3,V0), P_not-{F}(V6,V5), P_implies-{F}(V4,V6,V5), P_implies-{F}(V0,V5,V7), P_not-{F}(V7,V8), P_not-{F}(V9,V5) | P_big_hat-{T}(V9,V1,V8)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #184: mergings( V3 == V4, V4 == V5; #181 ), references = 7, size of lhs = 8:
% 3.95/4.13 P_truth-{F}(V0), P_not-{F}(V1,V2), P_implies-{F}(V2,V3,V0), P_implies-{F}(V4,V1,V5), P_implies-{F}(V0,V5,V6), P_not-{F}(V4,V7), P_implies-{F}(V3,V7,V8), P_implies-{F}(V5,V8,V0) | P_implies-{T}(V2,V7,V6)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #191: mergings( V3 == V4; #189 ), references = 3, size of lhs = 11:
% 3.95/4.13 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,V9,V0), P_implies-{F}(V9,V3,V6), P_implies-{F}(V8,V10,V0), P_implies-{F}(V10,V3,V6) | P_implies-{T}(V2,V5,V7)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #201: mergings( V3 == V4, V4 == V5; #198 ), references = 3, size of lhs = 6:
% 3.95/4.13 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)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #212: mergings( V3 == V4, V4 == V5; #209 ), references = 2, size of lhs = 12:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_not-{F}(V1,V2), P_not-{F}(V3,V4), P_big_V-{F}(V2,V4,V5), P_implies-{F}(V0,V6,V5), P_implies-{F}(V7,V5,V6), P_not-{F}(V7,V8), P_implies-{F}(V0,V8,V9), P_not-{F}(V10,V9), P_not-{F}(V11,V6), P_big_hat-{F}(V10,V11,V12) | P_big_hat-{T}(V1,V3,V12)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #235: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V16 == V18, V19 == V21; #223 ), references = 1, size of lhs = 21:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_x-{F}(V1), P_y-{F}(V2), P_big_V-{F}(V1,V2,V3), P_not-{F}(V3,V4), P_not-{F}(V0,V4), P_not-{F}(V1,V5), P_not-{F}(V2,V5), P_implies-{F}(V0,V4,V6), P_implies-{F}(V6,V0,V0), P_not-{F}(V7,V6), P_not-{F}(V8,V6), P_implies-{F}(V8,V5,V9), P_implies-{F}(V0,V9,V10), P_implies-{F}(V10,V6,V0), P_implies-{F}(V0,V6,V11), P_implies-{F}(V9,V11,V0), P_not-{F}(V12,V13), P_big_V-{F}(V13,V14,V5), P_not-{F}(V15,V14) | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #249: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V0, V0 == V9; #240 ), references = 1, size of lhs = 5:
% 3.95/4.13 P_x-{F}(V0), P_implies-{F}(V0,V0,V0), P_y-{F}(V0), P_big_V-{F}(V0,V0,V0), P_truth-{F}(V0) | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #272: mergings( V2 == V3, V3 == V4; #269 ), references = 3, size of lhs = 8:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_not-{F}(V1,V0), P_implies-{F}(V2,V1,V3), P_implies-{F}(V2,V4,V5), P_implies-{F}(V0,V5,V6), P_implies-{F}(V3,V6,V7), V7 == V0 | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #303: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V12 == V13, V13 == V19, V14 == V16; #291 ), references = 5, size of lhs = 16:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_not-{F}(V0,V1), P_implies-{F}(V1,V1,V0), P_implies-{F}(V0,V1,V2), P_implies-{F}(V2,V0,V0), P_not-{F}(V3,V2), P_not-{F}(V4,V2), P_implies-{F}(V0,V2,V5), P_implies-{F}(V6,V2,V0), P_implies-{F}(V0,V7,V6), P_implies-{F}(V7,V5,V0), P_implies-{F}(V4,V8,V7), P_not-{F}(V9,V10), P_big_V-{F}(V10,V11,V8), P_not-{F}(V12,V11) | P_big_hat-{T}(V9,V12,V0)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #322: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V0, V0 == V8, V8 == V9, V9 == V10, V10 == V11; #311 ), references = 2, size of lhs = 14:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_implies-{F}(V0,V1,V0), P_implies-{F}(V0,V2,V0), P_not-{F}(V3,V4), P_not-{F}(V4,V5), P_implies-{F}(V0,V3,V6), P_implies-{F}(V1,V5,V6), P_implies-{F}(V2,V5,V6), P_implies-{F}(V0,V6,V7), P_implies-{F}(V4,V8,V9), P_implies-{F}(V0,V9,V10), P_implies-{F}(V7,V10,V11), V11 == V0 | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #326: exists( #11, #128 ), references = 1, size of lhs = 10:
% 3.95/4.13 P_truth-{F}(V0), P_not-{F}(V1,V2), P_not-{F}(V3,V4), P_implies-{F}(V4,V5,V0), P_implies-{F}(V5,V6,V2), P_not-{F}(V7,V6), P_implies-{F}(V7,V3,V8), P_not-{F}(V9,V8), P_implies-{F}(V0,V8,V10), P_big_hat-{F}(V1,V9,V11) | P_not-{T}(V10,V11)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #340: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8; #334 ), references = 1, size of lhs = 13:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_x-{F}(V1), P_y-{F}(V2), P_big_V-{F}(V1,V2,V3), P_not-{F}(V3,V4), P_not-{F}(V0,V4), P_not-{F}(V1,V5), P_not-{F}(V5,V0), P_not-{F}(V2,V6), P_not-{F}(V7,V8), P_big_V-{F}(V8,V9,V6), P_not-{F}(V10,V9) | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #352: mergings( V2 == V3, V3 == V4, V4 == V6, V5 == V6, V6 == V7, V7 == V8, V8 == V9; #344 ), references = 1, size of lhs = 9:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_x-{F}(V1), P_y-{F}(V2), P_big_V-{F}(V1,V2,V3), P_not-{F}(V3,V4), P_not-{F}(V0,V4), P_not-{F}(V1,V5), P_not-{F}(V5,V0) | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #368: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V0, V0 == V7, V7 == V8, V8 == V9; #359 ), references = 1, size of lhs = 5:
% 3.95/4.13 P_x-{F}(V0), P_implies-{F}(V0,V0,V0), P_truth-{F}(V0), P_y-{F}(V1), P_big_V-{F}(V0,V1,V0) | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #382: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10; #372 ), references = 1, size of lhs = 3:
% 3.95/4.13 P_x-{F}(V0), P_implies-{F}(V0,V0,V0), P_truth-{F}(V0) | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #386: exists( #9, #272 ), references = 9, size of lhs = 6:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_not-{F}(V1,V0), P_implies-{F}(V2,V1,V3), P_implies-{F}(V2,V4,V5), P_implies-{F}(V0,V5,V6) | P_implies-{T}(V3,V6,V0)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #387: exists( #9, #322 ), references = 1, size of lhs = 12:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_implies-{F}(V0,V1,V0), P_implies-{F}(V0,V2,V0), P_not-{F}(V3,V4), P_not-{F}(V4,V5), P_implies-{F}(V0,V3,V6), P_implies-{F}(V1,V5,V6), P_implies-{F}(V2,V5,V6), P_implies-{F}(V0,V6,V7), P_implies-{F}(V4,V8,V9), P_implies-{F}(V0,V9,V10) | P_implies-{T}(V7,V10,V0)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #395: exists( #11, #128 ), references = 1, size of lhs = 10:
% 3.95/4.13 P_truth-{F}(V0), P_not-{F}(V1,V2), P_not-{F}(V3,V4), P_implies-{F}(V4,V5,V0), P_implies-{F}(V5,V6,V2), P_not-{F}(V7,V6), P_implies-{F}(V7,V3,V8), P_not-{F}(V9,V8), P_implies-{F}(V0,V8,V10), P_big_hat-{F}(V1,V9,V11) | P_not-{T}(V10,V11)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #416: mergings( V3 == V4, V4 == V5; #412 ), references = 5, size of lhs = 14:
% 3.95/4.13 P_truth-{F}(V0), P_not-{F}(V1,V0), P_not-{F}(V2,V0), P_not-{F}(V3,V2), P_not-{F}(V4,V5), P_not-{F}(V6,V7), P_big_V-{F}(V5,V7,V8), P_implies-{F}(V3,V8,V9), P_implies-{F}(V0,V9,V10), P_implies-{F}(V8,V1,V11), P_not-{F}(V11,V10), P_implies-{F}(V11,V2,V12), P_implies-{F}(V9,V12,V0), P_implies-{F}(V0,V11,V13) | P_big_hat-{T}(V4,V6,V13)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #420: mergings( V3 == V4, V4 == V6, V6 == V7; #413 ), references = 1, size of lhs = 15:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_not-{F}(V1,V0), P_not-{F}(V2,V0), P_implies-{F}(V0,V1,V3), P_not-{F}(V4,V3), P_not-{F}(V5,V6), P_not-{F}(V7,V8), P_big_V-{F}(V6,V8,V9), P_implies-{F}(V9,V2,V10), P_implies-{F}(V4,V9,V11), P_implies-{F}(V0,V11,V12), P_implies-{F}(V12,V3,V13), P_implies-{F}(V10,V3,V14), P_implies-{F}(V11,V14,V0) | P_big_hat-{T}(V5,V7,V13)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #432: mergings( V3 == V4, V4 == V5; #429 ), references = 4, size of lhs = 13:
% 3.95/4.13 P_truth-{F}(V0), P_not-{F}(V1,V2), P_implies-{F}(V3,V1,V4), P_implies-{F}(V0,V4,V5), P_not-{F}(V5,V6), P_not-{F}(V3,V7), P_not-{F}(V7,V8), P_implies-{F}(V8,V6,V2), P_implies-{F}(V7,V5,V9), P_implies-{F}(V9,V5,V10), P_implies-{F}(V4,V10,V0), P_implies-{F}(V7,V2,V11), P_implies-{F}(V11,V2,V12) | P_implies-{T}(V5,V7,V12)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #456: mergings( V15 == V17, V16 == V0, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V10, V10 == V11, V11 == V12, V12 == V18; #443 ), references = 1, size of lhs = 16:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_not-{F}(V1,V0), P_x-{F}(V2), P_implies-{F}(V0,V2,V2), P_y-{F}(V3), P_implies-{F}(V0,V1,V3), P_not-{F}(V3,V0), P_not-{F}(V0,V3), P_not-{F}(V4,V3), P_implies-{F}(V3,V2,V5), P_implies-{F}(V5,V2,V2), P_implies-{F}(V4,V2,V6), P_implies-{F}(V0,V6,V2), P_implies-{F}(V6,V2,V0), P_not-{F}(V7,V3) | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #479: mergings( V3 == V4, V4 == V5; #476 ), references = 1, size of lhs = 12:
% 3.95/4.13 P_truth-{F}(V0), P_x-{F}(V1), P_y-{F}(V2), P_big_V-{F}(V1,V2,V3), P_not-{F}(V1,V4), P_not-{F}(V4,V5), P_not-{F}(V2,V6), P_not-{F}(V6,V7), P_big_V-{F}(V5,V7,V3), P_not-{F}(V8,V9), P_big_V-{F}(V9,V10,V3), P_not-{F}(V11,V10) | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #489: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8; #483 ), references = 2, size of lhs = 13:
% 3.95/4.13 P_truth-{F}(V0), P_x-{F}(V1), P_y-{F}(V2), P_implies-{F}(V1,V2,V3), P_not-{F}(V1,V4), P_not-{F}(V4,V1), P_not-{F}(V2,V5), P_not-{F}(V5,V2), P_implies-{F}(V6,V2,V3), P_implies-{F}(V2,V6,V7), P_not-{F}(V8,V6), P_implies-{F}(V9,V6,V7), P_not-{F}(V10,V9) | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #502: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V1 == V11, V0 == V10, V10 == V12; #492 ), references = 1, size of lhs = 8:
% 3.95/4.13 P_truth-{F}(V0), P_x-{F}(V1), P_not-{F}(V1,V1), P_y-{F}(V2), P_implies-{F}(V2,V2,V0), P_not-{F}(V2,V2), P_not-{F}(V3,V1), P_not-{F}(V4,V2) | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #505: exists( #9, #489 ), references = 2, size of lhs = 11:
% 3.95/4.13 P_truth-{F}(V0), P_x-{F}(V1), P_y-{F}(V2), P_not-{F}(V1,V3), P_not-{F}(V3,V1), P_not-{F}(V2,V4), P_not-{F}(V4,V2), P_implies-{F}(V2,V1,V5), P_not-{F}(V6,V1), P_implies-{F}(V7,V1,V5), P_not-{F}(V8,V7) | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #509: exists( #9, #505 ), references = 1, size of lhs = 9:
% 3.95/4.13 P_truth-{F}(V0), P_x-{F}(V1), P_y-{F}(V2), P_not-{F}(V1,V3), P_not-{F}(V3,V1), P_not-{F}(V2,V4), P_not-{F}(V4,V2), P_not-{F}(V5,V1), P_not-{F}(V6,V2) | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #526: mergings( V16 == V18, V17 == V0, V2 == V3, V3 == V4, V4 == V5, V5 == V7, V7 == V8; #518 ), references = 1, size of lhs = 19:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_not-{F}(V1,V0), P_x-{F}(V2), P_implies-{F}(V0,V2,V2), P_y-{F}(V3), P_not-{F}(V3,V4), P_not-{F}(V4,V3), P_not-{F}(V5,V3), P_not-{F}(V0,V6), P_implies-{F}(V0,V1,V6), P_not-{F}(V6,V0), P_not-{F}(V7,V6), P_not-{F}(V8,V6), P_implies-{F}(V7,V2,V9), P_implies-{F}(V0,V9,V2), P_implies-{F}(V9,V2,V0), P_implies-{F}(V6,V2,V10), P_implies-{F}(V10,V2,V2) | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #544: mergings( V9 == V13, V13 == V14, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V0, V0 == V7, V7 == V8; #534 ), references = 2, size of lhs = 11:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_x-{F}(V1), P_implies-{F}(V0,V1,V1), P_implies-{F}(V1,V1,V0), P_y-{F}(V2), P_not-{F}(V2,V3), P_not-{F}(V3,V2), P_not-{F}(V4,V2), P_implies-{F}(V0,V5,V1), P_implies-{F}(V0,V6,V5) | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #584: mergings( V7 == V9, V9 == V11, V2 == V3, V3 == V4, V4 == V5, V5 == V0, V0 == V6, V8 == V10, V22 == V23, V24 == V26, V14 == V27; #571 ), references = 1, size of lhs = 22:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_implies-{F}(V0,V1,V1), P_not-{F}(V1,V2), P_implies-{F}(V0,V2,V3), P_not-{F}(V4,V3), P_implies-{F}(V0,V3,V5), P_implies-{F}(V0,V4,V6), P_implies-{F}(V0,V6,V1), P_implies-{F}(V6,V1,V0), P_implies-{F}(V0,V5,V7), P_implies-{F}(V0,V7,V2), P_implies-{F}(V7,V5,V0), P_not-{F}(V5,V8), V1 == V8, P_implies-{F}(V0,V9,V1), P_implies-{F}(V0,V10,V9), P_implies-{F}(V0,V11,V3), P_implies-{F}(V0,V12,V11), P_not-{F}(V13,V14), P_big_V-{F}(V14,V15,V5), P_not-{F}(V16,V15) | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #597: mergings( V8 == V10, V10 == V12, V2 == V3, V3 == V4, V4 == V5, V5 == V0, V0 == V6, V19 == V25, V9 == V11, V11 == V13, V16 == V18, V21 == V23; #572 ), references = 1, size of lhs = 24:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_implies-{F}(V0,V1,V0), P_implies-{F}(V0,V2,V2), P_not-{F}(V2,V3), P_implies-{F}(V0,V3,V4), P_not-{F}(V5,V4), P_implies-{F}(V0,V4,V6), P_not-{F}(V7,V6), P_implies-{F}(V1,V3,V8), P_big_V-{F}(V8,V6,V6), P_not-{F}(V9,V8), P_implies-{F}(V0,V5,V10), P_implies-{F}(V0,V10,V2), P_implies-{F}(V10,V2,V0), P_implies-{F}(V0,V6,V11), P_implies-{F}(V0,V11,V3), P_implies-{F}(V11,V6,V0), P_not-{F}(V11,V12), V2 == V12, P_implies-{F}(V0,V13,V2), P_implies-{F}(V0,V14,V13), P_implies-{F}(V0,V15,V4), P_implies-{F}(V0,V16,V15) | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #614: mergings( V10 == V12, V12 == V14, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V11 == V13, V28 == V29, V30 == V32, V17 == V26; #600 ), references = 1, size of lhs = 23:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_implies-{F}(V0,V1,V1), P_not-{F}(V1,V2), P_implies-{F}(V0,V2,V3), P_not-{F}(V4,V3), P_implies-{F}(V0,V3,V5), P_implies-{F}(V0,V4,V6), P_implies-{F}(V0,V6,V1), P_implies-{F}(V6,V1,V0), P_implies-{F}(V0,V5,V7), P_implies-{F}(V0,V7,V2), P_implies-{F}(V7,V5,V0), P_implies-{F}(V0,V8,V1), P_implies-{F}(V0,V9,V8), P_implies-{F}(V0,V10,V3), P_implies-{F}(V0,V11,V10), P_not-{F}(V12,V13), P_big_V-{F}(V13,V14,V5), P_not-{F}(V15,V14), P_not-{F}(V16,V17), P_big_V-{F}(V17,V18,V5), P_not-{F}(V19,V18) | P_big_hat-{T}(V12,V15,V1)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #628: mergings( V11 == V13, V13 == V15, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V22 == V27, V12 == V14, V14 == V16, V19 == V21, V23 == V25; #601 ), references = 1, size of lhs = 25:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_implies-{F}(V0,V1,V0), P_implies-{F}(V0,V2,V2), P_not-{F}(V2,V3), P_implies-{F}(V0,V3,V4), P_not-{F}(V5,V4), P_implies-{F}(V0,V4,V6), P_not-{F}(V7,V6), P_implies-{F}(V1,V3,V8), P_big_V-{F}(V8,V6,V6), P_not-{F}(V9,V8), P_implies-{F}(V0,V5,V10), P_implies-{F}(V0,V10,V2), P_implies-{F}(V10,V2,V0), P_implies-{F}(V0,V6,V11), P_implies-{F}(V0,V11,V3), P_implies-{F}(V11,V6,V0), P_implies-{F}(V0,V12,V2), P_implies-{F}(V0,V13,V12), P_implies-{F}(V0,V14,V4), P_implies-{F}(V0,V15,V14), P_not-{F}(V16,V17), P_big_V-{F}(V17,V18,V11), P_not-{F}(V19,V18) | P_big_hat-{T}(V16,V19,V2)
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #646: mergings( V0 == V13, V13 == V14, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11; #634 ), references = 2, size of lhs = 12:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_x-{F}(V1), P_implies-{F}(V0,V1,V1), P_implies-{F}(V1,V1,V0), P_y-{F}(V2), P_implies-{F}(V0,V2,V2), P_implies-{F}(V2,V2,V0), P_implies-{F}(V0,V3,V1), P_implies-{F}(V0,V4,V3), P_implies-{F}(V0,V5,V2), P_implies-{F}(V0,V6,V5) | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #650: exists( #15, #648 ), references = 1, size of lhs = 7:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0), P_x-{F}(V1), P_implies-{F}(V0,V1,V1), P_implies-{F}(V1,V1,V0), P_implies-{F}(V0,V2,V1), P_implies-{F}(V0,V3,V2) | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #654: exists( #14, #652 ), references = 1, size of lhs = 2:
% 3.95/4.13 P_truth-{F}(V0), P_implies-{F}(V0,V0,V0) | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 #657: exists( #10, #655 ), references = 1, size of lhs = 0:
% 3.95/4.13 FALSE | FALSE
% 3.95/4.13 (used 0 times, uses = {})
% 3.95/4.13
% 3.95/4.13 number of learnt formulas = 55
% 3.95/4.13
% 3.95/4.13
% 3.95/4.13 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.95/4.13
% 3.95/4.13 randbase = 1
%------------------------------------------------------------------------------