TSTP Solution File: SET962+1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : SET962+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 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 06:17:01 EDT 2022
% Result : Theorem 8.42s 8.66s
% Output : Refutation 8.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET962+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.03/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Jul 23 01:41:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 8.42/8.66 GeoParameters:
% 8.42/8.66
% 8.42/8.66 tptp_input = 1
% 8.42/8.66 tptp_output = 0
% 8.42/8.66 nonempty = 1
% 8.42/8.66 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.42/8.66 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 8.42/8.66
% 8.42/8.66
% 8.42/8.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.42/8.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.42/8.66
% 8.42/8.66 RuleSystem INPUT:
% 8.42/8.66
% 8.42/8.66 Initial Rules:
% 8.42/8.66 #0: input, references = 7, size of lhs = 2:
% 8.42/8.66 in-{F}(V0,V1), in-{F}(V1,V0) | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #1: input, references = 4, size of lhs = 3:
% 8.42/8.66 P_unordered_pair-{F}(V0,V1,V2), P_unordered_pair-{F}(V1,V0,V3), V2 == V3 | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #2: input, references = 5, size of lhs = 5:
% 8.42/8.66 P_ordered_pair-{F}(V0,V1,V2), P_unordered_pair-{F}(V0,V1,V3), P_singleton-{F}(V0,V4), P_unordered_pair-{F}(V3,V4,V5), V2 == V5 | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #3: input, references = 3, size of lhs = 2:
% 8.42/8.66 P_ordered_pair-{F}(V0,V1,V2), empty-{F}(V2) | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #4: input, references = 19, size of lhs = 3:
% 8.42/8.66 P_ordered_pair-{F}(V0,V1,V4), P_cartesian_product2-{F}(V2,V3,V5), in-{F}(V4,V5) | pppp0-{T}(V0,V1,V2,V3)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #5: input, references = 19, size of lhs = 3:
% 8.42/8.66 P_ordered_pair-{F}(V0,V1,V4), P_cartesian_product2-{F}(V2,V3,V5), pppp0-{F}(V0,V1,V2,V3) | in-{T}(V4,V5)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #6: input, references = 10, size of lhs = 1:
% 8.42/8.66 pppp0-{F}(V0,V1,V2,V3) | in-{T}(V0,V2)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #7: input, references = 11, size of lhs = 1:
% 8.42/8.66 pppp0-{F}(V0,V1,V2,V3) | in-{T}(V1,V3)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #8: input, references = 11, size of lhs = 2:
% 8.42/8.66 in-{F}(V0,V2), in-{F}(V1,V3) | pppp0-{T}(V0,V1,V2,V3)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #9: input, references = 3, size of lhs = 0:
% 8.42/8.66 FALSE | EXISTS V0: pppp1-{T}(V0)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #10: input, references = 3, size of lhs = 1:
% 8.42/8.66 pppp1-{F}(V0) | empty-{T}(V0)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #11: input, references = 3, size of lhs = 0:
% 8.42/8.66 FALSE | EXISTS V0: pppp2-{T}(V0)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #12: input, references = 3, size of lhs = 2:
% 8.42/8.66 pppp2-{F}(V0), empty-{F}(V0) | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #13: input, references = 4, size of lhs = 0:
% 8.42/8.66 FALSE | EXISTS V0: pppp4-{T}(V0)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #14: input, references = 4, size of lhs = 1:
% 8.42/8.66 pppp4-{F}(V0) | EXISTS V1: pppp3-{T}(V0,V1)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #15: input, references = 4, size of lhs = 3:
% 8.42/8.66 pppp3-{F}(V1,V1), P_cartesian_product2-{F}(V1,V1,V2), P_cartesian_product2-{F}(V1,V1,V3) | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #16: input, references = 4, size of lhs = 4:
% 8.42/8.66 pppp3-{F}(V0,V1), P_cartesian_product2-{F}(V0,V0,V2), P_cartesian_product2-{F}(V1,V1,V3), V2 == V3 | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #17: input, references = 5, size of lhs = 3:
% 8.42/8.66 #-{F} V0, #-{F} V1, V0 == V1 | EXISTS V2: pppp5-{T}(V0,V1,V2)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #18: input, references = 5, size of lhs = 3:
% 8.42/8.66 pppp5-{F}(V0,V1,V2), in-{F}(V2,V1), in-{F}(V2,V0) | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #19: input, references = 7, size of lhs = 1:
% 8.42/8.66 pppp5-{F}(V0,V1,V2) | in-{T}(V2,V0), in-{T}(V2,V1)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #20: input, references = 5, size of lhs = 2:
% 8.42/8.66 #-{F} V0, #-{F} V1 | EXISTS V2: P_unordered_pair-{T}(V0,V1,V2)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #21: input, references = 11, size of lhs = 2:
% 8.42/8.66 #-{F} V0, #-{F} V1 | EXISTS V2: P_ordered_pair-{T}(V0,V1,V2)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #22: input, references = 4, size of lhs = 1:
% 8.42/8.66 #-{F} V0 | EXISTS V1: P_singleton-{T}(V0,V1)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #23: input, references = 8, size of lhs = 2:
% 8.42/8.66 #-{F} V0, #-{F} V1 | EXISTS V2: P_cartesian_product2-{T}(V0,V1,V2)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 number of initial rules = 24
% 8.42/8.66
% 8.42/8.66 Simplifiers:
% 8.42/8.66 #24: unsound, references = 3, size of lhs = 3:
% 8.42/8.66 empty-{F}(V0), empty-{F}(V1), V0 == V1 | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #25: unsound, references = 3, size of lhs = 3:
% 8.42/8.66 P_unordered_pair-{F}(V0,V1,V2), P_unordered_pair-{F}(V0,V1,V5), V2 == V5 | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #26: unsound, references = 3, size of lhs = 3:
% 8.42/8.66 P_ordered_pair-{F}(V0,V1,V2), P_ordered_pair-{F}(V0,V1,V5), V2 == V5 | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #27: unsound, references = 3, size of lhs = 3:
% 8.42/8.66 P_singleton-{F}(V0,V1), P_singleton-{F}(V0,V3), V1 == V3 | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #28: unsound, references = 3, size of lhs = 3:
% 8.42/8.66 P_cartesian_product2-{F}(V0,V1,V2), P_cartesian_product2-{F}(V0,V1,V5), V2 == V5 | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #29: unsound, references = 3, size of lhs = 3:
% 8.42/8.66 pppp1-{F}(V0), pppp1-{F}(V1), V0 == V1 | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #30: unsound, references = 3, size of lhs = 3:
% 8.42/8.66 pppp2-{F}(V0), pppp2-{F}(V1), V0 == V1 | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #31: unsound, references = 3, size of lhs = 3:
% 8.42/8.66 pppp3-{F}(V0,V1), pppp3-{F}(V0,V3), V1 == V3 | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #32: unsound, references = 3, size of lhs = 3:
% 8.42/8.66 pppp3-{F}(V0,V1), pppp3-{F}(V2,V3), V0 == V2 | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #33: unsound, references = 3, size of lhs = 3:
% 8.42/8.66 pppp4-{F}(V0), pppp4-{F}(V1), V0 == V1 | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #34: unsound, references = 3, size of lhs = 3:
% 8.42/8.66 pppp5-{F}(V0,V1,V2), pppp5-{F}(V0,V1,V5), V2 == V5 | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 number of simplifiers = 11
% 8.42/8.66
% 8.42/8.66 Learnt:
% 8.42/8.66 #36: exists( #20, #1 ), references = 6, size of lhs = 1:
% 8.42/8.66 P_unordered_pair-{F}(V0,V1,V2) | P_unordered_pair-{T}(V1,V0,V2)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #39: exists( #20, #37 ), references = 8, size of lhs = 3:
% 8.42/8.66 P_singleton-{F}(V0,V1), P_ordered_pair-{F}(V0,V2,V3), P_unordered_pair-{F}(V0,V2,V4) | P_unordered_pair-{T}(V1,V4,V3)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #41: exists( #21, #2 ), references = 8, size of lhs = 3:
% 8.42/8.66 P_singleton-{F}(V0,V1), P_unordered_pair-{F}(V0,V2,V3), P_unordered_pair-{F}(V3,V1,V4) | P_ordered_pair-{T}(V0,V2,V4)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #51: disj( #19, #4+#6+#0 ), references = 1, size of lhs = 3:
% 8.42/8.66 P_ordered_pair-{F}(V0,V1,V2), P_cartesian_product2-{F}(V0,V3,V4), pppp5-{F}(V4,V5,V2) | in-{T}(V2,V5)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #63: exists( #21, #61 ), references = 3, size of lhs = 5:
% 8.42/8.66 in-{F}(V0,V1), pppp5-{F}(V2,V1,V0), P_cartesian_product2-{F}(V2,V3,V4), P_cartesian_product2-{F}(V5,V6,V4), pppp0-{F}(V0,V7,V5,V6) | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #121: exists( #23, #119 ), references = 4, size of lhs = 3:
% 8.42/8.66 P_ordered_pair-{F}(V0,V1,V2), pppp0-{F}(V0,V1,V3,V4), P_ordered_pair-{F}(V5,V4,V2) | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #153: exists( #23, #151 ), references = 2, size of lhs = 5:
% 8.42/8.66 P_ordered_pair-{F}(V0,V1,V2), pppp0-{F}(V0,V1,V3,V4), P_ordered_pair-{F}(V2,V5,V6), P_ordered_pair-{F}(V7,V5,V2), P_ordered_pair-{F}(V8,V4,V6) | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #170: disj( #19, input ), references = 1, size of lhs = 1:
% 8.42/8.66 pppp5-{F}(V0,V1,V0) | in-{T}(V0,V1)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #226: disj( #19, input ), references = 1, size of lhs = 1:
% 8.42/8.66 pppp5-{F}(V0,V1,V1) | in-{T}(V1,V0)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #270: disj( #19, #8+#63 ), references = 3, size of lhs = 4:
% 8.42/8.66 P_cartesian_product2-{F}(V0,V0,V1), pppp5-{F}(V2,V0,V3), pppp5-{F}(V4,V0,V3), P_cartesian_product2-{F}(V4,V5,V1) | in-{T}(V3,V2)
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #330: exists( #21, #324 ), references = 1, size of lhs = 10:
% 8.42/8.66 P_singleton-{F}(V0,V1), P_singleton-{F}(V2,V1), P_unordered_pair-{F}(V0,V3,V4), P_unordered_pair-{F}(V2,V5,V4), in-{F}(V6,V7), P_ordered_pair-{F}(V3,V6,V8), P_cartesian_product2-{F}(V9,V7,V8), pppp0-{F}(V2,V5,V10,V11), P_cartesian_product2-{F}(V10,V11,V12), P_cartesian_product2-{F}(V13,V9,V12) | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #331: exists( #21, #325 ), references = 3, size of lhs = 9:
% 8.42/8.66 P_singleton-{F}(V0,V1), P_singleton-{F}(V2,V1), P_unordered_pair-{F}(V0,V3,V4), P_unordered_pair-{F}(V2,V5,V4), P_ordered_pair-{F}(V3,V3,V6), pppp0-{F}(V2,V5,V7,V8), P_cartesian_product2-{F}(V7,V8,V9), P_cartesian_product2-{F}(V10,V11,V9), P_ordered_pair-{F}(V12,V11,V6) | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #332: exists( #21, #326 ), references = 1, size of lhs = 11:
% 8.42/8.66 P_singleton-{F}(V0,V1), P_singleton-{F}(V2,V1), P_unordered_pair-{F}(V0,V3,V4), P_unordered_pair-{F}(V2,V5,V4), P_ordered_pair-{F}(V3,V3,V6), pppp0-{F}(V2,V5,V7,V8), P_cartesian_product2-{F}(V7,V8,V9), P_cartesian_product2-{F}(V10,V11,V9), P_ordered_pair-{F}(V6,V12,V13), P_ordered_pair-{F}(V14,V12,V6), P_ordered_pair-{F}(V15,V11,V13) | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #347: exists( #21, #345 ), references = 2, size of lhs = 7:
% 8.42/8.66 P_singleton-{F}(V0,V1), P_unordered_pair-{F}(V0,V2,V3), P_singleton-{F}(V4,V3), P_unordered_pair-{F}(V4,V5,V1), pppp0-{F}(V4,V5,V6,V7), P_cartesian_product2-{F}(V6,V7,V8), P_cartesian_product2-{F}(V0,V9,V8) | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #389: exists( #22, #331 ), references = 2, size of lhs = 7:
% 8.42/8.66 P_ordered_pair-{F}(V0,V0,V1), P_unordered_pair-{F}(V2,V0,V3), P_unordered_pair-{F}(V2,V4,V3), pppp0-{F}(V2,V4,V5,V6), P_cartesian_product2-{F}(V5,V6,V7), P_cartesian_product2-{F}(V8,V9,V7), P_ordered_pair-{F}(V10,V9,V1) | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #429: exists( #21, #425 ), references = 2, size of lhs = 5:
% 8.42/8.66 in-{F}(V0,V1), pppp5-{F}(V1,V2,V0), P_cartesian_product2-{F}(V2,V3,V4), P_cartesian_product2-{F}(V5,V6,V4), pppp0-{F}(V0,V7,V5,V6) | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #431: mergings( V5 == V8; #428 ), references = 1, size of lhs = 5:
% 8.42/8.66 P_cartesian_product2-{F}(V0,V1,V2), pppp5-{F}(V3,V0,V4), P_cartesian_product2-{F}(V3,V5,V2), P_cartesian_product2-{F}(V6,V7,V2), pppp0-{F}(V4,V8,V6,V7) | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #438: exists( #17, #434 ), references = 3, size of lhs = 6:
% 8.42/8.66 P_cartesian_product2-{F}(V0,V0,V1), P_cartesian_product2-{F}(V2,V3,V1), V2 == V0, in-{F}(V4,V5), P_cartesian_product2-{F}(V2,V5,V6), P_cartesian_product2-{F}(V0,V7,V6) | FALSE
% 8.42/8.66 (used 0 times, uses = {})
% 8.42/8.66
% 8.42/8.66 #467: exists( #21, #465 ), references = 1, size of lhs = 8:
% 8.42/8.66 P_cartesian_product2-{F}(V0,V0,V1), P_cartesian_product2-{F}(V2,V3,V1), V2 == V0, P_cartesian_product2-{F}(V0,V4,V5), P_cartesian_product2-{F}(V2,V6,V5), P_cartesian_product2-{F}(V7,V6,V8), P_cartesian_product2-{F}(V9,V10,V8), pppp0-{F}(V11,V12,V9,V10) | FALSE
% 8.42/8.67 (used 0 times, uses = {})
% 8.42/8.67
% 8.42/8.67 #521: exists( #23, #16 ), references = 1, size of lhs = 2:
% 8.42/8.67 pppp3-{F}(V0,V1), P_cartesian_product2-{F}(V0,V0,V2) | P_cartesian_product2-{T}(V1,V1,V2)
% 8.42/8.67 (used 0 times, uses = {})
% 8.42/8.67
% 8.42/8.67 #545: exists( #23, #539 ), references = 2, size of lhs = 10:
% 8.42/8.67 in-{F}(V0,V1), P_unordered_pair-{F}(V0,V2,V3), P_unordered_pair-{F}(V0,V4,V3), P_ordered_pair-{F}(V4,V4,V5), P_ordered_pair-{F}(V2,V6,V7), P_ordered_pair-{F}(V8,V9,V7), pppp0-{F}(V8,V9,V10,V11), P_cartesian_product2-{F}(V1,V10,V12), P_cartesian_product2-{F}(V13,V14,V12), P_ordered_pair-{F}(V15,V14,V5) | FALSE
% 8.42/8.67 (used 0 times, uses = {})
% 8.42/8.67
% 8.42/8.67 #546: exists( #23, #540 ), references = 2, size of lhs = 12:
% 8.42/8.67 in-{F}(V0,V1), P_singleton-{F}(V0,V2), P_singleton-{F}(V3,V2), P_unordered_pair-{F}(V0,V4,V5), P_unordered_pair-{F}(V3,V6,V5), P_ordered_pair-{F}(V6,V6,V7), P_ordered_pair-{F}(V4,V8,V9), P_ordered_pair-{F}(V10,V11,V9), pppp0-{F}(V10,V11,V12,V13), P_cartesian_product2-{F}(V1,V12,V14), P_cartesian_product2-{F}(V15,V16,V14), P_ordered_pair-{F}(V17,V16,V7) | FALSE
% 8.42/8.67 (used 0 times, uses = {})
% 8.42/8.67
% 8.42/8.67 #547: exists( #23, #541 ), references = 1, size of lhs = 7:
% 8.42/8.67 P_singleton-{F}(V0,V1), P_unordered_pair-{F}(V0,V2,V3), P_singleton-{F}(V4,V3), P_unordered_pair-{F}(V4,V5,V1), P_ordered_pair-{F}(V4,V5,V6), P_ordered_pair-{F}(V7,V8,V6), pppp0-{F}(V7,V8,V0,V9) | FALSE
% 8.42/8.67 (used 0 times, uses = {})
% 8.42/8.67
% 8.42/8.67 #558: exists( #21, #556 ), references = 1, size of lhs = 5:
% 8.42/8.67 P_singleton-{F}(V0,V1), P_singleton-{F}(V2,V1), P_unordered_pair-{F}(V2,V3,V4), P_unordered_pair-{F}(V0,V5,V4), pppp0-{F}(V2,V3,V6,V5) | FALSE
% 8.42/8.67 (used 0 times, uses = {})
% 8.42/8.67
% 8.42/8.67 #653: exists( #21, #649 ), references = 1, size of lhs = 16:
% 8.42/8.67 P_singleton-{F}(V0,V1), P_unordered_pair-{F}(V0,V2,V3), P_singleton-{F}(V4,V3), P_unordered_pair-{F}(V4,V5,V1), P_ordered_pair-{F}(V6,V6,V7), P_unordered_pair-{F}(V2,V6,V8), P_unordered_pair-{F}(V2,V9,V8), pppp0-{F}(V4,V5,V10,V11), P_cartesian_product2-{F}(V10,V11,V12), P_cartesian_product2-{F}(V13,V14,V12), P_ordered_pair-{F}(V9,V15,V16), P_ordered_pair-{F}(V17,V18,V16), pppp0-{F}(V17,V18,V19,V20), P_cartesian_product2-{F}(V14,V19,V21), P_ordered_pair-{F}(V22,V23,V7), P_cartesian_product2-{F}(V24,V23,V21) | FALSE
% 8.42/8.67 (used 0 times, uses = {})
% 8.42/8.67
% 8.42/8.67 #654: exists( #21, #650 ), references = 1, size of lhs = 18:
% 8.42/8.67 P_singleton-{F}(V0,V1), P_unordered_pair-{F}(V0,V2,V3), P_singleton-{F}(V4,V3), P_unordered_pair-{F}(V4,V5,V1), P_singleton-{F}(V2,V6), P_singleton-{F}(V7,V6), pppp0-{F}(V4,V5,V8,V9), P_cartesian_product2-{F}(V8,V9,V10), P_cartesian_product2-{F}(V11,V12,V10), P_unordered_pair-{F}(V2,V13,V14), P_unordered_pair-{F}(V7,V15,V14), P_ordered_pair-{F}(V15,V15,V16), P_ordered_pair-{F}(V13,V17,V18), P_ordered_pair-{F}(V19,V20,V18), pppp0-{F}(V19,V20,V21,V22), P_cartesian_product2-{F}(V12,V21,V23), P_ordered_pair-{F}(V24,V25,V16), P_cartesian_product2-{F}(V26,V25,V23) | FALSE
% 8.42/8.67 (used 0 times, uses = {})
% 8.42/8.67
% 8.42/8.67 #685: exists( #17, #681 ), references = 1, size of lhs = 8:
% 8.42/8.67 P_cartesian_product2-{F}(V0,V0,V1), P_cartesian_product2-{F}(V2,V3,V1), V2 == V0, P_cartesian_product2-{F}(V4,V4,V5), P_cartesian_product2-{F}(V6,V7,V5), V6 == V4, P_cartesian_product2-{F}(V6,V2,V8), P_cartesian_product2-{F}(V4,V9,V8) | FALSE
% 8.42/8.67 (used 0 times, uses = {})
% 8.42/8.67
% 8.42/8.67 #688: exists( #14, #686 ), references = 1, size of lhs = 5:
% 8.42/8.67 pppp4-{F}(V0), P_cartesian_product2-{F}(V0,V0,V1), P_cartesian_product2-{F}(V2,V3,V1), P_cartesian_product2-{F}(V4,V2,V1), P_cartesian_product2-{F}(V4,V5,V1) | pppp3-{T}(V0,V2), pppp3-{T}(V0,V4)
% 8.42/8.67 (used 0 times, uses = {})
% 8.42/8.67
% 8.42/8.67 #692: mergings( V1 == V5, V5 == V6; #689 ), references = 1, size of lhs = 5:
% 8.42/8.67 pppp4-{F}(V0), P_cartesian_product2-{F}(V0,V0,V1), P_cartesian_product2-{F}(V0,V2,V1), P_cartesian_product2-{F}(V3,V0,V1), P_cartesian_product2-{F}(V3,V4,V1) | pppp3-{T}(V0,V3)
% 8.42/8.67 (used 0 times, uses = {})
% 8.42/8.67
% 8.42/8.67 #695: exists( #23, #693 ), references = 1, size of lhs = 1:
% 8.42/8.67 pppp4-{F}(V0) | FALSE
% 8.42/8.67 (used 0 times, uses = {})
% 8.42/8.67
% 8.42/8.67 #697: exists( #13, #694 ), references = 1, size of lhs = 0:
% 8.42/8.67 FALSE | FALSE
% 8.42/8.67 (used 0 times, uses = {})
% 8.42/8.67
% 8.42/8.67 number of learnt formulas = 31
% 8.42/8.67
% 8.42/8.67
% 8.42/8.67 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.42/8.67
% 8.42/8.67 randbase = 1
%------------------------------------------------------------------------------