TSTP Solution File: GRA002+3 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : GRA002+3 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n010.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 06:02:46 EDT 2022
% Result : Theorem 1.15s 1.34s
% Output : Refutation 1.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRA002+3 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.03/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n010.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 : Fri Jul 22 07:43:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.15/1.34 GeoParameters:
% 1.15/1.34
% 1.15/1.34 tptp_input = 1
% 1.15/1.34 tptp_output = 0
% 1.15/1.34 nonempty = 1
% 1.15/1.34 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.15/1.34 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 1.15/1.34
% 1.15/1.34
% 1.15/1.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.15/1.34 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.15/1.34
% 1.15/1.34 RuleSystem INPUT:
% 1.15/1.34
% 1.15/1.34 Initial Rules:
% 1.15/1.34 #0: input, references = 3, size of lhs = 3:
% 1.15/1.34 P_head_of-{F}(V0,V2), P_tail_of-{F}(V0,V2), edge-{F}(V0) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #1: input, references = 3, size of lhs = 3:
% 1.15/1.34 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), edge-{F}(V0) | vertex-{T}(V1)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #2: input, references = 3, size of lhs = 3:
% 1.15/1.34 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), edge-{F}(V0) | vertex-{T}(V2)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #3: input, references = 3, size of lhs = 4:
% 1.15/1.34 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0 | EXISTS V2: pppp9-{T}(V1,V0,V2)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #4: input, references = 3, size of lhs = 1:
% 1.15/1.34 pppp9-{F}(V0,V1,V2) | pppp8-{T}(V2,V0,V1)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #5: input, references = 3, size of lhs = 3:
% 1.15/1.34 pppp8-{F}(V0,V1,V2), pppp1-{F}(V0,V1,V2), pppp0-{F}(V0,V1,V2) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #6: input, references = 3, size of lhs = 1:
% 1.15/1.34 pppp8-{F}(V0,V1,V2) | pppp0-{T}(V0,V1,V2), pppp1-{T}(V0,V1,V2)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #7: input, references = 3, size of lhs = 1:
% 1.15/1.34 pppp8-{F}(V0,V1,V2) | edge-{T}(V0)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #8: input, references = 3, size of lhs = 4:
% 1.15/1.34 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp1-{F}(V0,V1,V2), V2 == V3 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #9: input, references = 3, size of lhs = 4:
% 1.15/1.34 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp1-{F}(V0,V1,V2), V1 == V4 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #10: input, references = 3, size of lhs = 2:
% 1.15/1.34 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | pppp1-{T}(V0,V4,V3)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #11: input, references = 3, size of lhs = 4:
% 1.15/1.34 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp0-{F}(V0,V1,V2), V1 == V3 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #12: input, references = 4, size of lhs = 4:
% 1.15/1.34 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp0-{F}(V0,V1,V2), V2 == V4 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #13: input, references = 3, size of lhs = 2:
% 1.15/1.34 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | pppp0-{T}(V0,V3,V4)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #14: input, references = 3, size of lhs = 7:
% 1.15/1.34 P_empty-{F}(V0), vertex-{F}(V6), vertex-{F}(V5), P_tail_of-{F}(V4,V5), P_head_of-{F}(V4,V6), P_path_cons-{F}(V4,V0,V7), edge-{F}(V4) | path-{T}(V5,V6,V7)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #15: input, references = 3, size of lhs = 9:
% 1.15/1.34 P_empty-{F}(V0), vertex-{F}(V1), vertex-{F}(V5), P_tail_of-{F}(V4,V5), P_head_of-{F}(V4,V6), P_path_cons-{F}(V4,V0,V7), edge-{F}(V4), P_path_cons-{F}(V4,V8,V9), path-{F}(V6,V1,V8) | path-{T}(V5,V1,V9)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #16: input, references = 3, size of lhs = 2:
% 1.15/1.34 P_empty-{F}(V0), path-{F}(V1,V2,V3) | vertex-{T}(V1)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #17: input, references = 3, size of lhs = 2:
% 1.15/1.34 P_empty-{F}(V0), path-{F}(V1,V2,V3) | vertex-{T}(V2)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #18: input, references = 3, size of lhs = 2:
% 1.15/1.34 P_empty-{F}(V0), path-{F}(V1,V2,V3) | EXISTS V4: pppp11-{T}(V1,V2,V3,V4)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #19: input, references = 4, size of lhs = 2:
% 1.15/1.34 pppp11-{F}(V0,V1,V2,V3), P_tail_of-{F}(V3,V4) | pppp10-{T}(V3,V0,V1,V2,V4)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #20: input, references = 3, size of lhs = 3:
% 1.15/1.34 pppp10-{F}(V0,V1,V2,V3,V4), pppp3-{F}(V0,V2,V3), pppp2-{F}(V0,V2,V3) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #21: input, references = 3, size of lhs = 1:
% 1.15/1.34 pppp10-{F}(V0,V1,V2,V3,V4) | pppp2-{T}(V0,V2,V3), pppp3-{T}(V0,V2,V3)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #22: input, references = 4, size of lhs = 2:
% 1.15/1.34 pppp10-{F}(V0,V1,V2,V3,V4), V1 == V4 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #23: input, references = 3, size of lhs = 1:
% 1.15/1.34 pppp10-{F}(V0,V1,V2,V3,V4) | edge-{T}(V0)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #24: input, references = 3, size of lhs = 3:
% 1.15/1.34 P_empty-{F}(V0), P_head_of-{F}(V1,V4), pppp3-{F}(V1,V2,V3) | EXISTS V5: pppp12-{T}(V1,V2,V3,V5,V4)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #25: input, references = 3, size of lhs = 4:
% 1.15/1.34 P_empty-{F}(V0), P_head_of-{F}(V1,V4), P_path_cons-{F}(V1,V5,V6), path-{F}(V4,V2,V5) | pppp3-{T}(V1,V2,V6)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #26: input, references = 3, size of lhs = 3:
% 1.15/1.34 pppp12-{F}(V0,V1,V2,V3,V4), P_path_cons-{F}(V0,V3,V5), V2 == V5 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #27: input, references = 3, size of lhs = 2:
% 1.15/1.34 pppp12-{F}(V0,V1,V2,V3,V4), P_path_cons-{F}(V0,V3,V5) | path-{T}(V4,V1,V3)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #28: input, references = 4, size of lhs = 5:
% 1.15/1.34 P_empty-{F}(V0), P_head_of-{F}(V1,V4), P_path_cons-{F}(V1,V0,V5), pppp2-{F}(V1,V2,V3), V2 == V4 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #29: input, references = 4, size of lhs = 5:
% 1.15/1.34 P_empty-{F}(V0), P_head_of-{F}(V1,V4), P_path_cons-{F}(V1,V0,V5), pppp2-{F}(V1,V2,V3), V3 == V5 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #30: input, references = 3, size of lhs = 3:
% 1.15/1.34 P_empty-{F}(V0), P_head_of-{F}(V1,V4), P_path_cons-{F}(V1,V0,V5) | pppp2-{T}(V1,V4,V5)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #31: input, references = 3, size of lhs = 5:
% 1.15/1.34 P_empty-{F}(V0), path-{F}(V3,V2,V1), P_head_of-{F}(V4,V5), P_tail_of-{F}(V4,V6), on_path-{F}(V4,V1) | edge-{T}(V4)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #32: input, references = 3, size of lhs = 5:
% 1.15/1.34 P_empty-{F}(V0), path-{F}(V3,V2,V1), P_head_of-{F}(V4,V5), P_tail_of-{F}(V4,V6), on_path-{F}(V4,V1) | in_path-{T}(V5,V1)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #33: input, references = 3, size of lhs = 5:
% 1.15/1.34 P_empty-{F}(V0), path-{F}(V3,V2,V1), P_head_of-{F}(V4,V5), P_tail_of-{F}(V4,V6), on_path-{F}(V4,V1) | in_path-{T}(V6,V1)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #34: input, references = 3, size of lhs = 3:
% 1.15/1.34 P_empty-{F}(V0), path-{F}(V3,V2,V1), in_path-{F}(V4,V1) | vertex-{T}(V4)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #35: input, references = 3, size of lhs = 3:
% 1.15/1.34 P_empty-{F}(V0), path-{F}(V3,V2,V1), in_path-{F}(V4,V1) | EXISTS V5: pppp13-{T}(V5,V1,V4)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #36: input, references = 4, size of lhs = 5:
% 1.15/1.34 pppp13-{F}(V0,V1,V2), P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), V2 == V3, V2 == V4 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #37: input, references = 3, size of lhs = 3:
% 1.15/1.34 pppp13-{F}(V0,V1,V2), P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | on_path-{T}(V0,V1)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #38: input, references = 3, size of lhs = 2:
% 1.15/1.34 P_empty-{F}(V0), sequential-{F}(V1,V2) | pppp4-{T}(V1,V2)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #39: input, references = 3, size of lhs = 2:
% 1.15/1.34 P_empty-{F}(V0), pppp4-{F}(V1,V2) | sequential-{T}(V1,V2)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #40: input, references = 3, size of lhs = 3:
% 1.15/1.34 P_empty-{F}(V0), P_head_of-{F}(V1,V3), P_tail_of-{F}(V2,V4) | pppp14-{T}(V1,V2,V3,V4)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #41: input, references = 3, size of lhs = 4:
% 1.15/1.34 pppp14-{F}(V0,V1,V3,V3), edge-{F}(V0), edge-{F}(V1), V0 == V1 | pppp4-{T}(V0,V1)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #42: input, references = 3, size of lhs = 3:
% 1.15/1.34 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1), V2 == V3 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #43: input, references = 3, size of lhs = 2:
% 1.15/1.34 pppp14-{F}(V1,V1,V2,V3), pppp4-{F}(V1,V1) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #44: input, references = 3, size of lhs = 2:
% 1.15/1.34 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1) | edge-{T}(V1)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #45: input, references = 3, size of lhs = 2:
% 1.15/1.34 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1) | edge-{T}(V0)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #46: input, references = 4, size of lhs = 5:
% 1.15/1.34 P_empty-{F}(V0), on_path-{F}(V2,V1), on_path-{F}(V3,V1), sequential-{F}(V3,V2), path-{F}(V5,V4,V1) | precedes-{T}(V3,V2,V1)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #47: input, references = 3, size of lhs = 6:
% 1.15/1.34 P_empty-{F}(V0), on_path-{F}(V2,V1), on_path-{F}(V3,V1), sequential-{F}(V3,V4), precedes-{F}(V4,V2,V1), path-{F}(V6,V5,V1) | precedes-{T}(V3,V2,V1)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #48: input, references = 3, size of lhs = 3:
% 1.15/1.34 P_empty-{F}(V0), precedes-{F}(V2,V3,V1), path-{F}(V5,V4,V1) | pppp15-{T}(V1,V2,V3)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #49: input, references = 3, size of lhs = 3:
% 1.15/1.34 pppp15-{F}(V0,V1,V2), pppp5-{F}(V0,V1,V2), sequential-{F}(V1,V2) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #50: input, references = 3, size of lhs = 1:
% 1.15/1.34 pppp15-{F}(V0,V1,V2) | sequential-{T}(V1,V2), pppp5-{T}(V0,V1,V2)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #51: input, references = 3, size of lhs = 1:
% 1.15/1.34 pppp15-{F}(V0,V1,V2) | on_path-{T}(V2,V0)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #52: input, references = 3, size of lhs = 1:
% 1.15/1.34 pppp15-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #53: input, references = 3, size of lhs = 2:
% 1.15/1.34 P_empty-{F}(V0), pppp5-{F}(V1,V2,V3) | EXISTS V4: pppp16-{T}(V1,V2,V3,V4)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #54: input, references = 3, size of lhs = 3:
% 1.15/1.34 P_empty-{F}(V0), sequential-{F}(V2,V4), precedes-{F}(V4,V3,V1) | pppp5-{T}(V1,V2,V3)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #55: input, references = 3, size of lhs = 1:
% 1.15/1.34 pppp16-{F}(V0,V1,V2,V3) | precedes-{T}(V3,V2,V0)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #56: input, references = 3, size of lhs = 1:
% 1.15/1.34 pppp16-{F}(V0,V1,V2,V3) | sequential-{T}(V1,V3)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #57: input, references = 6, size of lhs = 2:
% 1.15/1.34 P_empty-{F}(V0), shortest_path-{F}(V1,V2,V3) | pppp6-{T}(V1,V2,V3)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #58: input, references = 3, size of lhs = 2:
% 1.15/1.34 P_empty-{F}(V0), pppp6-{F}(V1,V2,V3) | shortest_path-{T}(V1,V2,V3)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #59: input, references = 6, size of lhs = 3:
% 1.15/1.34 P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V1,V2,V3) | path-{T}(V1,V2,V3)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #60: input, references = 3, size of lhs = 3:
% 1.15/1.34 P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V2,V2,V3) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #61: input, references = 3, size of lhs = 5:
% 1.15/1.34 P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V1,V2,V3), P_length_of-{F}(V5,V6), path-{F}(V1,V2,V5) | less_or_equal-{T}(V4,V6)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #62: input, references = 3, size of lhs = 4:
% 1.15/1.34 P_empty-{F}(V0), P_length_of-{F}(V3,V4), path-{F}(V1,V2,V3), V1 == V2 | pppp6-{T}(V1,V2,V3), pppp25-{T}(V1,V2,V4)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #63: input, references = 3, size of lhs = 1:
% 1.15/1.34 pppp25-{F}(V0,V1,V2) | EXISTS V3: pppp17-{T}(V0,V1,V3,V2)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #64: input, references = 3, size of lhs = 3:
% 1.15/1.34 pppp17-{F}(V0,V1,V2,V3), P_length_of-{F}(V2,V4), less_or_equal-{F}(V3,V4) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #65: input, references = 3, size of lhs = 2:
% 1.15/1.34 pppp17-{F}(V0,V1,V2,V3), P_length_of-{F}(V2,V4) | path-{T}(V0,V1,V2)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #66: input, references = 4, size of lhs = 7:
% 1.15/1.34 P_empty-{F}(V0), shortest_path-{F}(V3,V2,V1), P_tail_of-{F}(V5,V6), P_head_of-{F}(V4,V7), precedes-{F}(V5,V4,V1), P_tail_of-{F}(V8,V6), P_head_of-{F}(V8,V7) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #67: input, references = 3, size of lhs = 6:
% 1.15/1.34 P_empty-{F}(V0), shortest_path-{F}(V3,V2,V1), P_tail_of-{F}(V5,V6), P_head_of-{F}(V4,V7), precedes-{F}(V5,V4,V1), precedes-{F}(V4,V5,V1) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #68: input, references = 3, size of lhs = 2:
% 1.15/1.34 P_empty-{F}(V0), triangle-{F}(V1,V2,V3) | pppp7-{T}(V1,V2,V3)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #69: input, references = 3, size of lhs = 2:
% 1.15/1.34 P_empty-{F}(V0), pppp7-{F}(V1,V2,V3) | triangle-{T}(V1,V2,V3)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #70: input, references = 3, size of lhs = 2:
% 1.15/1.34 P_empty-{F}(V0), pppp7-{F}(V1,V2,V3) | pppp18-{T}(V1,V2,V3)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #71: input, references = 3, size of lhs = 7:
% 1.15/1.34 P_empty-{F}(V0), edge-{F}(V1), edge-{F}(V2), edge-{F}(V3), sequential-{F}(V1,V2), sequential-{F}(V2,V3), sequential-{F}(V3,V1) | pppp7-{T}(V1,V2,V3)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #72: input, references = 3, size of lhs = 1:
% 1.15/1.34 pppp18-{F}(V0,V1,V2) | sequential-{T}(V2,V0)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #73: input, references = 3, size of lhs = 1:
% 1.15/1.34 pppp18-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #74: input, references = 3, size of lhs = 1:
% 1.15/1.34 pppp18-{F}(V0,V1,V2) | sequential-{T}(V0,V1)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #75: input, references = 3, size of lhs = 1:
% 1.15/1.34 pppp18-{F}(V0,V1,V2) | edge-{T}(V2)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #76: input, references = 3, size of lhs = 1:
% 1.15/1.34 pppp18-{F}(V0,V1,V2) | edge-{T}(V1)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #77: input, references = 3, size of lhs = 1:
% 1.15/1.34 pppp18-{F}(V0,V1,V2) | edge-{T}(V0)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #78: input, references = 4, size of lhs = 6:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), P_number_of_in-{F}(V1,V2,V4), path-{F}(V6,V5,V2), V3 == V4 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #79: input, references = 4, size of lhs = 9:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_number_of_in-{F}(V2,V4,V5), P_length_of-{F}(V4,V6), P_minus-{F}(V6,V3,V7), path-{F}(V9,V8,V4), V5 == V7 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #80: input, references = 4, size of lhs = 9:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_number_of_in-{F}(V2,V5,V6), P_number_of_in-{F}(V4,V5,V7), path-{F}(V10,V9,V5), V6 == V7 | EXISTS V8: pppp20-{T}(V5,V8)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #81: input, references = 4, size of lhs = 1:
% 1.15/1.34 pppp20-{F}(V0,V1) | EXISTS V2: pppp19-{T}(V0,V2,V1)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #82: input, references = 4, size of lhs = 1:
% 1.15/1.34 pppp20-{F}(V0,V1) | on_path-{T}(V1,V0)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #83: input, references = 4, size of lhs = 2:
% 1.15/1.34 pppp19-{F}(V0,V1,V2), triangle-{F}(V1,V2,V3) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #84: input, references = 4, size of lhs = 1:
% 1.15/1.34 pppp19-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #85: input, references = 4, size of lhs = 1:
% 1.15/1.34 pppp19-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #86: input, references = 5, size of lhs = 8:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_graph-{F}(V5), P_number_of_in-{F}(V6,V7,V8), P_number_of_in-{F}(V6,V5,V9) | less_or_equal-{T}(V8,V9)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #87: input, references = 4, size of lhs = 10:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_graph-{F}(V5), complete-{F}(), sequential-{F}(V6,V7), precedes-{F}(V6,V7,V9), shortest_path-{F}(V11,V10,V9) | EXISTS V8: pppp21-{T}(V6,V7,V8)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #88: input, references = 4, size of lhs = 1:
% 1.15/1.34 pppp21-{F}(V0,V1,V2) | triangle-{T}(V0,V1,V2)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #89: input, references = 5, size of lhs = 7:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_graph-{F}(V5), P_number_of_in-{F}(V4,V5,V6) | complete-{T}()
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #90: input, references = 5, size of lhs = 7:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_graph-{F}(V5), P_number_of_in-{F}(V4,V5,V6) | EXISTS V7: pppp24-{T}(V7,V3,V6)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #91: input, references = 6, size of lhs = 3:
% 1.15/1.34 pppp24-{F}(V0,V1,V2), P_length_of-{F}(V0,V3), P_minus-{F}(V3,V1,V4) | EXISTS V5: pppp23-{T}(V0,V5)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #92: input, references = 5, size of lhs = 4:
% 1.15/1.34 pppp24-{F}(V0,V1,V2), P_length_of-{F}(V0,V3), P_minus-{F}(V3,V1,V4), less_or_equal-{F}(V4,V2) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #93: input, references = 6, size of lhs = 1:
% 1.15/1.34 pppp23-{F}(V0,V1) | EXISTS V2: pppp22-{T}(V1,V0,V2)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #94: input, references = 6, size of lhs = 1:
% 1.15/1.34 pppp22-{F}(V0,V1,V2) | shortest_path-{T}(V2,V0,V1)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #95: input, references = 5, size of lhs = 1:
% 1.15/1.34 #-{F} V0 | EXISTS V1: P_head_of-{T}(V0,V1)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #96: input, references = 6, size of lhs = 1:
% 1.15/1.34 #-{F} V0 | EXISTS V1: P_tail_of-{T}(V0,V1)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #97: input, references = 4, size of lhs = 2:
% 1.15/1.34 #-{F} V0, #-{F} V1 | EXISTS V2: P_path_cons-{T}(V0,V1,V2)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #98: input, references = 4, size of lhs = 0:
% 1.15/1.34 FALSE | EXISTS V0: P_empty-{T}(V0)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #99: input, references = 5, size of lhs = 1:
% 1.15/1.34 #-{F} V0 | EXISTS V1: P_length_of-{T}(V0,V1)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #100: input, references = 10, size of lhs = 2:
% 1.15/1.34 #-{F} V0, #-{F} V1 | EXISTS V2: P_number_of_in-{T}(V0,V1,V2)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #101: input, references = 4, size of lhs = 0:
% 1.15/1.34 FALSE | EXISTS V0: P_edges-{T}(V0)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #102: input, references = 4, size of lhs = 0:
% 1.15/1.34 FALSE | EXISTS V0: P_sequential_pairs-{T}(V0)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #103: input, references = 4, size of lhs = 2:
% 1.15/1.34 #-{F} V0, #-{F} V1 | EXISTS V2: P_minus-{T}(V0,V1,V2)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #104: input, references = 5, size of lhs = 0:
% 1.15/1.34 FALSE | EXISTS V0: P_n1-{T}(V0)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #105: input, references = 5, size of lhs = 0:
% 1.15/1.34 FALSE | EXISTS V0: P_triangles-{T}(V0)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #106: input, references = 5, size of lhs = 0:
% 1.15/1.34 FALSE | EXISTS V0: P_graph-{T}(V0)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 number of initial rules = 107
% 1.15/1.34
% 1.15/1.34 Simplifiers:
% 1.15/1.34 #107: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 P_head_of-{F}(V0,V1), P_head_of-{F}(V0,V3), V1 == V3 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #108: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 P_tail_of-{F}(V0,V1), P_tail_of-{F}(V0,V3), V1 == V3 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #109: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 P_path_cons-{F}(V0,V1,V2), P_path_cons-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #110: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 P_empty-{F}(V0), P_empty-{F}(V1), V0 == V1 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #111: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 P_length_of-{F}(V0,V1), P_length_of-{F}(V0,V3), V1 == V3 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #112: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 P_number_of_in-{F}(V0,V1,V2), P_number_of_in-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #113: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 P_edges-{F}(V0), P_edges-{F}(V1), V0 == V1 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #114: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 P_sequential_pairs-{F}(V0), P_sequential_pairs-{F}(V1), V0 == V1 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #115: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 P_minus-{F}(V0,V1,V2), P_minus-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #116: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 P_n1-{F}(V0), P_n1-{F}(V1), V0 == V1 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #117: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 P_triangles-{F}(V0), P_triangles-{F}(V1), V0 == V1 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #118: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 P_graph-{F}(V0), P_graph-{F}(V1), V0 == V1 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #119: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp8-{F}(V0,V1,V2), pppp8-{F}(V3,V1,V2), V0 == V3 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #120: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp9-{F}(V0,V1,V2), pppp9-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #121: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V5,V1,V2,V3,V9), V0 == V5 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #122: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #123: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp11-{F}(V0,V1,V2,V3), pppp11-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #124: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V1,V2,V8,V4), V3 == V8 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #125: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #126: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp13-{F}(V0,V1,V2), pppp13-{F}(V3,V1,V2), V0 == V3 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #127: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp14-{F}(V0,V1,V2,V3), pppp14-{F}(V0,V5,V6,V7), V2 == V6 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #128: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp14-{F}(V0,V1,V2,V3), pppp14-{F}(V4,V1,V6,V7), V3 == V7 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #129: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp16-{F}(V0,V1,V2,V3), pppp16-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #130: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp17-{F}(V0,V1,V2,V3), pppp17-{F}(V0,V1,V6,V3), V2 == V6 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #131: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp19-{F}(V0,V1,V2), pppp19-{F}(V0,V4,V2), V1 == V4 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #132: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp19-{F}(V0,V1,V2), pppp19-{F}(V0,V4,V5), V2 == V5 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #133: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp20-{F}(V0,V1), pppp20-{F}(V0,V3), V1 == V3 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #134: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp21-{F}(V0,V1,V2), pppp21-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #135: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp22-{F}(V0,V1,V2), pppp22-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #136: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp22-{F}(V0,V1,V2), pppp22-{F}(V3,V1,V5), V0 == V3 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #137: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp23-{F}(V0,V1), pppp23-{F}(V0,V3), V1 == V3 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #138: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp24-{F}(V0,V1,V2), pppp24-{F}(V3,V1,V2), V0 == V3 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #139: unsound, references = 3, size of lhs = 3:
% 1.15/1.34 pppp24-{F}(V0,V1,V2), pppp24-{F}(V3,V4,V5), V1 == V4 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 number of simplifiers = 33
% 1.15/1.34
% 1.15/1.34 Learnt:
% 1.15/1.34 #148: mergings( V3 == V4, V4 == V5, V7 == V8; #144 ), references = 1, size of lhs = 6:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), pppp23-{F}(V2,V3), P_length_of-{F}(V2,V4), P_number_of_in-{F}(V1,V2,V5), V4 == V5 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #154: mergings( V6 == V7, V7 == V8, V3 == V10, V10 == V11; #149 ), references = 2, size of lhs = 7:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), P_number_of_in-{F}(V1,V2,V4), V3 == V4, pppp24-{F}(V2,V5,V6), P_minus-{F}(V3,V5,V7) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #160: mergings( V3 == V4, V4 == V5, V6 == V7, V7 == V8; #155 ), references = 1, size of lhs = 5:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), pppp24-{F}(V2,V4,V5), P_minus-{F}(V3,V4,V6) | P_number_of_in-{T}(V1,V2,V3)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #171: mergings( V3 == V4, V4 == V5, V9 == V11; #167 ), references = 1, size of lhs = 9:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp23-{F}(V4,V5), P_number_of_in-{F}(V2,V4,V6), P_length_of-{F}(V4,V7), P_minus-{F}(V7,V3,V8), V6 == V8 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #177: mergings( V6 == V7, V7 == V8, V3 == V12, V12 == V14; #172 ), references = 2, size of lhs = 10:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_number_of_in-{F}(V2,V4,V5), P_length_of-{F}(V4,V6), P_minus-{F}(V6,V3,V7), V5 == V7, pppp24-{F}(V4,V8,V9), P_minus-{F}(V6,V8,V10) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #181: exists( #103, #154 ), references = 1, size of lhs = 6:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), P_number_of_in-{F}(V1,V2,V4), V3 == V4, pppp24-{F}(V2,V5,V6) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #182: exists( #103, #177 ), references = 4, size of lhs = 7:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_number_of_in-{F}(V2,V4,V5), P_length_of-{F}(V4,V6), pppp24-{F}(V4,V3,V7) | P_minus-{T}(V6,V3,V5)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #184: exists( #100, #179 ), references = 1, size of lhs = 4:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), pppp24-{F}(V2,V4,V5) | P_number_of_in-{T}(V1,V2,V3)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #203: exists( #96, #201 ), references = 1, size of lhs = 1:
% 1.15/1.34 pppp11-{F}(V0,V1,V2,V3) | P_tail_of-{T}(V3,V0)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #224: exists( #97, #28 ), references = 1, size of lhs = 4:
% 1.15/1.34 P_empty-{F}(V0), P_head_of-{F}(V1,V2), pppp2-{F}(V1,V3,V4), V3 == V2 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #226: mergings( V4 == V3; #223 ), references = 1, size of lhs = 3:
% 1.15/1.34 P_empty-{F}(V0), P_head_of-{F}(V1,V2), pppp2-{F}(V1,V2,V3) | P_path_cons-{T}(V1,V0,V3)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #228: exists( #95, #222 ), references = 1, size of lhs = 2:
% 1.15/1.34 P_empty-{F}(V0), pppp2-{F}(V1,V2,V3) | P_head_of-{T}(V1,V2)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #230: exists( #96, #12 ), references = 1, size of lhs = 2:
% 1.15/1.34 P_head_of-{F}(V0,V1), pppp0-{F}(V0,V2,V3) | P_tail_of-{T}(V0,V3)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #244: exists( #96, #36 ), references = 1, size of lhs = 3:
% 1.15/1.34 P_head_of-{F}(V0,V1), pppp13-{F}(V0,V2,V3), V3 == V1 | P_tail_of-{T}(V0,V3)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #247: exists( #95, #245 ), references = 1, size of lhs = 7:
% 1.15/1.34 P_empty-{F}(V0), P_tail_of-{F}(V1,V2), P_head_of-{F}(V1,V3), P_head_of-{F}(V4,V3), pppp13-{F}(V5,V6,V2), precedes-{F}(V5,V4,V7), shortest_path-{F}(V8,V9,V7) | P_head_of-{T}(V5,V2)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #255: exists( #87, #253 ), references = 1, size of lhs = 11:
% 1.15/1.34 complete-{F}(), P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_graph-{F}(V5), sequential-{F}(V6,V7), precedes-{F}(V6,V7,V8), pppp19-{F}(V9,V6,V7), shortest_path-{F}(V10,V11,V8) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #261: mergings( V3 == V4; #259 ), references = 1, size of lhs = 11:
% 1.15/1.34 complete-{F}(), P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_graph-{F}(V5), on_path-{F}(V6,V7), pppp20-{F}(V7,V6), path-{F}(V8,V9,V7), shortest_path-{F}(V10,V11,V7) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #270: mergings( V0 == V11, V11 == V12, V1 == V13, V2 == V14, V3 == V15, V4 == V16; #263 ), references = 1, size of lhs = 13:
% 1.15/1.34 complete-{F}(), P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_graph-{F}(V5), P_number_of_in-{F}(V2,V6,V7), P_number_of_in-{F}(V4,V6,V8), V7 == V8, path-{F}(V9,V10,V6), path-{F}(V11,V12,V6), shortest_path-{F}(V13,V14,V6) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #283: mergings( V3 == V4, V4 == V5, V5 == V10, V10 == V11, V6 == V12, V7 == V13, V8 == V14, V9 == V15; #274 ), references = 1, size of lhs = 12:
% 1.15/1.34 complete-{F}(), P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_graph-{F}(V5), pppp23-{F}(V6,V7), P_length_of-{F}(V6,V8), P_number_of_in-{F}(V2,V6,V9), P_number_of_in-{F}(V4,V6,V10), V9 == V10 | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #294: mergings( V6 == V7, V7 == V8, V8 == V13, V13 == V14, V3 == V20, V9 == V15, V10 == V16, V11 == V17, V12 == V18; #284 ), references = 2, size of lhs = 13:
% 1.15/1.34 complete-{F}(), P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_graph-{F}(V5), P_length_of-{F}(V6,V7), P_number_of_in-{F}(V2,V6,V8), P_number_of_in-{F}(V4,V6,V9), V8 == V9, pppp24-{F}(V6,V10,V11), P_minus-{F}(V7,V10,V12) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #305: mergings( V3 == V4, V4 == V5, V5 == V9, V9 == V10, V16 == V17, V6 == V11, V7 == V12, V8 == V13, V0 == V14; #295 ), references = 1, size of lhs = 11:
% 1.15/1.34 complete-{F}(), P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_graph-{F}(V5), P_length_of-{F}(V6,V7), P_number_of_in-{F}(V2,V6,V8), pppp24-{F}(V6,V9,V10), P_minus-{F}(V7,V9,V11) | P_number_of_in-{T}(V4,V6,V8)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #331: mergings( V2 == V4, V4 == V7, V7 == V8, V8 == V9, V9 == V13, V13 == V14, V14 == V20, V3 == V5, V5 == V10, V10 == V15, V15 == V21, V21 == V16, V16 == V22, V6 == V11, V11 == V17, V17 == V23, V12 == V18, V18 == V24, V19 == V25, V23 == V29; #310 ), references = 1, size of lhs = 12:
% 1.15/1.34 complete-{F}(), P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_graph-{F}(V4), P_number_of_in-{F}(V3,V4,V5), pppp24-{F}(V6,V2,V5), pppp24-{F}(V6,V2,V7), pppp24-{F}(V6,V2,V8), pppp24-{F}(V6,V2,V9) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #357: mergings( V0 == V8, V8 == V10, V10 == V12, V12 == V13, V13 == V14, V14 == V18, V18 == V19, V19 == V25, V1 == V9, V9 == V11, V11 == V15, V15 == V20, V20 == V26, V2 == V26, V26 == V21, V21 == V27, V3 == V16, V16 == V22, V22 == V28, V4 == V17, V17 == V23, V23 == V29, V5 == V24, V24 == V30; #332 ), references = 1, size of lhs = 8:
% 1.15/1.34 complete-{F}(), P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_graph-{F}(V4), P_number_of_in-{F}(V3,V4,V5) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #386: mergings( V3 == V7, V7 == V10, V10 == V12, V12 == V15, V15 == V16, V16 == V17, V17 == V20, V20 == V21, V21 == V27, V4 == V8, V8 == V11, V11 == V13, V13 == V18, V18 == V22, V22 == V28, V5 == V9, V9 == V28, V28 == V23, V23 == V29, V6 == V14, V14 == V19, V19 == V24, V24 == V30, V0 == V25, V25 == V31, V26 == V1; #359 ), references = 1, size of lhs = 6:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_graph-{F}(V4) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #413: mergings( V1 == V5, V5 == V8, V8 == V10, V10 == V13, V13 == V14, V14 == V15, V15 == V19, V19 == V20, V20 == V25, V2 == V6, V6 == V9, V9 == V11, V11 == V16, V16 == V21, V21 == V26, V3 == V7, V7 == V26, V26 == V22, V22 == V27, V4 == V12, V12 == V17, V17 == V23, V23 == V28, V18 == V24, V24 == V29; #387 ), references = 1, size of lhs = 5:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #438: mergings( V1 == V5, V5 == V8, V8 == V10, V10 == V13, V13 == V14, V14 == V15, V15 == V18, V18 == V19, V19 == V23, V2 == V6, V6 == V9, V9 == V11, V11 == V16, V16 == V20, V20 == V24, V3 == V7, V7 == V24, V24 == V21, V21 == V25, V4 == V12, V12 == V17, V17 == V22, V22 == V26; #414 ), references = 1, size of lhs = 4:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V1), P_n1-{F}(V2) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #459: mergings( V1 == V4, V4 == V7, V7 == V9, V9 == V11, V11 == V12, V12 == V13, V13 == V15, V15 == V16, V16 == V19, V2 == V5, V5 == V8, V8 == V10, V10 == V14, V14 == V17, V17 == V20, V3 == V6, V6 == V20, V20 == V18, V18 == V21; #439 ), references = 1, size of lhs = 3:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V1) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #465: mergings( V3 == V6, V4 == V7, V5 == V8; #461 ), references = 2, size of lhs = 11:
% 1.15/1.34 complete-{F}(), P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_graph-{F}(V5), pppp24-{F}(V6,V3,V7), P_length_of-{F}(V6,V8), P_number_of_in-{F}(V4,V6,V9), pppp24-{F}(V6,V3,V10) | P_number_of_in-{T}(V2,V6,V9)
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #482: mergings( V3 == V9, V9 == V13, V19 == V21, V4 == V10, V10 == V14, V5 == V15, V6 == V11, V11 == V16, V7 == V0, V8 == V12; #471 ), references = 1, size of lhs = 14:
% 1.15/1.34 complete-{F}(), P_triangles-{F}(V0), P_graph-{F}(V1), P_empty-{F}(V2), P_edges-{F}(V3), P_sequential_pairs-{F}(V4), P_n1-{F}(V5), P_number_of_in-{F}(V0,V1,V6), pppp24-{F}(V7,V5,V6), P_length_of-{F}(V7,V8), P_length_of-{F}(V9,V8), pppp24-{F}(V9,V5,V10), pppp24-{F}(V9,V5,V11), pppp24-{F}(V9,V5,V12) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #493: mergings( V2 == V8, V8 == V13, V3 == V9, V9 == V14, V4 == V15, V5 == V10, V10 == V16, V6 == V11, V7 == V12; #483 ), references = 1, size of lhs = 12:
% 1.15/1.34 complete-{F}(), P_triangles-{F}(V0), P_graph-{F}(V1), P_empty-{F}(V2), P_edges-{F}(V3), P_sequential_pairs-{F}(V4), P_n1-{F}(V5), P_number_of_in-{F}(V0,V1,V6), pppp24-{F}(V7,V5,V6), pppp24-{F}(V7,V5,V8), pppp24-{F}(V7,V5,V9), pppp24-{F}(V7,V5,V10) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #508: mergings( V0 == V8, V8 == V14, V14 == V18, V1 == V9, V9 == V15, V15 == V19, V2 == V10, V10 == V20, V11 == V3, V4 == V12, V12 == V16, V5 == V13, V13 == V17; #494 ), references = 1, size of lhs = 8:
% 1.15/1.34 complete-{F}(), P_triangles-{F}(V0), P_graph-{F}(V1), P_number_of_in-{F}(V0,V1,V2), P_empty-{F}(V3), P_edges-{F}(V4), P_sequential_pairs-{F}(V5), P_n1-{F}(V6) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #526: mergings( V3 == V7, V7 == V10, V10 == V15, V15 == V18, V4 == V8, V8 == V11, V11 == V16, V16 == V19, V5 == V9, V9 == V12, V12 == V20, V6 == V13, V13 == V21, V14 == V0, V1 == V17; #510 ), references = 1, size of lhs = 6:
% 1.15/1.34 P_triangles-{F}(V0), P_graph-{F}(V1), P_empty-{F}(V2), P_edges-{F}(V3), P_sequential_pairs-{F}(V4), P_n1-{F}(V5) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #542: mergings( V1 == V5, V5 == V8, V8 == V13, V13 == V16, V2 == V6, V6 == V9, V9 == V14, V14 == V17, V3 == V7, V7 == V10, V10 == V18, V4 == V11, V11 == V19, V12 == V15; #527 ), references = 1, size of lhs = 5:
% 1.15/1.34 P_triangles-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #557: mergings( V1 == V5, V5 == V8, V8 == V12, V12 == V14, V2 == V6, V6 == V9, V9 == V13, V13 == V15, V3 == V7, V7 == V10, V10 == V16, V4 == V11, V11 == V17; #543 ), references = 1, size of lhs = 4:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #570: mergings( V1 == V4, V4 == V7, V7 == V10, V10 == V12, V2 == V5, V5 == V8, V8 == V11, V11 == V13, V3 == V6, V6 == V9, V9 == V14; #558 ), references = 1, size of lhs = 3:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #580: mergings( V1 == V3, V3 == V5, V5 == V7, V7 == V9, V2 == V4, V4 == V6, V6 == V8, V8 == V10; #571 ), references = 1, size of lhs = 2:
% 1.15/1.34 P_empty-{F}(V0), P_edges-{F}(V1) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #586: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5; #581 ), references = 1, size of lhs = 1:
% 1.15/1.34 P_empty-{F}(V0) | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 #588: exists( #98, #581 ), references = 1, size of lhs = 0:
% 1.15/1.34 FALSE | FALSE
% 1.15/1.34 (used 0 times, uses = {})
% 1.15/1.34
% 1.15/1.34 number of learnt formulas = 38
% 1.15/1.34
% 1.15/1.34
% 1.15/1.34 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.15/1.34
% 1.15/1.34 randbase = 1
%------------------------------------------------------------------------------