TSTP Solution File: GRA009+2 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : GRA009+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n024.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 06:02:48 EDT 2022
% Result : Theorem 19.17s 19.34s
% Output : Refutation 19.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRA009+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.03/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n024.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 07:51:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 19.17/19.34 GeoParameters:
% 19.17/19.34
% 19.17/19.34 tptp_input = 1
% 19.17/19.34 tptp_output = 0
% 19.17/19.34 nonempty = 1
% 19.17/19.34 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.17/19.34 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 19.17/19.34
% 19.17/19.34
% 19.17/19.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.17/19.34 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.17/19.34
% 19.17/19.34 RuleSystem INPUT:
% 19.17/19.34
% 19.17/19.34 Initial Rules:
% 19.17/19.34 #0: input, references = 4, size of lhs = 3:
% 19.17/19.34 P_head_of-{F}(V0,V2), P_tail_of-{F}(V0,V2), edge-{F}(V0) | FALSE
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #1: input, references = 6, size of lhs = 3:
% 19.17/19.34 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), edge-{F}(V0) | vertex-{T}(V1)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #2: input, references = 7, size of lhs = 3:
% 19.17/19.34 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), edge-{F}(V0) | vertex-{T}(V2)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #3: input, references = 5, size of lhs = 4:
% 19.17/19.34 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0 | EXISTS V2: pppp9-{T}(V1,V0,V2)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #4: input, references = 14, size of lhs = 1:
% 19.17/19.34 pppp9-{F}(V0,V1,V2) | pppp8-{T}(V2,V0,V1)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #5: input, references = 5, size of lhs = 3:
% 19.17/19.34 pppp8-{F}(V0,V1,V2), pppp1-{F}(V0,V1,V2), pppp0-{F}(V0,V1,V2) | FALSE
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #6: input, references = 10, size of lhs = 1:
% 19.17/19.34 pppp8-{F}(V0,V1,V2) | pppp0-{T}(V0,V1,V2), pppp1-{T}(V0,V1,V2)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #7: input, references = 5, size of lhs = 1:
% 19.17/19.34 pppp8-{F}(V0,V1,V2) | edge-{T}(V0)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #8: input, references = 5, size of lhs = 4:
% 19.17/19.34 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp1-{F}(V0,V1,V2), V2 == V3 | FALSE
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #9: input, references = 6, size of lhs = 4:
% 19.17/19.34 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp1-{F}(V0,V1,V2), V1 == V4 | FALSE
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #10: input, references = 6, size of lhs = 2:
% 19.17/19.34 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | pppp1-{T}(V0,V4,V3)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #11: input, references = 4, size of lhs = 4:
% 19.17/19.34 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp0-{F}(V0,V1,V2), V1 == V3 | FALSE
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #12: input, references = 4, size of lhs = 4:
% 19.17/19.34 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp0-{F}(V0,V1,V2), V2 == V4 | FALSE
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #13: input, references = 3, size of lhs = 2:
% 19.17/19.34 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | pppp0-{T}(V0,V3,V4)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #14: input, references = 4, size of lhs = 7:
% 19.17/19.34 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)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #15: input, references = 4, size of lhs = 9:
% 19.17/19.34 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)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #16: input, references = 3, size of lhs = 2:
% 19.17/19.34 P_empty-{F}(V0), path-{F}(V1,V2,V3) | vertex-{T}(V1)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #17: input, references = 3, size of lhs = 2:
% 19.17/19.34 P_empty-{F}(V0), path-{F}(V1,V2,V3) | vertex-{T}(V2)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #18: input, references = 3, size of lhs = 2:
% 19.17/19.34 P_empty-{F}(V0), path-{F}(V1,V2,V3) | EXISTS V4: pppp11-{T}(V1,V2,V3,V4)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #19: input, references = 4, size of lhs = 2:
% 19.17/19.34 pppp11-{F}(V0,V1,V2,V3), P_tail_of-{F}(V3,V4) | pppp10-{T}(V3,V0,V1,V2,V4)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #20: input, references = 3, size of lhs = 3:
% 19.17/19.34 pppp10-{F}(V0,V1,V2,V3,V4), pppp3-{F}(V0,V2,V3), pppp2-{F}(V0,V2,V3) | FALSE
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #21: input, references = 3, size of lhs = 1:
% 19.17/19.34 pppp10-{F}(V0,V1,V2,V3,V4) | pppp2-{T}(V0,V2,V3), pppp3-{T}(V0,V2,V3)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #22: input, references = 4, size of lhs = 2:
% 19.17/19.34 pppp10-{F}(V0,V1,V2,V3,V4), V1 == V4 | FALSE
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #23: input, references = 3, size of lhs = 1:
% 19.17/19.34 pppp10-{F}(V0,V1,V2,V3,V4) | edge-{T}(V0)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #24: input, references = 3, size of lhs = 3:
% 19.17/19.34 P_empty-{F}(V0), P_head_of-{F}(V1,V4), pppp3-{F}(V1,V2,V3) | EXISTS V5: pppp12-{T}(V1,V2,V3,V5,V4)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #25: input, references = 3, size of lhs = 4:
% 19.17/19.34 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)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #26: input, references = 4, size of lhs = 3:
% 19.17/19.34 pppp12-{F}(V0,V1,V2,V3,V4), P_path_cons-{F}(V0,V3,V5), V2 == V5 | FALSE
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #27: input, references = 3, size of lhs = 2:
% 19.17/19.34 pppp12-{F}(V0,V1,V2,V3,V4), P_path_cons-{F}(V0,V3,V5) | path-{T}(V4,V1,V3)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #28: input, references = 3, size of lhs = 5:
% 19.17/19.34 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
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #29: input, references = 4, size of lhs = 5:
% 19.17/19.34 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
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #30: input, references = 3, size of lhs = 3:
% 19.17/19.34 P_empty-{F}(V0), P_head_of-{F}(V1,V4), P_path_cons-{F}(V1,V0,V5) | pppp2-{T}(V1,V4,V5)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #31: input, references = 7, size of lhs = 5:
% 19.17/19.34 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)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #32: input, references = 3, size of lhs = 5:
% 19.17/19.34 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)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #33: input, references = 3, size of lhs = 5:
% 19.17/19.34 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)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #34: input, references = 3, size of lhs = 3:
% 19.17/19.34 P_empty-{F}(V0), path-{F}(V3,V2,V1), in_path-{F}(V4,V1) | vertex-{T}(V4)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #35: input, references = 3, size of lhs = 3:
% 19.17/19.34 P_empty-{F}(V0), path-{F}(V3,V2,V1), in_path-{F}(V4,V1) | EXISTS V5: pppp13-{T}(V5,V1,V4)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #36: input, references = 5, size of lhs = 5:
% 19.17/19.34 pppp13-{F}(V0,V1,V2), P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), V2 == V3, V2 == V4 | FALSE
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #37: input, references = 3, size of lhs = 3:
% 19.17/19.34 pppp13-{F}(V0,V1,V2), P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | on_path-{T}(V0,V1)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #38: input, references = 4, size of lhs = 2:
% 19.17/19.34 P_empty-{F}(V0), sequential-{F}(V1,V2) | pppp4-{T}(V1,V2)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #39: input, references = 12, size of lhs = 2:
% 19.17/19.34 P_empty-{F}(V0), pppp4-{F}(V1,V2) | sequential-{T}(V1,V2)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #40: input, references = 15, size of lhs = 3:
% 19.17/19.34 P_empty-{F}(V0), P_head_of-{F}(V1,V3), P_tail_of-{F}(V2,V4) | pppp14-{T}(V1,V2,V3,V4)
% 19.17/19.34 (used 0 times, uses = {})
% 19.17/19.34
% 19.17/19.34 #41: input, references = 12, size of lhs = 4:
% 19.17/19.34 pppp14-{F}(V0,V1,V3,V3), edge-{F}(V0), edge-{F}(V1), V0 == V1 | pppp4-{T}(V0,V1)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #42: input, references = 4, size of lhs = 3:
% 19.17/19.35 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1), V2 == V3 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #43: input, references = 3, size of lhs = 2:
% 19.17/19.35 pppp14-{F}(V1,V1,V2,V3), pppp4-{F}(V1,V1) | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #44: input, references = 3, size of lhs = 2:
% 19.17/19.35 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1) | edge-{T}(V1)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #45: input, references = 5, size of lhs = 2:
% 19.17/19.35 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1) | edge-{T}(V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #46: input, references = 7, size of lhs = 5:
% 19.17/19.35 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)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #47: input, references = 6, size of lhs = 6:
% 19.17/19.35 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)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #48: input, references = 4, size of lhs = 3:
% 19.17/19.35 P_empty-{F}(V0), precedes-{F}(V2,V3,V1), path-{F}(V5,V4,V1) | pppp15-{T}(V1,V2,V3)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #49: input, references = 4, size of lhs = 3:
% 19.17/19.35 pppp15-{F}(V0,V1,V2), pppp5-{F}(V0,V1,V2), sequential-{F}(V1,V2) | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #50: input, references = 3, size of lhs = 1:
% 19.17/19.35 pppp15-{F}(V0,V1,V2) | sequential-{T}(V1,V2), pppp5-{T}(V0,V1,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #51: input, references = 3, size of lhs = 1:
% 19.17/19.35 pppp15-{F}(V0,V1,V2) | on_path-{T}(V2,V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #52: input, references = 3, size of lhs = 1:
% 19.17/19.35 pppp15-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #53: input, references = 3, size of lhs = 2:
% 19.17/19.35 P_empty-{F}(V0), pppp5-{F}(V1,V2,V3) | EXISTS V4: pppp16-{T}(V1,V2,V3,V4)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #54: input, references = 4, size of lhs = 3:
% 19.17/19.35 P_empty-{F}(V0), sequential-{F}(V2,V4), precedes-{F}(V4,V3,V1) | pppp5-{T}(V1,V2,V3)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #55: input, references = 3, size of lhs = 1:
% 19.17/19.35 pppp16-{F}(V0,V1,V2,V3) | precedes-{T}(V3,V2,V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #56: input, references = 3, size of lhs = 1:
% 19.17/19.35 pppp16-{F}(V0,V1,V2,V3) | sequential-{T}(V1,V3)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #57: input, references = 7, size of lhs = 2:
% 19.17/19.35 P_empty-{F}(V0), shortest_path-{F}(V1,V2,V3) | pppp6-{T}(V1,V2,V3)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #58: input, references = 3, size of lhs = 2:
% 19.17/19.35 P_empty-{F}(V0), pppp6-{F}(V1,V2,V3) | shortest_path-{T}(V1,V2,V3)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #59: input, references = 7, size of lhs = 3:
% 19.17/19.35 P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V1,V2,V3) | path-{T}(V1,V2,V3)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #60: input, references = 3, size of lhs = 3:
% 19.17/19.35 P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V2,V2,V3) | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #61: input, references = 3, size of lhs = 5:
% 19.17/19.35 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)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #62: input, references = 3, size of lhs = 4:
% 19.17/19.35 P_empty-{F}(V0), P_length_of-{F}(V3,V4), path-{F}(V1,V2,V3), V1 == V2 | pppp6-{T}(V1,V2,V3), pppp26-{T}(V1,V2,V4)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #63: input, references = 3, size of lhs = 1:
% 19.17/19.35 pppp26-{F}(V0,V1,V2) | EXISTS V3: pppp17-{T}(V0,V1,V3,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #64: input, references = 3, size of lhs = 3:
% 19.17/19.35 pppp17-{F}(V0,V1,V2,V3), P_length_of-{F}(V2,V4), less_or_equal-{F}(V3,V4) | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #65: input, references = 3, size of lhs = 2:
% 19.17/19.35 pppp17-{F}(V0,V1,V2,V3), P_length_of-{F}(V2,V4) | path-{T}(V0,V1,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #66: input, references = 8, size of lhs = 7:
% 19.17/19.35 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
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #67: input, references = 5, size of lhs = 6:
% 19.17/19.35 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
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #68: input, references = 3, size of lhs = 2:
% 19.17/19.35 P_empty-{F}(V0), triangle-{F}(V1,V2,V3) | pppp7-{T}(V1,V2,V3)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #69: input, references = 5, size of lhs = 2:
% 19.17/19.35 P_empty-{F}(V0), pppp7-{F}(V1,V2,V3) | triangle-{T}(V1,V2,V3)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #70: input, references = 3, size of lhs = 2:
% 19.17/19.35 P_empty-{F}(V0), pppp7-{F}(V1,V2,V3) | pppp18-{T}(V1,V2,V3)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #71: input, references = 5, size of lhs = 7:
% 19.17/19.35 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)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #72: input, references = 3, size of lhs = 1:
% 19.17/19.35 pppp18-{F}(V0,V1,V2) | sequential-{T}(V2,V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #73: input, references = 3, size of lhs = 1:
% 19.17/19.35 pppp18-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #74: input, references = 3, size of lhs = 1:
% 19.17/19.35 pppp18-{F}(V0,V1,V2) | sequential-{T}(V0,V1)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #75: input, references = 3, size of lhs = 1:
% 19.17/19.35 pppp18-{F}(V0,V1,V2) | edge-{T}(V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #76: input, references = 3, size of lhs = 1:
% 19.17/19.35 pppp18-{F}(V0,V1,V2) | edge-{T}(V1)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #77: input, references = 3, size of lhs = 1:
% 19.17/19.35 pppp18-{F}(V0,V1,V2) | edge-{T}(V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #78: input, references = 6, size of lhs = 6:
% 19.17/19.35 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
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #79: input, references = 6, size of lhs = 9:
% 19.17/19.35 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
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #80: input, references = 3, size of lhs = 9:
% 19.17/19.35 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)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #81: input, references = 3, size of lhs = 1:
% 19.17/19.35 pppp20-{F}(V0,V1) | EXISTS V2: pppp19-{T}(V0,V2,V1)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #82: input, references = 3, size of lhs = 1:
% 19.17/19.35 pppp20-{F}(V0,V1) | on_path-{T}(V1,V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #83: input, references = 4, size of lhs = 2:
% 19.17/19.35 pppp19-{F}(V0,V1,V2), triangle-{F}(V1,V2,V3) | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #84: input, references = 3, size of lhs = 1:
% 19.17/19.35 pppp19-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #85: input, references = 3, size of lhs = 1:
% 19.17/19.35 pppp19-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #86: input, references = 3, size of lhs = 8:
% 19.17/19.35 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)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #87: input, references = 4, size of lhs = 6:
% 19.17/19.35 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-{T}()
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #88: input, references = 4, size of lhs = 6:
% 19.17/19.35 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) | EXISTS V6: pppp25-{T}(V6)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #89: input, references = 6, size of lhs = 1:
% 19.17/19.35 pppp25-{F}(V0) | EXISTS V1: pppp24-{T}(V0,V1)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #90: input, references = 4, size of lhs = 1:
% 19.17/19.35 pppp25-{F}(V0) | EXISTS V1: pppp22-{T}(V0,V1)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #91: input, references = 7, size of lhs = 1:
% 19.17/19.35 pppp24-{F}(V0,V1) | EXISTS V2: pppp23-{T}(V1,V0,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #92: input, references = 7, size of lhs = 1:
% 19.17/19.35 pppp23-{F}(V0,V1,V2) | shortest_path-{T}(V2,V0,V1)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #93: input, references = 4, size of lhs = 1:
% 19.17/19.35 pppp22-{F}(V0,V1) | EXISTS V2: pppp21-{T}(V0,V2,V1)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #94: input, references = 4, size of lhs = 1:
% 19.17/19.35 pppp22-{F}(V0,V1) | on_path-{T}(V1,V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #95: input, references = 4, size of lhs = 2:
% 19.17/19.35 pppp21-{F}(V0,V1,V2), triangle-{F}(V1,V2,V3) | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #96: input, references = 5, size of lhs = 1:
% 19.17/19.35 pppp21-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #97: input, references = 4, size of lhs = 1:
% 19.17/19.35 pppp21-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #98: input, references = 11, size of lhs = 1:
% 19.17/19.35 #-{F} V0 | EXISTS V1: P_head_of-{T}(V0,V1)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #99: input, references = 9, size of lhs = 1:
% 19.17/19.35 #-{F} V0 | EXISTS V1: P_tail_of-{T}(V0,V1)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #100: input, references = 6, size of lhs = 2:
% 19.17/19.35 #-{F} V0, #-{F} V1 | EXISTS V2: P_path_cons-{T}(V0,V1,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #101: input, references = 4, size of lhs = 0:
% 19.17/19.35 FALSE | EXISTS V0: P_empty-{T}(V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #102: input, references = 5, size of lhs = 1:
% 19.17/19.35 #-{F} V0 | EXISTS V1: P_length_of-{T}(V0,V1)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #103: input, references = 6, size of lhs = 2:
% 19.17/19.35 #-{F} V0, #-{F} V1 | EXISTS V2: P_number_of_in-{T}(V0,V1,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #104: input, references = 4, size of lhs = 0:
% 19.17/19.35 FALSE | EXISTS V0: P_edges-{T}(V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #105: input, references = 4, size of lhs = 0:
% 19.17/19.35 FALSE | EXISTS V0: P_sequential_pairs-{T}(V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #106: input, references = 4, size of lhs = 2:
% 19.17/19.35 #-{F} V0, #-{F} V1 | EXISTS V2: P_minus-{T}(V0,V1,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #107: input, references = 4, size of lhs = 0:
% 19.17/19.35 FALSE | EXISTS V0: P_n1-{T}(V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #108: input, references = 4, size of lhs = 0:
% 19.17/19.35 FALSE | EXISTS V0: P_triangles-{T}(V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #109: input, references = 4, size of lhs = 0:
% 19.17/19.35 FALSE | EXISTS V0: P_graph-{T}(V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 number of initial rules = 110
% 19.17/19.35
% 19.17/19.35 Simplifiers:
% 19.17/19.35 #110: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 P_head_of-{F}(V0,V1), P_head_of-{F}(V0,V3), V1 == V3 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #111: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 P_tail_of-{F}(V0,V1), P_tail_of-{F}(V0,V3), V1 == V3 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #112: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 P_path_cons-{F}(V0,V1,V2), P_path_cons-{F}(V0,V1,V5), V2 == V5 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #113: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 P_empty-{F}(V0), P_empty-{F}(V1), V0 == V1 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #114: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 P_length_of-{F}(V0,V1), P_length_of-{F}(V0,V3), V1 == V3 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #115: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 P_number_of_in-{F}(V0,V1,V2), P_number_of_in-{F}(V0,V1,V5), V2 == V5 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #116: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 P_edges-{F}(V0), P_edges-{F}(V1), V0 == V1 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #117: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 P_sequential_pairs-{F}(V0), P_sequential_pairs-{F}(V1), V0 == V1 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #118: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 P_minus-{F}(V0,V1,V2), P_minus-{F}(V0,V1,V5), V2 == V5 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #119: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 P_n1-{F}(V0), P_n1-{F}(V1), V0 == V1 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #120: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 P_triangles-{F}(V0), P_triangles-{F}(V1), V0 == V1 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #121: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 P_graph-{F}(V0), P_graph-{F}(V1), V0 == V1 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #122: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp8-{F}(V0,V1,V2), pppp8-{F}(V3,V1,V2), V0 == V3 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #123: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp9-{F}(V0,V1,V2), pppp9-{F}(V0,V1,V5), V2 == V5 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #124: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V5,V1,V2,V3,V9), V0 == V5 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #125: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #126: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp11-{F}(V0,V1,V2,V3), pppp11-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #127: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V1,V2,V8,V4), V3 == V8 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #128: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #129: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp13-{F}(V0,V1,V2), pppp13-{F}(V3,V1,V2), V0 == V3 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #130: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp14-{F}(V0,V1,V2,V3), pppp14-{F}(V0,V5,V6,V7), V2 == V6 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #131: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp14-{F}(V0,V1,V2,V3), pppp14-{F}(V4,V1,V6,V7), V3 == V7 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #132: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp16-{F}(V0,V1,V2,V3), pppp16-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #133: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp17-{F}(V0,V1,V2,V3), pppp17-{F}(V0,V1,V6,V3), V2 == V6 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #134: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp19-{F}(V0,V1,V2), pppp19-{F}(V0,V4,V2), V1 == V4 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #135: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp19-{F}(V0,V1,V2), pppp19-{F}(V0,V4,V5), V2 == V5 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #136: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp20-{F}(V0,V1), pppp20-{F}(V0,V3), V1 == V3 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #137: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp21-{F}(V0,V1,V2), pppp21-{F}(V0,V4,V2), V1 == V4 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #138: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp21-{F}(V0,V1,V2), pppp21-{F}(V0,V4,V5), V2 == V5 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #139: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp21-{F}(V0,V1,V2), pppp21-{F}(V3,V4,V5), V0 == V3 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #140: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp22-{F}(V0,V1), pppp22-{F}(V0,V3), V1 == V3 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #141: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp22-{F}(V0,V1), pppp22-{F}(V2,V3), V0 == V2 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #142: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp23-{F}(V0,V1,V2), pppp23-{F}(V0,V1,V5), V2 == V5 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #143: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp23-{F}(V0,V1,V2), pppp23-{F}(V3,V1,V5), V0 == V3 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #144: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp23-{F}(V0,V1,V2), pppp23-{F}(V3,V4,V5), V1 == V4 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #145: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp24-{F}(V0,V1), pppp24-{F}(V0,V3), V1 == V3 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #146: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp24-{F}(V0,V1), pppp24-{F}(V2,V3), V0 == V2 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #147: unsound, references = 3, size of lhs = 3:
% 19.17/19.35 pppp25-{F}(V0), pppp25-{F}(V1), V0 == V1 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 number of simplifiers = 38
% 19.17/19.35
% 19.17/19.35 Learnt:
% 19.17/19.35 #157: mergings( V3 == V4, V4 == V5, V9 == V11; #153 ), references = 2, size of lhs = 9:
% 19.17/19.35 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp24-{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
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #162: mergings( V2 == V3, V3 == V4, V8 == V10; #158 ), references = 2, size of lhs = 9:
% 19.17/19.35 pppp25-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), P_number_of_in-{F}(V3,V0,V5), P_length_of-{F}(V0,V6), P_minus-{F}(V6,V4,V7), V5 == V7 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #167: mergings( V3 == V4, V4 == V5, V8 == V9; #163 ), references = 1, size of lhs = 7:
% 19.17/19.35 pppp25-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), P_length_of-{F}(V0,V5), P_minus-{F}(V5,V4,V6) | P_number_of_in-{T}(V3,V0,V6)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #177: mergings( V3 == V4, V4 == V5, V7 == V8; #173 ), references = 2, size of lhs = 6:
% 19.17/19.35 P_empty-{F}(V0), P_edges-{F}(V1), pppp24-{F}(V2,V3), P_length_of-{F}(V2,V4), P_number_of_in-{F}(V1,V2,V5), V4 == V5 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #182: mergings( V2 == V3, V3 == V4, V6 == V7; #178 ), references = 2, size of lhs = 6:
% 19.17/19.35 pppp25-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_length_of-{F}(V0,V3), P_number_of_in-{F}(V2,V0,V4), V3 == V4 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #188: exists( #103, #182 ), references = 1, size of lhs = 4:
% 19.17/19.35 pppp25-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_length_of-{F}(V0,V3) | P_number_of_in-{T}(V2,V0,V3)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #189: exists( #103, #177 ), references = 1, size of lhs = 4:
% 19.17/19.35 P_empty-{F}(V0), P_edges-{F}(V1), pppp24-{F}(V2,V3), P_length_of-{F}(V2,V4) | P_number_of_in-{T}(V1,V2,V4)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #220: mergings( V12 == V16, V16 == V18, V13 == V15, V15 == V17, V3 == V4, V4 == V5, V5 == V6, V6 == V7; #211 ), references = 1, size of lhs = 14:
% 19.17/19.35 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), on_path-{F}(V4,V5), pppp24-{F}(V5,V6), P_length_of-{F}(V5,V7), P_tail_of-{F}(V4,V8), P_head_of-{F}(V4,V9), P_path_cons-{F}(V4,V0,V10), P_number_of_in-{F}(V2,V10,V11), P_length_of-{F}(V10,V12), P_minus-{F}(V12,V3,V13), V11 == V13 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #230: mergings( V11 == V15, V15 == V17, V12 == V14, V14 == V16, V2 == V3, V3 == V4, V4 == V5, V5 == V6; #221 ), references = 1, size of lhs = 13:
% 19.17/19.35 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), on_path-{F}(V4,V5), pppp24-{F}(V5,V6), P_tail_of-{F}(V4,V7), P_head_of-{F}(V4,V8), P_path_cons-{F}(V4,V0,V9), P_number_of_in-{F}(V2,V9,V10), P_length_of-{F}(V9,V11), P_minus-{F}(V11,V3,V12), V10 == V12 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #246: exists( #106, #162 ), references = 1, size of lhs = 7:
% 19.17/19.35 pppp25-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), P_number_of_in-{F}(V3,V0,V5), P_length_of-{F}(V0,V6) | P_minus-{T}(V6,V4,V5)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #247: exists( #106, #157 ), references = 1, size of lhs = 7:
% 19.17/19.35 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp24-{F}(V4,V5), P_number_of_in-{F}(V2,V4,V6), P_length_of-{F}(V4,V7) | P_minus-{T}(V7,V3,V6)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #248: exists( #106, #79 ), references = 1, size of lhs = 7:
% 19.17/19.35 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), path-{F}(V7,V8,V4) | P_minus-{T}(V6,V3,V5)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #265: exists( #98, #263 ), references = 1, size of lhs = 3:
% 19.17/19.35 P_empty-{F}(V0), pppp4-{F}(V1,V2), P_tail_of-{F}(V2,V3) | P_head_of-{T}(V1,V3)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #305: exists( #99, #303 ), references = 1, size of lhs = 1:
% 19.17/19.35 pppp11-{F}(V0,V1,V2,V3) | P_tail_of-{T}(V3,V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #342: exists( #98, #36 ), references = 1, size of lhs = 3:
% 19.17/19.35 P_tail_of-{F}(V0,V1), pppp13-{F}(V0,V2,V3), V3 == V1 | P_head_of-{T}(V0,V3)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #385: disj( #6, input ), references = 3, size of lhs = 4:
% 19.17/19.35 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), pppp8-{F}(V0,V3,V4), V3 == V1 | pppp1-{T}(V0,V3,V4)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #387: mergings( V1 == V3; #384 ), references = 1, size of lhs = 4:
% 19.17/19.35 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), pppp8-{F}(V0,V1,V3), V3 == V2 | pppp1-{T}(V0,V1,V3)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #443: mergings( V2 == V3; #441 ), references = 5, size of lhs = 3:
% 19.17/19.35 P_tail_of-{F}(V0,V1), pppp8-{F}(V0,V2,V3), V2 == V1 | P_head_of-{T}(V0,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #513: exists( #103, #78 ), references = 1, size of lhs = 4:
% 19.17/19.35 P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), path-{F}(V4,V5,V2) | P_number_of_in-{T}(V1,V2,V3)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #569: exists( #99, #8 ), references = 7, size of lhs = 3:
% 19.17/19.35 P_head_of-{F}(V0,V1), pppp1-{F}(V0,V2,V3), V3 == V1 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #571: mergings( V4 == V2; #568 ), references = 5, size of lhs = 2:
% 19.17/19.35 P_head_of-{F}(V0,V1), pppp1-{F}(V0,V2,V1) | P_tail_of-{T}(V0,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #573: exists( #98, #567 ), references = 1, size of lhs = 1:
% 19.17/19.35 pppp1-{F}(V0,V1,V2) | P_head_of-{T}(V0,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #582: disj( #6, #572+#571+#385+#569 ), references = 3, size of lhs = 4:
% 19.17/19.35 pppp8-{F}(V0,V1,V2), pppp8-{F}(V0,V3,V4), V3 == V2, V4 == V2 | pppp0-{T}(V0,V1,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #661: exists( #100, #29 ), references = 1, size of lhs = 3:
% 19.17/19.35 P_empty-{F}(V0), P_head_of-{F}(V1,V2), pppp2-{F}(V1,V3,V4) | P_path_cons-{T}(V1,V0,V4)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #725: exists( #99, #11 ), references = 6, size of lhs = 3:
% 19.17/19.35 P_head_of-{F}(V0,V1), pppp0-{F}(V0,V2,V3), V2 == V1 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #727: mergings( V3 == V2; #724 ), references = 4, size of lhs = 2:
% 19.17/19.35 P_head_of-{F}(V0,V1), pppp0-{F}(V0,V1,V2) | P_tail_of-{T}(V0,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #791: exists( #98, #725 ), references = 3, size of lhs = 1:
% 19.17/19.35 pppp0-{F}(V0,V1,V2) | P_head_of-{T}(V0,V1)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #1196: exists( #100, #26 ), references = 1, size of lhs = 1:
% 19.17/19.35 pppp12-{F}(V0,V1,V2,V3,V4) | P_path_cons-{T}(V0,V3,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #1466: mergings( V3 == V6, V6 == V7, V7 == V8; #1462 ), references = 1, size of lhs = 16:
% 19.17/19.35 edge-{F}(V0), P_head_of-{F}(V0,V1), edge-{F}(V2), V0 == V2, pppp8-{F}(V2,V1,V3), P_head_of-{F}(V2,V4), P_empty-{F}(V5), on_path-{F}(V0,V6), on_path-{F}(V7,V6), precedes-{F}(V2,V7,V6), P_tail_of-{F}(V0,V8), P_head_of-{F}(V7,V9), P_tail_of-{F}(V10,V8), P_head_of-{F}(V10,V9), path-{F}(V11,V12,V6), shortest_path-{F}(V13,V14,V6) | pppp0-{T}(V2,V1,V3)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #1616: disj( #6, #571+#66 ), references = 1, size of lhs = 8:
% 19.17/19.35 P_empty-{F}(V0), P_head_of-{F}(V1,V2), pppp8-{F}(V1,V3,V2), P_tail_of-{F}(V4,V3), P_head_of-{F}(V4,V5), P_head_of-{F}(V6,V5), precedes-{F}(V1,V6,V7), shortest_path-{F}(V8,V9,V7) | pppp0-{T}(V1,V3,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #1849: disj( #6, #1834+#727+#10+#443+#569 ), references = 1, size of lhs = 4:
% 19.17/19.35 pppp8-{F}(V0,V1,V2), pppp8-{F}(V0,V3,V4), V3 == V2, V1 == V3 | pppp1-{T}(V0,V1,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2077: disj( #6, exists( #99, #11 ) ), references = 6, size of lhs = 3:
% 19.17/19.35 P_head_of-{F}(V0,V1), pppp8-{F}(V0,V2,V3), V2 == V1 | pppp1-{T}(V0,V2,V3)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2224: mergings( V1 == V8; #2222 ), references = 1, size of lhs = 12:
% 19.17/19.35 vertex-{F}(V0), vertex-{F}(V1), edge-{F}(V2), P_tail_of-{F}(V2,V1), P_head_of-{F}(V2,V3), path-{F}(V3,V0,V4), P_path_cons-{F}(V2,V4,V5), P_empty-{F}(V6), P_edges-{F}(V7), P_length_of-{F}(V5,V8), P_number_of_in-{F}(V7,V5,V9), V8 == V9 | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2232: disj( #6, #2225+#571+#66 ), references = 5, size of lhs = 6:
% 19.17/19.35 P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_tail_of-{F}(V3,V4), pppp8-{F}(V5,V4,V2), precedes-{F}(V3,V1,V6), shortest_path-{F}(V7,V8,V6) | pppp0-{T}(V5,V4,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2233: disj( #6, #2225+#571+#36 ), references = 1, size of lhs = 4:
% 19.17/19.35 pppp8-{F}(V0,V1,V2), pppp13-{F}(V0,V3,V4), V4 == V2, V4 == V1 | pppp0-{T}(V0,V1,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2315: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V14; #2308 ), references = 1, size of lhs = 15:
% 19.17/19.35 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0, edge-{F}(V2), P_tail_of-{F}(V2,V1), P_tail_of-{F}(V3,V1), edge-{F}(V4), sequential-{F}(V2,V4), P_head_of-{F}(V4,V0), P_head_of-{F}(V5,V0), precedes-{F}(V3,V5,V6), P_empty-{F}(V7), pppp19-{F}(V8,V2,V4), shortest_path-{F}(V9,V10,V6) | pppp9-{T}(V1,V0,V4), pppp9-{T}(V1,V0,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2333: mergings( V17 == V18, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V13; #2323 ), references = 1, size of lhs = 18:
% 19.17/19.35 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0, edge-{F}(V2), P_tail_of-{F}(V2,V1), P_tail_of-{F}(V3,V1), edge-{F}(V4), sequential-{F}(V2,V4), P_head_of-{F}(V4,V0), P_head_of-{F}(V5,V0), precedes-{F}(V3,V5,V6), P_empty-{F}(V7), pppp19-{F}(V8,V2,V4), P_head_of-{F}(V2,V9), V1 == V9, V0 == V9, shortest_path-{F}(V10,V11,V6) | pppp9-{T}(V1,V0,V4)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2340: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V13; #2324 ), references = 1, size of lhs = 20:
% 19.17/19.35 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0, edge-{F}(V2), P_tail_of-{F}(V2,V1), P_tail_of-{F}(V3,V1), edge-{F}(V4), sequential-{F}(V2,V4), P_head_of-{F}(V4,V0), P_head_of-{F}(V5,V0), precedes-{F}(V3,V5,V6), P_empty-{F}(V7), pppp19-{F}(V8,V2,V4), P_head_of-{F}(V2,V9), V1 == V9, shortest_path-{F}(V10,V11,V6), pppp8-{F}(V2,V12,V13), V12 == V0, V13 == V0 | pppp9-{T}(V1,V0,V4)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2347: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V13; #2325 ), references = 1, size of lhs = 20:
% 19.17/19.35 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0, edge-{F}(V2), P_tail_of-{F}(V2,V1), P_tail_of-{F}(V3,V1), edge-{F}(V4), sequential-{F}(V2,V4), P_head_of-{F}(V4,V0), P_head_of-{F}(V5,V0), precedes-{F}(V3,V5,V6), P_empty-{F}(V7), pppp19-{F}(V8,V2,V4), P_head_of-{F}(V2,V9), V1 == V9, shortest_path-{F}(V10,V11,V6), pppp8-{F}(V2,V12,V13), V12 == V0, V13 == V0 | pppp9-{T}(V1,V0,V4)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2459: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V14; #2452 ), references = 1, size of lhs = 15:
% 19.17/19.35 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0, edge-{F}(V2), P_tail_of-{F}(V2,V1), P_tail_of-{F}(V3,V1), edge-{F}(V4), sequential-{F}(V2,V4), P_head_of-{F}(V4,V0), P_head_of-{F}(V5,V0), precedes-{F}(V3,V5,V6), P_empty-{F}(V7), pppp21-{F}(V8,V2,V4), shortest_path-{F}(V9,V10,V6) | pppp9-{T}(V1,V0,V2), pppp9-{T}(V1,V0,V4)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2477: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V13, V19 == V0; #2467 ), references = 1, size of lhs = 18:
% 19.17/19.35 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V0 == V1, edge-{F}(V2), P_tail_of-{F}(V2,V1), P_tail_of-{F}(V3,V1), edge-{F}(V4), sequential-{F}(V2,V4), P_head_of-{F}(V4,V0), P_head_of-{F}(V5,V0), precedes-{F}(V3,V5,V6), P_empty-{F}(V7), pppp21-{F}(V8,V2,V4), P_tail_of-{F}(V4,V9), V1 == V9, pppp1-{F}(V4,V10,V0), shortest_path-{F}(V11,V12,V6) | pppp9-{T}(V1,V0,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2485: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V13, V18 == V0; #2468 ), references = 1, size of lhs = 18:
% 19.17/19.35 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V0 == V1, edge-{F}(V2), P_tail_of-{F}(V2,V1), P_tail_of-{F}(V3,V1), edge-{F}(V4), sequential-{F}(V2,V4), P_head_of-{F}(V4,V0), P_head_of-{F}(V5,V0), precedes-{F}(V3,V5,V6), P_empty-{F}(V7), pppp21-{F}(V8,V2,V4), P_tail_of-{F}(V4,V9), V1 == V9, pppp0-{F}(V4,V0,V10), shortest_path-{F}(V11,V12,V6) | pppp9-{T}(V1,V0,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2494: mergings( V0 == V18, V17 == V19, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V13; #2469 ), references = 1, size of lhs = 17:
% 19.17/19.35 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0, edge-{F}(V2), P_tail_of-{F}(V2,V1), P_tail_of-{F}(V3,V1), edge-{F}(V4), sequential-{F}(V2,V4), P_head_of-{F}(V4,V0), P_head_of-{F}(V5,V0), precedes-{F}(V3,V5,V6), P_empty-{F}(V7), pppp21-{F}(V8,V2,V4), P_tail_of-{F}(V4,V9), V1 == V9, shortest_path-{F}(V10,V11,V6) | pppp9-{T}(V1,V0,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2520: mergings( V2 == V16, V16 == V17, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V13, V21 == V3; #2508 ), references = 1, size of lhs = 15:
% 19.17/19.35 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), edge-{F}(V2), sequential-{F}(V1,V2), P_head_of-{F}(V2,V0), P_head_of-{F}(V3,V0), precedes-{F}(V1,V3,V4), P_empty-{F}(V5), pppp21-{F}(V6,V1,V2), P_tail_of-{F}(V2,V7), P_head_of-{F}(V1,V8), V0 == V8, pppp1-{F}(V2,V9,V0), shortest_path-{F}(V10,V11,V4) | P_tail_of-{T}(V1,V0), P_tail_of-{T}(V1,V7), P_tail_of-{T}(V1,V8)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2530: mergings( V2 == V18, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V13, V13 == V16, V23 == V3; #2509 ), references = 1, size of lhs = 17:
% 19.17/19.35 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), edge-{F}(V2), sequential-{F}(V1,V2), P_head_of-{F}(V2,V0), P_head_of-{F}(V3,V0), precedes-{F}(V1,V3,V4), pppp21-{F}(V5,V1,V2), P_tail_of-{F}(V2,V6), P_empty-{F}(V7), P_head_of-{F}(V8,V0), P_head_of-{F}(V1,V9), precedes-{F}(V1,V8,V10), pppp1-{F}(V2,V11,V0), shortest_path-{F}(V12,V13,V4), shortest_path-{F}(V14,V15,V10) | P_tail_of-{T}(V1,V0), P_tail_of-{T}(V1,V6), P_tail_of-{T}(V1,V9)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2540: mergings( V2 == V19, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V13, V13 == V16, V23 == V3; #2510 ), references = 1, size of lhs = 17:
% 19.17/19.35 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), edge-{F}(V2), sequential-{F}(V1,V2), P_head_of-{F}(V2,V0), P_head_of-{F}(V3,V0), precedes-{F}(V1,V3,V4), pppp21-{F}(V5,V1,V2), P_tail_of-{F}(V2,V6), P_empty-{F}(V7), P_head_of-{F}(V8,V0), precedes-{F}(V1,V8,V9), P_head_of-{F}(V1,V10), pppp1-{F}(V2,V11,V0), shortest_path-{F}(V12,V13,V4), shortest_path-{F}(V14,V15,V9) | P_tail_of-{T}(V1,V0), P_tail_of-{T}(V1,V6), P_tail_of-{T}(V1,V10)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2555: mergings( V14 == V8, V8 == V16, V16 == V15, V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V12, V20 == V0; #2541 ), references = 1, size of lhs = 15:
% 19.17/19.35 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_head_of-{F}(V1,V0), P_head_of-{F}(V2,V0), P_empty-{F}(V3), P_tail_of-{F}(V1,V4), V0 == V4, edge-{F}(V5), sequential-{F}(V5,V1), P_head_of-{F}(V5,V4), precedes-{F}(V5,V2,V6), pppp21-{F}(V7,V5,V1), pppp1-{F}(V1,V8,V0), shortest_path-{F}(V9,V10,V6) | P_tail_of-{T}(V5,V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2566: mergings( V8 == V16, V16 == V15, V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V12, V12 == V21, V20 == V0; #2543 ), references = 1, size of lhs = 20:
% 19.17/19.35 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_head_of-{F}(V1,V0), P_head_of-{F}(V2,V0), P_tail_of-{F}(V1,V3), P_empty-{F}(V4), P_tail_of-{F}(V5,V3), P_head_of-{F}(V5,V6), P_head_of-{F}(V7,V6), edge-{F}(V8), sequential-{F}(V8,V1), precedes-{F}(V8,V2,V9), pppp21-{F}(V10,V8,V1), precedes-{F}(V8,V7,V11), P_head_of-{F}(V8,V12), V0 == V12, pppp1-{F}(V1,V13,V0), shortest_path-{F}(V14,V15,V9), shortest_path-{F}(V16,V17,V11) | P_tail_of-{T}(V8,V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2578: mergings( V14 == V8, V8 == V15, V15 == V16, V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V12, V12 == V21, V20 == V0; #2542 ), references = 1, size of lhs = 20:
% 19.17/19.35 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_head_of-{F}(V1,V0), P_head_of-{F}(V2,V0), P_tail_of-{F}(V1,V3), V0 == V3, edge-{F}(V4), sequential-{F}(V4,V1), P_head_of-{F}(V4,V3), precedes-{F}(V4,V2,V5), pppp21-{F}(V6,V4,V1), P_empty-{F}(V7), P_tail_of-{F}(V8,V3), P_head_of-{F}(V8,V9), P_head_of-{F}(V10,V9), precedes-{F}(V4,V10,V11), pppp1-{F}(V1,V12,V0), shortest_path-{F}(V13,V14,V5), shortest_path-{F}(V15,V16,V11) | P_tail_of-{T}(V4,V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2604: mergings( V0 == V27, V10 == V12, V12 == V15, V15 == V16, V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V9, V9 == V21, V21 == V23, V23 == V24, V24 == V25, V20 == V27; #2587 ), references = 1, size of lhs = 23:
% 19.17/19.35 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_head_of-{F}(V1,V0), P_head_of-{F}(V2,V0), P_tail_of-{F}(V1,V3), V0 == V3, edge-{F}(V4), P_head_of-{F}(V4,V0), edge-{F}(V5), V4 == V5, sequential-{F}(V5,V1), P_head_of-{F}(V5,V3), precedes-{F}(V5,V2,V6), pppp21-{F}(V7,V5,V1), P_empty-{F}(V8), on_path-{F}(V4,V9), on_path-{F}(V5,V9), precedes-{F}(V5,V4,V9), pppp1-{F}(V1,V10,V0), shortest_path-{F}(V11,V12,V6), path-{F}(V13,V14,V9), shortest_path-{F}(V15,V16,V9) | P_tail_of-{T}(V5,V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2619: mergings( V10 == V12, V12 == V15, V15 == V16, V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V9, V9 == V21, V21 == V23, V23 == V24, V24 == V25, V20 == V0; #2588 ), references = 1, size of lhs = 27:
% 19.17/19.35 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_head_of-{F}(V1,V0), P_head_of-{F}(V2,V0), P_tail_of-{F}(V1,V3), V0 == V3, edge-{F}(V4), P_head_of-{F}(V4,V0), edge-{F}(V5), V4 == V5, sequential-{F}(V5,V1), P_head_of-{F}(V5,V3), precedes-{F}(V5,V2,V6), pppp21-{F}(V7,V5,V1), P_empty-{F}(V8), on_path-{F}(V4,V9), on_path-{F}(V10,V9), precedes-{F}(V5,V10,V9), P_tail_of-{F}(V4,V11), P_head_of-{F}(V10,V12), P_tail_of-{F}(V13,V11), P_head_of-{F}(V13,V12), pppp1-{F}(V1,V14,V0), shortest_path-{F}(V15,V16,V6), path-{F}(V17,V18,V9), shortest_path-{F}(V19,V20,V9) | P_tail_of-{T}(V5,V0)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2665: mergings( V21 == V22, V22 == V25, V25 == V26, V26 == V31, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19; #2642 ), references = 1, size of lhs = 22:
% 19.17/19.35 complete-{F}(), P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_head_of-{F}(V3,V2), on_path-{F}(V3,V4), on_path-{F}(V3,V5), sequential-{F}(V6,V3), V3 == V6, on_path-{F}(V6,V5), precedes-{F}(V6,V3,V5), pppp4-{F}(V6,V3), precedes-{F}(V6,V1,V7), pppp21-{F}(V8,V6,V3), on_path-{F}(V3,V9), on_path-{F}(V6,V9), precedes-{F}(V6,V3,V9), path-{F}(V10,V11,V4), shortest_path-{F}(V12,V13,V7), path-{F}(V14,V15,V5), shortest_path-{F}(V16,V17,V5), path-{F}(V18,V19,V9), shortest_path-{F}(V20,V21,V9) | P_tail_of-{T}(V3,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2687: mergings( V21 == V22, V22 == V25, V25 == V26, V26 == V32, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19; #2643 ), references = 1, size of lhs = 23:
% 19.17/19.35 complete-{F}(), P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_head_of-{F}(V3,V2), on_path-{F}(V3,V4), precedes-{F}(V5,V3,V4), sequential-{F}(V5,V6), V6 == V5, pppp4-{F}(V5,V6), on_path-{F}(V6,V4), P_head_of-{F}(V6,V2), on_path-{F}(V6,V7), on_path-{F}(V6,V8), on_path-{F}(V5,V8), precedes-{F}(V5,V6,V8), precedes-{F}(V5,V1,V9), pppp21-{F}(V10,V5,V6), path-{F}(V11,V12,V7), shortest_path-{F}(V13,V14,V9), path-{F}(V15,V16,V8), shortest_path-{F}(V17,V18,V8), path-{F}(V19,V20,V4), shortest_path-{F}(V21,V22,V4) | P_tail_of-{T}(V6,V2)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2709: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V20; #2690 ), references = 1, size of lhs = 22:
% 19.17/19.35 complete-{F}(), P_empty-{F}(V0), sequential-{F}(V1,V2), V2 == V1, pppp4-{F}(V1,V2), on_path-{F}(V2,V3), on_path-{F}(V2,V4), on_path-{F}(V1,V4), precedes-{F}(V1,V2,V4), precedes-{F}(V1,V2,V5), pppp21-{F}(V6,V1,V2), on_path-{F}(V2,V7), on_path-{F}(V1,V7), precedes-{F}(V1,V2,V7), on_path-{F}(V2,V8), path-{F}(V9,V10,V3), shortest_path-{F}(V11,V12,V5), path-{F}(V13,V14,V4), shortest_path-{F}(V15,V16,V4), path-{F}(V17,V18,V7), shortest_path-{F}(V19,V20,V7), path-{F}(V21,V22,V8) | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2735: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V20, V20 == V21, V21 == V22, V22 == V23; #2714 ), references = 1, size of lhs = 14:
% 19.17/19.35 complete-{F}(), P_empty-{F}(V0), on_path-{F}(V1,V2), on_path-{F}(V1,V3), pppp22-{F}(V3,V1), on_path-{F}(V1,V4), path-{F}(V5,V6,V3), path-{F}(V7,V8,V2), shortest_path-{F}(V9,V10,V3), path-{F}(V11,V12,V3), shortest_path-{F}(V13,V14,V3), path-{F}(V15,V16,V3), shortest_path-{F}(V17,V18,V3), path-{F}(V19,V20,V4) | pppp21-{T}(V3,V1,V1)
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2770: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V20, V20 == V21, V21 == V22, V22 == V23, V23 == V24, V24 == V25, V25 == V26, V26 == V27, V27 == V28; #2744 ), references = 1, size of lhs = 6:
% 19.17/19.35 complete-{F}(), P_empty-{F}(V0), pppp24-{F}(V1,V2), pppp22-{F}(V1,V3), on_path-{F}(V3,V1), P_length_of-{F}(V1,V4) | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2797: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V20, V20 == V21, V21 == V22, V22 == V23, V23 == V24, V24 == V25, V25 == V26, V26 == V27; #2771 ), references = 1, size of lhs = 5:
% 19.17/19.35 complete-{F}(), P_empty-{F}(V0), pppp24-{F}(V1,V2), pppp22-{F}(V1,V3), on_path-{F}(V3,V1) | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2825: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V20, V20 == V21, V21 == V22, V22 == V23, V23 == V24, V24 == V25, V25 == V26, V26 == V27; #2799 ), references = 1, size of lhs = 4:
% 19.17/19.35 complete-{F}(), pppp25-{F}(V0), P_empty-{F}(V1), pppp24-{F}(V0,V2) | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2852: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V20, V20 == V21, V21 == V22, V22 == V23, V23 == V24, V24 == V25, V25 == V26, V26 == V27; #2826 ), references = 1, size of lhs = 3:
% 19.17/19.35 complete-{F}(), pppp25-{F}(V0), P_empty-{F}(V1) | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2880: mergings( V0 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V20, V20 == V21, V21 == V22, V22 == V23, V23 == V24, V24 == V25, V25 == V26, V26 == V27, V27 == V28, V28 == V29, V29 == V30, V30 == V31, V31 == V32; #2853 ), references = 1, size of lhs = 7:
% 19.17/19.35 complete-{F}(), P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_graph-{F}(V4), P_empty-{F}(V5) | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2914: mergings( V1 == V6, V6 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V20, V20 == V21, V21 == V22, V22 == V23, V23 == V24, V24 == V25, V25 == V26, V26 == V27, V27 == V28, V28 == V29, V29 == V30, V30 == V31, V31 == V32, V32 == V33, V33 == V34, V34 == V35, V35 == V36, V2 == V7, V3 == V8, V4 == V9, V5 == V10; #2882 ), references = 1, size of lhs = 5:
% 19.17/19.35 P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_empty-{F}(V4) | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2946: mergings( V1 == V5, V5 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V20, V20 == V21, V21 == V22, V22 == V23, V23 == V24, V24 == V25, V25 == V26, V26 == V27, V27 == V28, V28 == V29, V29 == V30, V30 == V31, V31 == V32, V32 == V33, V33 == V34, V2 == V6, V3 == V7, V4 == V8; #2915 ), references = 1, size of lhs = 4:
% 19.17/19.35 P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_empty-{F}(V3) | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #2977: mergings( V1 == V4, V4 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V20, V20 == V21, V21 == V22, V22 == V23, V23 == V24, V24 == V25, V25 == V26, V26 == V27, V27 == V28, V28 == V29, V29 == V30, V30 == V31, V31 == V32, V2 == V5, V3 == V6; #2947 ), references = 1, size of lhs = 3:
% 19.17/19.35 P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_empty-{F}(V2) | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #3007: mergings( V1 == V3, V3 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V20, V20 == V21, V21 == V22, V22 == V23, V23 == V24, V24 == V25, V25 == V26, V26 == V27, V27 == V28, V28 == V29, V29 == V30, V2 == V4; #2978 ), references = 1, size of lhs = 2:
% 19.17/19.35 P_edges-{F}(V0), P_empty-{F}(V1) | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #3036: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V20, V20 == V21, V21 == V22, V22 == V23, V23 == V24, V24 == V25, V25 == V26, V26 == V27, V27 == V28; #3008 ), references = 1, size of lhs = 1:
% 19.17/19.35 P_empty-{F}(V0) | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 #3038: exists( #101, #3008 ), references = 1, size of lhs = 0:
% 19.17/19.35 FALSE | FALSE
% 19.17/19.35 (used 0 times, uses = {})
% 19.17/19.35
% 19.17/19.35 number of learnt formulas = 66
% 19.17/19.35
% 19.17/19.35
% 19.17/19.35 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.17/19.35
% 19.17/19.35 randbase = 1
%------------------------------------------------------------------------------