TSTP Solution File: GRA012+1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : GRA012+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n012.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 17.21s 17.41s
% Output : Refutation 17.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRA012+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.03/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n012.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 07:50:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 17.21/17.41 GeoParameters:
% 17.21/17.41
% 17.21/17.41 tptp_input = 1
% 17.21/17.41 tptp_output = 0
% 17.21/17.41 nonempty = 1
% 17.21/17.41 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.21/17.41 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 17.21/17.41
% 17.21/17.41
% 17.21/17.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.21/17.41 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.21/17.41
% 17.21/17.41 RuleSystem INPUT:
% 17.21/17.41
% 17.21/17.41 Initial Rules:
% 17.21/17.41 #0: input, references = 6, size of lhs = 3:
% 17.21/17.41 P_head_of-{F}(V0,V2), P_tail_of-{F}(V0,V2), edge-{F}(V0) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1: input, references = 8, size of lhs = 3:
% 17.21/17.41 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), edge-{F}(V0) | vertex-{T}(V1)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #2: input, references = 5, size of lhs = 3:
% 17.21/17.41 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), edge-{F}(V0) | vertex-{T}(V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #3: input, references = 4, size of lhs = 4:
% 17.21/17.41 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0 | EXISTS V2: pppp9-{T}(V1,V0,V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #4: input, references = 11, size of lhs = 1:
% 17.21/17.41 pppp9-{F}(V0,V1,V2) | pppp8-{T}(V2,V0,V1)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #5: input, references = 4, size of lhs = 3:
% 17.21/17.41 pppp8-{F}(V0,V1,V2), pppp1-{F}(V0,V1,V2), pppp0-{F}(V0,V1,V2) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #6: input, references = 6, size of lhs = 1:
% 17.21/17.41 pppp8-{F}(V0,V1,V2) | pppp0-{T}(V0,V1,V2), pppp1-{T}(V0,V1,V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #7: input, references = 4, size of lhs = 1:
% 17.21/17.41 pppp8-{F}(V0,V1,V2) | edge-{T}(V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #8: input, references = 5, size of lhs = 4:
% 17.21/17.41 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp1-{F}(V0,V1,V2), V2 == V3 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #9: input, references = 7, size of lhs = 4:
% 17.21/17.41 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp1-{F}(V0,V1,V2), V1 == V4 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #10: input, references = 12, size of lhs = 2:
% 17.21/17.41 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | pppp1-{T}(V0,V4,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #11: input, references = 5, size of lhs = 4:
% 17.21/17.41 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp0-{F}(V0,V1,V2), V1 == V3 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #12: input, references = 6, size of lhs = 4:
% 17.21/17.41 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp0-{F}(V0,V1,V2), V2 == V4 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #13: input, references = 3, size of lhs = 2:
% 17.21/17.41 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | pppp0-{T}(V0,V3,V4)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #14: input, references = 3, size of lhs = 7:
% 17.21/17.41 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)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #15: input, references = 3, size of lhs = 9:
% 17.21/17.41 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)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #16: input, references = 3, size of lhs = 2:
% 17.21/17.41 P_empty-{F}(V0), path-{F}(V1,V2,V3) | vertex-{T}(V1)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #17: input, references = 3, size of lhs = 2:
% 17.21/17.41 P_empty-{F}(V0), path-{F}(V1,V2,V3) | vertex-{T}(V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #18: input, references = 3, size of lhs = 2:
% 17.21/17.41 P_empty-{F}(V0), path-{F}(V1,V2,V3) | EXISTS V4: pppp11-{T}(V1,V2,V3,V4)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #19: input, references = 4, size of lhs = 2:
% 17.21/17.41 pppp11-{F}(V0,V1,V2,V3), P_tail_of-{F}(V3,V4) | pppp10-{T}(V3,V0,V1,V2,V4)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #20: input, references = 3, size of lhs = 3:
% 17.21/17.41 pppp10-{F}(V0,V1,V2,V3,V4), pppp3-{F}(V0,V2,V3), pppp2-{F}(V0,V2,V3) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #21: input, references = 5, size of lhs = 1:
% 17.21/17.41 pppp10-{F}(V0,V1,V2,V3,V4) | pppp2-{T}(V0,V2,V3), pppp3-{T}(V0,V2,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #22: input, references = 4, size of lhs = 2:
% 17.21/17.41 pppp10-{F}(V0,V1,V2,V3,V4), V1 == V4 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #23: input, references = 3, size of lhs = 1:
% 17.21/17.41 pppp10-{F}(V0,V1,V2,V3,V4) | edge-{T}(V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #24: input, references = 3, size of lhs = 3:
% 17.21/17.41 P_empty-{F}(V0), P_head_of-{F}(V1,V4), pppp3-{F}(V1,V2,V3) | EXISTS V5: pppp12-{T}(V1,V2,V3,V5,V4)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #25: input, references = 3, size of lhs = 4:
% 17.21/17.41 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)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #26: input, references = 4, size of lhs = 3:
% 17.21/17.41 pppp12-{F}(V0,V1,V2,V3,V4), P_path_cons-{F}(V0,V3,V5), V2 == V5 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #27: input, references = 3, size of lhs = 2:
% 17.21/17.41 pppp12-{F}(V0,V1,V2,V3,V4), P_path_cons-{F}(V0,V3,V5) | path-{T}(V4,V1,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #28: input, references = 4, size of lhs = 5:
% 17.21/17.41 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
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #29: input, references = 4, size of lhs = 5:
% 17.21/17.41 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
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #30: input, references = 3, size of lhs = 3:
% 17.21/17.41 P_empty-{F}(V0), P_head_of-{F}(V1,V4), P_path_cons-{F}(V1,V0,V5) | pppp2-{T}(V1,V4,V5)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #31: input, references = 7, size of lhs = 5:
% 17.21/17.41 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)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #32: input, references = 3, size of lhs = 5:
% 17.21/17.41 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)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #33: input, references = 3, size of lhs = 5:
% 17.21/17.41 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)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #34: input, references = 3, size of lhs = 3:
% 17.21/17.41 P_empty-{F}(V0), path-{F}(V3,V2,V1), in_path-{F}(V4,V1) | vertex-{T}(V4)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #35: input, references = 3, size of lhs = 3:
% 17.21/17.41 P_empty-{F}(V0), path-{F}(V3,V2,V1), in_path-{F}(V4,V1) | EXISTS V5: pppp13-{T}(V5,V1,V4)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #36: input, references = 6, size of lhs = 5:
% 17.21/17.41 pppp13-{F}(V0,V1,V2), P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), V2 == V3, V2 == V4 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #37: input, references = 3, size of lhs = 3:
% 17.21/17.41 pppp13-{F}(V0,V1,V2), P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | on_path-{T}(V0,V1)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #38: input, references = 6, size of lhs = 2:
% 17.21/17.41 P_empty-{F}(V0), sequential-{F}(V1,V2) | pppp4-{T}(V1,V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #39: input, references = 8, size of lhs = 2:
% 17.21/17.41 P_empty-{F}(V0), pppp4-{F}(V1,V2) | sequential-{T}(V1,V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #40: input, references = 13, size of lhs = 3:
% 17.21/17.41 P_empty-{F}(V0), P_head_of-{F}(V1,V3), P_tail_of-{F}(V2,V4) | pppp14-{T}(V1,V2,V3,V4)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #41: input, references = 8, size of lhs = 4:
% 17.21/17.41 pppp14-{F}(V0,V1,V3,V3), edge-{F}(V0), edge-{F}(V1), V0 == V1 | pppp4-{T}(V0,V1)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #42: input, references = 6, size of lhs = 3:
% 17.21/17.41 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1), V2 == V3 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #43: input, references = 4, size of lhs = 2:
% 17.21/17.41 pppp14-{F}(V1,V1,V2,V3), pppp4-{F}(V1,V1) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #44: input, references = 3, size of lhs = 2:
% 17.21/17.41 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1) | edge-{T}(V1)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #45: input, references = 4, size of lhs = 2:
% 17.21/17.41 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1) | edge-{T}(V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #46: input, references = 10, size of lhs = 5:
% 17.21/17.41 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)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #47: input, references = 4, size of lhs = 6:
% 17.21/17.41 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)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #48: input, references = 3, size of lhs = 3:
% 17.21/17.41 P_empty-{F}(V0), precedes-{F}(V2,V3,V1), path-{F}(V5,V4,V1) | pppp15-{T}(V1,V2,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #49: input, references = 3, size of lhs = 3:
% 17.21/17.41 pppp15-{F}(V0,V1,V2), pppp5-{F}(V0,V1,V2), sequential-{F}(V1,V2) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #50: input, references = 3, size of lhs = 1:
% 17.21/17.41 pppp15-{F}(V0,V1,V2) | sequential-{T}(V1,V2), pppp5-{T}(V0,V1,V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #51: input, references = 3, size of lhs = 1:
% 17.21/17.41 pppp15-{F}(V0,V1,V2) | on_path-{T}(V2,V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #52: input, references = 3, size of lhs = 1:
% 17.21/17.41 pppp15-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #53: input, references = 3, size of lhs = 2:
% 17.21/17.41 P_empty-{F}(V0), pppp5-{F}(V1,V2,V3) | EXISTS V4: pppp16-{T}(V1,V2,V3,V4)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #54: input, references = 3, size of lhs = 3:
% 17.21/17.41 P_empty-{F}(V0), sequential-{F}(V2,V4), precedes-{F}(V4,V3,V1) | pppp5-{T}(V1,V2,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #55: input, references = 3, size of lhs = 1:
% 17.21/17.41 pppp16-{F}(V0,V1,V2,V3) | precedes-{T}(V3,V2,V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #56: input, references = 3, size of lhs = 1:
% 17.21/17.41 pppp16-{F}(V0,V1,V2,V3) | sequential-{T}(V1,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #57: input, references = 6, size of lhs = 2:
% 17.21/17.41 P_empty-{F}(V0), shortest_path-{F}(V1,V2,V3) | pppp6-{T}(V1,V2,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #58: input, references = 3, size of lhs = 2:
% 17.21/17.41 P_empty-{F}(V0), pppp6-{F}(V1,V2,V3) | shortest_path-{T}(V1,V2,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #59: input, references = 6, size of lhs = 3:
% 17.21/17.41 P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V1,V2,V3) | path-{T}(V1,V2,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #60: input, references = 3, size of lhs = 3:
% 17.21/17.41 P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V2,V2,V3) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #61: input, references = 4, size of lhs = 5:
% 17.21/17.41 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)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #62: input, references = 4, size of lhs = 4:
% 17.21/17.41 P_empty-{F}(V0), P_length_of-{F}(V3,V4), path-{F}(V1,V2,V3), V1 == V2 | pppp6-{T}(V1,V2,V3), pppp24-{T}(V1,V2,V4)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #63: input, references = 4, size of lhs = 1:
% 17.21/17.41 pppp24-{F}(V0,V1,V2) | EXISTS V3: pppp17-{T}(V0,V1,V3,V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #64: input, references = 4, size of lhs = 3:
% 17.21/17.41 pppp17-{F}(V0,V1,V2,V3), P_length_of-{F}(V2,V4), less_or_equal-{F}(V3,V4) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #65: input, references = 4, size of lhs = 2:
% 17.21/17.41 pppp17-{F}(V0,V1,V2,V3), P_length_of-{F}(V2,V4) | path-{T}(V0,V1,V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #66: input, references = 7, size of lhs = 7:
% 17.21/17.41 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
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #67: input, references = 6, size of lhs = 6:
% 17.21/17.41 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
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #68: input, references = 3, size of lhs = 2:
% 17.21/17.41 P_empty-{F}(V0), triangle-{F}(V1,V2,V3) | pppp7-{T}(V1,V2,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #69: input, references = 4, size of lhs = 2:
% 17.21/17.41 P_empty-{F}(V0), pppp7-{F}(V1,V2,V3) | triangle-{T}(V1,V2,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #70: input, references = 3, size of lhs = 2:
% 17.21/17.41 P_empty-{F}(V0), pppp7-{F}(V1,V2,V3) | pppp18-{T}(V1,V2,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #71: input, references = 4, size of lhs = 7:
% 17.21/17.41 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)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #72: input, references = 3, size of lhs = 1:
% 17.21/17.41 pppp18-{F}(V0,V1,V2) | sequential-{T}(V2,V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #73: input, references = 3, size of lhs = 1:
% 17.21/17.41 pppp18-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #74: input, references = 3, size of lhs = 1:
% 17.21/17.41 pppp18-{F}(V0,V1,V2) | sequential-{T}(V0,V1)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #75: input, references = 3, size of lhs = 1:
% 17.21/17.41 pppp18-{F}(V0,V1,V2) | edge-{T}(V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #76: input, references = 3, size of lhs = 1:
% 17.21/17.41 pppp18-{F}(V0,V1,V2) | edge-{T}(V1)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #77: input, references = 3, size of lhs = 1:
% 17.21/17.41 pppp18-{F}(V0,V1,V2) | edge-{T}(V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #78: input, references = 5, size of lhs = 6:
% 17.21/17.41 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
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #79: input, references = 5, size of lhs = 9:
% 17.21/17.41 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
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #80: input, references = 4, size of lhs = 9:
% 17.21/17.41 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)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #81: input, references = 4, size of lhs = 1:
% 17.21/17.41 pppp20-{F}(V0,V1) | EXISTS V2: pppp19-{T}(V0,V2,V1)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #82: input, references = 4, size of lhs = 1:
% 17.21/17.41 pppp20-{F}(V0,V1) | on_path-{T}(V1,V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #83: input, references = 4, size of lhs = 2:
% 17.21/17.41 pppp19-{F}(V0,V1,V2), triangle-{F}(V1,V2,V3) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #84: input, references = 10, size of lhs = 1:
% 17.21/17.41 pppp19-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #85: input, references = 4, size of lhs = 1:
% 17.21/17.41 pppp19-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #86: input, references = 3, size of lhs = 8:
% 17.21/17.41 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)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #87: input, references = 6, size of lhs = 6:
% 17.21/17.41 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}()
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #88: input, references = 7, size of lhs = 6:
% 17.21/17.41 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: pppp23-{T}(V6,V3,V4)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #89: input, references = 6, size of lhs = 4:
% 17.21/17.41 pppp23-{F}(V0,V1,V2), P_number_of_in-{F}(V2,V0,V3), P_length_of-{F}(V0,V4), P_minus-{F}(V4,V1,V5) | EXISTS V6: pppp22-{T}(V0,V6)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #90: input, references = 7, size of lhs = 4:
% 17.21/17.41 pppp23-{F}(V0,V1,V2), P_number_of_in-{F}(V2,V0,V5), P_length_of-{F}(V0,V4), P_minus-{F}(V4,V1,V5) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #91: input, references = 6, size of lhs = 1:
% 17.21/17.41 pppp22-{F}(V0,V1) | EXISTS V2: pppp21-{T}(V1,V0,V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #92: input, references = 6, size of lhs = 1:
% 17.21/17.41 pppp21-{F}(V0,V1,V2) | shortest_path-{T}(V2,V0,V1)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #93: input, references = 13, size of lhs = 1:
% 17.21/17.41 #-{F} V0 | EXISTS V1: P_head_of-{T}(V0,V1)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #94: input, references = 13, size of lhs = 1:
% 17.21/17.41 #-{F} V0 | EXISTS V1: P_tail_of-{T}(V0,V1)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #95: input, references = 5, size of lhs = 2:
% 17.21/17.41 #-{F} V0, #-{F} V1 | EXISTS V2: P_path_cons-{T}(V0,V1,V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #96: input, references = 4, size of lhs = 0:
% 17.21/17.41 FALSE | EXISTS V0: P_empty-{T}(V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #97: input, references = 8, size of lhs = 1:
% 17.21/17.41 #-{F} V0 | EXISTS V1: P_length_of-{T}(V0,V1)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #98: input, references = 17, size of lhs = 2:
% 17.21/17.41 #-{F} V0, #-{F} V1 | EXISTS V2: P_number_of_in-{T}(V0,V1,V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #99: input, references = 4, size of lhs = 0:
% 17.21/17.41 FALSE | EXISTS V0: P_edges-{T}(V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #100: input, references = 4, size of lhs = 0:
% 17.21/17.41 FALSE | EXISTS V0: P_sequential_pairs-{T}(V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #101: input, references = 7, size of lhs = 2:
% 17.21/17.41 #-{F} V0, #-{F} V1 | EXISTS V2: P_minus-{T}(V0,V1,V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #102: input, references = 5, size of lhs = 0:
% 17.21/17.41 FALSE | EXISTS V0: P_n1-{T}(V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #103: input, references = 5, size of lhs = 0:
% 17.21/17.41 FALSE | EXISTS V0: P_triangles-{T}(V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #104: input, references = 7, size of lhs = 0:
% 17.21/17.41 FALSE | EXISTS V0: P_graph-{T}(V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 number of initial rules = 105
% 17.21/17.41
% 17.21/17.41 Simplifiers:
% 17.21/17.41 #105: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 P_head_of-{F}(V0,V1), P_head_of-{F}(V0,V3), V1 == V3 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #106: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 P_tail_of-{F}(V0,V1), P_tail_of-{F}(V0,V3), V1 == V3 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #107: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 P_path_cons-{F}(V0,V1,V2), P_path_cons-{F}(V0,V1,V5), V2 == V5 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #108: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 P_empty-{F}(V0), P_empty-{F}(V1), V0 == V1 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #109: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 P_length_of-{F}(V0,V1), P_length_of-{F}(V0,V3), V1 == V3 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #110: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 P_number_of_in-{F}(V0,V1,V2), P_number_of_in-{F}(V0,V1,V5), V2 == V5 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #111: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 P_edges-{F}(V0), P_edges-{F}(V1), V0 == V1 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #112: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 P_sequential_pairs-{F}(V0), P_sequential_pairs-{F}(V1), V0 == V1 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #113: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 P_minus-{F}(V0,V1,V2), P_minus-{F}(V0,V1,V5), V2 == V5 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #114: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 P_n1-{F}(V0), P_n1-{F}(V1), V0 == V1 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #115: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 P_triangles-{F}(V0), P_triangles-{F}(V1), V0 == V1 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #116: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 P_graph-{F}(V0), P_graph-{F}(V1), V0 == V1 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #117: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp8-{F}(V0,V1,V2), pppp8-{F}(V3,V1,V2), V0 == V3 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #118: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp9-{F}(V0,V1,V2), pppp9-{F}(V0,V1,V5), V2 == V5 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #119: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V5,V1,V2,V3,V9), V0 == V5 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #120: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #121: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp11-{F}(V0,V1,V2,V3), pppp11-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #122: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V1,V2,V8,V4), V3 == V8 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #123: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #124: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp13-{F}(V0,V1,V2), pppp13-{F}(V3,V1,V2), V0 == V3 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #125: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp14-{F}(V0,V1,V2,V3), pppp14-{F}(V0,V5,V6,V7), V2 == V6 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #126: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp14-{F}(V0,V1,V2,V3), pppp14-{F}(V4,V1,V6,V7), V3 == V7 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #127: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp16-{F}(V0,V1,V2,V3), pppp16-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #128: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp17-{F}(V0,V1,V2,V3), pppp17-{F}(V0,V1,V6,V3), V2 == V6 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #129: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp19-{F}(V0,V1,V2), pppp19-{F}(V0,V4,V2), V1 == V4 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #130: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp19-{F}(V0,V1,V2), pppp19-{F}(V0,V4,V5), V2 == V5 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #131: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp20-{F}(V0,V1), pppp20-{F}(V0,V3), V1 == V3 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #132: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp21-{F}(V0,V1,V2), pppp21-{F}(V0,V1,V5), V2 == V5 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #133: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp21-{F}(V0,V1,V2), pppp21-{F}(V3,V1,V5), V0 == V3 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #134: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp22-{F}(V0,V1), pppp22-{F}(V0,V3), V1 == V3 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #135: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp23-{F}(V0,V1,V2), pppp23-{F}(V3,V1,V2), V0 == V3 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #136: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp23-{F}(V0,V1,V2), pppp23-{F}(V3,V4,V5), V1 == V4 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #137: unsound, references = 3, size of lhs = 3:
% 17.21/17.41 pppp23-{F}(V0,V1,V2), pppp23-{F}(V3,V4,V5), V2 == V5 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 number of simplifiers = 33
% 17.21/17.41
% 17.21/17.41 Learnt:
% 17.21/17.41 #145: mergings( V3 == V4, V4 == V5, V7 == V8; #141 ), references = 1, size of lhs = 6:
% 17.21/17.41 P_empty-{F}(V0), P_edges-{F}(V1), pppp22-{F}(V2,V3), P_length_of-{F}(V2,V4), P_number_of_in-{F}(V1,V2,V5), V4 == V5 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #151: mergings( V7 == V8, V8 == V9, V4 == V11, V11 == V12; #146 ), references = 2, size of lhs = 8:
% 17.21/17.41 P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), P_number_of_in-{F}(V1,V2,V4), V3 == V4, pppp23-{F}(V2,V5,V6), P_number_of_in-{F}(V6,V2,V7), P_minus-{F}(V3,V5,V8) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #157: mergings( V3 == V4, V4 == V5, V6 == V7, V7 == V8; #152 ), references = 1, size of lhs = 6:
% 17.21/17.41 P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), pppp23-{F}(V2,V4,V5), P_number_of_in-{F}(V5,V2,V6), P_minus-{F}(V3,V4,V7) | P_number_of_in-{T}(V1,V2,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #167: mergings( V3 == V4, V4 == V5, V9 == V11; #163 ), references = 1, size of lhs = 9:
% 17.21/17.41 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp22-{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
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #173: mergings( V7 == V8, V8 == V9, V4 == V13, V13 == V15; #168 ), references = 5, size of lhs = 11:
% 17.21/17.41 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, pppp23-{F}(V4,V8,V9), P_number_of_in-{F}(V9,V4,V10), P_minus-{F}(V6,V8,V11) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #189: mergings( V3 == V4, V4 == V5, V5 == V7, V7 == V8, V8 == V9, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V6 == V10, V19 == V21, V20 == V22; #175 ), references = 2, size of lhs = 9:
% 17.21/17.41 P_sequential_pairs-{F}(V0), P_edges-{F}(V0), P_empty-{F}(V1), P_n1-{F}(V2), P_length_of-{F}(V3,V4), P_minus-{F}(V4,V2,V5), V4 == V5, pppp23-{F}(V3,V6,V7), P_minus-{F}(V4,V6,V8) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #192: exists( #101, #151 ), references = 2, size of lhs = 7:
% 17.21/17.41 P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), P_number_of_in-{F}(V1,V2,V4), V3 == V4, pppp23-{F}(V2,V5,V6), P_number_of_in-{F}(V6,V2,V7) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #194: exists( #98, #190 ), references = 2, size of lhs = 5:
% 17.21/17.41 P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), pppp23-{F}(V2,V4,V5), P_number_of_in-{F}(V5,V2,V6) | P_number_of_in-{T}(V1,V2,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #197: exists( #101, #189 ), references = 1, size of lhs = 6:
% 17.21/17.41 P_sequential_pairs-{F}(V0), P_edges-{F}(V0), P_empty-{F}(V1), P_n1-{F}(V2), P_length_of-{F}(V3,V4), pppp23-{F}(V3,V2,V5) | P_minus-{T}(V4,V2,V4)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #212: exists( #95, #26 ), references = 1, size of lhs = 1:
% 17.21/17.41 pppp12-{F}(V0,V1,V2,V3,V4) | P_path_cons-{T}(V0,V3,V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #215: exists( #94, #213 ), references = 1, size of lhs = 1:
% 17.21/17.41 pppp11-{F}(V0,V1,V2,V3) | P_tail_of-{T}(V3,V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #223: exists( #98, #78 ), references = 1, size of lhs = 4:
% 17.21/17.41 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)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #226: exists( #95, #28 ), references = 1, size of lhs = 4:
% 17.21/17.41 P_empty-{F}(V0), P_head_of-{F}(V1,V2), pppp2-{F}(V1,V3,V4), V3 == V2 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #228: mergings( V4 == V3; #225 ), references = 1, size of lhs = 3:
% 17.21/17.41 P_empty-{F}(V0), P_head_of-{F}(V1,V2), pppp2-{F}(V1,V2,V3) | P_path_cons-{T}(V1,V0,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #230: exists( #93, #224 ), references = 1, size of lhs = 2:
% 17.21/17.41 P_empty-{F}(V0), pppp2-{F}(V1,V2,V3) | P_head_of-{T}(V1,V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #232: exists( #94, #9 ), references = 1, size of lhs = 2:
% 17.21/17.41 P_head_of-{F}(V0,V1), pppp1-{F}(V0,V2,V3) | P_tail_of-{T}(V0,V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #235: exists( #101, #79 ), references = 1, size of lhs = 7:
% 17.21/17.41 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)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #248: exists( #94, #36 ), references = 2, size of lhs = 3:
% 17.21/17.41 P_head_of-{F}(V0,V1), pppp13-{F}(V0,V2,V3), V3 == V1 | P_tail_of-{T}(V0,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #251: exists( #93, #249 ), references = 1, size of lhs = 3:
% 17.21/17.41 pppp13-{F}(V0,V1,V2), pppp13-{F}(V0,V3,V4), V4 == V2 | P_head_of-{T}(V0,V2), P_head_of-{T}(V0,V4)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #256: disj( #250, #40+#42 ), references = 1, size of lhs = 7:
% 17.21/17.41 P_empty-{F}(V0), pppp4-{F}(V1,V2), P_tail_of-{F}(V2,V3), pppp13-{F}(V1,V4,V5), V5 == V3, pppp13-{F}(V1,V6,V7), V7 == V5 | P_head_of-{T}(V1,V7)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #257: disj( #250, #248+#66 ), references = 1, size of lhs = 9:
% 17.21/17.41 P_empty-{F}(V0), P_head_of-{F}(V1,V2), pppp13-{F}(V3,V4,V2), precedes-{F}(V3,V1,V5), pppp13-{F}(V3,V6,V7), V7 == V2, pppp13-{F}(V3,V8,V9), V9 == V2, shortest_path-{F}(V10,V11,V5) | P_head_of-{T}(V3,V7)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #275: exists( #94, #66 ), references = 5, size of lhs = 5:
% 17.21/17.41 P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_head_of-{F}(V3,V2), precedes-{F}(V3,V1,V4), shortest_path-{F}(V5,V6,V4) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #279: exists( #93, #277 ), references = 4, size of lhs = 3:
% 17.21/17.41 P_empty-{F}(V0), pppp4-{F}(V1,V2), P_tail_of-{F}(V2,V3) | P_head_of-{T}(V1,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #310: disj( #21, input ), references = 1, size of lhs = 5:
% 17.21/17.41 P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_path_cons-{F}(V1,V0,V3), pppp10-{F}(V1,V4,V5,V6,V7), V6 == V3 | pppp3-{T}(V1,V5,V6)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #380: exists( #93, #36 ), references = 1, size of lhs = 3:
% 17.21/17.41 P_tail_of-{F}(V0,V1), pppp13-{F}(V0,V2,V3), V3 == V1 | P_head_of-{T}(V0,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #421: exists( #97, #419 ), references = 1, size of lhs = 5:
% 17.21/17.41 P_empty-{F}(V0), P_length_of-{F}(V1,V2), pppp6-{F}(V3,V4,V1), pppp17-{F}(V3,V4,V5,V6), pppp17-{F}(V7,V8,V5,V2) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #423: exists( #63, #420 ), references = 1, size of lhs = 4:
% 17.21/17.41 P_empty-{F}(V0), P_length_of-{F}(V1,V2), pppp24-{F}(V3,V4,V2), pppp6-{F}(V3,V4,V1) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #426: mergings( V0 == V5; #424 ), references = 1, size of lhs = 6:
% 17.21/17.41 P_empty-{F}(V0), P_length_of-{F}(V1,V2), P_length_of-{F}(V3,V2), path-{F}(V4,V5,V1), V4 == V5, pppp6-{F}(V4,V5,V3) | pppp6-{T}(V4,V5,V1)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #429: exists( #94, #8 ), references = 6, size of lhs = 3:
% 17.21/17.41 P_head_of-{F}(V0,V1), pppp1-{F}(V0,V2,V3), V3 == V1 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #431: exists( #93, #427 ), references = 1, size of lhs = 1:
% 17.21/17.41 pppp1-{F}(V0,V1,V2) | P_head_of-{T}(V0,V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #549: disj( #6, input ), references = 4, size of lhs = 4:
% 17.21/17.41 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), pppp8-{F}(V0,V3,V4), V3 == V1 | pppp1-{T}(V0,V3,V4)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #602: mergings( V2 == V3; #600 ), references = 8, size of lhs = 3:
% 17.21/17.41 P_head_of-{F}(V0,V1), pppp8-{F}(V0,V2,V3), V2 == V1 | P_tail_of-{T}(V0,V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #637: exists( #93, #633 ), references = 6, size of lhs = 3:
% 17.21/17.41 P_tail_of-{F}(V0,V1), pppp8-{F}(V0,V2,V3), V1 == V2 | P_head_of-{T}(V0,V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #680: disj( #6, exists( #94, #8 ) ), references = 4, size of lhs = 3:
% 17.21/17.41 P_head_of-{F}(V0,V1), pppp8-{F}(V0,V2,V3), V3 == V1 | pppp0-{T}(V0,V2,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #682: mergings( V2 == V3; #679 ), references = 1, size of lhs = 4:
% 17.21/17.41 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), pppp8-{F}(V0,V3,V1), V3 == V2 | pppp0-{T}(V0,V3,V1)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #748: exists( #94, #12 ), references = 2, size of lhs = 2:
% 17.21/17.41 P_head_of-{F}(V0,V1), pppp0-{F}(V0,V2,V3) | P_tail_of-{T}(V0,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #850: disj( #6, #847+#275 ), references = 1, size of lhs = 5:
% 17.21/17.41 P_empty-{F}(V0), P_head_of-{F}(V1,V2), pppp8-{F}(V3,V4,V2), precedes-{F}(V3,V1,V5), shortest_path-{F}(V6,V7,V5) | pppp0-{T}(V3,V4,V2)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #856: exists( #93, #852 ), references = 1, size of lhs = 2:
% 17.21/17.41 pppp8-{F}(V0,V1,V2), pppp8-{F}(V0,V3,V4) | P_head_of-{T}(V0,V1), P_head_of-{T}(V0,V4), P_head_of-{T}(V0,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #857: exists( #93, #853 ), references = 1, size of lhs = 3:
% 17.21/17.41 pppp8-{F}(V0,V1,V2), pppp0-{F}(V0,V3,V4), V4 == V1 | P_head_of-{T}(V0,V1)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #880: mergings( V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V14, V14 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V20, V20 == V25; #868 ), references = 1, size of lhs = 24:
% 17.21/17.41 edge-{F}(V0), P_tail_of-{F}(V0,V1), edge-{F}(V2), sequential-{F}(V0,V2), P_head_of-{F}(V2,V3), V3 == V1, pppp19-{F}(V4,V0,V2), edge-{F}(V5), P_tail_of-{F}(V5,V6), edge-{F}(V7), sequential-{F}(V5,V7), P_head_of-{F}(V7,V8), V8 == V6, edge-{F}(V9), V9 == V0, V2 == V9, V9 == V5, V7 == V9, pppp8-{F}(V9,V1,V10), pppp8-{F}(V9,V6,V11), pppp8-{F}(V9,V12,V3), pppp8-{F}(V9,V13,V8), P_empty-{F}(V14), pppp19-{F}(V15,V5,V7) | P_head_of-{T}(V9,V11)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #898: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V10, V10 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V19, V19 == V21; #885 ), references = 1, size of lhs = 21:
% 17.21/17.41 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0, edge-{F}(V2), P_tail_of-{F}(V2,V1), edge-{F}(V3), sequential-{F}(V2,V3), P_head_of-{F}(V3,V0), pppp19-{F}(V4,V2,V3), edge-{F}(V5), P_tail_of-{F}(V5,V1), edge-{F}(V6), sequential-{F}(V5,V6), P_head_of-{F}(V6,V0), pppp19-{F}(V7,V5,V6), P_empty-{F}(V8), P_head_of-{F}(V9,V0), P_tail_of-{F}(V10,V1), precedes-{F}(V10,V9,V11), shortest_path-{F}(V12,V13,V11) | pppp9-{T}(V1,V0,V2), pppp9-{T}(V1,V0,V3), pppp9-{T}(V1,V0,V5), pppp9-{T}(V1,V0,V6)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #931: mergings( V26 == V27, V29 == V30, V1 == V28, V28 == V31, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V9, V9 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V18, V18 == V20; #906 ), references = 1, size of lhs = 27:
% 17.21/17.41 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0, edge-{F}(V2), P_tail_of-{F}(V2,V1), edge-{F}(V3), sequential-{F}(V2,V3), P_head_of-{F}(V3,V0), pppp19-{F}(V4,V2,V3), edge-{F}(V5), P_tail_of-{F}(V5,V1), edge-{F}(V6), sequential-{F}(V5,V6), P_head_of-{F}(V6,V0), pppp19-{F}(V7,V5,V6), P_empty-{F}(V8), P_head_of-{F}(V9,V0), P_tail_of-{F}(V10,V1), precedes-{F}(V10,V9,V11), P_head_of-{F}(V2,V12), V0 == V12, V1 == V12, P_head_of-{F}(V5,V13), V0 == V13, V1 == V13, shortest_path-{F}(V14,V15,V11) | pppp9-{T}(V1,V0,V3), pppp9-{T}(V1,V0,V6)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #948: mergings( V26 == V27, V29 == V31, V1 == V28, V28 == V30, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V9, V9 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V18, V18 == V20; #907 ), references = 1, size of lhs = 27:
% 17.21/17.41 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0, edge-{F}(V2), P_tail_of-{F}(V2,V1), edge-{F}(V3), sequential-{F}(V2,V3), P_head_of-{F}(V3,V0), pppp19-{F}(V4,V2,V3), edge-{F}(V5), P_tail_of-{F}(V5,V1), edge-{F}(V6), sequential-{F}(V5,V6), P_head_of-{F}(V6,V0), pppp19-{F}(V7,V5,V6), P_empty-{F}(V8), P_head_of-{F}(V9,V0), P_tail_of-{F}(V10,V1), precedes-{F}(V10,V9,V11), P_head_of-{F}(V2,V12), V0 == V12, V1 == V12, P_head_of-{F}(V5,V13), V1 == V13, V0 == V13, shortest_path-{F}(V14,V15,V11) | pppp9-{T}(V1,V0,V3), pppp9-{T}(V1,V0,V6)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #965: mergings( V26 == V28, V29 == V30, V1 == V27, V27 == V31, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V9, V9 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V18, V18 == V20; #909 ), references = 1, size of lhs = 27:
% 17.21/17.41 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0, edge-{F}(V2), P_tail_of-{F}(V2,V1), edge-{F}(V3), sequential-{F}(V2,V3), P_head_of-{F}(V3,V0), pppp19-{F}(V4,V2,V3), edge-{F}(V5), P_tail_of-{F}(V5,V1), edge-{F}(V6), sequential-{F}(V5,V6), P_head_of-{F}(V6,V0), pppp19-{F}(V7,V5,V6), P_empty-{F}(V8), P_head_of-{F}(V9,V0), P_tail_of-{F}(V10,V1), precedes-{F}(V10,V9,V11), P_head_of-{F}(V2,V12), V1 == V12, V0 == V12, P_head_of-{F}(V5,V13), V0 == V13, V1 == V13, shortest_path-{F}(V14,V15,V11) | pppp9-{T}(V1,V0,V3), pppp9-{T}(V1,V0,V6)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #994: mergings( V24 == V25, V27 == V28, V1 == V26, V26 == V29, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V9, V9 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V18, V18 == V20, V34 == V0; #974 ), references = 1, size of lhs = 30:
% 17.21/17.41 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V0 == V1, edge-{F}(V2), P_tail_of-{F}(V2,V1), edge-{F}(V3), sequential-{F}(V2,V3), P_head_of-{F}(V3,V0), pppp19-{F}(V4,V2,V3), edge-{F}(V5), P_tail_of-{F}(V5,V1), edge-{F}(V6), sequential-{F}(V5,V6), P_head_of-{F}(V6,V0), pppp19-{F}(V7,V5,V6), P_empty-{F}(V8), P_head_of-{F}(V9,V0), P_tail_of-{F}(V10,V1), precedes-{F}(V10,V9,V11), P_head_of-{F}(V2,V12), V0 == V12, V1 == V12, P_head_of-{F}(V5,V13), V0 == V13, V1 == V13, P_tail_of-{F}(V3,V14), V14 == V1, pppp1-{F}(V3,V15,V0), shortest_path-{F}(V16,V17,V11) | pppp9-{T}(V1,V0,V6)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1012: mergings( V0 == V32, V24 == V25, V27 == V28, V1 == V26, V26 == V29, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V9, V9 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V18, V18 == V20; #975 ), references = 1, size of lhs = 29:
% 17.21/17.41 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0, edge-{F}(V2), P_tail_of-{F}(V2,V1), sequential-{F}(V2,V3), edge-{F}(V3), P_head_of-{F}(V3,V0), pppp19-{F}(V4,V2,V3), edge-{F}(V5), P_tail_of-{F}(V5,V1), edge-{F}(V6), sequential-{F}(V5,V6), P_head_of-{F}(V6,V0), pppp19-{F}(V7,V5,V6), P_empty-{F}(V8), P_head_of-{F}(V9,V0), P_tail_of-{F}(V10,V1), precedes-{F}(V10,V9,V11), P_head_of-{F}(V2,V12), V0 == V12, V1 == V12, P_head_of-{F}(V5,V13), V0 == V13, V1 == V13, P_tail_of-{F}(V3,V14), V14 == V1, shortest_path-{F}(V15,V16,V11) | pppp9-{T}(V1,V0,V6)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1031: mergings( V0 == V32, V24 == V25, V27 == V28, V1 == V26, V26 == V29, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V9, V9 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V18, V18 == V20, V35 == V32; #976 ), references = 1, size of lhs = 30:
% 17.21/17.41 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V0 == V1, edge-{F}(V2), P_tail_of-{F}(V2,V1), edge-{F}(V3), sequential-{F}(V2,V3), P_head_of-{F}(V3,V0), pppp19-{F}(V4,V2,V3), edge-{F}(V5), P_tail_of-{F}(V5,V1), edge-{F}(V6), sequential-{F}(V5,V6), P_head_of-{F}(V6,V0), pppp19-{F}(V7,V5,V6), P_empty-{F}(V8), P_head_of-{F}(V9,V0), P_tail_of-{F}(V10,V1), precedes-{F}(V10,V9,V11), P_head_of-{F}(V2,V12), V0 == V12, V1 == V12, P_head_of-{F}(V5,V13), V0 == V13, V1 == V13, P_tail_of-{F}(V3,V14), V14 == V1, pppp1-{F}(V3,V15,V0), shortest_path-{F}(V16,V17,V11) | pppp9-{T}(V1,V0,V6)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1067: mergings( V2 == V23, V3 == V28, V23 == V24, V24 == V25, V25 == V26, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V10, V10 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V18, V18 == V20, V33 == V28; #1046 ), references = 1, size of lhs = 20:
% 17.21/17.41 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_head_of-{F}(V1,V0), edge-{F}(V2), sequential-{F}(V2,V1), pppp19-{F}(V3,V2,V1), sequential-{F}(V2,V4), edge-{F}(V4), P_head_of-{F}(V4,V0), pppp19-{F}(V5,V2,V4), P_empty-{F}(V6), P_head_of-{F}(V7,V0), precedes-{F}(V2,V7,V8), P_head_of-{F}(V2,V9), V0 == V9, P_tail_of-{F}(V1,V10), P_tail_of-{F}(V4,V11), pppp1-{F}(V1,V12,V0), shortest_path-{F}(V13,V14,V8) | P_tail_of-{T}(V2,V0), P_tail_of-{T}(V2,V9), P_tail_of-{T}(V2,V10), P_tail_of-{T}(V2,V11)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1086: mergings( V2 == V23, V23 == V24, V24 == V25, V25 == V26, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V10, V10 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V18, V18 == V20, V32 == V3, V34 == V3; #1047 ), references = 1, size of lhs = 21:
% 17.21/17.41 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_head_of-{F}(V1,V0), edge-{F}(V2), sequential-{F}(V2,V1), pppp19-{F}(V3,V2,V1), edge-{F}(V4), sequential-{F}(V2,V4), P_head_of-{F}(V4,V0), pppp19-{F}(V5,V2,V4), P_empty-{F}(V6), P_head_of-{F}(V7,V0), precedes-{F}(V2,V7,V8), P_head_of-{F}(V2,V9), V0 == V9, P_tail_of-{F}(V1,V10), P_tail_of-{F}(V4,V11), pppp1-{F}(V1,V12,V0), pppp1-{F}(V4,V13,V0), shortest_path-{F}(V14,V15,V8) | P_tail_of-{T}(V2,V0), P_tail_of-{T}(V2,V9), P_tail_of-{T}(V2,V10), P_tail_of-{T}(V2,V11)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1123: mergings( V0 == V27, V26 == V28, V28 == V14, V14 == V22, V22 == V24, V24 == V23, V23 == V25, V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V17, V17 == V19, V32 == V27; #1087 ), references = 3, size of lhs = 20:
% 17.21/17.41 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_head_of-{F}(V1,V0), edge-{F}(V2), P_head_of-{F}(V2,V0), P_empty-{F}(V3), P_head_of-{F}(V4,V0), P_tail_of-{F}(V1,V5), V0 == V5, P_tail_of-{F}(V2,V5), edge-{F}(V6), sequential-{F}(V6,V1), sequential-{F}(V6,V2), P_head_of-{F}(V6,V5), pppp19-{F}(V7,V6,V1), pppp19-{F}(V8,V6,V2), precedes-{F}(V6,V4,V9), pppp1-{F}(V1,V10,V0), shortest_path-{F}(V11,V12,V9) | P_tail_of-{T}(V6,V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1144: mergings( V0 == V27, V26 == V14, V14 == V22, V22 == V24, V24 == V23, V23 == V25, V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V17, V17 == V19, V19 == V33, V32 == V27; #1088 ), references = 1, size of lhs = 25:
% 17.21/17.41 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_head_of-{F}(V1,V0), edge-{F}(V2), P_head_of-{F}(V2,V0), P_head_of-{F}(V3,V0), P_tail_of-{F}(V1,V4), V0 == V4, P_tail_of-{F}(V2,V5), edge-{F}(V6), sequential-{F}(V6,V1), sequential-{F}(V6,V2), P_head_of-{F}(V6,V4), pppp19-{F}(V7,V6,V1), pppp19-{F}(V8,V6,V2), precedes-{F}(V6,V3,V9), P_empty-{F}(V10), P_tail_of-{F}(V11,V5), P_head_of-{F}(V11,V12), P_head_of-{F}(V13,V12), precedes-{F}(V6,V13,V14), pppp1-{F}(V1,V15,V0), shortest_path-{F}(V16,V17,V9), shortest_path-{F}(V18,V19,V14) | P_tail_of-{T}(V6,V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1165: mergings( V0 == V27, V28 == V14, V14 == V22, V22 == V24, V24 == V23, V23 == V25, V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V17, V17 == V19, V19 == V33, V32 == V27; #1089 ), references = 1, size of lhs = 25:
% 17.21/17.41 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_head_of-{F}(V1,V0), edge-{F}(V2), P_head_of-{F}(V2,V0), P_head_of-{F}(V3,V0), P_tail_of-{F}(V1,V4), P_tail_of-{F}(V2,V5), V0 == V5, P_empty-{F}(V6), P_tail_of-{F}(V7,V4), P_head_of-{F}(V7,V8), P_head_of-{F}(V9,V8), edge-{F}(V10), sequential-{F}(V10,V1), sequential-{F}(V10,V2), P_head_of-{F}(V10,V5), pppp19-{F}(V11,V10,V1), pppp19-{F}(V12,V10,V2), precedes-{F}(V10,V3,V13), precedes-{F}(V10,V9,V14), pppp1-{F}(V1,V15,V0), shortest_path-{F}(V16,V17,V13), shortest_path-{F}(V18,V19,V14) | P_tail_of-{T}(V10,V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1217: mergings( V0 == V18, V18 == V39, V39 == V50, V17 == V19, V19 == V21, V21 == V25, V25 == V26, V26 == V27, V27 == V28, V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V14, V14 == V15, V15 == V33, V33 == V35, V35 == V36, V36 == V37, V37 == V44, V44 == V46, V46 == V47, V47 == V48, V32 == V50; #1182 ), references = 1, size of lhs = 36:
% 17.21/17.41 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_head_of-{F}(V1,V0), edge-{F}(V2), P_head_of-{F}(V2,V0), P_head_of-{F}(V3,V0), P_tail_of-{F}(V1,V4), V0 == V4, P_tail_of-{F}(V2,V4), edge-{F}(V5), P_head_of-{F}(V5,V0), on_path-{F}(V5,V6), edge-{F}(V7), P_head_of-{F}(V7,V0), edge-{F}(V8), V5 == V8, V7 == V8, sequential-{F}(V8,V1), sequential-{F}(V8,V2), on_path-{F}(V8,V6), precedes-{F}(V8,V5,V6), P_head_of-{F}(V8,V4), pppp19-{F}(V9,V8,V1), pppp19-{F}(V10,V8,V2), precedes-{F}(V8,V3,V11), P_empty-{F}(V12), on_path-{F}(V7,V13), on_path-{F}(V8,V13), precedes-{F}(V8,V7,V13), pppp1-{F}(V1,V14,V0), shortest_path-{F}(V15,V16,V11), path-{F}(V17,V18,V6), shortest_path-{F}(V19,V20,V6), path-{F}(V21,V22,V13), shortest_path-{F}(V23,V24,V13) | P_tail_of-{T}(V8,V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1248: mergings( V0 == V18, V18 == V40, V40 == V51, V17 == V19, V19 == V21, V21 == V25, V25 == V26, V26 == V27, V27 == V28, V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V14, V14 == V15, V15 == V33, V33 == V35, V35 == V36, V36 == V37, V37 == V45, V45 == V47, V47 == V48, V48 == V49, V32 == V51; #1179 ), references = 1, size of lhs = 37:
% 17.21/17.41 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_head_of-{F}(V1,V0), edge-{F}(V2), P_head_of-{F}(V2,V0), P_head_of-{F}(V3,V0), P_tail_of-{F}(V1,V4), V0 == V4, P_tail_of-{F}(V2,V4), edge-{F}(V5), P_head_of-{F}(V5,V0), on_path-{F}(V5,V6), on_path-{F}(V7,V6), P_head_of-{F}(V7,V0), edge-{F}(V8), P_head_of-{F}(V8,V0), edge-{F}(V9), V5 == V9, V8 == V9, sequential-{F}(V9,V1), sequential-{F}(V9,V2), precedes-{F}(V9,V7,V6), P_head_of-{F}(V9,V4), pppp19-{F}(V10,V9,V1), pppp19-{F}(V11,V9,V2), precedes-{F}(V9,V3,V12), P_empty-{F}(V13), on_path-{F}(V8,V14), on_path-{F}(V9,V14), precedes-{F}(V9,V8,V14), pppp1-{F}(V1,V15,V0), shortest_path-{F}(V16,V17,V12), path-{F}(V18,V19,V6), shortest_path-{F}(V20,V21,V6), path-{F}(V22,V23,V14), shortest_path-{F}(V24,V25,V14) | P_tail_of-{T}(V9,V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1279: mergings( V0 == V18, V18 == V39, V39 == V51, V17 == V19, V19 == V21, V21 == V25, V25 == V26, V26 == V27, V27 == V28, V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V14, V14 == V15, V15 == V33, V33 == V35, V35 == V36, V36 == V37, V37 == V44, V44 == V46, V46 == V47, V47 == V48, V32 == V51; #1181 ), references = 1, size of lhs = 37:
% 17.21/17.41 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_head_of-{F}(V1,V0), edge-{F}(V2), P_head_of-{F}(V2,V0), P_head_of-{F}(V3,V0), P_tail_of-{F}(V1,V4), V0 == V4, P_tail_of-{F}(V2,V4), edge-{F}(V5), P_head_of-{F}(V5,V0), on_path-{F}(V5,V6), edge-{F}(V7), P_head_of-{F}(V7,V0), edge-{F}(V8), V5 == V8, V7 == V8, sequential-{F}(V8,V1), sequential-{F}(V8,V2), on_path-{F}(V8,V6), precedes-{F}(V8,V5,V6), P_head_of-{F}(V8,V4), pppp19-{F}(V9,V8,V1), pppp19-{F}(V10,V8,V2), precedes-{F}(V8,V3,V11), P_empty-{F}(V12), on_path-{F}(V7,V13), on_path-{F}(V14,V13), precedes-{F}(V8,V14,V13), P_head_of-{F}(V14,V0), pppp1-{F}(V1,V15,V0), shortest_path-{F}(V16,V17,V11), path-{F}(V18,V19,V6), shortest_path-{F}(V20,V21,V6), path-{F}(V22,V23,V13), shortest_path-{F}(V24,V25,V13) | P_tail_of-{T}(V8,V0)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1353: mergings( V7 == V30, V30 == V32, V32 == V33, V33 == V34, V34 == V40, V31 == V36, V3 == V4, V4 == V5, V5 == V6, V6 == 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 == V37, V37 == V38, V38 == V39; #1316 ), references = 4, size of lhs = 18:
% 17.21/17.41 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_head_of-{F}(V1,V0), pppp1-{F}(V1,V2,V0), P_tail_of-{F}(V1,V3), V0 == V3, P_empty-{F}(V4), on_path-{F}(V1,V5), pppp20-{F}(V5,V1), path-{F}(V6,V7,V5), shortest_path-{F}(V8,V9,V5), path-{F}(V10,V11,V5), shortest_path-{F}(V12,V13,V5), path-{F}(V14,V15,V5), shortest_path-{F}(V16,V17,V5), path-{F}(V18,V19,V5), shortest_path-{F}(V20,V21,V5) | pppp19-{T}(V5,V1,V1)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1408: mergings( V33 == V34, V34 == V35, V35 == V36, 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, V30 == V31, V31 == V32, V32 == V37, V37 == V38, V38 == V39, V39 == V41; #1371 ), references = 1, size of lhs = 17:
% 17.21/17.41 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_tail_of-{F}(V1,V2), V0 == V2, on_path-{F}(V1,V3), pppp20-{F}(V3,V1), P_empty-{F}(V4), path-{F}(V5,V6,V3), shortest_path-{F}(V7,V8,V3), path-{F}(V9,V10,V3), shortest_path-{F}(V11,V12,V3), path-{F}(V13,V14,V3), shortest_path-{F}(V15,V16,V3), path-{F}(V17,V18,V3), shortest_path-{F}(V19,V20,V3), pppp10-{F}(V1,V21,V0,V22,V23) | pppp3-{T}(V1,V0,V22)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1443: mergings( V33 == V34, V34 == V35, V35 == V36, 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, V30 == V31, V31 == V32, V32 == V37, V37 == V38, V38 == V39, V39 == V41; #1372 ), references = 1, size of lhs = 17:
% 17.21/17.41 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_tail_of-{F}(V1,V2), V0 == V2, on_path-{F}(V1,V3), pppp20-{F}(V3,V1), P_empty-{F}(V4), path-{F}(V5,V6,V3), shortest_path-{F}(V7,V8,V3), path-{F}(V9,V10,V3), shortest_path-{F}(V11,V12,V3), path-{F}(V13,V14,V3), shortest_path-{F}(V15,V16,V3), path-{F}(V17,V18,V3), shortest_path-{F}(V19,V20,V3), pppp10-{F}(V1,V21,V0,V22,V23) | pppp3-{T}(V1,V0,V22)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1477: mergings( V32 == V33, V33 == V34, 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, V30 == V31, V31 == V35, V35 == V36, V36 == V37, V37 == V39, V39 == V40; #1373 ), references = 1, size of lhs = 20:
% 17.21/17.41 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_tail_of-{F}(V1,V2), V0 == V2, on_path-{F}(V1,V3), pppp20-{F}(V3,V1), P_empty-{F}(V4), on_path-{F}(V1,V5), path-{F}(V6,V7,V3), shortest_path-{F}(V8,V9,V3), path-{F}(V10,V11,V3), shortest_path-{F}(V12,V13,V3), path-{F}(V14,V15,V3), shortest_path-{F}(V16,V17,V3), path-{F}(V18,V19,V3), shortest_path-{F}(V20,V21,V3), path-{F}(V22,V23,V5), shortest_path-{F}(V24,V25,V5), pppp10-{F}(V1,V26,V0,V27,V28) | pppp3-{T}(V1,V0,V27)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1494: exists( #94, #1488 ), references = 1, size of lhs = 3:
% 17.21/17.41 P_empty-{F}(V0), pppp4-{F}(V1,V2), pppp1-{F}(V1,V3,V4) | P_tail_of-{T}(V2,V4)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1495: exists( #94, #1490 ), references = 1, size of lhs = 4:
% 17.21/17.41 P_empty-{F}(V0), pppp4-{F}(V1,V2), P_tail_of-{F}(V1,V3), pppp0-{F}(V1,V4,V5) | P_tail_of-{T}(V2,V4)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1508: mergings( V5 == V10, V2 == V3, V3 == V10, V14 == V10; #1502 ), references = 1, size of lhs = 12:
% 17.21/17.41 complete-{F}(), edge-{F}(V0), P_empty-{F}(V1), P_tail_of-{F}(V0,V2), edge-{F}(V3), sequential-{F}(V3,V0), P_head_of-{F}(V3,V2), pppp19-{F}(V4,V3,V0), pppp19-{F}(V5,V3,V0), precedes-{F}(V3,V0,V6), pppp1-{F}(V3,V7,V2), shortest_path-{F}(V8,V9,V6) | P_head_of-{T}(V0,V2), P_head_of-{T}(V0,V7)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1512: mergings( V5 == V10, V2 == V3, V3 == V10; #1503 ), references = 1, size of lhs = 12:
% 17.21/17.41 complete-{F}(), edge-{F}(V0), P_empty-{F}(V1), P_tail_of-{F}(V0,V2), edge-{F}(V3), sequential-{F}(V3,V0), P_head_of-{F}(V3,V2), pppp19-{F}(V4,V3,V0), pppp19-{F}(V5,V3,V0), precedes-{F}(V3,V0,V6), shortest_path-{F}(V7,V8,V6), pppp0-{F}(V3,V9,V10) | P_head_of-{T}(V0,V2), P_head_of-{T}(V0,V10)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1519: mergings( V4 == V9, V1 == V2, V2 == V9, V3 == V14, V13 == V9; #1513 ), references = 1, size of lhs = 17:
% 17.21/17.41 complete-{F}(), edge-{F}(V0), P_tail_of-{F}(V0,V1), edge-{F}(V2), sequential-{F}(V2,V0), P_head_of-{F}(V2,V1), pppp19-{F}(V3,V2,V0), pppp19-{F}(V4,V2,V0), precedes-{F}(V2,V0,V5), P_empty-{F}(V6), P_head_of-{F}(V7,V1), P_tail_of-{F}(V7,V8), P_tail_of-{F}(V9,V8), precedes-{F}(V9,V0,V10), pppp1-{F}(V2,V11,V1), shortest_path-{F}(V12,V13,V5), shortest_path-{F}(V14,V15,V10) | P_head_of-{T}(V0,V11)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1554: mergings( V6 == V8, V8 == V11, V2 == V3, V3 == V4, V4 == V5; #1546 ), references = 1, size of lhs = 18:
% 17.21/17.41 complete-{F}(), P_empty-{F}(V0), on_path-{F}(V1,V2), on_path-{F}(V1,V3), pppp20-{F}(V3,V1), on_path-{F}(V1,V4), P_head_of-{F}(V1,V5), path-{F}(V6,V7,V2), path-{F}(V8,V9,V3), shortest_path-{F}(V10,V11,V3), path-{F}(V12,V13,V3), shortest_path-{F}(V14,V15,V3), path-{F}(V16,V17,V3), shortest_path-{F}(V18,V19,V3), path-{F}(V20,V21,V3), shortest_path-{F}(V22,V23,V3), path-{F}(V24,V25,V4), shortest_path-{F}(V26,V27,V4) | P_tail_of-{T}(V1,V5)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1560: mergings( V6 == V8, V8 == V11, V2 == V3, V3 == V4, V4 == V5; #1547 ), references = 1, size of lhs = 18:
% 17.21/17.41 complete-{F}(), P_empty-{F}(V0), on_path-{F}(V1,V2), on_path-{F}(V1,V3), pppp20-{F}(V3,V1), on_path-{F}(V1,V4), P_head_of-{F}(V1,V5), path-{F}(V6,V7,V2), path-{F}(V8,V9,V3), shortest_path-{F}(V10,V11,V3), path-{F}(V12,V13,V3), shortest_path-{F}(V14,V15,V3), path-{F}(V16,V17,V3), shortest_path-{F}(V18,V19,V3), path-{F}(V20,V21,V3), shortest_path-{F}(V22,V23,V3), path-{F}(V24,V25,V4), shortest_path-{F}(V26,V27,V4) | P_tail_of-{T}(V1,V5)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1566: mergings( V6 == V7, V7 == V9, V2 == V3, V3 == V4, V4 == V5; #1548 ), references = 1, size of lhs = 18:
% 17.21/17.41 complete-{F}(), P_empty-{F}(V0), on_path-{F}(V1,V2), P_head_of-{F}(V1,V3), on_path-{F}(V1,V4), pppp20-{F}(V4,V1), on_path-{F}(V1,V5), path-{F}(V6,V7,V2), path-{F}(V8,V9,V4), shortest_path-{F}(V10,V11,V4), path-{F}(V12,V13,V4), shortest_path-{F}(V14,V15,V4), path-{F}(V16,V17,V4), shortest_path-{F}(V18,V19,V4), path-{F}(V20,V21,V4), shortest_path-{F}(V22,V23,V4), path-{F}(V24,V25,V5), shortest_path-{F}(V26,V27,V5) | P_tail_of-{T}(V1,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1574: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6; #1569 ), references = 1, size of lhs = 19:
% 17.21/17.41 complete-{F}(), P_empty-{F}(V0), on_path-{F}(V1,V2), on_path-{F}(V1,V3), pppp20-{F}(V3,V1), on_path-{F}(V1,V4), on_path-{F}(V1,V5), path-{F}(V6,V7,V2), path-{F}(V8,V9,V3), shortest_path-{F}(V10,V11,V3), path-{F}(V12,V13,V3), shortest_path-{F}(V14,V15,V3), path-{F}(V16,V17,V3), shortest_path-{F}(V18,V19,V3), path-{F}(V20,V21,V3), shortest_path-{F}(V22,V23,V3), path-{F}(V24,V25,V4), shortest_path-{F}(V26,V27,V4), path-{F}(V28,V29,V5) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1582: mergings( V0 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15; #1576 ), references = 1, size of lhs = 22:
% 17.21/17.41 complete-{F}(), P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_empty-{F}(V4), P_number_of_in-{F}(V1,V5,V6), P_number_of_in-{F}(V3,V5,V7), V6 == V7, path-{F}(V8,V9,V5), path-{F}(V10,V11,V5), path-{F}(V12,V13,V5), shortest_path-{F}(V14,V15,V5), path-{F}(V16,V17,V5), shortest_path-{F}(V18,V19,V5), path-{F}(V20,V21,V5), shortest_path-{F}(V22,V23,V5), path-{F}(V24,V25,V5), shortest_path-{F}(V26,V27,V5), path-{F}(V28,V29,V5), shortest_path-{F}(V30,V31,V5), path-{F}(V32,V33,V5) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1594: mergings( V3 == V4, V4 == V5, V5 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14; #1586 ), references = 1, size of lhs = 11:
% 17.21/17.41 complete-{F}(), P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_empty-{F}(V4), pppp22-{F}(V5,V6), P_length_of-{F}(V5,V7), P_number_of_in-{F}(V1,V5,V8), P_number_of_in-{F}(V3,V5,V9), V8 == V9 | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1604: mergings( V7 == V8, V8 == V9, V9 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V4 == V19; #1595 ), references = 4, size of lhs = 13:
% 17.21/17.41 complete-{F}(), P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_empty-{F}(V4), P_length_of-{F}(V5,V6), P_number_of_in-{F}(V1,V5,V7), P_number_of_in-{F}(V3,V5,V8), V7 == V8, pppp23-{F}(V5,V9,V10), P_number_of_in-{F}(V10,V5,V11), P_minus-{F}(V6,V9,V12) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1619: mergings( V3 == V5, V5 == V6, V6 == V7, V7 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V15 == V16, V16 == V17, V4 == V8, V18 == V19; #1606 ), references = 1, size of lhs = 9:
% 17.21/17.41 complete-{F}(), P_sequential_pairs-{F}(V0), P_edges-{F}(V0), P_n1-{F}(V1), P_triangles-{F}(V2), P_empty-{F}(V3), P_length_of-{F}(V4,V5), pppp23-{F}(V4,V6,V2), P_minus-{F}(V5,V6,V7) | P_number_of_in-{T}(V2,V4,V5)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1637: mergings( V3 == V5, V5 == V7, V7 == V8, V8 == V9, V9 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V2 == V6, V6 == V10, V4 == V11, V11 == V18, V12 == V19; #1622 ), references = 1, size of lhs = 7:
% 17.21/17.41 complete-{F}(), P_sequential_pairs-{F}(V0), P_edges-{F}(V0), P_n1-{F}(V1), P_triangles-{F}(V2), P_empty-{F}(V3), pppp23-{F}(V4,V1,V2) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1654: mergings( V0 == V8, V8 == V9, V9 == V11, V11 == V12, V12 == V13, V13 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V20, V1 == V7, V7 == V10, V10 == V14, V2 == V14, V3 == V15; #1638 ), references = 1, size of lhs = 7:
% 17.21/17.41 complete-{F}(), P_graph-{F}(V0), P_sequential_pairs-{F}(V1), P_edges-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_empty-{F}(V4) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1677: mergings( V1 == V6, V6 == V10, V10 == V12, V12 == V14, V14 == V15, V15 == V16, V16 == V20, V20 == V21, V21 == V22, V22 == V23, V23 == V24, V2 == V7, V7 == V9, V9 == V13, V13 == V17, V3 == V8, V8 == V17, V4 == V11, V11 == V18, V5 == V19; #1656 ), references = 1, size of lhs = 5:
% 17.21/17.41 P_sequential_pairs-{F}(V0), P_edges-{F}(V0), P_n1-{F}(V1), P_triangles-{F}(V2), P_empty-{F}(V3) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1698: mergings( V1 == V5, V5 == V9, V9 == V11, V11 == V13, V13 == V14, V14 == V15, V15 == V18, V18 == V19, V19 == V20, V20 == V21, V21 == V22, V2 == V6, V6 == V8, V8 == V12, V12 == V16, V3 == V7, V7 == V16, V4 == V10, V10 == V17; #1678 ), references = 1, size of lhs = 4:
% 17.21/17.41 P_sequential_pairs-{F}(V0), P_edges-{F}(V0), P_n1-{F}(V1), P_empty-{F}(V2) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1717: mergings( V1 == V4, V4 == V8, V8 == V9, V9 == V11, V11 == V12, V12 == V13, V13 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19, V2 == V5, V5 == V7, V7 == V10, V10 == V14, V3 == V6, V6 == V14; #1699 ), references = 1, size of lhs = 3:
% 17.21/17.41 P_sequential_pairs-{F}(V0), P_edges-{F}(V0), P_empty-{F}(V1) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1719: exists( #98, #173 ), references = 1, size of lhs = 8:
% 17.21/17.41 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_length_of-{F}(V4,V5), P_minus-{F}(V5,V3,V6), pppp23-{F}(V4,V7,V2), P_minus-{F}(V5,V7,V8) | P_number_of_in-{T}(V2,V4,V6)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1723: exists( #98, #192 ), references = 1, size of lhs = 6:
% 17.21/17.41 P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), P_number_of_in-{F}(V1,V2,V4), V3 == V4, pppp23-{F}(V2,V5,V6) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1725: exists( #98, #1722 ), references = 2, size of lhs = 4:
% 17.21/17.41 P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), pppp23-{F}(V2,V4,V5) | P_number_of_in-{T}(V1,V2,V3)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1727: exists( #101, #173 ), references = 6, size of lhs = 8:
% 17.21/17.41 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), pppp23-{F}(V4,V3,V7), P_number_of_in-{F}(V7,V4,V8) | P_minus-{T}(V6,V3,V5)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1730: exists( #98, #1728 ), references = 1, size of lhs = 6:
% 17.21/17.41 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp23-{F}(V4,V3,V2), P_length_of-{F}(V4,V5) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1732: exists( #97, #1729 ), references = 1, size of lhs = 5:
% 17.21/17.41 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp23-{F}(V4,V3,V2) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1737: mergings( V0 == V7, V1 == V8, V2 == V4; #1733 ), references = 1, size of lhs = 6:
% 17.21/17.41 P_triangles-{F}(V0), P_sequential_pairs-{F}(V0), P_graph-{F}(V1), P_empty-{F}(V2), P_edges-{F}(V3), P_n1-{F}(V4) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1742: mergings( V1 == V5, V2 == V6, V3 == V4; #1738 ), references = 1, size of lhs = 5:
% 17.21/17.41 P_triangles-{F}(V0), P_sequential_pairs-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_n1-{F}(V3) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1751: mergings( V3 == V9, V4 == V6, V5 == V7, V11 == V14, V12 == V15; #1745 ), references = 2, size of lhs = 10:
% 17.21/17.41 complete-{F}(), P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_empty-{F}(V4), P_length_of-{F}(V5,V6), P_number_of_in-{F}(V3,V5,V7), pppp23-{F}(V5,V2,V8), P_number_of_in-{F}(V8,V5,V9) | P_number_of_in-{T}(V1,V5,V7)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1766: mergings( V2 == V4, V4 == V9, V9 == V10, V3 == V5, V5 == V7, V7 == V11, V6 == V8, V8 == V13, V13 == V14, V11 == V15; #1755 ), references = 1, size of lhs = 7:
% 17.21/17.41 complete-{F}(), P_triangles-{F}(V0), P_edges-{F}(V0), P_empty-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp23-{F}(V4,V3,V0) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1778: mergings( V0 == V7, V7 == V8, V8 == V12, V12 == V13, V1 == V4, V4 == V9, V9 == V10, V10 == V14, V2 == V15, V11 == V3; #1767 ), references = 1, size of lhs = 7:
% 17.21/17.41 complete-{F}(), P_graph-{F}(V0), P_triangles-{F}(V1), P_edges-{F}(V1), P_empty-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1796: mergings( V1 == V6, V6 == V9, V9 == V11, V11 == V15, V15 == V16, V2 == V7, V7 == V10, V10 == V12, V12 == V13, V13 == V17, V3 == V8, V8 == V18, V4 == V14, V14 == V19, V5 == V17; #1780 ), references = 1, size of lhs = 5:
% 17.21/17.41 P_triangles-{F}(V0), P_edges-{F}(V0), P_empty-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1798: exists( #98, #1604 ), references = 2, size of lhs = 10:
% 17.21/17.41 complete-{F}(), P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_empty-{F}(V4), P_length_of-{F}(V5,V6), P_number_of_in-{F}(V1,V5,V7), pppp23-{F}(V5,V8,V3), P_minus-{F}(V6,V8,V9) | P_number_of_in-{T}(V3,V5,V7)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1808: mergings( V6 == V7, V10 == V13, V3 == V8, V4 == V9, V11 == V15, V12 == V16; #1801 ), references = 1, size of lhs = 10:
% 17.21/17.41 complete-{F}(), P_triangles-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), P_length_of-{F}(V5,V6), P_minus-{F}(V6,V4,V7), pppp23-{F}(V5,V8,V0), P_minus-{F}(V6,V8,V9) | P_number_of_in-{T}(V3,V5,V7)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1821: mergings( V3 == V10, V4 == V7, V5 == V8, V11 == V13, V6 == V9; #1814 ), references = 1, size of lhs = 9:
% 17.21/17.41 complete-{F}(), P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_empty-{F}(V4), pppp23-{F}(V5,V2,V3), P_length_of-{F}(V5,V6), P_number_of_in-{F}(V1,V5,V7) | P_number_of_in-{T}(V3,V5,V7)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1829: mergings( V5 == V6, V6 == V9, V13 == V14, V3 == V7, V7 == V10, V8 == V11, V4 == V12; #1815 ), references = 1, size of lhs = 9:
% 17.21/17.41 complete-{F}(), P_triangles-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), pppp23-{F}(V5,V4,V0), P_length_of-{F}(V5,V6), P_number_of_in-{F}(V3,V5,V7) | P_number_of_in-{T}(V0,V5,V7)
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1840: mergings( V3 == V9, V9 == V11, V10 == V14, V4 == V6, V6 == V12, V5 == V7, V7 == V13; #1832 ), references = 1, size of lhs = 8:
% 17.21/17.41 complete-{F}(), P_triangles-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), pppp23-{F}(V5,V4,V0), P_length_of-{F}(V5,V6) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1848: mergings( V2 == V8, V8 == V9, V3 == V5, V5 == V10, V4 == V6, V6 == V12; #1841 ), references = 1, size of lhs = 7:
% 17.21/17.41 complete-{F}(), P_triangles-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), pppp23-{F}(V5,V4,V0) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1858: mergings( V0 == V7, V7 == V11, V11 == V12, V1 == V8, V8 == V9, V9 == V13, V2 == V14, V10 == V3; #1849 ), references = 1, size of lhs = 7:
% 17.21/17.41 complete-{F}(), P_graph-{F}(V0), P_triangles-{F}(V1), P_empty-{F}(V2), P_edges-{F}(V3), P_sequential_pairs-{F}(V4), P_n1-{F}(V5) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1874: mergings( V1 == V6, V6 == V9, V9 == V14, V14 == V15, V2 == V7, V7 == V10, V10 == V11, V11 == V16, V3 == V8, V8 == V17, V4 == V12, V12 == V18, V5 == V13; #1860 ), references = 1, size of lhs = 5:
% 17.21/17.41 P_triangles-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1888: mergings( V1 == V5, V5 == V8, V8 == V12, V12 == V13, V2 == V6, V6 == V9, V9 == V10, V10 == V14, V3 == V7, V7 == V15, V4 == V11, V11 == V16; #1875 ), references = 1, size of lhs = 4:
% 17.21/17.41 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1900: mergings( V1 == V4, V4 == V7, V7 == V10, V10 == V11, V2 == V5, V5 == V8, V8 == V9, V9 == V12, V3 == V6, V6 == V13; #1889 ), references = 1, size of lhs = 3:
% 17.21/17.41 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1910: mergings( V1 == V3, V3 == V5, V5 == V8, V8 == V9, V2 == V4, V4 == V6, V6 == V7, V7 == V10; #1901 ), references = 1, size of lhs = 2:
% 17.21/17.41 P_empty-{F}(V0), P_edges-{F}(V1) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1916: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5; #1911 ), references = 1, size of lhs = 1:
% 17.21/17.41 P_empty-{F}(V0) | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 #1918: exists( #96, #1911 ), references = 1, size of lhs = 0:
% 17.21/17.41 FALSE | FALSE
% 17.21/17.41 (used 0 times, uses = {})
% 17.21/17.41
% 17.21/17.41 number of learnt formulas = 102
% 17.21/17.41
% 17.21/17.41
% 17.21/17.41 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.21/17.41
% 17.21/17.41 randbase = 1
%------------------------------------------------------------------------------