TSTP Solution File: GRA002+1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : GRA002+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jul 23 06:02:46 EDT 2022
% Result : Theorem 3.63s 3.79s
% Output : Refutation 3.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRA002+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.06/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jul 22 08:03:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.63/3.79 GeoParameters:
% 3.63/3.79
% 3.63/3.79 tptp_input = 1
% 3.63/3.79 tptp_output = 0
% 3.63/3.79 nonempty = 1
% 3.63/3.79 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.63/3.79 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 3.63/3.79
% 3.63/3.79
% 3.63/3.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.63/3.79 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.63/3.79
% 3.63/3.79 RuleSystem INPUT:
% 3.63/3.79
% 3.63/3.79 Initial Rules:
% 3.63/3.79 #0: input, references = 5, size of lhs = 3:
% 3.63/3.79 P_head_of-{F}(V0,V2), P_tail_of-{F}(V0,V2), edge-{F}(V0) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #1: input, references = 5, size of lhs = 3:
% 3.63/3.79 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), edge-{F}(V0) | vertex-{T}(V1)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #2: input, references = 5, size of lhs = 3:
% 3.63/3.79 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), edge-{F}(V0) | vertex-{T}(V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #3: input, references = 4, size of lhs = 4:
% 3.63/3.79 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0 | EXISTS V2: pppp9-{T}(V1,V0,V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #4: input, references = 9, size of lhs = 1:
% 3.63/3.79 pppp9-{F}(V0,V1,V2) | pppp8-{T}(V2,V0,V1)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #5: input, references = 3, size of lhs = 3:
% 3.63/3.79 pppp8-{F}(V0,V1,V2), pppp1-{F}(V0,V1,V2), pppp0-{F}(V0,V1,V2) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #6: input, references = 7, size of lhs = 1:
% 3.63/3.79 pppp8-{F}(V0,V1,V2) | pppp0-{T}(V0,V1,V2), pppp1-{T}(V0,V1,V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #7: input, references = 4, size of lhs = 1:
% 3.63/3.79 pppp8-{F}(V0,V1,V2) | edge-{T}(V0)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #8: input, references = 5, size of lhs = 4:
% 3.63/3.79 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp1-{F}(V0,V1,V2), V2 == V3 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #9: input, references = 4, size of lhs = 4:
% 3.63/3.79 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp1-{F}(V0,V1,V2), V1 == V4 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #10: input, references = 3, size of lhs = 2:
% 3.63/3.79 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | pppp1-{T}(V0,V4,V3)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #11: input, references = 6, size of lhs = 4:
% 3.63/3.79 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp0-{F}(V0,V1,V2), V1 == V3 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #12: input, references = 5, size of lhs = 4:
% 3.63/3.79 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp0-{F}(V0,V1,V2), V2 == V4 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #13: input, references = 3, size of lhs = 2:
% 3.63/3.79 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | pppp0-{T}(V0,V3,V4)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #14: input, references = 3, size of lhs = 7:
% 3.63/3.79 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)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #15: input, references = 5, size of lhs = 9:
% 3.63/3.79 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)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #16: input, references = 3, size of lhs = 2:
% 3.63/3.79 P_empty-{F}(V0), path-{F}(V1,V2,V3) | vertex-{T}(V1)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #17: input, references = 3, size of lhs = 2:
% 3.63/3.79 P_empty-{F}(V0), path-{F}(V1,V2,V3) | vertex-{T}(V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #18: input, references = 3, size of lhs = 2:
% 3.63/3.79 P_empty-{F}(V0), path-{F}(V1,V2,V3) | EXISTS V4: pppp11-{T}(V1,V2,V3,V4)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #19: input, references = 4, size of lhs = 2:
% 3.63/3.79 pppp11-{F}(V0,V1,V2,V3), P_tail_of-{F}(V3,V4) | pppp10-{T}(V3,V0,V1,V2,V4)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #20: input, references = 3, size of lhs = 3:
% 3.63/3.79 pppp10-{F}(V0,V1,V2,V3,V4), pppp3-{F}(V0,V2,V3), pppp2-{F}(V0,V2,V3) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #21: input, references = 3, size of lhs = 1:
% 3.63/3.79 pppp10-{F}(V0,V1,V2,V3,V4) | pppp2-{T}(V0,V2,V3), pppp3-{T}(V0,V2,V3)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #22: input, references = 4, size of lhs = 2:
% 3.63/3.79 pppp10-{F}(V0,V1,V2,V3,V4), V1 == V4 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #23: input, references = 3, size of lhs = 1:
% 3.63/3.79 pppp10-{F}(V0,V1,V2,V3,V4) | edge-{T}(V0)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #24: input, references = 3, size of lhs = 3:
% 3.63/3.79 P_empty-{F}(V0), P_head_of-{F}(V1,V4), pppp3-{F}(V1,V2,V3) | EXISTS V5: pppp12-{T}(V1,V2,V3,V5,V4)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #25: input, references = 3, size of lhs = 4:
% 3.63/3.79 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)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #26: input, references = 3, size of lhs = 3:
% 3.63/3.79 pppp12-{F}(V0,V1,V2,V3,V4), P_path_cons-{F}(V0,V3,V5), V2 == V5 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #27: input, references = 3, size of lhs = 2:
% 3.63/3.79 pppp12-{F}(V0,V1,V2,V3,V4), P_path_cons-{F}(V0,V3,V5) | path-{T}(V4,V1,V3)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #28: input, references = 4, size of lhs = 5:
% 3.63/3.79 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
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #29: input, references = 4, size of lhs = 5:
% 3.63/3.79 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
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #30: input, references = 3, size of lhs = 3:
% 3.63/3.79 P_empty-{F}(V0), P_head_of-{F}(V1,V4), P_path_cons-{F}(V1,V0,V5) | pppp2-{T}(V1,V4,V5)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #31: input, references = 4, size of lhs = 5:
% 3.63/3.79 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)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #32: input, references = 3, size of lhs = 5:
% 3.63/3.79 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)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #33: input, references = 3, size of lhs = 5:
% 3.63/3.79 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)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #34: input, references = 3, size of lhs = 3:
% 3.63/3.79 P_empty-{F}(V0), path-{F}(V3,V2,V1), in_path-{F}(V4,V1) | vertex-{T}(V4)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #35: input, references = 3, size of lhs = 3:
% 3.63/3.79 P_empty-{F}(V0), path-{F}(V3,V2,V1), in_path-{F}(V4,V1) | EXISTS V5: pppp13-{T}(V5,V1,V4)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #36: input, references = 4, size of lhs = 5:
% 3.63/3.79 pppp13-{F}(V0,V1,V2), P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), V2 == V3, V2 == V4 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #37: input, references = 3, size of lhs = 3:
% 3.63/3.79 pppp13-{F}(V0,V1,V2), P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | on_path-{T}(V0,V1)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #38: input, references = 8, size of lhs = 2:
% 3.63/3.79 P_empty-{F}(V0), sequential-{F}(V1,V2) | pppp4-{T}(V1,V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #39: input, references = 7, size of lhs = 2:
% 3.63/3.79 P_empty-{F}(V0), pppp4-{F}(V1,V2) | sequential-{T}(V1,V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #40: input, references = 13, size of lhs = 3:
% 3.63/3.79 P_empty-{F}(V0), P_head_of-{F}(V1,V3), P_tail_of-{F}(V2,V4) | pppp14-{T}(V1,V2,V3,V4)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #41: input, references = 7, size of lhs = 4:
% 3.63/3.79 pppp14-{F}(V0,V1,V3,V3), edge-{F}(V0), edge-{F}(V1), V0 == V1 | pppp4-{T}(V0,V1)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #42: input, references = 4, size of lhs = 3:
% 3.63/3.79 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1), V2 == V3 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #43: input, references = 4, size of lhs = 2:
% 3.63/3.79 pppp14-{F}(V1,V1,V2,V3), pppp4-{F}(V1,V1) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #44: input, references = 3, size of lhs = 2:
% 3.63/3.79 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1) | edge-{T}(V1)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #45: input, references = 7, size of lhs = 2:
% 3.63/3.79 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1) | edge-{T}(V0)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #46: input, references = 10, size of lhs = 5:
% 3.63/3.79 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)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #47: input, references = 3, size of lhs = 6:
% 3.63/3.79 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)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #48: input, references = 3, size of lhs = 3:
% 3.63/3.79 P_empty-{F}(V0), precedes-{F}(V2,V3,V1), path-{F}(V5,V4,V1) | pppp15-{T}(V1,V2,V3)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #49: input, references = 3, size of lhs = 3:
% 3.63/3.79 pppp15-{F}(V0,V1,V2), pppp5-{F}(V0,V1,V2), sequential-{F}(V1,V2) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #50: input, references = 3, size of lhs = 1:
% 3.63/3.79 pppp15-{F}(V0,V1,V2) | sequential-{T}(V1,V2), pppp5-{T}(V0,V1,V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #51: input, references = 3, size of lhs = 1:
% 3.63/3.79 pppp15-{F}(V0,V1,V2) | on_path-{T}(V2,V0)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #52: input, references = 3, size of lhs = 1:
% 3.63/3.79 pppp15-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #53: input, references = 3, size of lhs = 2:
% 3.63/3.79 P_empty-{F}(V0), pppp5-{F}(V1,V2,V3) | EXISTS V4: pppp16-{T}(V1,V2,V3,V4)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #54: input, references = 3, size of lhs = 3:
% 3.63/3.79 P_empty-{F}(V0), sequential-{F}(V2,V4), precedes-{F}(V4,V3,V1) | pppp5-{T}(V1,V2,V3)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #55: input, references = 3, size of lhs = 1:
% 3.63/3.79 pppp16-{F}(V0,V1,V2,V3) | precedes-{T}(V3,V2,V0)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #56: input, references = 3, size of lhs = 1:
% 3.63/3.79 pppp16-{F}(V0,V1,V2,V3) | sequential-{T}(V1,V3)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #57: input, references = 6, size of lhs = 2:
% 3.63/3.79 P_empty-{F}(V0), shortest_path-{F}(V1,V2,V3) | pppp6-{T}(V1,V2,V3)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #58: input, references = 3, size of lhs = 2:
% 3.63/3.79 P_empty-{F}(V0), pppp6-{F}(V1,V2,V3) | shortest_path-{T}(V1,V2,V3)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #59: input, references = 6, size of lhs = 3:
% 3.63/3.79 P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V1,V2,V3) | path-{T}(V1,V2,V3)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #60: input, references = 3, size of lhs = 3:
% 3.63/3.79 P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V2,V2,V3) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #61: input, references = 3, size of lhs = 5:
% 3.63/3.79 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)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #62: input, references = 3, size of lhs = 4:
% 3.63/3.79 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)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #63: input, references = 3, size of lhs = 1:
% 3.63/3.79 pppp24-{F}(V0,V1,V2) | EXISTS V3: pppp17-{T}(V0,V1,V3,V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #64: input, references = 3, size of lhs = 3:
% 3.63/3.79 pppp17-{F}(V0,V1,V2,V3), P_length_of-{F}(V2,V4), less_or_equal-{F}(V3,V4) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #65: input, references = 3, size of lhs = 2:
% 3.63/3.79 pppp17-{F}(V0,V1,V2,V3), P_length_of-{F}(V2,V4) | path-{T}(V0,V1,V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #66: input, references = 7, size of lhs = 7:
% 3.63/3.79 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
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #67: input, references = 5, size of lhs = 6:
% 3.63/3.79 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
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #68: input, references = 3, size of lhs = 2:
% 3.63/3.79 P_empty-{F}(V0), triangle-{F}(V1,V2,V3) | pppp7-{T}(V1,V2,V3)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #69: input, references = 4, size of lhs = 2:
% 3.63/3.79 P_empty-{F}(V0), pppp7-{F}(V1,V2,V3) | triangle-{T}(V1,V2,V3)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #70: input, references = 3, size of lhs = 2:
% 3.63/3.79 P_empty-{F}(V0), pppp7-{F}(V1,V2,V3) | pppp18-{T}(V1,V2,V3)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #71: input, references = 4, size of lhs = 7:
% 3.63/3.79 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)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #72: input, references = 3, size of lhs = 1:
% 3.63/3.79 pppp18-{F}(V0,V1,V2) | sequential-{T}(V2,V0)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #73: input, references = 3, size of lhs = 1:
% 3.63/3.79 pppp18-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #74: input, references = 3, size of lhs = 1:
% 3.63/3.79 pppp18-{F}(V0,V1,V2) | sequential-{T}(V0,V1)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #75: input, references = 3, size of lhs = 1:
% 3.63/3.79 pppp18-{F}(V0,V1,V2) | edge-{T}(V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #76: input, references = 3, size of lhs = 1:
% 3.63/3.79 pppp18-{F}(V0,V1,V2) | edge-{T}(V1)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #77: input, references = 3, size of lhs = 1:
% 3.63/3.79 pppp18-{F}(V0,V1,V2) | edge-{T}(V0)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #78: input, references = 5, size of lhs = 6:
% 3.63/3.79 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
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #79: input, references = 5, size of lhs = 9:
% 3.63/3.79 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
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #80: input, references = 4, size of lhs = 9:
% 3.63/3.79 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)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #81: input, references = 5, size of lhs = 1:
% 3.63/3.79 pppp20-{F}(V0,V1) | EXISTS V2: pppp19-{T}(V0,V2,V1)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #82: input, references = 4, size of lhs = 1:
% 3.63/3.79 pppp20-{F}(V0,V1) | on_path-{T}(V1,V0)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #83: input, references = 4, size of lhs = 2:
% 3.63/3.79 pppp19-{F}(V0,V1,V2), triangle-{F}(V1,V2,V3) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #84: input, references = 9, size of lhs = 1:
% 3.63/3.79 pppp19-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #85: input, references = 7, size of lhs = 1:
% 3.63/3.79 pppp19-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #86: input, references = 6, size of lhs = 8:
% 3.63/3.79 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)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #87: input, references = 6, size of lhs = 7:
% 3.63/3.79 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_graph-{F}(V5), P_number_of_in-{F}(V4,V5,V6) | complete-{T}()
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #88: input, references = 6, size of lhs = 7:
% 3.63/3.79 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_graph-{F}(V5), P_number_of_in-{F}(V4,V5,V6) | EXISTS V7: pppp23-{T}(V7,V3,V6)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #89: input, references = 6, size of lhs = 3:
% 3.63/3.79 pppp23-{F}(V0,V1,V2), P_length_of-{F}(V0,V3), P_minus-{F}(V3,V1,V4) | EXISTS V5: pppp22-{T}(V0,V5)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #90: input, references = 6, size of lhs = 4:
% 3.63/3.79 pppp23-{F}(V0,V1,V2), P_length_of-{F}(V0,V3), P_minus-{F}(V3,V1,V4), less_or_equal-{F}(V4,V2) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #91: input, references = 6, size of lhs = 1:
% 3.63/3.79 pppp22-{F}(V0,V1) | EXISTS V2: pppp21-{T}(V1,V0,V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #92: input, references = 6, size of lhs = 1:
% 3.63/3.79 pppp21-{F}(V0,V1,V2) | shortest_path-{T}(V2,V0,V1)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #93: input, references = 11, size of lhs = 1:
% 3.63/3.79 #-{F} V0 | EXISTS V1: P_head_of-{T}(V0,V1)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #94: input, references = 12, size of lhs = 1:
% 3.63/3.79 #-{F} V0 | EXISTS V1: P_tail_of-{T}(V0,V1)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #95: input, references = 6, size of lhs = 2:
% 3.63/3.79 #-{F} V0, #-{F} V1 | EXISTS V2: P_path_cons-{T}(V0,V1,V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #96: input, references = 4, size of lhs = 0:
% 3.63/3.79 FALSE | EXISTS V0: P_empty-{T}(V0)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #97: input, references = 6, size of lhs = 1:
% 3.63/3.79 #-{F} V0 | EXISTS V1: P_length_of-{T}(V0,V1)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #98: input, references = 12, size of lhs = 2:
% 3.63/3.79 #-{F} V0, #-{F} V1 | EXISTS V2: P_number_of_in-{T}(V0,V1,V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #99: input, references = 4, size of lhs = 0:
% 3.63/3.79 FALSE | EXISTS V0: P_edges-{T}(V0)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #100: input, references = 4, size of lhs = 0:
% 3.63/3.79 FALSE | EXISTS V0: P_sequential_pairs-{T}(V0)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #101: input, references = 4, size of lhs = 2:
% 3.63/3.79 #-{F} V0, #-{F} V1 | EXISTS V2: P_minus-{T}(V0,V1,V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #102: input, references = 5, size of lhs = 0:
% 3.63/3.79 FALSE | EXISTS V0: P_n1-{T}(V0)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #103: input, references = 5, size of lhs = 0:
% 3.63/3.79 FALSE | EXISTS V0: P_triangles-{T}(V0)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #104: input, references = 6, size of lhs = 0:
% 3.63/3.79 FALSE | EXISTS V0: P_graph-{T}(V0)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 number of initial rules = 105
% 3.63/3.79
% 3.63/3.79 Simplifiers:
% 3.63/3.79 #105: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 P_head_of-{F}(V0,V1), P_head_of-{F}(V0,V3), V1 == V3 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #106: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 P_tail_of-{F}(V0,V1), P_tail_of-{F}(V0,V3), V1 == V3 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #107: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 P_path_cons-{F}(V0,V1,V2), P_path_cons-{F}(V0,V1,V5), V2 == V5 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #108: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 P_empty-{F}(V0), P_empty-{F}(V1), V0 == V1 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #109: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 P_length_of-{F}(V0,V1), P_length_of-{F}(V0,V3), V1 == V3 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #110: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 P_number_of_in-{F}(V0,V1,V2), P_number_of_in-{F}(V0,V1,V5), V2 == V5 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #111: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 P_edges-{F}(V0), P_edges-{F}(V1), V0 == V1 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #112: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 P_sequential_pairs-{F}(V0), P_sequential_pairs-{F}(V1), V0 == V1 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #113: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 P_minus-{F}(V0,V1,V2), P_minus-{F}(V0,V1,V5), V2 == V5 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #114: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 P_n1-{F}(V0), P_n1-{F}(V1), V0 == V1 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #115: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 P_triangles-{F}(V0), P_triangles-{F}(V1), V0 == V1 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #116: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 P_graph-{F}(V0), P_graph-{F}(V1), V0 == V1 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #117: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 pppp8-{F}(V0,V1,V2), pppp8-{F}(V3,V1,V2), V0 == V3 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #118: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 pppp9-{F}(V0,V1,V2), pppp9-{F}(V0,V1,V5), V2 == V5 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #119: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V5,V1,V2,V3,V9), V0 == V5 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #120: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #121: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 pppp11-{F}(V0,V1,V2,V3), pppp11-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #122: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V1,V2,V8,V4), V3 == V8 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #123: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #124: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 pppp13-{F}(V0,V1,V2), pppp13-{F}(V3,V1,V2), V0 == V3 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #125: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 pppp14-{F}(V0,V1,V2,V3), pppp14-{F}(V0,V5,V6,V7), V2 == V6 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #126: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 pppp14-{F}(V0,V1,V2,V3), pppp14-{F}(V4,V1,V6,V7), V3 == V7 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #127: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 pppp16-{F}(V0,V1,V2,V3), pppp16-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #128: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 pppp17-{F}(V0,V1,V2,V3), pppp17-{F}(V0,V1,V6,V3), V2 == V6 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #129: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 pppp19-{F}(V0,V1,V2), pppp19-{F}(V0,V4,V2), V1 == V4 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #130: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 pppp19-{F}(V0,V1,V2), pppp19-{F}(V0,V4,V5), V2 == V5 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #131: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 pppp20-{F}(V0,V1), pppp20-{F}(V0,V3), V1 == V3 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #132: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 pppp21-{F}(V0,V1,V2), pppp21-{F}(V0,V1,V5), V2 == V5 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #133: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 pppp21-{F}(V0,V1,V2), pppp21-{F}(V3,V1,V5), V0 == V3 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #134: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 pppp22-{F}(V0,V1), pppp22-{F}(V0,V3), V1 == V3 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #135: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 pppp23-{F}(V0,V1,V2), pppp23-{F}(V3,V1,V2), V0 == V3 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #136: unsound, references = 3, size of lhs = 3:
% 3.63/3.79 pppp23-{F}(V0,V1,V2), pppp23-{F}(V3,V4,V5), V1 == V4 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 number of simplifiers = 32
% 3.63/3.79
% 3.63/3.79 Learnt:
% 3.63/3.79 #145: mergings( V3 == V4, V4 == V5, V7 == V8; #141 ), references = 1, size of lhs = 6:
% 3.63/3.79 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
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #151: mergings( V6 == V7, V7 == V8, V3 == V10, V10 == V11; #146 ), references = 2, size of lhs = 7:
% 3.63/3.79 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_minus-{F}(V3,V5,V7) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #157: mergings( V3 == V4, V4 == V5, V6 == V7, V7 == V8; #152 ), references = 1, size of lhs = 5:
% 3.63/3.79 P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), pppp23-{F}(V2,V4,V5), P_minus-{F}(V3,V4,V6) | P_number_of_in-{T}(V1,V2,V3)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #168: mergings( V3 == V4, V4 == V5, V9 == V11; #164 ), references = 1, size of lhs = 9:
% 3.63/3.79 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
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #174: mergings( V6 == V7, V7 == V8, V3 == V12, V12 == V14; #169 ), references = 3, size of lhs = 10:
% 3.63/3.79 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_minus-{F}(V6,V8,V10) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #178: exists( #101, #151 ), references = 1, size of lhs = 6:
% 3.63/3.79 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
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #179: exists( #101, #174 ), references = 5, size of lhs = 7:
% 3.63/3.79 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_minus-{T}(V6,V3,V5)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #181: exists( #98, #176 ), references = 2, size of lhs = 4:
% 3.63/3.79 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)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #200: exists( #94, #198 ), references = 1, size of lhs = 1:
% 3.63/3.79 pppp11-{F}(V0,V1,V2,V3) | P_tail_of-{T}(V3,V0)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #221: exists( #95, #28 ), references = 1, size of lhs = 4:
% 3.63/3.79 P_empty-{F}(V0), P_head_of-{F}(V1,V2), pppp2-{F}(V1,V3,V4), V3 == V2 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #223: mergings( V4 == V3; #220 ), references = 1, size of lhs = 3:
% 3.63/3.79 P_empty-{F}(V0), P_head_of-{F}(V1,V2), pppp2-{F}(V1,V2,V3) | P_path_cons-{T}(V1,V0,V3)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #225: exists( #93, #219 ), references = 1, size of lhs = 2:
% 3.63/3.79 P_empty-{F}(V0), pppp2-{F}(V1,V2,V3) | P_head_of-{T}(V1,V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #227: exists( #94, #12 ), references = 1, size of lhs = 2:
% 3.63/3.79 P_head_of-{F}(V0,V1), pppp0-{F}(V0,V2,V3) | P_tail_of-{T}(V0,V3)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #241: exists( #94, #36 ), references = 1, size of lhs = 3:
% 3.63/3.79 P_head_of-{F}(V0,V1), pppp13-{F}(V0,V2,V3), V3 == V1 | P_tail_of-{T}(V0,V3)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #244: exists( #93, #242 ), references = 1, size of lhs = 7:
% 3.63/3.79 P_empty-{F}(V0), P_tail_of-{F}(V1,V2), P_head_of-{F}(V1,V3), P_head_of-{F}(V4,V3), pppp13-{F}(V5,V6,V2), precedes-{F}(V5,V4,V7), shortest_path-{F}(V8,V9,V7) | P_head_of-{T}(V5,V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #274: disj( #6, input ), references = 4, size of lhs = 4:
% 3.63/3.79 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), pppp8-{F}(V0,V3,V4), V4 == V1 | pppp0-{T}(V0,V3,V4)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #295: mergings( V2 == V3; #293 ), references = 3, size of lhs = 4:
% 3.63/3.79 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), pppp8-{F}(V0,V3,V1), V3 == V2 | pppp0-{T}(V0,V3,V1)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #309: exists( #94, #9 ), references = 3, size of lhs = 2:
% 3.63/3.79 P_head_of-{F}(V0,V1), pppp1-{F}(V0,V2,V3) | P_tail_of-{T}(V0,V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #313: exists( #93, #311 ), references = 1, size of lhs = 2:
% 3.63/3.79 pppp1-{F}(V0,V1,V2), pppp1-{F}(V0,V3,V4) | P_head_of-{T}(V0,V4)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #317: disj( #6, #312+#309+#66 ), references = 1, size of lhs = 6:
% 3.63/3.79 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)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #333: exists( #93, #12 ), references = 5, size of lhs = 3:
% 3.63/3.79 P_tail_of-{F}(V0,V1), pppp0-{F}(V0,V2,V3), V3 == V1 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #335: mergings( V4 == V2; #331 ), references = 2, size of lhs = 2:
% 3.63/3.79 P_tail_of-{F}(V0,V1), pppp0-{F}(V0,V2,V1) | P_head_of-{T}(V0,V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #339: exists( #94, #333 ), references = 3, size of lhs = 1:
% 3.63/3.79 pppp0-{F}(V0,V1,V2) | P_tail_of-{T}(V0,V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #340: exists( #94, #11 ), references = 4, size of lhs = 3:
% 3.63/3.79 P_head_of-{F}(V0,V1), pppp0-{F}(V0,V2,V3), V2 == V1 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #361: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V14; #354 ), references = 1, size of lhs = 15:
% 3.63/3.79 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)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #379: mergings( V1 == V18, V18 == V19, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V13; #368 ), references = 2, size of lhs = 17:
% 3.63/3.79 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), pppp19-{F}(V8,V2,V4), P_head_of-{F}(V2,V9), V0 == V9, shortest_path-{F}(V10,V11,V6) | pppp9-{T}(V1,V0,V4)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #388: mergings( V17 == V19, V1 == V18, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V13; #369 ), references = 1, size of lhs = 18:
% 3.63/3.79 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), V0 == V9, V1 == V9, shortest_path-{F}(V10,V11,V6) | pppp9-{T}(V1,V0,V4)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #398: mergings( V17 == V19, V1 == V18, V18 == V20, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V13; #370 ), references = 1, size of lhs = 18:
% 3.63/3.79 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), V0 == V9, V1 == V9, shortest_path-{F}(V10,V11,V6) | pppp9-{T}(V1,V0,V4)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #422: mergings( V2 == V15, V16 == V17, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V13; #411 ), references = 1, size of lhs = 15:
% 3.63/3.79 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), pppp19-{F}(V6,V1,V2), P_head_of-{F}(V1,V7), V0 == V7, P_tail_of-{F}(V2,V8), V0 == V8, shortest_path-{F}(V9,V10,V4) | P_tail_of-{T}(V1,V0), P_tail_of-{T}(V1,V8)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #433: mergings( V8 == V14, V15 == V16, V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V12, V12 == V19; #423 ), references = 3, size of lhs = 20:
% 3.63/3.79 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), pppp19-{F}(V5,V1,V2), P_head_of-{F}(V1,V6), V0 == V6, P_tail_of-{F}(V2,V7), V0 == V7, P_empty-{F}(V8), P_tail_of-{F}(V9,V0), P_head_of-{F}(V9,V10), P_head_of-{F}(V11,V10), precedes-{F}(V1,V11,V12), shortest_path-{F}(V13,V14,V4), shortest_path-{F}(V15,V16,V12) | P_tail_of-{T}(V1,V7)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #444: exists( #93, #442 ), references = 5, size of lhs = 3:
% 3.63/3.79 P_empty-{F}(V0), pppp4-{F}(V1,V2), P_tail_of-{F}(V2,V3) | P_head_of-{T}(V1,V3)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #469: mergings( V7 == V10, V11 == V12, V3 == V4, V4 == V5, V5 == V6, V6 == V8; #461 ), references = 2, size of lhs = 14:
% 3.63/3.79 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_head_of-{F}(V1,V0), P_empty-{F}(V2), P_tail_of-{F}(V3,V0), P_head_of-{F}(V3,V0), on_path-{F}(V1,V4), pppp20-{F}(V4,V1), P_tail_of-{F}(V1,V5), V0 == V5, path-{F}(V6,V7,V4), shortest_path-{F}(V8,V9,V4), shortest_path-{F}(V10,V11,V4) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #479: mergings( V7 == V13, V13 == V16, V8 == V9, V9 == V10, V3 == V4, V4 == V5, V5 == V6, V6 == V11, V11 == V14; #462 ), references = 2, size of lhs = 17:
% 3.63/3.79 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_head_of-{F}(V1,V0), on_path-{F}(V1,V2), pppp20-{F}(V2,V1), P_tail_of-{F}(V1,V3), V0 == V3, P_tail_of-{F}(V4,V0), P_head_of-{F}(V4,V0), P_empty-{F}(V5), P_tail_of-{F}(V6,V3), P_head_of-{F}(V6,V0), path-{F}(V7,V8,V2), shortest_path-{F}(V9,V10,V2), shortest_path-{F}(V11,V12,V2), shortest_path-{F}(V13,V14,V2) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #483: exists( #93, #340 ), references = 1, size of lhs = 1:
% 3.63/3.79 pppp0-{F}(V0,V1,V2) | P_head_of-{T}(V0,V1)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #490: disj( #6, #482+#339+#469 ), references = 1, size of lhs = 13:
% 3.63/3.79 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), pppp8-{F}(V1,V0,V2), V0 == V2, P_empty-{F}(V3), P_tail_of-{F}(V4,V0), P_head_of-{F}(V4,V0), on_path-{F}(V1,V5), pppp20-{F}(V5,V1), path-{F}(V6,V7,V5), shortest_path-{F}(V8,V9,V5), shortest_path-{F}(V10,V11,V5) | pppp1-{T}(V1,V0,V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #491: disj( #6, #482+#339+#479 ), references = 1, size of lhs = 14:
% 3.63/3.79 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), pppp8-{F}(V1,V0,V2), V0 == V2, on_path-{F}(V1,V3), pppp20-{F}(V3,V1), P_tail_of-{F}(V4,V0), P_head_of-{F}(V4,V0), P_empty-{F}(V5), path-{F}(V6,V7,V3), shortest_path-{F}(V8,V9,V3), shortest_path-{F}(V10,V11,V3), shortest_path-{F}(V12,V13,V3) | pppp1-{T}(V1,V0,V2)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #499: mergings( V1 == V8; #497 ), references = 1, size of lhs = 12:
% 3.63/3.79 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
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #504: mergings( V1 == V8; #502 ), references = 1, size of lhs = 15:
% 3.63/3.79 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_sequential_pairs-{F}(V8), P_n1-{F}(V9), P_number_of_in-{F}(V8,V5,V10), P_length_of-{F}(V5,V11), P_minus-{F}(V11,V9,V12), V10 == V12 | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #555: mergings( V2 == V9, V10 == V11; #550 ), references = 1, size of lhs = 15:
% 3.63/3.79 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), pppp19-{F}(V6,V1,V2), P_head_of-{F}(V1,V7), V0 == V7, P_tail_of-{F}(V2,V8), V0 == V8, shortest_path-{F}(V9,V10,V4) | P_tail_of-{T}(V1,V0), P_tail_of-{T}(V1,V8)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #561: mergings( V9 == V2, V2 == V8, V8 == V10; #556 ), references = 1, size of lhs = 14:
% 3.63/3.79 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), pppp19-{F}(V7,V5,V1), shortest_path-{F}(V8,V9,V6) | P_tail_of-{T}(V5,V0)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #565: mergings( V2 == V8, V9 == V10, V6 == V13; #557 ), references = 1, size of lhs = 20:
% 3.63/3.79 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), pppp19-{F}(V5,V1,V2), P_head_of-{F}(V1,V6), V0 == V6, P_tail_of-{F}(V2,V7), V0 == V7, P_empty-{F}(V8), P_tail_of-{F}(V9,V7), P_head_of-{F}(V9,V10), P_head_of-{F}(V11,V10), precedes-{F}(V1,V11,V12), shortest_path-{F}(V13,V14,V4), shortest_path-{F}(V15,V16,V12) | P_tail_of-{T}(V1,V0)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #603: mergings( V7 == V16, V10 == V11, V11 == V12, V3 == V4, V4 == V5, V5 == V6, V6 == V8, V8 == V9, V9 == V13, V13 == V14, V14 == V15; #590 ), references = 3, size of lhs = 13:
% 3.63/3.79 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_head_of-{F}(V1,V0), P_tail_of-{F}(V1,V2), V0 == V2, P_empty-{F}(V3), on_path-{F}(V1,V4), pppp20-{F}(V4,V1), path-{F}(V5,V6,V4), shortest_path-{F}(V7,V8,V4), path-{F}(V9,V10,V4), shortest_path-{F}(V11,V12,V4) | pppp19-{T}(V4,V1,V1)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #614: mergings( V9 == V12, V12 == V13, V3 == V4, V4 == V5, V5 == V6, V6 == V8, V8 == V10, V10 == V14, V14 == V15, V15 == V16; #591 ), references = 1, size of lhs = 19:
% 3.63/3.79 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_head_of-{F}(V1,V0), edge-{F}(V2), P_head_of-{F}(V2,V0), on_path-{F}(V1,V3), pppp20-{F}(V3,V1), on_path-{F}(V2,V3), P_tail_of-{F}(V1,V4), V0 == V4, P_empty-{F}(V5), P_tail_of-{F}(V2,V6), P_tail_of-{F}(V7,V6), P_head_of-{F}(V7,V4), path-{F}(V8,V9,V3), shortest_path-{F}(V10,V11,V3), path-{F}(V12,V13,V3), shortest_path-{F}(V14,V15,V3) | pppp19-{T}(V3,V2,V1)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #663: mergings( V2 == V4, V4 == V5, V3 == V6, V6 == V8; #656 ), references = 2, size of lhs = 10:
% 3.63/3.79 complete-{F}(), edge-{F}(V0), P_tail_of-{F}(V0,V1), on_path-{F}(V0,V2), pppp20-{F}(V2,V0), P_empty-{F}(V3), path-{F}(V4,V5,V2), shortest_path-{F}(V6,V7,V2), path-{F}(V8,V9,V2), shortest_path-{F}(V10,V11,V2) | P_head_of-{T}(V0,V1)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #668: mergings( V2 == V3, V3 == V9, V4 == V6, V6 == V7; #658 ), references = 1, size of lhs = 13:
% 3.63/3.79 complete-{F}(), edge-{F}(V0), on_path-{F}(V0,V1), pppp20-{F}(V1,V0), P_empty-{F}(V2), on_path-{F}(V0,V3), P_tail_of-{F}(V0,V4), path-{F}(V5,V6,V1), shortest_path-{F}(V7,V8,V1), path-{F}(V9,V10,V1), shortest_path-{F}(V11,V12,V1), path-{F}(V13,V14,V3), shortest_path-{F}(V15,V16,V3) | P_head_of-{T}(V0,V4)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #679: exists( #94, #673 ), references = 1, size of lhs = 3:
% 3.63/3.79 P_empty-{F}(V0), pppp4-{F}(V1,V2), pppp0-{F}(V1,V3,V4) | P_tail_of-{T}(V2,V3)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #680: exists( #94, #674 ), references = 1, size of lhs = 4:
% 3.63/3.79 P_empty-{F}(V0), pppp4-{F}(V1,V2), P_tail_of-{F}(V1,V3), pppp1-{F}(V1,V4,V5) | P_tail_of-{T}(V2,V5)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #711: mergings( V2 == V3; #707 ), references = 1, size of lhs = 11:
% 3.63/3.79 complete-{F}(), P_empty-{F}(V0), P_head_of-{F}(V1,V2), on_path-{F}(V1,V3), on_path-{F}(V1,V4), pppp20-{F}(V4,V1), path-{F}(V5,V6,V3), path-{F}(V7,V8,V4), shortest_path-{F}(V9,V10,V4), path-{F}(V11,V12,V4), shortest_path-{F}(V13,V14,V4) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #714: mergings( V2 == V3; #712 ), references = 1, size of lhs = 10:
% 3.63/3.79 complete-{F}(), P_empty-{F}(V0), on_path-{F}(V1,V2), on_path-{F}(V1,V3), pppp20-{F}(V3,V1), path-{F}(V4,V5,V2), path-{F}(V6,V7,V3), shortest_path-{F}(V8,V9,V3), path-{F}(V10,V11,V3), shortest_path-{F}(V12,V13,V3) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #719: mergings( V0 == V11, V11 == V12; #716 ), references = 1, size of lhs = 15:
% 3.63/3.79 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) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #728: mergings( V3 == V4, V4 == V5, V5 == V10, V10 == V11; #723 ), references = 1, size of lhs = 11:
% 3.63/3.79 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
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #735: mergings( V6 == V7, V7 == V8, V8 == V13, V13 == V14, V3 == V15; #729 ), references = 3, size of lhs = 12:
% 3.63/3.79 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_minus-{F}(V6,V9,V11) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #742: mergings( V3 == V4, V4 == V5, V5 == V9, V9 == V10, V11 == V12; #736 ), references = 1, size of lhs = 10:
% 3.63/3.79 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,V9), P_minus-{F}(V6,V8,V10) | P_number_of_in-{T}(V3,V5,V7)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #763: mergings( V2 == V4, V4 == V7, V7 == V8, V8 == V9, V9 == V13, V13 == V14, V14 == V15, V3 == V5, V5 == V10, V10 == V16, V16 == V17, V6 == V11, V11 == V18, V12 == V19, V18 == V24; #747 ), references = 1, size of lhs = 12:
% 3.63/3.79 complete-{F}(), P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_graph-{F}(V4), P_number_of_in-{F}(V3,V4,V5), pppp23-{F}(V6,V2,V5), pppp23-{F}(V6,V2,V7), pppp23-{F}(V6,V2,V8), pppp23-{F}(V6,V2,V9) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #784: mergings( V0 == V8, V8 == V10, V10 == V12, V12 == V13, V13 == V14, V14 == V18, V18 == V19, V19 == V20, V1 == V9, V9 == V11, V11 == V15, V15 == V21, V2 == V21, V21 == V22, V3 == V16, V16 == V23, V4 == V17, V17 == V24, V5 == V25; #764 ), references = 1, size of lhs = 8:
% 3.63/3.79 complete-{F}(), P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_graph-{F}(V4), P_number_of_in-{F}(V3,V4,V5) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #808: mergings( V3 == V7, V7 == V10, V10 == V12, V12 == V15, V15 == V16, V16 == V17, V17 == V20, V20 == V21, V21 == V22, V4 == V8, V8 == V11, V11 == V13, V13 == V18, V18 == V23, V5 == V9, V9 == V23, V23 == V24, V6 == V14, V14 == V19, V19 == V25, V0 == V26; #786 ), references = 1, size of lhs = 6:
% 3.63/3.79 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_graph-{F}(V4) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #831: mergings( V1 == V5, V5 == V8, V8 == V10, V10 == V13, V13 == V14, V14 == V15, V15 == V19, V19 == V20, V20 == V21, V2 == V6, V6 == V9, V9 == V11, V11 == V16, V16 == V22, V3 == V7, V7 == V22, V22 == V23, V4 == V12, V12 == V17, V17 == V24, V18 == V25; #809 ), references = 1, size of lhs = 5:
% 3.63/3.79 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #853: mergings( V1 == V5, V5 == V8, V8 == V10, V10 == V13, V13 == V14, V14 == V15, V15 == V18, V18 == V19, V19 == V20, V2 == V6, V6 == V9, V9 == V11, V11 == V16, V16 == V21, V3 == V7, V7 == V21, V21 == V22, V4 == V12, V12 == V17, V17 == V23; #832 ), references = 1, size of lhs = 4:
% 3.63/3.79 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V1), P_n1-{F}(V2) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #872: mergings( V1 == V4, V4 == V7, V7 == V9, V9 == V11, V11 == V12, V12 == V13, V13 == V15, V15 == V16, V16 == V17, V2 == V5, V5 == V8, V8 == V10, V10 == V14, V14 == V18, V3 == V6, V6 == V18, V18 == V19; #854 ), references = 1, size of lhs = 3:
% 3.63/3.79 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V1) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #877: exists( #98, #174 ), references = 1, size of lhs = 8:
% 3.63/3.79 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,V8), P_minus-{F}(V5,V7,V9) | P_number_of_in-{T}(V2,V4,V6)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #878: exists( #98, #735 ), references = 1, size of lhs = 10:
% 3.63/3.79 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,V8,V9), P_minus-{F}(V6,V8,V10) | P_number_of_in-{T}(V1,V5,V7)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #889: mergings( V3 == V9, V4 == V6, V5 == V7; #885 ), references = 2, size of lhs = 10:
% 3.63/3.79 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,V6), P_length_of-{F}(V5,V7), P_number_of_in-{F}(V3,V5,V8), pppp23-{F}(V5,V2,V9) | P_number_of_in-{T}(V1,V5,V8)
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #909: mergings( V2 == V4, V4 == V10, V10 == V15, V15 == V16, V3 == V5, V5 == V11, V11 == V13, V13 == V17, V6 == V18, V7 == V12, V12 == V14, V14 == V19, V17 == V8, V19 == V24; #894 ), references = 1, size of lhs = 13:
% 3.63/3.79 complete-{F}(), P_triangles-{F}(V0), P_edges-{F}(V0), P_graph-{F}(V1), P_empty-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), P_number_of_in-{F}(V0,V1,V5), pppp23-{F}(V6,V4,V5), pppp23-{F}(V6,V4,V7), pppp23-{F}(V6,V4,V8), pppp23-{F}(V6,V4,V9), pppp23-{F}(V6,V4,V10) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #928: mergings( V0 == V8, V8 == V10, V10 == V16, V16 == V20, V20 == V21, V1 == V9, V9 == V11, V11 == V17, V17 == V18, V18 == V22, V2 == V12, V12 == V23, V13 == V19, V19 == V3, V4 == V22, V22 == V14, V5 == V15; #910 ), references = 1, size of lhs = 8:
% 3.63/3.79 complete-{F}(), P_triangles-{F}(V0), P_edges-{F}(V0), P_graph-{F}(V1), P_number_of_in-{F}(V0,V1,V2), P_empty-{F}(V3), P_sequential_pairs-{F}(V4), P_n1-{F}(V5) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #950: mergings( V3 == V7, V7 == V10, V10 == V11, V11 == V16, V16 == V20, V20 == V21, V4 == V8, V8 == V0, V0 == V12, V12 == V17, V17 == V18, V18 == V22, V5 == V9, V9 == V13, V13 == V23, V6 == V14, V14 == V19, V19 == V24, V22 == V15; #930 ), references = 1, size of lhs = 6:
% 3.63/3.79 P_triangles-{F}(V0), P_edges-{F}(V0), P_graph-{F}(V1), P_empty-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #971: mergings( V1 == V5, V5 == V8, V8 == V10, V10 == V15, V15 == V19, V19 == V20, V2 == V6, V6 == V9, V9 == V11, V11 == V16, V16 == V17, V17 == V21, V3 == V7, V7 == V12, V12 == V22, V4 == V13, V13 == V18, V18 == V23, V21 == V14; #951 ), references = 1, size of lhs = 5:
% 3.63/3.79 P_triangles-{F}(V0), P_edges-{F}(V0), P_empty-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #987: mergings( V3 == V11, V11 == V12, V18 == V20, V4 == V9, V9 == V13, V5 == V14, V6 == V10, V10 == V15, V7 == V0; #977 ), references = 1, size of lhs = 14:
% 3.63/3.79 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), P_number_of_in-{F}(V1,V0,V6), pppp23-{F}(V7,V5,V6), P_length_of-{F}(V7,V8), P_length_of-{F}(V9,V8), pppp23-{F}(V9,V5,V10), pppp23-{F}(V9,V5,V11), pppp23-{F}(V9,V5,V12) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #997: mergings( V2 == V11, V11 == V12, V3 == V8, V8 == V13, V4 == V14, V5 == V9, V9 == V15, V6 == V10; #988 ), references = 1, size of lhs = 12:
% 3.63/3.79 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), P_number_of_in-{F}(V1,V0,V6), pppp23-{F}(V7,V5,V6), pppp23-{F}(V7,V5,V8), pppp23-{F}(V7,V5,V9), pppp23-{F}(V7,V5,V10) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #1011: mergings( V0 == V8, V8 == V16, V16 == V17, V1 == V9, V9 == V14, V14 == V18, V2 == V10, V10 == V19, V11 == V3, V4 == V12, V12 == V15, V5 == V13; #998 ), references = 1, size of lhs = 8:
% 3.63/3.79 complete-{F}(), P_graph-{F}(V0), P_triangles-{F}(V1), P_number_of_in-{F}(V1,V0,V2), P_empty-{F}(V3), P_edges-{F}(V4), P_sequential_pairs-{F}(V5), P_n1-{F}(V6) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #1028: mergings( V3 == V7, V7 == V10, V10 == V16, V16 == V17, V4 == V8, V8 == V11, V11 == V15, V15 == V18, V5 == V9, V9 == V12, V12 == V19, V6 == V13, V13 == V20, V14 == V0; #1013 ), references = 1, size of lhs = 6:
% 3.63/3.79 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
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #1044: mergings( V1 == V5, V5 == V8, V8 == V15, V15 == V16, V2 == V6, V6 == V9, V9 == V13, V13 == V17, V3 == V7, V7 == V10, V10 == V18, V4 == V11, V11 == V19, V12 == V14; #1029 ), references = 1, size of lhs = 5:
% 3.63/3.79 P_triangles-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #1059: mergings( V1 == V5, V5 == V8, V8 == V13, V13 == V14, V2 == V6, V6 == V9, V9 == V12, V12 == V15, V3 == V7, V7 == V10, V10 == V16, V4 == V11, V11 == V17; #1045 ), references = 1, size of lhs = 4:
% 3.63/3.79 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #1072: mergings( V1 == V4, V4 == V7, V7 == V11, V11 == V12, V2 == V5, V5 == V8, V8 == V10, V10 == V13, V3 == V6, V6 == V9, V9 == V14; #1060 ), references = 1, size of lhs = 3:
% 3.63/3.79 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #1082: mergings( V1 == V3, V3 == V5, V5 == V8, V8 == V9, V2 == V4, V4 == V6, V6 == V7, V7 == V10; #1073 ), references = 1, size of lhs = 2:
% 3.63/3.79 P_empty-{F}(V0), P_edges-{F}(V1) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #1088: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5; #1083 ), references = 1, size of lhs = 1:
% 3.63/3.79 P_empty-{F}(V0) | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 #1090: exists( #96, #1083 ), references = 1, size of lhs = 0:
% 3.63/3.79 FALSE | FALSE
% 3.63/3.79 (used 0 times, uses = {})
% 3.63/3.79
% 3.63/3.79 number of learnt formulas = 76
% 3.63/3.79
% 3.63/3.79
% 3.63/3.79 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.63/3.79
% 3.63/3.79 randbase = 1
%------------------------------------------------------------------------------