TSTP Solution File: GRA008+1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : GRA008+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n008.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 06:02:47 EDT 2022
% Result : Theorem 4.92s 5.17s
% Output : Refutation 4.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRA008+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.11/0.13 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jul 22 07:54:53 EDT 2022
% 0.13/0.33 % CPUTime :
% 4.92/5.17 GeoParameters:
% 4.92/5.17
% 4.92/5.17 tptp_input = 1
% 4.92/5.17 tptp_output = 0
% 4.92/5.17 nonempty = 1
% 4.92/5.17 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.92/5.17 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 4.92/5.17
% 4.92/5.17
% 4.92/5.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.92/5.17 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.92/5.17
% 4.92/5.17 RuleSystem INPUT:
% 4.92/5.17
% 4.92/5.17 Initial Rules:
% 4.92/5.17 #0: input, references = 6, size of lhs = 3:
% 4.92/5.17 P_head_of-{F}(V0,V2), P_tail_of-{F}(V0,V2), edge-{F}(V0) | FALSE
% 4.92/5.17 (used 0 times, uses = {})
% 4.92/5.17
% 4.92/5.17 #1: input, references = 7, size of lhs = 3:
% 4.92/5.17 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), edge-{F}(V0) | vertex-{T}(V1)
% 4.92/5.17 (used 0 times, uses = {})
% 4.92/5.17
% 4.92/5.17 #2: input, references = 5, size of lhs = 3:
% 4.92/5.17 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), edge-{F}(V0) | vertex-{T}(V2)
% 4.92/5.17 (used 0 times, uses = {})
% 4.92/5.17
% 4.92/5.17 #3: input, references = 4, size of lhs = 4:
% 4.92/5.17 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0 | EXISTS V2: pppp9-{T}(V1,V0,V2)
% 4.92/5.17 (used 0 times, uses = {})
% 4.92/5.17
% 4.92/5.17 #4: input, references = 8, size of lhs = 1:
% 4.92/5.17 pppp9-{F}(V0,V1,V2) | pppp8-{T}(V2,V0,V1)
% 4.92/5.17 (used 0 times, uses = {})
% 4.92/5.17
% 4.92/5.17 #5: input, references = 3, size of lhs = 3:
% 4.92/5.17 pppp8-{F}(V0,V1,V2), pppp1-{F}(V0,V1,V2), pppp0-{F}(V0,V1,V2) | FALSE
% 4.92/5.17 (used 0 times, uses = {})
% 4.92/5.17
% 4.92/5.17 #6: input, references = 6, size of lhs = 1:
% 4.92/5.17 pppp8-{F}(V0,V1,V2) | pppp0-{T}(V0,V1,V2), pppp1-{T}(V0,V1,V2)
% 4.92/5.17 (used 0 times, uses = {})
% 4.92/5.17
% 4.92/5.17 #7: input, references = 4, size of lhs = 1:
% 4.92/5.17 pppp8-{F}(V0,V1,V2) | edge-{T}(V0)
% 4.92/5.17 (used 0 times, uses = {})
% 4.92/5.17
% 4.92/5.17 #8: input, references = 5, size of lhs = 4:
% 4.92/5.17 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp1-{F}(V0,V1,V2), V2 == V3 | FALSE
% 4.92/5.17 (used 0 times, uses = {})
% 4.92/5.17
% 4.92/5.17 #9: input, references = 5, size of lhs = 4:
% 4.92/5.17 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp1-{F}(V0,V1,V2), V1 == V4 | FALSE
% 4.92/5.17 (used 0 times, uses = {})
% 4.92/5.17
% 4.92/5.17 #10: input, references = 4, size of lhs = 2:
% 4.92/5.17 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | pppp1-{T}(V0,V4,V3)
% 4.92/5.17 (used 0 times, uses = {})
% 4.92/5.17
% 4.92/5.17 #11: input, references = 7, size of lhs = 4:
% 4.92/5.18 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp0-{F}(V0,V1,V2), V1 == V3 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #12: input, references = 9, size of lhs = 4:
% 4.92/5.18 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp0-{F}(V0,V1,V2), V2 == V4 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #13: input, references = 5, size of lhs = 2:
% 4.92/5.18 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | pppp0-{T}(V0,V3,V4)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #14: input, references = 4, size of lhs = 7:
% 4.92/5.18 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)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #15: input, references = 6, size of lhs = 9:
% 4.92/5.18 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)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #16: input, references = 3, size of lhs = 2:
% 4.92/5.18 P_empty-{F}(V0), path-{F}(V1,V2,V3) | vertex-{T}(V1)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #17: input, references = 3, size of lhs = 2:
% 4.92/5.18 P_empty-{F}(V0), path-{F}(V1,V2,V3) | vertex-{T}(V2)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #18: input, references = 3, size of lhs = 2:
% 4.92/5.18 P_empty-{F}(V0), path-{F}(V1,V2,V3) | EXISTS V4: pppp11-{T}(V1,V2,V3,V4)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #19: input, references = 4, size of lhs = 2:
% 4.92/5.18 pppp11-{F}(V0,V1,V2,V3), P_tail_of-{F}(V3,V4) | pppp10-{T}(V3,V0,V1,V2,V4)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #20: input, references = 3, size of lhs = 3:
% 4.92/5.18 pppp10-{F}(V0,V1,V2,V3,V4), pppp3-{F}(V0,V2,V3), pppp2-{F}(V0,V2,V3) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #21: input, references = 3, size of lhs = 1:
% 4.92/5.18 pppp10-{F}(V0,V1,V2,V3,V4) | pppp2-{T}(V0,V2,V3), pppp3-{T}(V0,V2,V3)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #22: input, references = 4, size of lhs = 2:
% 4.92/5.18 pppp10-{F}(V0,V1,V2,V3,V4), V1 == V4 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #23: input, references = 3, size of lhs = 1:
% 4.92/5.18 pppp10-{F}(V0,V1,V2,V3,V4) | edge-{T}(V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #24: input, references = 3, size of lhs = 3:
% 4.92/5.18 P_empty-{F}(V0), P_head_of-{F}(V1,V4), pppp3-{F}(V1,V2,V3) | EXISTS V5: pppp12-{T}(V1,V2,V3,V5,V4)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #25: input, references = 3, size of lhs = 4:
% 4.92/5.18 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)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #26: input, references = 3, size of lhs = 3:
% 4.92/5.18 pppp12-{F}(V0,V1,V2,V3,V4), P_path_cons-{F}(V0,V3,V5), V2 == V5 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #27: input, references = 3, size of lhs = 2:
% 4.92/5.18 pppp12-{F}(V0,V1,V2,V3,V4), P_path_cons-{F}(V0,V3,V5) | path-{T}(V4,V1,V3)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #28: input, references = 3, size of lhs = 5:
% 4.92/5.18 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
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #29: input, references = 3, size of lhs = 5:
% 4.92/5.18 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
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #30: input, references = 3, size of lhs = 3:
% 4.92/5.18 P_empty-{F}(V0), P_head_of-{F}(V1,V4), P_path_cons-{F}(V1,V0,V5) | pppp2-{T}(V1,V4,V5)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #31: input, references = 3, size of lhs = 5:
% 4.92/5.18 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)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #32: input, references = 3, size of lhs = 5:
% 4.92/5.18 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)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #33: input, references = 3, size of lhs = 5:
% 4.92/5.18 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)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #34: input, references = 3, size of lhs = 3:
% 4.92/5.18 P_empty-{F}(V0), path-{F}(V3,V2,V1), in_path-{F}(V4,V1) | vertex-{T}(V4)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #35: input, references = 3, size of lhs = 3:
% 4.92/5.18 P_empty-{F}(V0), path-{F}(V3,V2,V1), in_path-{F}(V4,V1) | EXISTS V5: pppp13-{T}(V5,V1,V4)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #36: input, references = 7, size of lhs = 5:
% 4.92/5.18 pppp13-{F}(V0,V1,V2), P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), V2 == V3, V2 == V4 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #37: input, references = 3, size of lhs = 3:
% 4.92/5.18 pppp13-{F}(V0,V1,V2), P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | on_path-{T}(V0,V1)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #38: input, references = 5, size of lhs = 2:
% 4.92/5.18 P_empty-{F}(V0), sequential-{F}(V1,V2) | pppp4-{T}(V1,V2)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #39: input, references = 6, size of lhs = 2:
% 4.92/5.18 P_empty-{F}(V0), pppp4-{F}(V1,V2) | sequential-{T}(V1,V2)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #40: input, references = 11, size of lhs = 3:
% 4.92/5.18 P_empty-{F}(V0), P_head_of-{F}(V1,V3), P_tail_of-{F}(V2,V4) | pppp14-{T}(V1,V2,V3,V4)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #41: input, references = 6, size of lhs = 4:
% 4.92/5.18 pppp14-{F}(V0,V1,V3,V3), edge-{F}(V0), edge-{F}(V1), V0 == V1 | pppp4-{T}(V0,V1)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #42: input, references = 5, size of lhs = 3:
% 4.92/5.18 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1), V2 == V3 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #43: input, references = 3, size of lhs = 2:
% 4.92/5.18 pppp14-{F}(V1,V1,V2,V3), pppp4-{F}(V1,V1) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #44: input, references = 5, size of lhs = 2:
% 4.92/5.18 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1) | edge-{T}(V1)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #45: input, references = 5, size of lhs = 2:
% 4.92/5.18 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1) | edge-{T}(V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #46: input, references = 4, size of lhs = 5:
% 4.92/5.18 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)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #47: input, references = 3, size of lhs = 6:
% 4.92/5.18 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)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #48: input, references = 4, size of lhs = 3:
% 4.92/5.18 P_empty-{F}(V0), precedes-{F}(V2,V3,V1), path-{F}(V5,V4,V1) | pppp15-{T}(V1,V2,V3)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #49: input, references = 3, size of lhs = 3:
% 4.92/5.18 pppp15-{F}(V0,V1,V2), pppp5-{F}(V0,V1,V2), sequential-{F}(V1,V2) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #50: input, references = 3, size of lhs = 1:
% 4.92/5.18 pppp15-{F}(V0,V1,V2) | sequential-{T}(V1,V2), pppp5-{T}(V0,V1,V2)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #51: input, references = 4, size of lhs = 1:
% 4.92/5.18 pppp15-{F}(V0,V1,V2) | on_path-{T}(V2,V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #52: input, references = 4, size of lhs = 1:
% 4.92/5.18 pppp15-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #53: input, references = 3, size of lhs = 2:
% 4.92/5.18 P_empty-{F}(V0), pppp5-{F}(V1,V2,V3) | EXISTS V4: pppp16-{T}(V1,V2,V3,V4)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #54: input, references = 3, size of lhs = 3:
% 4.92/5.18 P_empty-{F}(V0), sequential-{F}(V2,V4), precedes-{F}(V4,V3,V1) | pppp5-{T}(V1,V2,V3)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #55: input, references = 3, size of lhs = 1:
% 4.92/5.18 pppp16-{F}(V0,V1,V2,V3) | precedes-{T}(V3,V2,V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #56: input, references = 3, size of lhs = 1:
% 4.92/5.18 pppp16-{F}(V0,V1,V2,V3) | sequential-{T}(V1,V3)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #57: input, references = 6, size of lhs = 2:
% 4.92/5.18 P_empty-{F}(V0), shortest_path-{F}(V1,V2,V3) | pppp6-{T}(V1,V2,V3)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #58: input, references = 3, size of lhs = 2:
% 4.92/5.18 P_empty-{F}(V0), pppp6-{F}(V1,V2,V3) | shortest_path-{T}(V1,V2,V3)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #59: input, references = 6, size of lhs = 3:
% 4.92/5.18 P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V1,V2,V3) | path-{T}(V1,V2,V3)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #60: input, references = 3, size of lhs = 3:
% 4.92/5.18 P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V2,V2,V3) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #61: input, references = 3, size of lhs = 5:
% 4.92/5.18 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)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #62: input, references = 3, size of lhs = 4:
% 4.92/5.18 P_empty-{F}(V0), P_length_of-{F}(V3,V4), path-{F}(V1,V2,V3), V1 == V2 | pppp6-{T}(V1,V2,V3), pppp26-{T}(V1,V2,V4)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #63: input, references = 3, size of lhs = 1:
% 4.92/5.18 pppp26-{F}(V0,V1,V2) | EXISTS V3: pppp17-{T}(V0,V1,V3,V2)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #64: input, references = 3, size of lhs = 3:
% 4.92/5.18 pppp17-{F}(V0,V1,V2,V3), P_length_of-{F}(V2,V4), less_or_equal-{F}(V3,V4) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #65: input, references = 3, size of lhs = 2:
% 4.92/5.18 pppp17-{F}(V0,V1,V2,V3), P_length_of-{F}(V2,V4) | path-{T}(V0,V1,V2)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #66: input, references = 4, size of lhs = 7:
% 4.92/5.18 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
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #67: input, references = 4, size of lhs = 6:
% 4.92/5.18 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
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #68: input, references = 3, size of lhs = 2:
% 4.92/5.18 P_empty-{F}(V0), triangle-{F}(V1,V2,V3) | pppp7-{T}(V1,V2,V3)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #69: input, references = 4, size of lhs = 2:
% 4.92/5.18 P_empty-{F}(V0), pppp7-{F}(V1,V2,V3) | triangle-{T}(V1,V2,V3)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #70: input, references = 3, size of lhs = 2:
% 4.92/5.18 P_empty-{F}(V0), pppp7-{F}(V1,V2,V3) | pppp18-{T}(V1,V2,V3)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #71: input, references = 4, size of lhs = 7:
% 4.92/5.18 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)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #72: input, references = 3, size of lhs = 1:
% 4.92/5.18 pppp18-{F}(V0,V1,V2) | sequential-{T}(V2,V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #73: input, references = 3, size of lhs = 1:
% 4.92/5.18 pppp18-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #74: input, references = 3, size of lhs = 1:
% 4.92/5.18 pppp18-{F}(V0,V1,V2) | sequential-{T}(V0,V1)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #75: input, references = 3, size of lhs = 1:
% 4.92/5.18 pppp18-{F}(V0,V1,V2) | edge-{T}(V2)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #76: input, references = 3, size of lhs = 1:
% 4.92/5.18 pppp18-{F}(V0,V1,V2) | edge-{T}(V1)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #77: input, references = 3, size of lhs = 1:
% 4.92/5.18 pppp18-{F}(V0,V1,V2) | edge-{T}(V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #78: input, references = 6, size of lhs = 6:
% 4.92/5.18 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
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #79: input, references = 7, size of lhs = 9:
% 4.92/5.18 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
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #80: input, references = 3, size of lhs = 9:
% 4.92/5.18 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)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #81: input, references = 3, size of lhs = 1:
% 4.92/5.18 pppp20-{F}(V0,V1) | EXISTS V2: pppp19-{T}(V0,V2,V1)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #82: input, references = 3, size of lhs = 1:
% 4.92/5.18 pppp20-{F}(V0,V1) | on_path-{T}(V1,V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #83: input, references = 3, size of lhs = 2:
% 4.92/5.18 pppp19-{F}(V0,V1,V2), triangle-{F}(V1,V2,V3) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #84: input, references = 3, size of lhs = 1:
% 4.92/5.18 pppp19-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #85: input, references = 3, size of lhs = 1:
% 4.92/5.18 pppp19-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #86: input, references = 3, size of lhs = 8:
% 4.92/5.18 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)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #87: input, references = 4, size of lhs = 6:
% 4.92/5.18 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}()
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #88: input, references = 4, size of lhs = 6:
% 4.92/5.18 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_graph-{F}(V5) | EXISTS V6: pppp25-{T}(V6)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #89: input, references = 5, size of lhs = 1:
% 4.92/5.18 pppp25-{F}(V0) | EXISTS V1: pppp24-{T}(V0,V1)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #90: input, references = 5, size of lhs = 1:
% 4.92/5.18 pppp24-{F}(V0,V1) | EXISTS V2: pppp23-{T}(V2,V0,V1)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #91: input, references = 4, size of lhs = 2:
% 4.92/5.18 pppp24-{F}(V0,V1), triangle-{F}(V0,V1,V2) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #92: input, references = 5, size of lhs = 1:
% 4.92/5.18 pppp24-{F}(V0,V1) | sequential-{T}(V0,V1)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #93: input, references = 6, size of lhs = 1:
% 4.92/5.18 pppp23-{F}(V0,V1,V2) | EXISTS V3: pppp22-{T}(V0,V3)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #94: input, references = 6, size of lhs = 1:
% 4.92/5.18 pppp23-{F}(V0,V1,V2) | precedes-{T}(V1,V2,V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #95: input, references = 6, size of lhs = 1:
% 4.92/5.18 pppp22-{F}(V0,V1) | EXISTS V2: pppp21-{T}(V1,V0,V2)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #96: input, references = 7, size of lhs = 1:
% 4.92/5.18 pppp21-{F}(V0,V1,V2) | shortest_path-{T}(V2,V0,V1)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #97: input, references = 11, size of lhs = 1:
% 4.92/5.18 #-{F} V0 | EXISTS V1: P_head_of-{T}(V0,V1)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #98: input, references = 13, size of lhs = 1:
% 4.92/5.18 #-{F} V0 | EXISTS V1: P_tail_of-{T}(V0,V1)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #99: input, references = 5, size of lhs = 2:
% 4.92/5.18 #-{F} V0, #-{F} V1 | EXISTS V2: P_path_cons-{T}(V0,V1,V2)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #100: input, references = 4, size of lhs = 0:
% 4.92/5.18 FALSE | EXISTS V0: P_empty-{T}(V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #101: input, references = 4, size of lhs = 1:
% 4.92/5.18 #-{F} V0 | EXISTS V1: P_length_of-{T}(V0,V1)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #102: input, references = 5, size of lhs = 2:
% 4.92/5.18 #-{F} V0, #-{F} V1 | EXISTS V2: P_number_of_in-{T}(V0,V1,V2)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #103: input, references = 4, size of lhs = 0:
% 4.92/5.18 FALSE | EXISTS V0: P_edges-{T}(V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #104: input, references = 4, size of lhs = 0:
% 4.92/5.18 FALSE | EXISTS V0: P_sequential_pairs-{T}(V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #105: input, references = 5, size of lhs = 2:
% 4.92/5.18 #-{F} V0, #-{F} V1 | EXISTS V2: P_minus-{T}(V0,V1,V2)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #106: input, references = 4, size of lhs = 0:
% 4.92/5.18 FALSE | EXISTS V0: P_n1-{T}(V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #107: input, references = 4, size of lhs = 0:
% 4.92/5.18 FALSE | EXISTS V0: P_triangles-{T}(V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #108: input, references = 4, size of lhs = 0:
% 4.92/5.18 FALSE | EXISTS V0: P_graph-{T}(V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 number of initial rules = 109
% 4.92/5.18
% 4.92/5.18 Simplifiers:
% 4.92/5.18 #109: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 P_head_of-{F}(V0,V1), P_head_of-{F}(V0,V3), V1 == V3 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #110: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 P_tail_of-{F}(V0,V1), P_tail_of-{F}(V0,V3), V1 == V3 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #111: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 P_path_cons-{F}(V0,V1,V2), P_path_cons-{F}(V0,V1,V5), V2 == V5 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #112: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 P_empty-{F}(V0), P_empty-{F}(V1), V0 == V1 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #113: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 P_length_of-{F}(V0,V1), P_length_of-{F}(V0,V3), V1 == V3 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #114: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 P_number_of_in-{F}(V0,V1,V2), P_number_of_in-{F}(V0,V1,V5), V2 == V5 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #115: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 P_edges-{F}(V0), P_edges-{F}(V1), V0 == V1 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #116: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 P_sequential_pairs-{F}(V0), P_sequential_pairs-{F}(V1), V0 == V1 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #117: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 P_minus-{F}(V0,V1,V2), P_minus-{F}(V0,V1,V5), V2 == V5 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #118: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 P_n1-{F}(V0), P_n1-{F}(V1), V0 == V1 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #119: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 P_triangles-{F}(V0), P_triangles-{F}(V1), V0 == V1 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #120: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 P_graph-{F}(V0), P_graph-{F}(V1), V0 == V1 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #121: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp8-{F}(V0,V1,V2), pppp8-{F}(V3,V1,V2), V0 == V3 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #122: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp9-{F}(V0,V1,V2), pppp9-{F}(V0,V1,V5), V2 == V5 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #123: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V5,V1,V2,V3,V9), V0 == V5 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #124: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #125: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp11-{F}(V0,V1,V2,V3), pppp11-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #126: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V1,V2,V8,V4), V3 == V8 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #127: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #128: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp13-{F}(V0,V1,V2), pppp13-{F}(V3,V1,V2), V0 == V3 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #129: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp14-{F}(V0,V1,V2,V3), pppp14-{F}(V0,V5,V6,V7), V2 == V6 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #130: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp14-{F}(V0,V1,V2,V3), pppp14-{F}(V4,V1,V6,V7), V3 == V7 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #131: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp16-{F}(V0,V1,V2,V3), pppp16-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #132: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp17-{F}(V0,V1,V2,V3), pppp17-{F}(V0,V1,V6,V3), V2 == V6 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #133: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp19-{F}(V0,V1,V2), pppp19-{F}(V0,V4,V2), V1 == V4 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #134: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp19-{F}(V0,V1,V2), pppp19-{F}(V0,V4,V5), V2 == V5 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #135: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp20-{F}(V0,V1), pppp20-{F}(V0,V3), V1 == V3 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #136: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp21-{F}(V0,V1,V2), pppp21-{F}(V0,V1,V5), V2 == V5 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #137: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp21-{F}(V0,V1,V2), pppp21-{F}(V3,V1,V5), V0 == V3 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #138: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp22-{F}(V0,V1), pppp22-{F}(V0,V3), V1 == V3 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #139: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp23-{F}(V0,V1,V2), pppp23-{F}(V3,V1,V2), V0 == V3 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #140: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp23-{F}(V0,V1,V2), pppp23-{F}(V3,V1,V5), V2 == V5 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #141: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp23-{F}(V0,V1,V2), pppp23-{F}(V3,V4,V5), V1 == V4 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #142: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp24-{F}(V0,V1), pppp24-{F}(V0,V3), V1 == V3 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #143: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp24-{F}(V0,V1), pppp24-{F}(V2,V3), V0 == V2 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #144: unsound, references = 3, size of lhs = 3:
% 4.92/5.18 pppp25-{F}(V0), pppp25-{F}(V1), V0 == V1 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 number of simplifiers = 36
% 4.92/5.18
% 4.92/5.18 Learnt:
% 4.92/5.18 #149: exists( #98, #147 ), references = 4, size of lhs = 3:
% 4.92/5.18 P_empty-{F}(V0), P_head_of-{F}(V1,V2), pppp4-{F}(V1,V3) | P_tail_of-{T}(V3,V2)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #160: mergings( V5 == V6, V6 == V7, V2 == V3, V3 == V4; #155 ), references = 1, size of lhs = 4:
% 4.92/5.18 pppp25-{F}(V0), P_empty-{F}(V1), P_head_of-{F}(V0,V2), P_tail_of-{F}(V0,V2) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #172: mergings( V11 == V13, V9 == V10, V10 == V12, V2 == V3, V3 == V4; #166 ), references = 1, size of lhs = 12:
% 4.92/5.18 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp4-{F}(V4,V5), P_tail_of-{F}(V5,V6), P_head_of-{F}(V5,V7), P_path_cons-{F}(V5,V0,V8), P_number_of_in-{F}(V2,V8,V9), P_length_of-{F}(V8,V10), P_minus-{F}(V10,V3,V11), V9 == V11 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #181: exists( #97, #177 ), references = 1, size of lhs = 3:
% 4.92/5.18 P_empty-{F}(V0), pppp4-{F}(V1,V2), P_tail_of-{F}(V2,V3) | P_head_of-{T}(V1,V3)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #182: exists( #97, #175 ), references = 1, size of lhs = 4:
% 4.92/5.18 P_empty-{F}(V0), pppp4-{F}(V1,V2), P_head_of-{F}(V2,V3), pppp1-{F}(V2,V4,V5) | P_head_of-{T}(V1,V4)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #183: exists( #97, #176 ), references = 1, size of lhs = 4:
% 4.92/5.18 P_empty-{F}(V0), pppp4-{F}(V1,V2), P_head_of-{F}(V2,V3), pppp0-{F}(V2,V4,V5) | P_head_of-{T}(V1,V5)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #196: exists( #102, #78 ), references = 1, size of lhs = 4:
% 4.92/5.18 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)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #201: exists( #105, #79 ), references = 1, size of lhs = 7:
% 4.92/5.18 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)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #215: exists( #98, #36 ), references = 3, size of lhs = 3:
% 4.92/5.18 P_head_of-{F}(V0,V1), pppp13-{F}(V0,V2,V3), V3 == V1 | P_tail_of-{T}(V0,V3)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #234: exists( #95, #232 ), references = 3, size of lhs = 7:
% 4.92/5.18 P_empty-{F}(V0), P_tail_of-{F}(V1,V2), P_tail_of-{F}(V3,V2), P_head_of-{F}(V3,V4), P_head_of-{F}(V5,V4), precedes-{F}(V1,V5,V6), pppp22-{F}(V6,V7) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #236: exists( #93, #233 ), references = 4, size of lhs = 7:
% 4.92/5.18 P_empty-{F}(V0), P_tail_of-{F}(V1,V2), P_tail_of-{F}(V3,V2), P_head_of-{F}(V3,V4), P_head_of-{F}(V5,V4), precedes-{F}(V1,V5,V6), pppp23-{F}(V6,V7,V8) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #257: exists( #97, #255 ), references = 1, size of lhs = 3:
% 4.92/5.18 pppp13-{F}(V0,V1,V2), pppp13-{F}(V0,V3,V4), V4 == V2 | P_head_of-{T}(V0,V2), P_head_of-{T}(V0,V4)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #275: mergings( V1 == V8; #272 ), references = 2, size of lhs = 12:
% 4.92/5.18 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
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #277: mergings( V1 == V8; #273 ), references = 1, size of lhs = 15:
% 4.92/5.18 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
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #282: disj( #6, input ), references = 4, size of lhs = 4:
% 4.92/5.18 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), pppp8-{F}(V0,V3,V4), V4 == V1 | pppp0-{T}(V0,V3,V4)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #284: mergings( V2 == V3; #281 ), references = 3, size of lhs = 4:
% 4.92/5.18 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), pppp8-{F}(V0,V3,V1), V3 == V2 | pppp0-{T}(V0,V3,V1)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #313: exists( #97, #310 ), references = 1, size of lhs = 3:
% 4.92/5.18 pppp13-{F}(V0,V1,V2), pppp8-{F}(V0,V3,V4), V4 == V2 | P_head_of-{T}(V0,V2), P_head_of-{T}(V0,V4)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #320: disj( #312, #215+#284+#12 ), references = 1, size of lhs = 7:
% 4.92/5.18 pppp13-{F}(V0,V1,V2), pppp8-{F}(V0,V3,V4), V4 == V2, pppp8-{F}(V0,V5,V4), pppp13-{F}(V0,V6,V7), V5 == V7, V4 == V7 | P_head_of-{T}(V0,V2)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #321: disj( #312, #215+#284+#11 ), references = 1, size of lhs = 8:
% 4.92/5.18 pppp13-{F}(V0,V1,V2), pppp8-{F}(V0,V3,V4), V4 == V2, pppp8-{F}(V0,V5,V4), V5 == V4, pppp13-{F}(V0,V6,V7), V7 == V4, V5 == V7 | P_head_of-{T}(V0,V2)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #341: mergings( V2 == V3; #338 ), references = 2, size of lhs = 4:
% 4.92/5.18 P_head_of-{F}(V0,V1), pppp8-{F}(V0,V2,V3), V3 == V1, V2 == V1 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #344: mergings( V2 == V3, V4 == V3; #339 ), references = 10, size of lhs = 3:
% 4.92/5.18 P_head_of-{F}(V0,V1), pppp8-{F}(V0,V1,V2), V2 == V1 | P_tail_of-{T}(V0,V2)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #352: exists( #97, #341 ), references = 4, size of lhs = 1:
% 4.92/5.18 pppp8-{F}(V0,V1,V2) | P_head_of-{T}(V0,V2), P_head_of-{T}(V0,V1)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #386: disj( #352, #344+#11 ), references = 1, size of lhs = 5:
% 4.92/5.18 pppp8-{F}(V0,V1,V2), pppp8-{F}(V0,V2,V3), V3 == V2, pppp0-{F}(V0,V4,V5), V4 == V2 | P_head_of-{T}(V0,V1)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #388: mergings( V4 == V2; #385 ), references = 1, size of lhs = 5:
% 4.92/5.18 pppp8-{F}(V0,V1,V2), pppp8-{F}(V0,V2,V3), V3 == V2, pppp0-{F}(V0,V2,V4), V4 == V3 | P_head_of-{T}(V0,V1)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #398: disj( #6, #384+#344+#236 ), references = 1, size of lhs = 12:
% 4.92/5.18 P_empty-{F}(V0), P_tail_of-{F}(V1,V2), P_head_of-{F}(V3,V4), V2 == V4, pppp8-{F}(V5,V4,V2), pppp8-{F}(V5,V4,V6), pppp8-{F}(V5,V6,V7), V7 == V6, precedes-{F}(V1,V3,V8), pppp8-{F}(V5,V9,V10), V9 == V6, pppp23-{F}(V8,V11,V12) | pppp1-{T}(V5,V9,V10)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #399: disj( #6, #384+#344+#234 ), references = 1, size of lhs = 12:
% 4.92/5.18 P_empty-{F}(V0), P_tail_of-{F}(V1,V2), P_head_of-{F}(V3,V4), V2 == V4, pppp8-{F}(V5,V4,V2), pppp8-{F}(V5,V4,V6), pppp8-{F}(V5,V6,V7), V7 == V6, precedes-{F}(V1,V3,V8), pppp22-{F}(V8,V9), pppp8-{F}(V5,V10,V11), V10 == V6 | pppp1-{T}(V5,V10,V11)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #409: disj( #352, #344+#8 ), references = 1, size of lhs = 5:
% 4.92/5.18 pppp8-{F}(V0,V1,V2), pppp8-{F}(V0,V2,V3), V3 == V2, pppp1-{F}(V0,V4,V5), V5 == V2 | P_head_of-{T}(V0,V1)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #434: disj( #352, #344+#236 ), references = 5, size of lhs = 8:
% 4.92/5.18 P_empty-{F}(V0), P_tail_of-{F}(V1,V2), P_head_of-{F}(V3,V4), V2 == V4, pppp8-{F}(V5,V4,V2), pppp8-{F}(V5,V4,V6), precedes-{F}(V1,V3,V7), pppp23-{F}(V7,V8,V9) | P_head_of-{T}(V5,V6)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #435: disj( #352, #344+#234 ), references = 1, size of lhs = 8:
% 4.92/5.18 P_empty-{F}(V0), P_tail_of-{F}(V1,V2), P_head_of-{F}(V3,V4), V2 == V4, pppp8-{F}(V5,V4,V2), pppp8-{F}(V5,V4,V6), precedes-{F}(V1,V3,V7), pppp22-{F}(V7,V8) | P_head_of-{T}(V5,V6)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #455: exists( #98, #11 ), references = 3, size of lhs = 3:
% 4.92/5.18 P_head_of-{F}(V0,V1), pppp0-{F}(V0,V2,V3), V2 == V1 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #457: mergings( V3 == V2; #454 ), references = 1, size of lhs = 2:
% 4.92/5.18 P_head_of-{F}(V0,V1), pppp0-{F}(V0,V1,V2) | P_tail_of-{T}(V0,V2)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #460: mergings( V2 == V3; #458 ), references = 1, size of lhs = 3:
% 4.92/5.18 P_head_of-{F}(V0,V1), pppp8-{F}(V0,V2,V1), V2 == V1 | pppp1-{T}(V0,V2,V1)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #481: exists( #98, #9 ), references = 1, size of lhs = 2:
% 4.92/5.18 P_head_of-{F}(V0,V1), pppp1-{F}(V0,V2,V3) | P_tail_of-{T}(V0,V2)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #502: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V11; #495 ), references = 1, size of lhs = 15:
% 4.92/5.18 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V0 == V1, edge-{F}(V2), P_tail_of-{F}(V2,V0), edge-{F}(V3), sequential-{F}(V2,V3), pppp24-{F}(V2,V3), P_head_of-{F}(V3,V1), P_empty-{F}(V4), P_head_of-{F}(V5,V1), P_tail_of-{F}(V6,V0), precedes-{F}(V6,V5,V7), pppp23-{F}(V7,V8,V9) | pppp9-{T}(V1,V0,V2), pppp9-{T}(V1,V0,V3)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #522: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V10, V10 == V16, V14 == V20, V15 == V21, V13 == V19; #511 ), references = 1, size of lhs = 20:
% 4.92/5.18 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V0 == V1, edge-{F}(V2), P_tail_of-{F}(V2,V0), edge-{F}(V3), sequential-{F}(V2,V3), pppp24-{F}(V2,V3), P_head_of-{F}(V3,V1), P_head_of-{F}(V4,V1), P_tail_of-{F}(V5,V0), precedes-{F}(V5,V4,V6), P_empty-{F}(V7), P_tail_of-{F}(V8,V0), P_head_of-{F}(V9,V1), precedes-{F}(V8,V9,V6), pppp23-{F}(V6,V10,V11), pppp0-{F}(V2,V12,V13), V12 == V0 | pppp9-{T}(V1,V0,V3)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #556: mergings( V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V11, V11 == V14, V14 == V17, V20 == V22, V21 == V23, V13 == V16, V22 == V26, V23 == V27, V16 == V19; #539 ), references = 2, size of lhs = 18:
% 4.92/5.18 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_tail_of-{F}(V1,V0), sequential-{F}(V1,V2), pppp24-{F}(V1,V2), edge-{F}(V2), P_tail_of-{F}(V2,V3), P_tail_of-{F}(V4,V0), precedes-{F}(V4,V2,V5), P_tail_of-{F}(V6,V0), precedes-{F}(V6,V2,V5), P_empty-{F}(V7), P_tail_of-{F}(V8,V0), precedes-{F}(V8,V2,V5), pppp0-{F}(V1,V9,V10), V9 == V0, pppp23-{F}(V5,V11,V12) | P_head_of-{T}(V2,V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #572: mergings( V2 == V11, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V12, V12 == V15, V15 == V18, V21 == V23, V22 == V24, V14 == V17, V23 == V27, V24 == V28, V17 == V20; #540 ), references = 1, size of lhs = 18:
% 4.92/5.18 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_tail_of-{F}(V1,V0), edge-{F}(V2), sequential-{F}(V1,V2), pppp24-{F}(V1,V2), P_tail_of-{F}(V2,V3), P_tail_of-{F}(V4,V0), precedes-{F}(V4,V2,V5), P_tail_of-{F}(V6,V0), precedes-{F}(V6,V2,V5), P_empty-{F}(V7), P_tail_of-{F}(V8,V0), precedes-{F}(V8,V2,V5), pppp0-{F}(V1,V9,V10), V9 == V0, pppp23-{F}(V5,V11,V12) | P_head_of-{T}(V2,V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #588: mergings( V2 == V11, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V12, V12 == V15, V15 == V18, V21 == V23, V22 == V24, V14 == V17, V23 == V27, V24 == V28, V17 == V20; #541 ), references = 1, size of lhs = 18:
% 4.92/5.18 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_tail_of-{F}(V1,V0), edge-{F}(V2), sequential-{F}(V1,V2), pppp24-{F}(V1,V2), P_tail_of-{F}(V2,V3), P_tail_of-{F}(V4,V0), precedes-{F}(V4,V2,V5), P_tail_of-{F}(V6,V0), precedes-{F}(V6,V2,V5), P_empty-{F}(V7), P_tail_of-{F}(V8,V0), precedes-{F}(V8,V2,V5), pppp0-{F}(V1,V9,V10), V9 == V0, pppp23-{F}(V5,V11,V12) | P_head_of-{T}(V2,V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #604: mergings( V1 == V11; #602 ), references = 1, size of lhs = 17:
% 4.92/5.18 vertex-{F}(V0), edge-{F}(V1), P_tail_of-{F}(V1,V0), P_head_of-{F}(V1,V2), vertex-{F}(V3), path-{F}(V2,V3,V4), P_path_cons-{F}(V1,V4,V5), vertex-{F}(V6), edge-{F}(V7), P_tail_of-{F}(V7,V6), P_head_of-{F}(V7,V0), P_path_cons-{F}(V7,V5,V8), P_empty-{F}(V9), P_edges-{F}(V10), P_length_of-{F}(V8,V11), P_number_of_in-{F}(V10,V8,V12), V11 == V12 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #615: exists( #98, #613 ), references = 1, size of lhs = 1:
% 4.92/5.18 pppp11-{F}(V0,V1,V2,V3) | P_tail_of-{T}(V3,V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #640: mergings( V3 == V4, V4 == V5, V7 == V8; #635 ), references = 2, size of lhs = 6:
% 4.92/5.18 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
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #644: mergings( V3 == V4, V4 == V5, V9 == V11; #636 ), references = 2, size of lhs = 9:
% 4.92/5.18 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
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #650: mergings( V4 == V5, V5 == V6, V8 == V9; #645 ), references = 2, size of lhs = 6:
% 4.92/5.18 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
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #654: mergings( V4 == V5, V5 == V6, V10 == V12; #646 ), references = 3, size of lhs = 9:
% 4.92/5.18 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) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #666: exists( #102, #650 ), references = 1, size of lhs = 4:
% 4.92/5.18 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)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #667: exists( #102, #654 ), references = 1, size of lhs = 7:
% 4.92/5.18 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_number_of_in-{T}(V2,V4,V6)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #668: exists( #102, #640 ), references = 1, size of lhs = 4:
% 4.92/5.18 P_empty-{F}(V0), P_edges-{F}(V1), pppp22-{F}(V2,V3), P_length_of-{F}(V2,V4) | P_number_of_in-{T}(V1,V2,V4)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #697: exists( #105, #654 ), references = 1, size of lhs = 7:
% 4.92/5.18 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,V7,V8) | P_minus-{T}(V6,V3,V5)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #698: exists( #105, #644 ), references = 1, size of lhs = 7:
% 4.92/5.18 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-{T}(V7,V3,V6)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #717: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7; #712 ), references = 1, size of lhs = 7:
% 4.92/5.18 P_empty-{F}(V0), sequential-{F}(V1,V2), precedes-{F}(V2,V1,V3), pppp22-{F}(V3,V4), P_length_of-{F}(V3,V5), P_tail_of-{F}(V2,V6), P_head_of-{F}(V1,V7) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #723: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6; #718 ), references = 1, size of lhs = 6:
% 4.92/5.18 P_empty-{F}(V0), sequential-{F}(V1,V2), precedes-{F}(V2,V1,V3), pppp22-{F}(V3,V4), P_tail_of-{F}(V2,V5), P_head_of-{F}(V1,V6) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #729: mergings( V4 == V5, V5 == V6, V6 == V7, V7 == V8; #724 ), references = 2, size of lhs = 6:
% 4.92/5.18 P_empty-{F}(V0), sequential-{F}(V1,V2), precedes-{F}(V2,V1,V3), P_tail_of-{F}(V2,V4), P_head_of-{F}(V1,V5), pppp23-{F}(V3,V6,V7) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #745: mergings( V3 == V14, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V4 == V0; #735 ), references = 1, size of lhs = 12:
% 4.92/5.18 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_tail_of-{F}(V1,V2), edge-{F}(V3), V1 == V3, sequential-{F}(V3,V1), pppp24-{F}(V3,V1), P_tail_of-{F}(V3,V0), P_empty-{F}(V4), pppp0-{F}(V3,V5,V6), V5 == V0 | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #757: mergings( V2 == V3, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13; #748 ), references = 1, size of lhs = 9:
% 4.92/5.18 complete-{F}(), edge-{F}(V0), P_tail_of-{F}(V0,V1), edge-{F}(V2), V0 == V2, sequential-{F}(V2,V0), pppp24-{F}(V2,V0), P_head_of-{F}(V2,V3), P_empty-{F}(V4) | P_tail_of-{T}(V2,V3)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #779: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11; #768 ), references = 1, size of lhs = 6:
% 4.92/5.18 complete-{F}(), P_empty-{F}(V0), sequential-{F}(V1,V2), V2 == V1, pppp24-{F}(V1,V2), pppp4-{F}(V1,V2) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #796: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12; #784 ), references = 1, size of lhs = 3:
% 4.92/5.18 complete-{F}(), pppp25-{F}(V0), P_empty-{F}(V1) | pppp24-{T}(V0,V0)
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #799: exists( #98, #729 ), references = 1, size of lhs = 5:
% 4.92/5.18 P_empty-{F}(V0), sequential-{F}(V1,V2), precedes-{F}(V2,V1,V3), P_head_of-{F}(V1,V4), pppp23-{F}(V3,V5,V6) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #800: exists( #98, #236 ), references = 1, size of lhs = 5:
% 4.92/5.18 P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_head_of-{F}(V3,V2), precedes-{F}(V1,V3,V4), pppp23-{F}(V4,V5,V6) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #803: exists( #97, #798 ), references = 1, size of lhs = 3:
% 4.92/5.18 P_empty-{F}(V0), precedes-{F}(V1,V1,V2), pppp23-{F}(V2,V3,V4) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #804: exists( #97, #797 ), references = 1, size of lhs = 4:
% 4.92/5.18 P_empty-{F}(V0), sequential-{F}(V1,V2), precedes-{F}(V2,V1,V3), pppp23-{F}(V3,V4,V5) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #809: exists( #90, #805 ), references = 1, size of lhs = 2:
% 4.92/5.18 pppp24-{F}(V0,V0), P_empty-{F}(V1) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #810: exists( #90, #806 ), references = 1, size of lhs = 3:
% 4.92/5.18 P_empty-{F}(V0), pppp24-{F}(V1,V2), sequential-{F}(V2,V1) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #828: mergings( V0 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18; #814 ), references = 1, size of lhs = 7:
% 4.92/5.18 complete-{F}(), P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_graph-{F}(V4), P_empty-{F}(V5) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #850: mergings( V1 == V6, V6 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V20, V20 == V21, V21 == V22, V2 == V7, V3 == V8, V4 == V9, V5 == V10; #831 ), references = 1, size of lhs = 5:
% 4.92/5.18 P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_empty-{F}(V4) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #869: mergings( V1 == V5, V5 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V20, V2 == V6, V3 == V7, V4 == V8; #851 ), references = 1, size of lhs = 4:
% 4.92/5.18 P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_empty-{F}(V3) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #887: mergings( V1 == V4, V4 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V2 == V5, V3 == V6; #870 ), references = 1, size of lhs = 3:
% 4.92/5.18 P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_empty-{F}(V2) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #904: mergings( V1 == V3, V3 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V2 == V4; #888 ), references = 1, size of lhs = 2:
% 4.92/5.18 P_edges-{F}(V0), P_empty-{F}(V1) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #920: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14; #905 ), references = 1, size of lhs = 1:
% 4.92/5.18 P_empty-{F}(V0) | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 #923: exists( #100, #905 ), references = 1, size of lhs = 0:
% 4.92/5.18 FALSE | FALSE
% 4.92/5.18 (used 0 times, uses = {})
% 4.92/5.18
% 4.92/5.18 number of learnt formulas = 69
% 4.92/5.18
% 4.92/5.18
% 4.92/5.18 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.92/5.18
% 4.92/5.18 randbase = 1
%------------------------------------------------------------------------------