TSTP Solution File: GRA007+2 by Geo-III---2018C

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Geo-III---2018C
% Problem  : GRA007+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : geo -tptp_input -nonempty -inputfile %s

% Computer : n028.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 7.22s 7.41s
% Output   : Refutation 7.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRA007+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.06/0.12  % Command  : geo -tptp_input -nonempty -inputfile %s
% 0.13/0.33  % Computer : n028.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 07:59:42 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 7.22/7.41  GeoParameters:
% 7.22/7.41  
% 7.22/7.41  tptp_input =     1
% 7.22/7.41  tptp_output =    0
% 7.22/7.41  nonempty =       1
% 7.22/7.41  inputfile =      /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.22/7.41  includepath =    /export/starexec/sandbox2/solver/bin/../../benchmark/
% 7.22/7.41  
% 7.22/7.41  
% 7.22/7.41  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.22/7.41  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.22/7.41  
% 7.22/7.41  RuleSystem INPUT:
% 7.22/7.41  
% 7.22/7.41  Initial Rules:
% 7.22/7.41  #0: input, references = 4, size of lhs = 3:
% 7.22/7.41     P_head_of-{F}(V0,V2), P_tail_of-{F}(V0,V2), edge-{F}(V0) | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #1: input, references = 7, size of lhs = 3:
% 7.22/7.41     P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), edge-{F}(V0) | vertex-{T}(V1)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #2: input, references = 8, size of lhs = 3:
% 7.22/7.41     P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), edge-{F}(V0) | vertex-{T}(V2)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #3: input, references = 4, size of lhs = 4:
% 7.22/7.41     complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0 | EXISTS V2: pppp9-{T}(V1,V0,V2)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #4: input, references = 4, size of lhs = 1:
% 7.22/7.41     pppp9-{F}(V0,V1,V2) | pppp8-{T}(V2,V0,V1)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #5: input, references = 3, size of lhs = 3:
% 7.22/7.41     pppp8-{F}(V0,V1,V2), pppp1-{F}(V0,V1,V2), pppp0-{F}(V0,V1,V2) | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #6: input, references = 10, size of lhs = 1:
% 7.22/7.41     pppp8-{F}(V0,V1,V2) | pppp0-{T}(V0,V1,V2), pppp1-{T}(V0,V1,V2)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #7: input, references = 4, size of lhs = 1:
% 7.22/7.41     pppp8-{F}(V0,V1,V2) | edge-{T}(V0)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #8: input, references = 4, size of lhs = 4:
% 7.22/7.41     P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp1-{F}(V0,V1,V2), V2 == V3 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #9: input, references = 7, size of lhs = 4:
% 7.22/7.41     P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp1-{F}(V0,V1,V2), V1 == V4 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #10: input, references = 3, size of lhs = 2:
% 7.22/7.41     P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | pppp1-{T}(V0,V4,V3)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #11: input, references = 9, size of lhs = 4:
% 7.22/7.41     P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp0-{F}(V0,V1,V2), V1 == V3 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #12: input, references = 6, size of lhs = 4:
% 7.22/7.41     P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp0-{F}(V0,V1,V2), V2 == V4 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #13: input, references = 3, size of lhs = 2:
% 7.22/7.41     P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | pppp0-{T}(V0,V3,V4)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #14: input, references = 6, size of lhs = 7:
% 7.22/7.41     P_empty-{F}(V0), vertex-{F}(V6), vertex-{F}(V5), P_tail_of-{F}(V4,V5), P_head_of-{F}(V4,V6), P_path_cons-{F}(V4,V0,V7), edge-{F}(V4) | path-{T}(V5,V6,V7)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #15: input, references = 3, size of lhs = 9:
% 7.22/7.41     P_empty-{F}(V0), vertex-{F}(V1), vertex-{F}(V5), P_tail_of-{F}(V4,V5), P_head_of-{F}(V4,V6), P_path_cons-{F}(V4,V0,V7), edge-{F}(V4), P_path_cons-{F}(V4,V8,V9), path-{F}(V6,V1,V8) | path-{T}(V5,V1,V9)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #16: input, references = 3, size of lhs = 2:
% 7.22/7.41     P_empty-{F}(V0), path-{F}(V1,V2,V3) | vertex-{T}(V1)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #17: input, references = 5, size of lhs = 2:
% 7.22/7.41     P_empty-{F}(V0), path-{F}(V1,V2,V3) | vertex-{T}(V2)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #18: input, references = 3, size of lhs = 2:
% 7.22/7.41     P_empty-{F}(V0), path-{F}(V1,V2,V3) | EXISTS V4: pppp11-{T}(V1,V2,V3,V4)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #19: input, references = 3, size of lhs = 2:
% 7.22/7.41     pppp11-{F}(V0,V1,V2,V3), P_tail_of-{F}(V3,V4) | pppp10-{T}(V3,V0,V1,V2,V4)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #20: input, references = 3, size of lhs = 3:
% 7.22/7.41     pppp10-{F}(V0,V1,V2,V3,V4), pppp3-{F}(V0,V2,V3), pppp2-{F}(V0,V2,V3) | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #21: input, references = 4, size of lhs = 1:
% 7.22/7.41     pppp10-{F}(V0,V1,V2,V3,V4) | pppp2-{T}(V0,V2,V3), pppp3-{T}(V0,V2,V3)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #22: input, references = 3, size of lhs = 2:
% 7.22/7.41     pppp10-{F}(V0,V1,V2,V3,V4), V1 == V4 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #23: input, references = 3, size of lhs = 1:
% 7.22/7.41     pppp10-{F}(V0,V1,V2,V3,V4) | edge-{T}(V0)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #24: input, references = 3, size of lhs = 3:
% 7.22/7.41     P_empty-{F}(V0), P_head_of-{F}(V1,V4), pppp3-{F}(V1,V2,V3) | EXISTS V5: pppp12-{T}(V1,V2,V3,V5,V4)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #25: input, references = 3, size of lhs = 4:
% 7.22/7.41     P_empty-{F}(V0), P_head_of-{F}(V1,V4), P_path_cons-{F}(V1,V5,V6), path-{F}(V4,V2,V5) | pppp3-{T}(V1,V2,V6)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #26: input, references = 3, size of lhs = 3:
% 7.22/7.41     pppp12-{F}(V0,V1,V2,V3,V4), P_path_cons-{F}(V0,V3,V5), V2 == V5 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #27: input, references = 3, size of lhs = 2:
% 7.22/7.41     pppp12-{F}(V0,V1,V2,V3,V4), P_path_cons-{F}(V0,V3,V5) | path-{T}(V4,V1,V3)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #28: input, references = 3, size of lhs = 5:
% 7.22/7.41     P_empty-{F}(V0), P_head_of-{F}(V1,V4), P_path_cons-{F}(V1,V0,V5), pppp2-{F}(V1,V2,V3), V2 == V4 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #29: input, references = 3, size of lhs = 5:
% 7.22/7.41     P_empty-{F}(V0), P_head_of-{F}(V1,V4), P_path_cons-{F}(V1,V0,V5), pppp2-{F}(V1,V2,V3), V3 == V5 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #30: input, references = 3, size of lhs = 3:
% 7.22/7.41     P_empty-{F}(V0), P_head_of-{F}(V1,V4), P_path_cons-{F}(V1,V0,V5) | pppp2-{T}(V1,V4,V5)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #31: input, references = 17, size of lhs = 5:
% 7.22/7.41     P_empty-{F}(V0), path-{F}(V3,V2,V1), P_head_of-{F}(V4,V5), P_tail_of-{F}(V4,V6), on_path-{F}(V4,V1) | edge-{T}(V4)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #32: input, references = 3, size of lhs = 5:
% 7.22/7.41     P_empty-{F}(V0), path-{F}(V3,V2,V1), P_head_of-{F}(V4,V5), P_tail_of-{F}(V4,V6), on_path-{F}(V4,V1) | in_path-{T}(V5,V1)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #33: input, references = 3, size of lhs = 5:
% 7.22/7.41     P_empty-{F}(V0), path-{F}(V3,V2,V1), P_head_of-{F}(V4,V5), P_tail_of-{F}(V4,V6), on_path-{F}(V4,V1) | in_path-{T}(V6,V1)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #34: input, references = 3, size of lhs = 3:
% 7.22/7.41     P_empty-{F}(V0), path-{F}(V3,V2,V1), in_path-{F}(V4,V1) | vertex-{T}(V4)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #35: input, references = 3, size of lhs = 3:
% 7.22/7.41     P_empty-{F}(V0), path-{F}(V3,V2,V1), in_path-{F}(V4,V1) | EXISTS V5: pppp13-{T}(V5,V1,V4)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #36: input, references = 5, size of lhs = 5:
% 7.22/7.41     pppp13-{F}(V0,V1,V2), P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), V2 == V3, V2 == V4 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #37: input, references = 3, size of lhs = 3:
% 7.22/7.41     pppp13-{F}(V0,V1,V2), P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | on_path-{T}(V0,V1)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #38: input, references = 3, size of lhs = 2:
% 7.22/7.41     P_empty-{F}(V0), sequential-{F}(V1,V2) | pppp4-{T}(V1,V2)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #39: input, references = 6, size of lhs = 2:
% 7.22/7.41     P_empty-{F}(V0), pppp4-{F}(V1,V2) | sequential-{T}(V1,V2)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #40: input, references = 5, size of lhs = 3:
% 7.22/7.41     P_empty-{F}(V0), P_head_of-{F}(V1,V3), P_tail_of-{F}(V2,V4) | pppp14-{T}(V1,V2,V3,V4)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #41: input, references = 6, size of lhs = 4:
% 7.22/7.41     pppp14-{F}(V0,V1,V3,V3), edge-{F}(V0), edge-{F}(V1), V0 == V1 | pppp4-{T}(V0,V1)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #42: input, references = 3, size of lhs = 3:
% 7.22/7.41     pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1), V2 == V3 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #43: input, references = 3, size of lhs = 2:
% 7.22/7.41     pppp14-{F}(V1,V1,V2,V3), pppp4-{F}(V1,V1) | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #44: input, references = 3, size of lhs = 2:
% 7.22/7.41     pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1) | edge-{T}(V1)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #45: input, references = 3, size of lhs = 2:
% 7.22/7.41     pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1) | edge-{T}(V0)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #46: input, references = 3, size of lhs = 5:
% 7.22/7.41     P_empty-{F}(V0), on_path-{F}(V2,V1), on_path-{F}(V3,V1), sequential-{F}(V3,V2), path-{F}(V5,V4,V1) | precedes-{T}(V3,V2,V1)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #47: input, references = 6, size of lhs = 6:
% 7.22/7.41     P_empty-{F}(V0), on_path-{F}(V2,V1), on_path-{F}(V3,V1), sequential-{F}(V3,V4), precedes-{F}(V4,V2,V1), path-{F}(V6,V5,V1) | precedes-{T}(V3,V2,V1)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #48: input, references = 13, size of lhs = 3:
% 7.22/7.41     P_empty-{F}(V0), precedes-{F}(V2,V3,V1), path-{F}(V5,V4,V1) | pppp15-{T}(V1,V2,V3)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #49: input, references = 3, size of lhs = 3:
% 7.22/7.41     pppp15-{F}(V0,V1,V2), pppp5-{F}(V0,V1,V2), sequential-{F}(V1,V2) | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #50: input, references = 3, size of lhs = 1:
% 7.22/7.41     pppp15-{F}(V0,V1,V2) | sequential-{T}(V1,V2), pppp5-{T}(V0,V1,V2)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #51: input, references = 10, size of lhs = 1:
% 7.22/7.41     pppp15-{F}(V0,V1,V2) | on_path-{T}(V2,V0)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #52: input, references = 10, size of lhs = 1:
% 7.22/7.41     pppp15-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #53: input, references = 3, size of lhs = 2:
% 7.22/7.41     P_empty-{F}(V0), pppp5-{F}(V1,V2,V3) | EXISTS V4: pppp16-{T}(V1,V2,V3,V4)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #54: input, references = 3, size of lhs = 3:
% 7.22/7.41     P_empty-{F}(V0), sequential-{F}(V2,V4), precedes-{F}(V4,V3,V1) | pppp5-{T}(V1,V2,V3)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #55: input, references = 3, size of lhs = 1:
% 7.22/7.41     pppp16-{F}(V0,V1,V2,V3) | precedes-{T}(V3,V2,V0)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #56: input, references = 3, size of lhs = 1:
% 7.22/7.41     pppp16-{F}(V0,V1,V2,V3) | sequential-{T}(V1,V3)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #57: input, references = 15, size of lhs = 2:
% 7.22/7.41     P_empty-{F}(V0), shortest_path-{F}(V1,V2,V3) | pppp6-{T}(V1,V2,V3)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #58: input, references = 3, size of lhs = 2:
% 7.22/7.41     P_empty-{F}(V0), pppp6-{F}(V1,V2,V3) | shortest_path-{T}(V1,V2,V3)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #59: input, references = 15, size of lhs = 3:
% 7.22/7.41     P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V1,V2,V3) | path-{T}(V1,V2,V3)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #60: input, references = 3, size of lhs = 3:
% 7.22/7.41     P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V2,V2,V3) | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #61: input, references = 3, size of lhs = 5:
% 7.22/7.41     P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V1,V2,V3), P_length_of-{F}(V5,V6), path-{F}(V1,V2,V5) | less_or_equal-{T}(V4,V6)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #62: input, references = 3, size of lhs = 4:
% 7.22/7.41     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)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #63: input, references = 3, size of lhs = 1:
% 7.22/7.41     pppp26-{F}(V0,V1,V2) | EXISTS V3: pppp17-{T}(V0,V1,V3,V2)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #64: input, references = 3, size of lhs = 3:
% 7.22/7.41     pppp17-{F}(V0,V1,V2,V3), P_length_of-{F}(V2,V4), less_or_equal-{F}(V3,V4) | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #65: input, references = 3, size of lhs = 2:
% 7.22/7.41     pppp17-{F}(V0,V1,V2,V3), P_length_of-{F}(V2,V4) | path-{T}(V0,V1,V2)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #66: input, references = 6, size of lhs = 7:
% 7.22/7.41     P_empty-{F}(V0), shortest_path-{F}(V3,V2,V1), P_tail_of-{F}(V5,V6), P_head_of-{F}(V4,V7), precedes-{F}(V5,V4,V1), P_tail_of-{F}(V8,V6), P_head_of-{F}(V8,V7) | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #67: input, references = 5, size of lhs = 6:
% 7.22/7.41     P_empty-{F}(V0), shortest_path-{F}(V3,V2,V1), P_tail_of-{F}(V5,V6), P_head_of-{F}(V4,V7), precedes-{F}(V5,V4,V1), precedes-{F}(V4,V5,V1) | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #68: input, references = 3, size of lhs = 2:
% 7.22/7.41     P_empty-{F}(V0), triangle-{F}(V1,V2,V3) | pppp7-{T}(V1,V2,V3)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #69: input, references = 3, size of lhs = 2:
% 7.22/7.41     P_empty-{F}(V0), pppp7-{F}(V1,V2,V3) | triangle-{T}(V1,V2,V3)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #70: input, references = 3, size of lhs = 2:
% 7.22/7.41     P_empty-{F}(V0), pppp7-{F}(V1,V2,V3) | pppp18-{T}(V1,V2,V3)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #71: input, references = 3, size of lhs = 7:
% 7.22/7.41     P_empty-{F}(V0), edge-{F}(V1), edge-{F}(V2), edge-{F}(V3), sequential-{F}(V1,V2), sequential-{F}(V2,V3), sequential-{F}(V3,V1) | pppp7-{T}(V1,V2,V3)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #72: input, references = 3, size of lhs = 1:
% 7.22/7.41     pppp18-{F}(V0,V1,V2) | sequential-{T}(V2,V0)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #73: input, references = 3, size of lhs = 1:
% 7.22/7.41     pppp18-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #74: input, references = 3, size of lhs = 1:
% 7.22/7.41     pppp18-{F}(V0,V1,V2) | sequential-{T}(V0,V1)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #75: input, references = 3, size of lhs = 1:
% 7.22/7.41     pppp18-{F}(V0,V1,V2) | edge-{T}(V2)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #76: input, references = 3, size of lhs = 1:
% 7.22/7.41     pppp18-{F}(V0,V1,V2) | edge-{T}(V1)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #77: input, references = 3, size of lhs = 1:
% 7.22/7.41     pppp18-{F}(V0,V1,V2) | edge-{T}(V0)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #78: input, references = 6, size of lhs = 6:
% 7.22/7.41     P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), P_number_of_in-{F}(V1,V2,V4), path-{F}(V6,V5,V2), V3 == V4 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #79: input, references = 7, size of lhs = 9:
% 7.22/7.41     P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_number_of_in-{F}(V2,V4,V5), P_length_of-{F}(V4,V6), P_minus-{F}(V6,V3,V7), path-{F}(V9,V8,V4), V5 == V7 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #80: input, references = 3, size of lhs = 9:
% 7.22/7.41     P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_number_of_in-{F}(V2,V5,V6), P_number_of_in-{F}(V4,V5,V7), path-{F}(V10,V9,V5), V6 == V7 | EXISTS V8: pppp20-{T}(V5,V8)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #81: input, references = 3, size of lhs = 1:
% 7.22/7.41     pppp20-{F}(V0,V1) | EXISTS V2: pppp19-{T}(V0,V2,V1)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #82: input, references = 3, size of lhs = 1:
% 7.22/7.41     pppp20-{F}(V0,V1) | on_path-{T}(V1,V0)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #83: input, references = 3, size of lhs = 2:
% 7.22/7.41     pppp19-{F}(V0,V1,V2), triangle-{F}(V1,V2,V3) | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #84: input, references = 3, size of lhs = 1:
% 7.22/7.41     pppp19-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #85: input, references = 3, size of lhs = 1:
% 7.22/7.41     pppp19-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #86: input, references = 3, size of lhs = 8:
% 7.22/7.41     P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_graph-{F}(V5), P_number_of_in-{F}(V6,V7,V8), P_number_of_in-{F}(V6,V5,V9) | less_or_equal-{T}(V8,V9)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #87: input, references = 3, size of lhs = 13:
% 7.22/7.41     P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_graph-{F}(V5), shortest_path-{F}(V8,V7,V6), P_tail_of-{F}(V10,V11), P_head_of-{F}(V9,V12), precedes-{F}(V10,V9,V6), P_tail_of-{F}(V13,V11), P_head_of-{F}(V13,V12), edge-{F}(V13) | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #88: input, references = 4, size of lhs = 6:
% 7.22/7.41     P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_graph-{F}(V5) | complete-{T}()
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #89: input, references = 4, size of lhs = 6:
% 7.22/7.41     P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_graph-{F}(V5) | EXISTS V6: pppp25-{T}(V6)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #90: input, references = 4, size of lhs = 1:
% 7.22/7.41     pppp25-{F}(V0) | EXISTS V1: pppp24-{T}(V0,V1)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #91: input, references = 7, size of lhs = 1:
% 7.22/7.41     pppp25-{F}(V0) | EXISTS V1: pppp22-{T}(V0,V1)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #92: input, references = 6, size of lhs = 1:
% 7.22/7.41     pppp24-{F}(V0,V1) | EXISTS V2: pppp23-{T}(V0,V2,V1)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #93: input, references = 4, size of lhs = 6:
% 7.22/7.41     pppp23-{F}(V0,V1,V2), P_head_of-{F}(V2,V3), P_tail_of-{F}(V1,V4), P_tail_of-{F}(V5,V3), P_head_of-{F}(V5,V4), edge-{F}(V5) | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #94: input, references = 12, size of lhs = 3:
% 7.22/7.41     pppp23-{F}(V0,V1,V2), P_head_of-{F}(V2,V3), P_tail_of-{F}(V1,V4) | precedes-{T}(V1,V2,V0)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #95: input, references = 14, size of lhs = 1:
% 7.22/7.41     pppp22-{F}(V0,V1) | EXISTS V2: pppp21-{T}(V1,V0,V2)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #96: input, references = 17, size of lhs = 1:
% 7.22/7.41     pppp21-{F}(V0,V1,V2) | shortest_path-{T}(V2,V0,V1)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #97: input, references = 15, size of lhs = 1:
% 7.22/7.41     #-{F} V0 | EXISTS V1: P_head_of-{T}(V0,V1)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #98: input, references = 13, size of lhs = 1:
% 7.22/7.41     #-{F} V0 | EXISTS V1: P_tail_of-{T}(V0,V1)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #99: input, references = 3, size of lhs = 2:
% 7.22/7.41     #-{F} V0, #-{F} V1 | EXISTS V2: P_path_cons-{T}(V0,V1,V2)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #100: input, references = 4, size of lhs = 0:
% 7.22/7.41     FALSE | EXISTS V0: P_empty-{T}(V0)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #101: input, references = 6, size of lhs = 1:
% 7.22/7.41     #-{F} V0 | EXISTS V1: P_length_of-{T}(V0,V1)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #102: input, references = 7, size of lhs = 2:
% 7.22/7.41     #-{F} V0, #-{F} V1 | EXISTS V2: P_number_of_in-{T}(V0,V1,V2)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #103: input, references = 4, size of lhs = 0:
% 7.22/7.41     FALSE | EXISTS V0: P_edges-{T}(V0)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #104: input, references = 4, size of lhs = 0:
% 7.22/7.41     FALSE | EXISTS V0: P_sequential_pairs-{T}(V0)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #105: input, references = 5, size of lhs = 2:
% 7.22/7.41     #-{F} V0, #-{F} V1 | EXISTS V2: P_minus-{T}(V0,V1,V2)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #106: input, references = 4, size of lhs = 0:
% 7.22/7.41     FALSE | EXISTS V0: P_n1-{T}(V0)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #107: input, references = 4, size of lhs = 0:
% 7.22/7.41     FALSE | EXISTS V0: P_triangles-{T}(V0)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #108: input, references = 4, size of lhs = 0:
% 7.22/7.41     FALSE | EXISTS V0: P_graph-{T}(V0)
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  number of initial rules = 109
% 7.22/7.41  
% 7.22/7.41  Simplifiers:
% 7.22/7.41  #109: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     P_head_of-{F}(V0,V1), P_head_of-{F}(V0,V3), V1 == V3 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #110: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     P_tail_of-{F}(V0,V1), P_tail_of-{F}(V0,V3), V1 == V3 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #111: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     P_path_cons-{F}(V0,V1,V2), P_path_cons-{F}(V0,V1,V5), V2 == V5 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #112: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     P_empty-{F}(V0), P_empty-{F}(V1), V0 == V1 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #113: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     P_length_of-{F}(V0,V1), P_length_of-{F}(V0,V3), V1 == V3 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #114: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     P_number_of_in-{F}(V0,V1,V2), P_number_of_in-{F}(V0,V1,V5), V2 == V5 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #115: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     P_edges-{F}(V0), P_edges-{F}(V1), V0 == V1 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #116: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     P_sequential_pairs-{F}(V0), P_sequential_pairs-{F}(V1), V0 == V1 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #117: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     P_minus-{F}(V0,V1,V2), P_minus-{F}(V0,V1,V5), V2 == V5 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #118: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     P_n1-{F}(V0), P_n1-{F}(V1), V0 == V1 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #119: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     P_triangles-{F}(V0), P_triangles-{F}(V1), V0 == V1 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #120: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     P_graph-{F}(V0), P_graph-{F}(V1), V0 == V1 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #121: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp8-{F}(V0,V1,V2), pppp8-{F}(V3,V1,V2), V0 == V3 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #122: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp9-{F}(V0,V1,V2), pppp9-{F}(V0,V1,V5), V2 == V5 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #123: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V5,V1,V2,V3,V9), V0 == V5 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #124: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #125: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp11-{F}(V0,V1,V2,V3), pppp11-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #126: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V1,V2,V8,V4), V3 == V8 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #127: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #128: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp13-{F}(V0,V1,V2), pppp13-{F}(V3,V1,V2), V0 == V3 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #129: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp14-{F}(V0,V1,V2,V3), pppp14-{F}(V0,V5,V6,V7), V2 == V6 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #130: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp14-{F}(V0,V1,V2,V3), pppp14-{F}(V4,V1,V6,V7), V3 == V7 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #131: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp16-{F}(V0,V1,V2,V3), pppp16-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #132: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp17-{F}(V0,V1,V2,V3), pppp17-{F}(V0,V1,V6,V3), V2 == V6 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #133: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp19-{F}(V0,V1,V2), pppp19-{F}(V0,V4,V2), V1 == V4 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #134: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp19-{F}(V0,V1,V2), pppp19-{F}(V0,V4,V5), V2 == V5 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #135: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp20-{F}(V0,V1), pppp20-{F}(V0,V3), V1 == V3 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #136: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp21-{F}(V0,V1,V2), pppp21-{F}(V0,V1,V5), V2 == V5 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #137: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp21-{F}(V0,V1,V2), pppp21-{F}(V3,V1,V5), V0 == V3 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #138: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp21-{F}(V0,V1,V2), pppp21-{F}(V3,V4,V5), V1 == V4 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #139: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp22-{F}(V0,V1), pppp22-{F}(V0,V3), V1 == V3 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #140: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp22-{F}(V0,V1), pppp22-{F}(V2,V3), V0 == V2 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #141: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp23-{F}(V0,V1,V2), pppp23-{F}(V0,V4,V2), V1 == V4 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #142: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp23-{F}(V0,V1,V2), pppp23-{F}(V0,V4,V5), V2 == V5 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #143: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp23-{F}(V0,V1,V2), pppp23-{F}(V3,V4,V5), V0 == V3 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #144: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp24-{F}(V0,V1), pppp24-{F}(V0,V3), V1 == V3 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #145: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp24-{F}(V0,V1), pppp24-{F}(V2,V3), V0 == V2 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  #146: unsound, references = 3, size of lhs = 3:
% 7.22/7.41     pppp25-{F}(V0), pppp25-{F}(V1), V0 == V1 | FALSE
% 7.22/7.41        (used 0 times, uses = {})
% 7.22/7.41  
% 7.22/7.41  number of simplifiers = 38
% 7.22/7.41  
% 7.22/7.41  Learnt:
% 7.22/7.41  #151: exists( #95, #147 ), references = 3, size of lhs = 6:
% 7.22/7.42     P_empty-{F}(V0), P_tail_of-{F}(V1,V2), P_head_of-{F}(V3,V4), precedes-{F}(V1,V3,V5), precedes-{F}(V3,V1,V5), pppp22-{F}(V5,V6) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #152: exists( #95, #148 ), references = 2, size of lhs = 7:
% 7.22/7.42     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
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #164: mergings( V3 == V4, V4 == V5, V9 == V11; #160 ), references = 2, size of lhs = 9:
% 7.22/7.42     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
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #169: mergings( V2 == V3, V3 == V4, V8 == V10; #165 ), references = 2, size of lhs = 9:
% 7.22/7.42     pppp25-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), P_number_of_in-{F}(V3,V0,V5), P_length_of-{F}(V0,V6), P_minus-{F}(V6,V4,V7), V5 == V7 | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #174: mergings( V3 == V4, V4 == V5, V8 == V9; #170 ), references = 1, size of lhs = 7:
% 7.22/7.42     pppp25-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), P_length_of-{F}(V0,V5), P_minus-{F}(V5,V4,V6) | P_number_of_in-{T}(V3,V0,V6)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #184: mergings( V3 == V4, V4 == V5, V7 == V8; #180 ), references = 2, size of lhs = 6:
% 7.22/7.42     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
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #189: mergings( V2 == V3, V3 == V4, V6 == V7; #185 ), references = 2, size of lhs = 6:
% 7.22/7.42     pppp25-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_length_of-{F}(V0,V3), P_number_of_in-{F}(V2,V0,V4), V3 == V4 | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #195: exists( #102, #189 ), references = 1, size of lhs = 4:
% 7.22/7.42     pppp25-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_length_of-{F}(V0,V3) | P_number_of_in-{T}(V2,V0,V3)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #196: exists( #102, #184 ), references = 1, size of lhs = 4:
% 7.22/7.42     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)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #219: mergings( V11 == V12, V12 == V15, V5 == V13, V13 == V14, V2 == V3, V3 == V4, V4 == V6; #211 ), references = 2, size of lhs = 15:
% 7.22/7.42     vertex-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), P_tail_of-{F}(V5,V0), P_head_of-{F}(V5,V6), P_path_cons-{F}(V5,V1,V7), P_number_of_in-{F}(V3,V7,V8), P_length_of-{F}(V7,V9), P_minus-{F}(V9,V4,V10), V8 == V10, pppp23-{F}(V11,V12,V5), path-{F}(V13,V14,V11), path-{F}(V15,V16,V11) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #235: mergings( V16 == V17, V17 == V20, V1 == V18, V18 == V19, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9; #224 ), references = 1, size of lhs = 14:
% 7.22/7.42     P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp22-{F}(V4,V5), P_length_of-{F}(V4,V6), P_tail_of-{F}(V7,V5), pppp23-{F}(V4,V8,V7), P_head_of-{F}(V7,V9), P_path_cons-{F}(V7,V0,V10), P_number_of_in-{F}(V2,V10,V11), P_length_of-{F}(V10,V12), P_minus-{F}(V12,V3,V13), V11 == V13 | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #247: mergings( V15 == V16, V16 == V19, V13 == V17, V17 == V18, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9; #236 ), references = 1, size of lhs = 14:
% 7.22/7.42     P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp24-{F}(V4,V5), pppp22-{F}(V4,V6), P_tail_of-{F}(V5,V6), P_length_of-{F}(V4,V7), P_head_of-{F}(V5,V8), P_path_cons-{F}(V5,V0,V9), P_number_of_in-{F}(V2,V9,V10), P_length_of-{F}(V9,V11), P_minus-{F}(V11,V3,V12), V10 == V12 | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #259: mergings( V14 == V15, V15 == V18, V13 == V16, V16 == V17, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8; #248 ), references = 1, size of lhs = 13:
% 7.22/7.42     P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp24-{F}(V4,V5), pppp22-{F}(V4,V6), 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
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #262: exists( #105, #169 ), references = 1, size of lhs = 7:
% 7.22/7.42     pppp25-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), P_number_of_in-{F}(V3,V0,V5), P_length_of-{F}(V0,V6) | P_minus-{T}(V6,V4,V5)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #263: exists( #105, #164 ), references = 1, size of lhs = 7:
% 7.22/7.42     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)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #283: mergings( V9 == V10, V10 == V12, V11 == V13, V2 == V3, V3 == V4, V20 == V25, V8 == V14, V12 == V15, V0 == V26; #273 ), references = 1, size of lhs = 16:
% 7.22/7.42     P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_tail_of-{F}(V4,V5), P_head_of-{F}(V4,V6), P_path_cons-{F}(V4,V0,V7), P_number_of_in-{F}(V2,V7,V8), P_length_of-{F}(V7,V9), P_minus-{F}(V9,V3,V10), V8 == V10, pppp23-{F}(V11,V12,V4), path-{F}(V13,V14,V11), path-{F}(V15,V16,V11), path-{F}(V17,V18,V11), path-{F}(V19,V20,V11) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #298: mergings( V14 == V15, V15 == V17, V16 == V18, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V13 == V19, V17 == V20, V12 == V25; #287 ), references = 1, size of lhs = 14:
% 7.22/7.42     P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp22-{F}(V4,V5), P_length_of-{F}(V4,V6), pppp23-{F}(V4,V7,V8), P_tail_of-{F}(V8,V9), P_head_of-{F}(V8,V10), P_path_cons-{F}(V8,V0,V11), P_number_of_in-{F}(V2,V11,V12), P_length_of-{F}(V11,V13), P_minus-{F}(V13,V3,V14), V12 == V14 | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #308: mergings( V13 == V14, V14 == V16, V16 == V18, V15 == V17, V3 == V4, V4 == V5, V5 == V6, V6 == V7; #299 ), references = 1, size of lhs = 14:
% 7.22/7.42     P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp24-{F}(V4,V5), pppp22-{F}(V4,V6), P_length_of-{F}(V4,V7), P_tail_of-{F}(V5,V8), P_head_of-{F}(V5,V9), P_path_cons-{F}(V5,V0,V10), P_number_of_in-{F}(V2,V10,V11), P_length_of-{F}(V10,V12), P_minus-{F}(V12,V3,V13), V11 == V13 | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #318: mergings( V12 == V13, V13 == V15, V15 == V17, V14 == V16, V2 == V3, V3 == V4, V4 == V5, V5 == V6; #309 ), references = 1, size of lhs = 13:
% 7.22/7.42     P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp24-{F}(V4,V5), pppp22-{F}(V4,V6), P_tail_of-{F}(V5,V7), P_head_of-{F}(V5,V8), P_path_cons-{F}(V5,V0,V9), P_number_of_in-{F}(V2,V9,V10), P_length_of-{F}(V9,V11), P_minus-{F}(V11,V3,V12), V10 == V12 | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #328: mergings( V11 == V12, V12 == V14, V14 == V16, V13 == V15, V2 == V3, V3 == V4, V4 == V5, V5 == V6; #319 ), references = 1, size of lhs = 13:
% 7.22/7.42     pppp25-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), pppp24-{F}(V0,V5), P_tail_of-{F}(V5,V6), P_head_of-{F}(V5,V7), P_path_cons-{F}(V5,V1,V8), P_number_of_in-{F}(V3,V8,V9), P_length_of-{F}(V8,V10), P_minus-{F}(V10,V4,V11), V9 == V11 | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #341: mergings( V8 == V10, V9 == V10, V3 == V4, V4 == V5, V5 == V6; #335 ), references = 1, size of lhs = 6:
% 7.22/7.42     P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_tail_of-{F}(V1,V2), precedes-{F}(V3,V1,V4), pppp22-{F}(V4,V5), P_length_of-{F}(V4,V6) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #366: disj( #21, input ), references = 1, size of lhs = 5:
% 7.22/7.42     P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_path_cons-{F}(V1,V0,V3), pppp10-{F}(V1,V4,V5,V6,V7), V6 == V3 | pppp3-{T}(V1,V5,V6)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #388: disj( #6, input ), references = 4, size of lhs = 4:
% 7.22/7.42     P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), pppp8-{F}(V0,V3,V4), V3 == V1 | pppp1-{T}(V0,V3,V4)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #390: mergings( V1 == V3; #387 ), references = 1, size of lhs = 4:
% 7.22/7.42     P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), pppp8-{F}(V0,V1,V3), V3 == V2 | pppp1-{T}(V0,V1,V3)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #453: exists( #98, #36 ), references = 1, size of lhs = 3:
% 7.22/7.42     P_head_of-{F}(V0,V1), pppp13-{F}(V0,V2,V3), V3 == V1 | P_tail_of-{T}(V0,V3)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #454: exists( #98, #12 ), references = 8, size of lhs = 2:
% 7.22/7.42     P_head_of-{F}(V0,V1), pppp0-{F}(V0,V2,V3) | P_tail_of-{T}(V0,V3)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #460: exists( #97, #457 ), references = 1, size of lhs = 3:
% 7.22/7.42     pppp13-{F}(V0,V1,V2), pppp8-{F}(V0,V3,V4), V3 == V2 | P_head_of-{T}(V0,V2), P_head_of-{T}(V0,V3)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #466: exists( #98, #8 ), references = 3, size of lhs = 3:
% 7.22/7.42     P_head_of-{F}(V0,V1), pppp1-{F}(V0,V2,V3), V3 == V1 | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #468: mergings( V4 == V2; #465 ), references = 3, size of lhs = 2:
% 7.22/7.42     P_head_of-{F}(V0,V1), pppp1-{F}(V0,V2,V1) | P_tail_of-{T}(V0,V2)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #470: disj( #6, exists( #98, #8 ) ), references = 9, size of lhs = 3:
% 7.22/7.42     P_head_of-{F}(V0,V1), pppp8-{F}(V0,V2,V3), V3 == V1 | pppp0-{T}(V0,V2,V3)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #475: disj( #459, #469+#454+#470+#11 ), references = 1, size of lhs = 8:
% 7.22/7.42     pppp13-{F}(V0,V1,V2), pppp8-{F}(V0,V3,V4), V3 == V2, pppp8-{F}(V0,V5,V6), V6 == V2, pppp8-{F}(V0,V7,V8), V8 == V2, V7 == V2 | P_head_of-{T}(V0,V3)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #498: exists( #97, #496 ), references = 1, size of lhs = 2:
% 7.22/7.42     pppp0-{F}(V0,V1,V2), pppp8-{F}(V0,V3,V4) | P_head_of-{T}(V0,V4), P_head_of-{T}(V0,V3)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #502: disj( #497, #454+#470+#11 ), references = 2, size of lhs = 6:
% 7.22/7.42     pppp0-{F}(V0,V1,V2), pppp8-{F}(V0,V3,V4), pppp0-{F}(V0,V5,V6), pppp8-{F}(V0,V7,V8), V8 == V4, V7 == V4 | P_head_of-{T}(V0,V3)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #507: disj( #6, #501+#454+#470+#11 ), references = 1, size of lhs = 8:
% 7.22/7.42     pppp8-{F}(V0,V1,V2), pppp8-{F}(V0,V3,V4), pppp8-{F}(V0,V5,V6), V6 == V4, V5 == V4, pppp8-{F}(V0,V7,V8), V8 == V3, V7 == V3 | pppp1-{T}(V0,V1,V2)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #575: exists( #97, #466 ), references = 1, size of lhs = 1:
% 7.22/7.42     pppp1-{F}(V0,V1,V2) | P_head_of-{T}(V0,V2)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #666: mergings( V4 == V3; #664 ), references = 1, size of lhs = 2:
% 7.22/7.42     pppp13-{F}(V0,V1,V2), pppp8-{F}(V0,V2,V3) | P_head_of-{T}(V0,V2), P_head_of-{T}(V0,V3)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #671: disj( #664, #470+#454+#388+#9, #470+#454+#388+#9 ), references = 1, size of lhs = 12:
% 7.22/7.42     pppp13-{F}(V0,V1,V2), pppp8-{F}(V0,V3,V4), pppp8-{F}(V0,V5,V6), V6 == V2, pppp8-{F}(V0,V7,V8), V7 == V2, V7 == V6, pppp8-{F}(V0,V9,V10), V10 == V4, pppp8-{F}(V0,V11,V12), V11 == V4, V11 == V10 | P_head_of-{T}(V0,V3)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #698: disj( #6, #502+#454+#388+#9 ), references = 1, size of lhs = 8:
% 7.22/7.42     pppp8-{F}(V0,V1,V2), pppp8-{F}(V0,V3,V4), pppp8-{F}(V0,V5,V6), V6 == V4, V5 == V4, pppp8-{F}(V0,V7,V8), V7 == V3, V7 == V2 | pppp1-{T}(V0,V1,V2)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #814: exists( #98, #11 ), references = 3, size of lhs = 3:
% 7.22/7.42     P_head_of-{F}(V0,V1), pppp0-{F}(V0,V2,V3), V2 == V1 | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #816: exists( #97, #813 ), references = 2, size of lhs = 1:
% 7.22/7.42     pppp0-{F}(V0,V1,V2) | P_head_of-{T}(V0,V1)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #824: disj( #6, #815+#470+#814 ), references = 1, size of lhs = 4:
% 7.22/7.42     pppp8-{F}(V0,V1,V2), pppp8-{F}(V0,V3,V4), V4 == V1, V3 == V1 | pppp1-{T}(V0,V1,V2)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #985: mergings( V3 == V1; #983 ), references = 1, size of lhs = 4:
% 7.22/7.42     pppp8-{F}(V0,V1,V2), pppp8-{F}(V0,V1,V3), V3 == V1, V3 == V2 | pppp1-{T}(V0,V1,V2)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1050: exists( #102, #78 ), references = 1, size of lhs = 4:
% 7.22/7.42     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)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1051: exists( #102, #79 ), references = 1, size of lhs = 7:
% 7.22/7.42     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), path-{F}(V7,V8,V4) | P_number_of_in-{T}(V2,V4,V6)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1064: disj( #6, #1054+#468+#66 ), references = 1, size of lhs = 6:
% 7.22/7.42     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)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1065: disj( #6, #1054+#468+#152 ), references = 1, size of lhs = 6:
% 7.22/7.42     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), pppp22-{F}(V6,V7) | pppp0-{T}(V5,V4,V2)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1072: exists( #3, #1070 ), references = 2, size of lhs = 12:
% 7.22/7.42     complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0, P_empty-{F}(V2), P_head_of-{F}(V3,V0), P_tail_of-{F}(V4,V1), precedes-{F}(V4,V3,V5), P_tail_of-{F}(V6,V1), P_head_of-{F}(V7,V0), pppp23-{F}(V8,V6,V7), shortest_path-{F}(V9,V10,V5) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1089: mergings( V12 == V14, V15 == V13, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8; #1081 ), references = 2, size of lhs = 14:
% 7.22/7.42     complete-{F}(), P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_head_of-{F}(V3,V2), pppp22-{F}(V4,V2), precedes-{F}(V5,V1,V4), P_tail_of-{F}(V5,V6), V6 == V2, P_tail_of-{F}(V7,V6), P_head_of-{F}(V7,V8), P_length_of-{F}(V4,V9), P_tail_of-{F}(V10,V6), pppp23-{F}(V11,V10,V3), precedes-{F}(V7,V12,V4) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1111: mergings( V10 == V12, V18 == V20, V11 == V13, V21 == V22, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8; #1101 ), references = 2, size of lhs = 16:
% 7.22/7.42     complete-{F}(), P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_tail_of-{F}(V1,V3), P_tail_of-{F}(V4,V3), P_tail_of-{F}(V5,V3), precedes-{F}(V1,V6,V7), pppp22-{F}(V7,V8), P_length_of-{F}(V7,V9), precedes-{F}(V4,V10,V7), P_head_of-{F}(V10,V11), V3 == V11, P_head_of-{F}(V6,V11), P_tail_of-{F}(V6,V12), P_head_of-{F}(V13,V11), pppp23-{F}(V14,V5,V13) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1121: mergings( V9 == V11, V18 == V20, V10 == V12, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7; #1112 ), references = 2, size of lhs = 15:
% 7.22/7.42     complete-{F}(), P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_tail_of-{F}(V1,V3), P_tail_of-{F}(V4,V3), P_tail_of-{F}(V5,V3), precedes-{F}(V1,V6,V7), pppp22-{F}(V7,V8), P_length_of-{F}(V7,V9), precedes-{F}(V4,V10,V7), P_head_of-{F}(V10,V11), V3 == V11, P_head_of-{F}(V6,V11), P_head_of-{F}(V12,V11), pppp23-{F}(V13,V5,V12) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1134: mergings( V10 == V12, V9 == V11, V11 == V13, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V15 == V18, V8 == V14; #1123 ), references = 1, size of lhs = 7:
% 7.22/7.42     complete-{F}(), P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_tail_of-{F}(V1,V3), pppp22-{F}(V4,V5), P_length_of-{F}(V4,V6), pppp23-{F}(V4,V1,V7) | P_head_of-{T}(V7,V3)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1165: mergings( V11 == V14, V14 == V16, V12 == V13, V13 == V15, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8; #1155 ), references = 1, size of lhs = 11:
% 7.22/7.42     P_empty-{F}(V0), P_edges-{F}(V1), P_tail_of-{F}(V2,V3), P_head_of-{F}(V2,V4), P_path_cons-{F}(V2,V0,V5), P_length_of-{F}(V5,V6), P_number_of_in-{F}(V1,V5,V7), V6 == V7, precedes-{F}(V2,V8,V9), pppp22-{F}(V9,V10), P_length_of-{F}(V9,V11) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1176: mergings( V10 == V13, V13 == V15, V11 == V12, V12 == V14, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8; #1166 ), references = 1, size of lhs = 9:
% 7.22/7.42     P_empty-{F}(V0), P_edges-{F}(V1), P_tail_of-{F}(V2,V3), P_head_of-{F}(V2,V4), P_path_cons-{F}(V2,V0,V5), P_length_of-{F}(V5,V6), precedes-{F}(V2,V7,V8), pppp22-{F}(V8,V9), P_length_of-{F}(V8,V10) | P_number_of_in-{T}(V1,V5,V6)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1196: mergings( V13 == V16, V16 == V18, V14 == V15, V15 == V17, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8; #1186 ), references = 2, size of lhs = 14:
% 7.22/7.42     P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_tail_of-{F}(V4,V5), P_head_of-{F}(V4,V6), P_path_cons-{F}(V4,V0,V7), P_number_of_in-{F}(V2,V7,V8), P_length_of-{F}(V7,V9), P_minus-{F}(V9,V3,V10), V8 == V10, precedes-{F}(V4,V11,V12), pppp22-{F}(V12,V13), P_length_of-{F}(V12,V14) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1201: exists( #105, #1196 ), references = 1, size of lhs = 12:
% 7.22/7.42     P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_tail_of-{F}(V4,V5), P_head_of-{F}(V4,V6), P_path_cons-{F}(V4,V0,V7), P_number_of_in-{F}(V2,V7,V8), P_length_of-{F}(V7,V9), precedes-{F}(V4,V10,V11), pppp22-{F}(V11,V12), P_length_of-{F}(V11,V13) | P_minus-{T}(V9,V3,V8)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1247: mergings( V15 == V20, V16 == V19, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10; #1235 ), references = 1, size of lhs = 10:
% 7.22/7.42     P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_tail_of-{F}(V1,V3), pppp14-{F}(V4,V1,V5,V5), V4 == V1, precedes-{F}(V1,V4,V6), pppp22-{F}(V6,V7), P_length_of-{F}(V6,V8), P_tail_of-{F}(V4,V9), P_head_of-{F}(V4,V10) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1258: mergings( V15 == V20, V16 == V19, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V1 == V21; #1236 ), references = 1, size of lhs = 10:
% 7.22/7.42     P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_tail_of-{F}(V1,V3), pppp14-{F}(V4,V1,V5,V5), V4 == V1, precedes-{F}(V1,V4,V6), P_length_of-{F}(V6,V7), P_tail_of-{F}(V4,V8), P_head_of-{F}(V4,V9), pppp22-{F}(V6,V10) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1268: mergings( V16 == V18, V15 == V19, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10; #1237 ), references = 1, size of lhs = 12:
% 7.22/7.42     P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_tail_of-{F}(V1,V3), P_tail_of-{F}(V4,V5), P_head_of-{F}(V4,V6), P_head_of-{F}(V7,V6), V7 == V1, P_tail_of-{F}(V7,V5), pppp14-{F}(V7,V1,V8,V8), precedes-{F}(V1,V7,V9), pppp22-{F}(V9,V10), P_length_of-{F}(V9,V11) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1280: mergings( V13 == V18, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9; #1269 ), references = 3, size of lhs = 9:
% 7.22/7.42     P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_tail_of-{F}(V1,V3), pppp14-{F}(V4,V1,V5,V5), V4 == V1, precedes-{F}(V1,V4,V6), pppp22-{F}(V6,V7), P_length_of-{F}(V6,V8), P_head_of-{F}(V4,V9) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1289: mergings( V13 == V14, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9; #1271 ), references = 1, size of lhs = 9:
% 7.22/7.42     P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_tail_of-{F}(V1,V3), P_head_of-{F}(V4,V5), V4 == V1, pppp14-{F}(V4,V1,V6,V6), precedes-{F}(V1,V4,V7), pppp22-{F}(V7,V8), P_length_of-{F}(V7,V9) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1299: mergings( V13 == V18, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V16 == V19; #1270 ), references = 1, size of lhs = 9:
% 7.22/7.42     P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_tail_of-{F}(V1,V3), pppp14-{F}(V4,V1,V5,V5), V4 == V1, precedes-{F}(V1,V4,V6), P_length_of-{F}(V6,V7), P_head_of-{F}(V4,V8), pppp22-{F}(V6,V9) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1318: mergings( V6 == V7, V4 == V10, V5 == V9; #1312 ), references = 1, size of lhs = 7:
% 7.22/7.42     complete-{F}(), P_empty-{F}(V0), P_head_of-{F}(V1,V2), pppp22-{F}(V3,V4), P_length_of-{F}(V3,V5), pppp23-{F}(V3,V1,V6), P_head_of-{F}(V6,V4) | P_tail_of-{T}(V1,V4)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1322: mergings( V6 == V9, V4 == V11, V5 == V10; #1313 ), references = 3, size of lhs = 7:
% 7.22/7.42     complete-{F}(), P_empty-{F}(V0), P_head_of-{F}(V1,V2), pppp22-{F}(V3,V4), P_length_of-{F}(V3,V5), pppp23-{F}(V3,V1,V6), P_head_of-{F}(V6,V7) | P_tail_of-{T}(V1,V7)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1326: mergings( V6 == V9, V4 == V12, V5 == V11; #1314 ), references = 1, size of lhs = 8:
% 7.22/7.42     complete-{F}(), P_empty-{F}(V0), P_head_of-{F}(V1,V2), pppp22-{F}(V3,V4), P_length_of-{F}(V3,V5), pppp23-{F}(V3,V1,V6), P_tail_of-{F}(V6,V7), P_head_of-{F}(V6,V8) | P_tail_of-{T}(V1,V8)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1350: mergings( V8 == V7, V7 == V14, V14 == V17, V2 == V3, V3 == V4, V5 == V13, V9 == V16, V17 == V15, V6 == V12, V11 == V13, V10 == V12; #1336 ), references = 1, size of lhs = 7:
% 7.22/7.42     complete-{F}(), P_empty-{F}(V0), pppp22-{F}(V1,V2), P_length_of-{F}(V1,V3), P_head_of-{F}(V4,V2), pppp23-{F}(V1,V5,V4), V4 == V5 | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1385: mergings( V9 == V12, V12 == V15, V2 == V3, V3 == V4, V5 == V11, V7 == V14, V6 == V13, V8 == V10; #1374 ), references = 1, size of lhs = 7:
% 7.22/7.42     complete-{F}(), P_empty-{F}(V0), pppp22-{F}(V1,V2), P_length_of-{F}(V1,V3), pppp23-{F}(V1,V4,V5), V5 == V4, P_head_of-{F}(V5,V6) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1394: mergings( V2 == V3, V3 == V4, V5 == V9, V7 == V11, V6 == V10; #1386 ), references = 1, size of lhs = 6:
% 7.22/7.42     complete-{F}(), P_empty-{F}(V0), pppp22-{F}(V1,V2), P_length_of-{F}(V1,V3), pppp23-{F}(V1,V4,V5), V5 == V4 | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1402: mergings( V3 == V4, V4 == V5, V7 == V9, V6 == V8; #1395 ), references = 1, size of lhs = 5:
% 7.22/7.42     complete-{F}(), P_empty-{F}(V0), pppp24-{F}(V1,V2), pppp22-{F}(V1,V3), P_length_of-{F}(V1,V4) | pppp23-{T}(V1,V2,V2)
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1415: mergings( V2 == V3, V4 == V7, V5 == V8; #1409 ), references = 1, size of lhs = 5:
% 7.22/7.42     complete-{F}(), P_empty-{F}(V0), P_length_of-{F}(V1,V2), pppp23-{F}(V1,V3,V3), pppp22-{F}(V1,V4) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1429: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V8 == V9, V9 == V10, V10 == V11; #1419 ), references = 1, size of lhs = 4:
% 7.22/7.42     complete-{F}(), P_empty-{F}(V0), pppp24-{F}(V1,V2), pppp22-{F}(V1,V3) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1437: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6; #1430 ), references = 1, size of lhs = 4:
% 7.22/7.42     complete-{F}(), pppp25-{F}(V0), P_empty-{F}(V1), pppp24-{F}(V0,V2) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1445: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6; #1438 ), references = 1, size of lhs = 3:
% 7.22/7.42     complete-{F}(), pppp25-{F}(V0), P_empty-{F}(V1) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1454: mergings( V0 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11; #1446 ), references = 1, size of lhs = 7:
% 7.22/7.42     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
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1471: mergings( V1 == V6, V6 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V2 == V7, V3 == V8, V4 == V9, V5 == V10; #1458 ), references = 1, size of lhs = 5:
% 7.22/7.42     P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_empty-{F}(V4) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1484: mergings( V1 == V5, V5 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V2 == V6, V3 == V7, V4 == V8; #1472 ), references = 1, size of lhs = 4:
% 7.22/7.42     P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_empty-{F}(V3) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1496: mergings( V1 == V4, V4 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V2 == V5, V3 == V6; #1485 ), references = 1, size of lhs = 3:
% 7.22/7.42     P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_empty-{F}(V2) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1507: mergings( V1 == V3, V3 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V2 == V4; #1497 ), references = 1, size of lhs = 2:
% 7.22/7.42     P_edges-{F}(V0), P_empty-{F}(V1) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1517: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7; #1508 ), references = 1, size of lhs = 1:
% 7.22/7.42     P_empty-{F}(V0) | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  #1521: exists( #100, #1508 ), references = 1, size of lhs = 0:
% 7.22/7.42     FALSE | FALSE
% 7.22/7.42        (used 0 times, uses = {})
% 7.22/7.42  
% 7.22/7.42  number of learnt formulas = 79
% 7.22/7.42  
% 7.22/7.42  
% 7.22/7.42  % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.22/7.42  
% 7.22/7.42  randbase = 1
%------------------------------------------------------------------------------