TSTP Solution File: GRA003+1 by Geo-III---2018C

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Geo-III---2018C
% Problem  : GRA003+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : geo -tptp_input -nonempty -inputfile %s

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat Jul 23 06:02:46 EDT 2022

% Result   : Theorem 0.93s 1.09s
% Output   : Refutation 0.93s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GRA003+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.03/0.12  % Command  : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33  % Computer : n007.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Fri Jul 22 07:35:26 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.93/1.09  GeoParameters:
% 0.93/1.09  
% 0.93/1.09  tptp_input =     1
% 0.93/1.09  tptp_output =    0
% 0.93/1.09  nonempty =       1
% 0.93/1.09  inputfile =      /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.93/1.09  includepath =    /export/starexec/sandbox2/solver/bin/../../benchmark/
% 0.93/1.09  
% 0.93/1.09  
% 0.93/1.09  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.93/1.09  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.93/1.09  
% 0.93/1.09  RuleSystem INPUT:
% 0.93/1.09  
% 0.93/1.09  Initial Rules:
% 0.93/1.09  #0: input, references = 4, size of lhs = 3:
% 0.93/1.09     P_head_of-{F}(V0,V2), P_tail_of-{F}(V0,V2), edge-{F}(V0) | FALSE
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #1: input, references = 4, size of lhs = 3:
% 0.93/1.09     P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), edge-{F}(V0) | vertex-{T}(V1)
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #2: input, references = 4, size of lhs = 3:
% 0.93/1.09     P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), edge-{F}(V0) | vertex-{T}(V2)
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #3: input, references = 3, size of lhs = 4:
% 0.93/1.09     complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0 | EXISTS V2: pppp9-{T}(V1,V0,V2)
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #4: input, references = 3, size of lhs = 1:
% 0.93/1.09     pppp9-{F}(V0,V1,V2) | pppp8-{T}(V2,V0,V1)
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #5: input, references = 3, size of lhs = 3:
% 0.93/1.09     pppp8-{F}(V0,V1,V2), pppp1-{F}(V0,V1,V2), pppp0-{F}(V0,V1,V2) | FALSE
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #6: input, references = 3, size of lhs = 1:
% 0.93/1.09     pppp8-{F}(V0,V1,V2) | pppp0-{T}(V0,V1,V2), pppp1-{T}(V0,V1,V2)
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #7: input, references = 3, size of lhs = 1:
% 0.93/1.09     pppp8-{F}(V0,V1,V2) | edge-{T}(V0)
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #8: input, references = 3, size of lhs = 4:
% 0.93/1.09     P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp1-{F}(V0,V1,V2), V2 == V3 | FALSE
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #9: input, references = 3, size of lhs = 4:
% 0.93/1.09     P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp1-{F}(V0,V1,V2), V1 == V4 | FALSE
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #10: input, references = 3, size of lhs = 2:
% 0.93/1.09     P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | pppp1-{T}(V0,V4,V3)
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #11: input, references = 3, size of lhs = 4:
% 0.93/1.09     P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp0-{F}(V0,V1,V2), V1 == V3 | FALSE
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #12: input, references = 3, size of lhs = 4:
% 0.93/1.09     P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp0-{F}(V0,V1,V2), V2 == V4 | FALSE
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #13: input, references = 3, size of lhs = 2:
% 0.93/1.09     P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | pppp0-{T}(V0,V3,V4)
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #14: input, references = 4, size of lhs = 7:
% 0.93/1.09     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)
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #15: input, references = 3, size of lhs = 9:
% 0.93/1.09     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)
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #16: input, references = 4, size of lhs = 2:
% 0.93/1.09     P_empty-{F}(V0), path-{F}(V1,V2,V3) | vertex-{T}(V1)
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #17: input, references = 4, size of lhs = 2:
% 0.93/1.09     P_empty-{F}(V0), path-{F}(V1,V2,V3) | vertex-{T}(V2)
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #18: input, references = 3, size of lhs = 2:
% 0.93/1.09     P_empty-{F}(V0), path-{F}(V1,V2,V3) | EXISTS V4: pppp11-{T}(V1,V2,V3,V4)
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #19: input, references = 3, size of lhs = 2:
% 0.93/1.09     pppp11-{F}(V0,V1,V2,V3), P_tail_of-{F}(V3,V4) | pppp10-{T}(V3,V0,V1,V2,V4)
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #20: input, references = 3, size of lhs = 3:
% 0.93/1.09     pppp10-{F}(V0,V1,V2,V3,V4), pppp3-{F}(V0,V2,V3), pppp2-{F}(V0,V2,V3) | FALSE
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #21: input, references = 3, size of lhs = 1:
% 0.93/1.09     pppp10-{F}(V0,V1,V2,V3,V4) | pppp2-{T}(V0,V2,V3), pppp3-{T}(V0,V2,V3)
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #22: input, references = 3, size of lhs = 2:
% 0.93/1.09     pppp10-{F}(V0,V1,V2,V3,V4), V1 == V4 | FALSE
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #23: input, references = 3, size of lhs = 1:
% 0.93/1.09     pppp10-{F}(V0,V1,V2,V3,V4) | edge-{T}(V0)
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #24: input, references = 3, size of lhs = 3:
% 0.93/1.09     P_empty-{F}(V0), P_head_of-{F}(V1,V4), pppp3-{F}(V1,V2,V3) | EXISTS V5: pppp12-{T}(V1,V2,V3,V5,V4)
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #25: input, references = 3, size of lhs = 4:
% 0.93/1.09     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)
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #26: input, references = 3, size of lhs = 3:
% 0.93/1.09     pppp12-{F}(V0,V1,V2,V3,V4), P_path_cons-{F}(V0,V3,V5), V2 == V5 | FALSE
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #27: input, references = 3, size of lhs = 2:
% 0.93/1.09     pppp12-{F}(V0,V1,V2,V3,V4), P_path_cons-{F}(V0,V3,V5) | path-{T}(V4,V1,V3)
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #28: input, references = 3, size of lhs = 5:
% 0.93/1.09     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
% 0.93/1.09        (used 0 times, uses = {})
% 0.93/1.09  
% 0.93/1.09  #29: input, references = 3, size of lhs = 5:
% 0.93/1.09     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
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #30: input, references = 3, size of lhs = 3:
% 0.93/1.10     P_empty-{F}(V0), P_head_of-{F}(V1,V4), P_path_cons-{F}(V1,V0,V5) | pppp2-{T}(V1,V4,V5)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #31: input, references = 7, size of lhs = 5:
% 0.93/1.10     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)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #32: input, references = 3, size of lhs = 5:
% 0.93/1.10     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)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #33: input, references = 3, size of lhs = 5:
% 0.93/1.10     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)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #34: input, references = 3, size of lhs = 3:
% 0.93/1.10     P_empty-{F}(V0), path-{F}(V3,V2,V1), in_path-{F}(V4,V1) | vertex-{T}(V4)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #35: input, references = 3, size of lhs = 3:
% 0.93/1.10     P_empty-{F}(V0), path-{F}(V3,V2,V1), in_path-{F}(V4,V1) | EXISTS V5: pppp13-{T}(V5,V1,V4)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #36: input, references = 3, size of lhs = 5:
% 0.93/1.10     pppp13-{F}(V0,V1,V2), P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), V2 == V3, V2 == V4 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #37: input, references = 3, size of lhs = 3:
% 0.93/1.10     pppp13-{F}(V0,V1,V2), P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | on_path-{T}(V0,V1)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #38: input, references = 3, size of lhs = 2:
% 0.93/1.10     P_empty-{F}(V0), sequential-{F}(V1,V2) | pppp4-{T}(V1,V2)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #39: input, references = 3, size of lhs = 2:
% 0.93/1.10     P_empty-{F}(V0), pppp4-{F}(V1,V2) | sequential-{T}(V1,V2)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #40: input, references = 3, size of lhs = 3:
% 0.93/1.10     P_empty-{F}(V0), P_head_of-{F}(V1,V3), P_tail_of-{F}(V2,V4) | pppp14-{T}(V1,V2,V3,V4)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #41: input, references = 3, size of lhs = 4:
% 0.93/1.10     pppp14-{F}(V0,V1,V3,V3), edge-{F}(V0), edge-{F}(V1), V0 == V1 | pppp4-{T}(V0,V1)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #42: input, references = 3, size of lhs = 3:
% 0.93/1.10     pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1), V2 == V3 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #43: input, references = 3, size of lhs = 2:
% 0.93/1.10     pppp14-{F}(V1,V1,V2,V3), pppp4-{F}(V1,V1) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #44: input, references = 3, size of lhs = 2:
% 0.93/1.10     pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1) | edge-{T}(V1)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #45: input, references = 3, size of lhs = 2:
% 0.93/1.10     pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1) | edge-{T}(V0)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #46: input, references = 3, size of lhs = 5:
% 0.93/1.10     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)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #47: input, references = 3, size of lhs = 6:
% 0.93/1.10     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)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #48: input, references = 6, size of lhs = 3:
% 0.93/1.10     P_empty-{F}(V0), precedes-{F}(V2,V3,V1), path-{F}(V5,V4,V1) | pppp15-{T}(V1,V2,V3)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #49: input, references = 3, size of lhs = 3:
% 0.93/1.10     pppp15-{F}(V0,V1,V2), pppp5-{F}(V0,V1,V2), sequential-{F}(V1,V2) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #50: input, references = 3, size of lhs = 1:
% 0.93/1.10     pppp15-{F}(V0,V1,V2) | sequential-{T}(V1,V2), pppp5-{T}(V0,V1,V2)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #51: input, references = 5, size of lhs = 1:
% 0.93/1.10     pppp15-{F}(V0,V1,V2) | on_path-{T}(V2,V0)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #52: input, references = 5, size of lhs = 1:
% 0.93/1.10     pppp15-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #53: input, references = 3, size of lhs = 2:
% 0.93/1.10     P_empty-{F}(V0), pppp5-{F}(V1,V2,V3) | EXISTS V4: pppp16-{T}(V1,V2,V3,V4)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #54: input, references = 3, size of lhs = 3:
% 0.93/1.10     P_empty-{F}(V0), sequential-{F}(V2,V4), precedes-{F}(V4,V3,V1) | pppp5-{T}(V1,V2,V3)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #55: input, references = 3, size of lhs = 1:
% 0.93/1.10     pppp16-{F}(V0,V1,V2,V3) | precedes-{T}(V3,V2,V0)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #56: input, references = 3, size of lhs = 1:
% 0.93/1.10     pppp16-{F}(V0,V1,V2,V3) | sequential-{T}(V1,V3)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #57: input, references = 9, size of lhs = 2:
% 0.93/1.10     P_empty-{F}(V0), shortest_path-{F}(V1,V2,V3) | pppp6-{T}(V1,V2,V3)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #58: input, references = 3, size of lhs = 2:
% 0.93/1.10     P_empty-{F}(V0), pppp6-{F}(V1,V2,V3) | shortest_path-{T}(V1,V2,V3)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #59: input, references = 8, size of lhs = 3:
% 0.93/1.10     P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V1,V2,V3) | path-{T}(V1,V2,V3)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #60: input, references = 4, size of lhs = 3:
% 0.93/1.10     P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V2,V2,V3) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #61: input, references = 3, size of lhs = 5:
% 0.93/1.10     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)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #62: input, references = 3, size of lhs = 4:
% 0.93/1.10     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)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #63: input, references = 3, size of lhs = 1:
% 0.93/1.10     pppp26-{F}(V0,V1,V2) | EXISTS V3: pppp17-{T}(V0,V1,V3,V2)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #64: input, references = 3, size of lhs = 3:
% 0.93/1.10     pppp17-{F}(V0,V1,V2,V3), P_length_of-{F}(V2,V4), less_or_equal-{F}(V3,V4) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #65: input, references = 3, size of lhs = 2:
% 0.93/1.10     pppp17-{F}(V0,V1,V2,V3), P_length_of-{F}(V2,V4) | path-{T}(V0,V1,V2)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #66: input, references = 4, size of lhs = 7:
% 0.93/1.10     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
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #67: input, references = 3, size of lhs = 6:
% 0.93/1.10     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
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #68: input, references = 3, size of lhs = 2:
% 0.93/1.10     P_empty-{F}(V0), triangle-{F}(V1,V2,V3) | pppp7-{T}(V1,V2,V3)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #69: input, references = 3, size of lhs = 2:
% 0.93/1.10     P_empty-{F}(V0), pppp7-{F}(V1,V2,V3) | triangle-{T}(V1,V2,V3)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #70: input, references = 3, size of lhs = 2:
% 0.93/1.10     P_empty-{F}(V0), pppp7-{F}(V1,V2,V3) | pppp18-{T}(V1,V2,V3)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #71: input, references = 3, size of lhs = 7:
% 0.93/1.10     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)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #72: input, references = 3, size of lhs = 1:
% 0.93/1.10     pppp18-{F}(V0,V1,V2) | sequential-{T}(V2,V0)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #73: input, references = 3, size of lhs = 1:
% 0.93/1.10     pppp18-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #74: input, references = 3, size of lhs = 1:
% 0.93/1.10     pppp18-{F}(V0,V1,V2) | sequential-{T}(V0,V1)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #75: input, references = 3, size of lhs = 1:
% 0.93/1.10     pppp18-{F}(V0,V1,V2) | edge-{T}(V2)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #76: input, references = 3, size of lhs = 1:
% 0.93/1.10     pppp18-{F}(V0,V1,V2) | edge-{T}(V1)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #77: input, references = 3, size of lhs = 1:
% 0.93/1.10     pppp18-{F}(V0,V1,V2) | edge-{T}(V0)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #78: input, references = 4, size of lhs = 6:
% 0.93/1.10     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
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #79: input, references = 5, size of lhs = 9:
% 0.93/1.10     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
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #80: input, references = 3, size of lhs = 9:
% 0.93/1.10     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)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #81: input, references = 3, size of lhs = 1:
% 0.93/1.10     pppp20-{F}(V0,V1) | EXISTS V2: pppp19-{T}(V0,V2,V1)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #82: input, references = 3, size of lhs = 1:
% 0.93/1.10     pppp20-{F}(V0,V1) | on_path-{T}(V1,V0)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #83: input, references = 3, size of lhs = 2:
% 0.93/1.10     pppp19-{F}(V0,V1,V2), triangle-{F}(V1,V2,V3) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #84: input, references = 3, size of lhs = 1:
% 0.93/1.10     pppp19-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #85: input, references = 3, size of lhs = 1:
% 0.93/1.10     pppp19-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #86: input, references = 3, size of lhs = 8:
% 0.93/1.10     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)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #87: input, references = 4, size of lhs = 6:
% 0.93/1.10     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)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #88: input, references = 5, size of lhs = 1:
% 0.93/1.10     pppp25-{F}(V0) | EXISTS V1: pppp24-{T}(V0,V1)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #89: input, references = 7, size of lhs = 1:
% 0.93/1.10     pppp24-{F}(V0,V1) | EXISTS V2: pppp23-{T}(V2,V0,V1)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #90: input, references = 9, size of lhs = 1:
% 0.93/1.10     pppp23-{F}(V0,V1,V2) | EXISTS V3: pppp22-{T}(V0,V1,V2,V3)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #91: input, references = 7, size of lhs = 1:
% 0.93/1.10     pppp23-{F}(V0,V1,V2) | precedes-{T}(V1,V2,V0)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #92: input, references = 9, size of lhs = 1:
% 0.93/1.10     pppp22-{F}(V0,V1,V2,V3) | EXISTS V4: pppp21-{T}(V4,V3,V0,V1,V2)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #93: input, references = 4, size of lhs = 8:
% 0.93/1.10     pppp21-{F}(V0,V1,V2,V3,V4), vertex-{F}(V0), vertex-{F}(V1), edge-{F}(V3), edge-{F}(V4), path-{F}(V0,V1,V2), V0 == V1, V3 == V4 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #94: input, references = 10, size of lhs = 1:
% 0.93/1.10     pppp21-{F}(V0,V1,V2,V3,V4) | shortest_path-{T}(V0,V1,V2)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #95: input, references = 6, size of lhs = 1:
% 0.93/1.10     #-{F} V0 | EXISTS V1: P_head_of-{T}(V0,V1)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #96: input, references = 6, size of lhs = 1:
% 0.93/1.10     #-{F} V0 | EXISTS V1: P_tail_of-{T}(V0,V1)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #97: input, references = 3, size of lhs = 2:
% 0.93/1.10     #-{F} V0, #-{F} V1 | EXISTS V2: P_path_cons-{T}(V0,V1,V2)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #98: input, references = 4, size of lhs = 0:
% 0.93/1.10     FALSE | EXISTS V0: P_empty-{T}(V0)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #99: input, references = 6, size of lhs = 1:
% 0.93/1.10     #-{F} V0 | EXISTS V1: P_length_of-{T}(V0,V1)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #100: input, references = 6, size of lhs = 2:
% 0.93/1.10     #-{F} V0, #-{F} V1 | EXISTS V2: P_number_of_in-{T}(V0,V1,V2)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #101: input, references = 4, size of lhs = 0:
% 0.93/1.10     FALSE | EXISTS V0: P_edges-{T}(V0)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #102: input, references = 4, size of lhs = 0:
% 0.93/1.10     FALSE | EXISTS V0: P_sequential_pairs-{T}(V0)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #103: input, references = 4, size of lhs = 2:
% 0.93/1.10     #-{F} V0, #-{F} V1 | EXISTS V2: P_minus-{T}(V0,V1,V2)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #104: input, references = 4, size of lhs = 0:
% 0.93/1.10     FALSE | EXISTS V0: P_n1-{T}(V0)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #105: input, references = 4, size of lhs = 0:
% 0.93/1.10     FALSE | EXISTS V0: P_triangles-{T}(V0)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #106: input, references = 4, size of lhs = 0:
% 0.93/1.10     FALSE | EXISTS V0: P_graph-{T}(V0)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  number of initial rules = 107
% 0.93/1.10  
% 0.93/1.10  Simplifiers:
% 0.93/1.10  #107: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp0-{F}(V0,V1,V2), pppp0-{F}(V0,V4,V5), V1 == V4 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #108: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp0-{F}(V0,V1,V2), pppp0-{F}(V0,V4,V5), V2 == V5 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #109: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp1-{F}(V0,V1,V2), pppp1-{F}(V0,V4,V5), V2 == V5 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #110: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp1-{F}(V0,V1,V2), pppp1-{F}(V0,V4,V5), V1 == V4 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #111: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     P_head_of-{F}(V0,V1), P_head_of-{F}(V0,V3), V1 == V3 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #112: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     P_tail_of-{F}(V0,V1), P_tail_of-{F}(V0,V3), V1 == V3 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #113: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     P_path_cons-{F}(V0,V1,V2), P_path_cons-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #114: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     P_empty-{F}(V0), P_empty-{F}(V1), V0 == V1 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #115: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     P_length_of-{F}(V0,V1), P_length_of-{F}(V0,V3), V1 == V3 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #116: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     P_number_of_in-{F}(V0,V1,V2), P_number_of_in-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #117: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     P_edges-{F}(V0), P_edges-{F}(V1), V0 == V1 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #118: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     P_sequential_pairs-{F}(V0), P_sequential_pairs-{F}(V1), V0 == V1 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #119: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     P_minus-{F}(V0,V1,V2), P_minus-{F}(V0,V1,V5), V2 == V5 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #120: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     P_n1-{F}(V0), P_n1-{F}(V1), V0 == V1 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #121: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     P_triangles-{F}(V0), P_triangles-{F}(V1), V0 == V1 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #122: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     P_graph-{F}(V0), P_graph-{F}(V1), V0 == V1 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #123: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V5,V1,V2,V3,V9), V0 == V5 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #124: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #125: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp11-{F}(V0,V1,V2,V3), pppp11-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #126: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V1,V2,V8,V4), V3 == V8 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #127: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #128: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp13-{F}(V0,V1,V2), pppp13-{F}(V3,V1,V2), V0 == V3 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #129: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp14-{F}(V0,V1,V2,V3), pppp14-{F}(V0,V5,V6,V7), V2 == V6 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #130: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp14-{F}(V0,V1,V2,V3), pppp14-{F}(V4,V1,V6,V7), V3 == V7 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #131: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp16-{F}(V0,V1,V2,V3), pppp16-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #132: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp17-{F}(V0,V1,V2,V3), pppp17-{F}(V0,V1,V6,V3), V2 == V6 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #133: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp19-{F}(V0,V1,V2), pppp19-{F}(V0,V4,V2), V1 == V4 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #134: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp19-{F}(V0,V1,V2), pppp19-{F}(V0,V4,V5), V2 == V5 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #135: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp20-{F}(V0,V1), pppp20-{F}(V0,V3), V1 == V3 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #136: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp21-{F}(V0,V1,V2,V3,V4), pppp21-{F}(V5,V1,V2,V3,V4), V0 == V5 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #137: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp21-{F}(V0,V1,V2,V3,V4), pppp21-{F}(V5,V6,V2,V3,V4), V1 == V6 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #138: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp21-{F}(V0,V1,V2,V3,V4), pppp21-{F}(V5,V6,V7,V3,V4), V2 == V7 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #139: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp21-{F}(V0,V1,V2,V3,V4), pppp21-{F}(V5,V6,V7,V3,V9), V4 == V9 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #140: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp21-{F}(V0,V1,V2,V3,V4), pppp21-{F}(V5,V6,V7,V8,V9), V3 == V8 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #141: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp22-{F}(V0,V1,V2,V3), pppp22-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #142: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp22-{F}(V0,V1,V2,V3), pppp22-{F}(V4,V1,V2,V7), V0 == V4 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #143: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp22-{F}(V0,V1,V2,V3), pppp22-{F}(V4,V1,V6,V7), V2 == V6 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #144: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp22-{F}(V0,V1,V2,V3), pppp22-{F}(V4,V5,V6,V7), V1 == V5 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #145: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp23-{F}(V0,V1,V2), pppp23-{F}(V3,V1,V2), V0 == V3 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #146: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp23-{F}(V0,V1,V2), pppp23-{F}(V3,V1,V5), V2 == V5 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #147: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp23-{F}(V0,V1,V2), pppp23-{F}(V3,V4,V5), V1 == V4 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #148: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp24-{F}(V0,V1), pppp24-{F}(V0,V3), V1 == V3 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #149: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp24-{F}(V0,V1), pppp24-{F}(V2,V3), V0 == V2 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #150: unsound, references = 3, size of lhs = 3:
% 0.93/1.10     pppp25-{F}(V0), pppp25-{F}(V1), V0 == V1 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  number of simplifiers = 44
% 0.93/1.10  
% 0.93/1.10  Learnt:
% 0.93/1.10  #153: exists( #92, #151 ), references = 1, size of lhs = 7:
% 0.93/1.10     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,V8,V9) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #155: exists( #90, #152 ), references = 1, size of lhs = 7:
% 0.93/1.10     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
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #158: exists( #89, #156 ), references = 2, size of lhs = 6:
% 0.93/1.10     P_empty-{F}(V0), pppp24-{F}(V1,V2), P_tail_of-{F}(V1,V3), P_tail_of-{F}(V4,V3), P_head_of-{F}(V4,V5), P_head_of-{F}(V2,V5) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #166: mergings( V5 == V6, V6 == V7, V11 == V13; #162 ), references = 2, size of lhs = 9:
% 0.93/1.10     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, pppp22-{F}(V4,V8,V9,V10) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #171: mergings( V4 == V5, V5 == V6, V10 == V12; #167 ), references = 3, size of lhs = 9:
% 0.93/1.10     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
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #179: mergings( V5 == V6, V6 == V7, V9 == V10; #175 ), references = 2, size of lhs = 6:
% 0.93/1.10     P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), P_number_of_in-{F}(V1,V2,V4), V3 == V4, pppp22-{F}(V2,V5,V6,V7) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #184: mergings( V3 == V4, V4 == V5, V6 == V7; #180 ), references = 1, size of lhs = 4:
% 0.93/1.10     P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), pppp22-{F}(V2,V4,V5,V6) | P_number_of_in-{T}(V1,V2,V3)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #189: exists( #103, #166 ), references = 1, size of lhs = 7:
% 0.93/1.10     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), pppp22-{F}(V4,V7,V8,V9) | P_minus-{T}(V6,V3,V5)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #190: exists( #103, #171 ), references = 1, size of lhs = 7:
% 0.93/1.10     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)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #205: mergings( V10 == V12, V11 == V12, V5 == V6, V6 == V7, V7 == V8; #199 ), references = 1, size of lhs = 6:
% 0.93/1.10     P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_tail_of-{F}(V1,V2), precedes-{F}(V1,V3,V4), P_length_of-{F}(V4,V5), pppp22-{F}(V4,V6,V7,V8) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #212: mergings( V7 == V9, V8 == V9, V2 == V3, V3 == V4, V4 == V5; #206 ), references = 1, size of lhs = 5:
% 0.93/1.10     P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_tail_of-{F}(V1,V2), precedes-{F}(V1,V3,V4), pppp22-{F}(V4,V5,V6,V7) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #219: mergings( V9 == V11, V10 == V11, V4 == V5, V5 == V6, V6 == V7; #213 ), references = 1, size of lhs = 5:
% 0.93/1.10     P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_tail_of-{F}(V1,V2), precedes-{F}(V1,V3,V4), pppp23-{F}(V4,V5,V6) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #227: mergings( V7 == V9, V8 == V9, V3 == V4, V4 == V5, V5 == V6; #221 ), references = 1, size of lhs = 4:
% 0.93/1.10     P_empty-{F}(V0), pppp24-{F}(V1,V2), P_head_of-{F}(V1,V3), P_tail_of-{F}(V1,V3) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #234: mergings( V6 == V8, V7 == V8, V2 == V3, V3 == V4, V4 == V5; #228 ), references = 1, size of lhs = 4:
% 0.93/1.10     pppp25-{F}(V0), P_empty-{F}(V1), P_head_of-{F}(V0,V2), P_tail_of-{F}(V0,V2) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #236: exists( #96, #158 ), references = 2, size of lhs = 4:
% 0.93/1.10     P_empty-{F}(V0), pppp24-{F}(V1,V2), P_head_of-{F}(V1,V3), P_head_of-{F}(V2,V3) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #238: exists( #100, #171 ), references = 1, size of lhs = 7:
% 0.93/1.10     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)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #240: exists( #90, #179 ), references = 2, size of lhs = 6:
% 0.93/1.10     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
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #243: exists( #100, #240 ), references = 1, size of lhs = 4:
% 0.93/1.10     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)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #274: mergings( V15 == V18, V18 == V20, V16 == V17, V17 == V19, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10; #263 ), references = 1, size of lhs = 14:
% 0.93/1.10     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}(V11,V4,V12), P_length_of-{F}(V12,V13), pppp22-{F}(V12,V14,V15,V16) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #285: mergings( V14 == V17, V17 == V19, V15 == V16, V16 == V18, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9; #275 ), references = 1, size of lhs = 14:
% 0.93/1.10     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}(V11,V4,V12), P_length_of-{F}(V12,V13), pppp23-{F}(V12,V14,V15) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #296: mergings( V12 == V15, V15 == V17, V13 == V14, V14 == V16, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7; #286 ), references = 1, size of lhs = 13:
% 0.93/1.10     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}(V11,V4,V12), pppp23-{F}(V12,V13,V14) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #308: mergings( V12 == V15, V15 == V17, V13 == V14, V14 == V16, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8; #298 ), references = 1, size of lhs = 12:
% 0.93/1.10     P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp24-{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
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #326: mergings( V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11; #319 ), references = 1, size of lhs = 9:
% 0.93/1.10     P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_tail_of-{F}(V1,V3), precedes-{F}(V1,V4,V5), V1 == V4, pppp22-{F}(V5,V1,V4,V6), P_length_of-{F}(V5,V7), P_head_of-{F}(V4,V8), P_tail_of-{F}(V4,V9) | pppp21-{T}(V6,V6,V5,V1,V4)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #340: mergings( V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V15 == V18; #330 ), references = 1, size of lhs = 9:
% 0.93/1.10     P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_tail_of-{F}(V1,V3), pppp23-{F}(V4,V1,V5), V1 == V5, precedes-{F}(V1,V5,V4), P_head_of-{F}(V5,V6), P_tail_of-{F}(V5,V7), P_length_of-{F}(V4,V8) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #350: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10; #341 ), references = 1, size of lhs = 8:
% 0.93/1.10     P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_tail_of-{F}(V1,V3), pppp23-{F}(V4,V1,V5), V1 == V5, precedes-{F}(V1,V5,V4), P_head_of-{F}(V5,V6), P_tail_of-{F}(V5,V7) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #360: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10; #351 ), references = 1, size of lhs = 7:
% 0.93/1.10     P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_tail_of-{F}(V1,V3), pppp23-{F}(V4,V1,V5), V1 == V5, precedes-{F}(V1,V5,V4), P_head_of-{F}(V5,V6) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #370: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10; #361 ), references = 1, size of lhs = 6:
% 0.93/1.10     P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_tail_of-{F}(V1,V3), pppp23-{F}(V4,V1,V5), V1 == V5, precedes-{F}(V1,V5,V4) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #381: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11; #372 ), references = 1, size of lhs = 5:
% 0.93/1.10     P_empty-{F}(V0), pppp24-{F}(V1,V2), V1 == V2, P_head_of-{F}(V1,V3), P_tail_of-{F}(V1,V4) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #391: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10; #382 ), references = 1, size of lhs = 4:
% 0.93/1.10     P_empty-{F}(V0), pppp24-{F}(V1,V2), V1 == V2, P_head_of-{F}(V1,V3) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #401: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10; #392 ), references = 1, size of lhs = 3:
% 0.93/1.10     P_empty-{F}(V0), pppp24-{F}(V1,V2), V1 == V2 | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #411: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10; #402 ), references = 1, size of lhs = 2:
% 0.93/1.10     pppp25-{F}(V0), P_empty-{F}(V1) | pppp24-{T}(V0,V0)
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #413: exists( #95, #236 ), references = 1, size of lhs = 2:
% 0.93/1.10     P_empty-{F}(V0), pppp24-{F}(V1,V1) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #426: mergings( V0 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16; #415 ), references = 1, size of lhs = 6:
% 0.93/1.10     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
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #438: mergings( V1 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15; #427 ), references = 1, size of lhs = 5:
% 0.93/1.10     P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_empty-{F}(V4) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #450: mergings( V1 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14; #439 ), references = 1, size of lhs = 4:
% 0.93/1.10     P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_empty-{F}(V3) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #462: mergings( V1 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13; #451 ), references = 1, size of lhs = 3:
% 0.93/1.10     P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_empty-{F}(V2) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #474: mergings( V1 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12; #463 ), references = 1, size of lhs = 2:
% 0.93/1.10     P_edges-{F}(V0), P_empty-{F}(V1) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #486: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11; #475 ), references = 1, size of lhs = 1:
% 0.93/1.10     P_empty-{F}(V0) | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  #488: exists( #98, #475 ), references = 1, size of lhs = 0:
% 0.93/1.10     FALSE | FALSE
% 0.93/1.10        (used 0 times, uses = {})
% 0.93/1.10  
% 0.93/1.10  number of learnt formulas = 39
% 0.93/1.10  
% 0.93/1.10  
% 0.93/1.10  % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.93/1.10  
% 0.93/1.10  randbase = 1
%------------------------------------------------------------------------------