TSTP Solution File: GRA008+2 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : GRA008+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n004.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 5.16s 5.32s
% Output : Refutation 5.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRA008+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.10/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n004.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 07:47:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 5.16/5.32 GeoParameters:
% 5.16/5.32
% 5.16/5.32 tptp_input = 1
% 5.16/5.32 tptp_output = 0
% 5.16/5.32 nonempty = 1
% 5.16/5.32 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.16/5.32 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 5.16/5.32
% 5.16/5.32
% 5.16/5.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.16/5.32 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.16/5.32
% 5.16/5.32 RuleSystem INPUT:
% 5.16/5.32
% 5.16/5.32 Initial Rules:
% 5.16/5.32 #0: input, references = 6, size of lhs = 3:
% 5.16/5.32 P_head_of-{F}(V0,V2), P_tail_of-{F}(V0,V2), edge-{F}(V0) | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #1: input, references = 7, size of lhs = 3:
% 5.16/5.32 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), edge-{F}(V0) | vertex-{T}(V1)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #2: input, references = 5, size of lhs = 3:
% 5.16/5.32 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), edge-{F}(V0) | vertex-{T}(V2)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #3: input, references = 4, size of lhs = 4:
% 5.16/5.32 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0 | EXISTS V2: pppp9-{T}(V1,V0,V2)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #4: input, references = 8, size of lhs = 1:
% 5.16/5.32 pppp9-{F}(V0,V1,V2) | pppp8-{T}(V2,V0,V1)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #5: input, references = 3, size of lhs = 3:
% 5.16/5.32 pppp8-{F}(V0,V1,V2), pppp1-{F}(V0,V1,V2), pppp0-{F}(V0,V1,V2) | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #6: input, references = 6, size of lhs = 1:
% 5.16/5.32 pppp8-{F}(V0,V1,V2) | pppp0-{T}(V0,V1,V2), pppp1-{T}(V0,V1,V2)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #7: input, references = 4, size of lhs = 1:
% 5.16/5.32 pppp8-{F}(V0,V1,V2) | edge-{T}(V0)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #8: input, references = 5, size of lhs = 4:
% 5.16/5.32 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp1-{F}(V0,V1,V2), V2 == V3 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #9: input, references = 5, size of lhs = 4:
% 5.16/5.32 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp1-{F}(V0,V1,V2), V1 == V4 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #10: input, references = 4, size of lhs = 2:
% 5.16/5.32 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | pppp1-{T}(V0,V4,V3)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #11: input, references = 7, size of lhs = 4:
% 5.16/5.32 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp0-{F}(V0,V1,V2), V1 == V3 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #12: input, references = 9, size of lhs = 4:
% 5.16/5.32 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp0-{F}(V0,V1,V2), V2 == V4 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #13: input, references = 5, size of lhs = 2:
% 5.16/5.32 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | pppp0-{T}(V0,V3,V4)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #14: input, references = 4, size of lhs = 7:
% 5.16/5.32 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)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #15: input, references = 6, size of lhs = 9:
% 5.16/5.32 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)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #16: input, references = 3, size of lhs = 2:
% 5.16/5.32 P_empty-{F}(V0), path-{F}(V1,V2,V3) | vertex-{T}(V1)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #17: input, references = 3, size of lhs = 2:
% 5.16/5.32 P_empty-{F}(V0), path-{F}(V1,V2,V3) | vertex-{T}(V2)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #18: input, references = 3, size of lhs = 2:
% 5.16/5.32 P_empty-{F}(V0), path-{F}(V1,V2,V3) | EXISTS V4: pppp11-{T}(V1,V2,V3,V4)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #19: input, references = 4, size of lhs = 2:
% 5.16/5.32 pppp11-{F}(V0,V1,V2,V3), P_tail_of-{F}(V3,V4) | pppp10-{T}(V3,V0,V1,V2,V4)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #20: input, references = 3, size of lhs = 3:
% 5.16/5.32 pppp10-{F}(V0,V1,V2,V3,V4), pppp3-{F}(V0,V2,V3), pppp2-{F}(V0,V2,V3) | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #21: input, references = 3, size of lhs = 1:
% 5.16/5.32 pppp10-{F}(V0,V1,V2,V3,V4) | pppp2-{T}(V0,V2,V3), pppp3-{T}(V0,V2,V3)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #22: input, references = 4, size of lhs = 2:
% 5.16/5.32 pppp10-{F}(V0,V1,V2,V3,V4), V1 == V4 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #23: input, references = 3, size of lhs = 1:
% 5.16/5.32 pppp10-{F}(V0,V1,V2,V3,V4) | edge-{T}(V0)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #24: input, references = 3, size of lhs = 3:
% 5.16/5.32 P_empty-{F}(V0), P_head_of-{F}(V1,V4), pppp3-{F}(V1,V2,V3) | EXISTS V5: pppp12-{T}(V1,V2,V3,V5,V4)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #25: input, references = 3, size of lhs = 4:
% 5.16/5.32 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)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #26: input, references = 3, size of lhs = 3:
% 5.16/5.32 pppp12-{F}(V0,V1,V2,V3,V4), P_path_cons-{F}(V0,V3,V5), V2 == V5 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #27: input, references = 3, size of lhs = 2:
% 5.16/5.32 pppp12-{F}(V0,V1,V2,V3,V4), P_path_cons-{F}(V0,V3,V5) | path-{T}(V4,V1,V3)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #28: input, references = 3, size of lhs = 5:
% 5.16/5.32 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
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #29: input, references = 3, size of lhs = 5:
% 5.16/5.32 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
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #30: input, references = 3, size of lhs = 3:
% 5.16/5.32 P_empty-{F}(V0), P_head_of-{F}(V1,V4), P_path_cons-{F}(V1,V0,V5) | pppp2-{T}(V1,V4,V5)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #31: input, references = 3, size of lhs = 5:
% 5.16/5.32 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)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #32: input, references = 3, size of lhs = 5:
% 5.16/5.32 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)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #33: input, references = 3, size of lhs = 5:
% 5.16/5.32 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)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #34: input, references = 3, size of lhs = 3:
% 5.16/5.32 P_empty-{F}(V0), path-{F}(V3,V2,V1), in_path-{F}(V4,V1) | vertex-{T}(V4)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #35: input, references = 3, size of lhs = 3:
% 5.16/5.32 P_empty-{F}(V0), path-{F}(V3,V2,V1), in_path-{F}(V4,V1) | EXISTS V5: pppp13-{T}(V5,V1,V4)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #36: input, references = 7, size of lhs = 5:
% 5.16/5.32 pppp13-{F}(V0,V1,V2), P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), V2 == V3, V2 == V4 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #37: input, references = 3, size of lhs = 3:
% 5.16/5.32 pppp13-{F}(V0,V1,V2), P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | on_path-{T}(V0,V1)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #38: input, references = 5, size of lhs = 2:
% 5.16/5.32 P_empty-{F}(V0), sequential-{F}(V1,V2) | pppp4-{T}(V1,V2)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #39: input, references = 6, size of lhs = 2:
% 5.16/5.32 P_empty-{F}(V0), pppp4-{F}(V1,V2) | sequential-{T}(V1,V2)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #40: input, references = 11, size of lhs = 3:
% 5.16/5.32 P_empty-{F}(V0), P_head_of-{F}(V1,V3), P_tail_of-{F}(V2,V4) | pppp14-{T}(V1,V2,V3,V4)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #41: input, references = 6, size of lhs = 4:
% 5.16/5.32 pppp14-{F}(V0,V1,V3,V3), edge-{F}(V0), edge-{F}(V1), V0 == V1 | pppp4-{T}(V0,V1)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #42: input, references = 5, size of lhs = 3:
% 5.16/5.32 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1), V2 == V3 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #43: input, references = 3, size of lhs = 2:
% 5.16/5.32 pppp14-{F}(V1,V1,V2,V3), pppp4-{F}(V1,V1) | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #44: input, references = 5, size of lhs = 2:
% 5.16/5.32 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1) | edge-{T}(V1)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #45: input, references = 5, size of lhs = 2:
% 5.16/5.32 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1) | edge-{T}(V0)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #46: input, references = 4, size of lhs = 5:
% 5.16/5.32 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)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #47: input, references = 3, size of lhs = 6:
% 5.16/5.32 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)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #48: input, references = 4, size of lhs = 3:
% 5.16/5.32 P_empty-{F}(V0), precedes-{F}(V2,V3,V1), path-{F}(V5,V4,V1) | pppp15-{T}(V1,V2,V3)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #49: input, references = 3, size of lhs = 3:
% 5.16/5.32 pppp15-{F}(V0,V1,V2), pppp5-{F}(V0,V1,V2), sequential-{F}(V1,V2) | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #50: input, references = 3, size of lhs = 1:
% 5.16/5.32 pppp15-{F}(V0,V1,V2) | sequential-{T}(V1,V2), pppp5-{T}(V0,V1,V2)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #51: input, references = 4, size of lhs = 1:
% 5.16/5.32 pppp15-{F}(V0,V1,V2) | on_path-{T}(V2,V0)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #52: input, references = 4, size of lhs = 1:
% 5.16/5.32 pppp15-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #53: input, references = 3, size of lhs = 2:
% 5.16/5.32 P_empty-{F}(V0), pppp5-{F}(V1,V2,V3) | EXISTS V4: pppp16-{T}(V1,V2,V3,V4)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #54: input, references = 3, size of lhs = 3:
% 5.16/5.32 P_empty-{F}(V0), sequential-{F}(V2,V4), precedes-{F}(V4,V3,V1) | pppp5-{T}(V1,V2,V3)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #55: input, references = 3, size of lhs = 1:
% 5.16/5.32 pppp16-{F}(V0,V1,V2,V3) | precedes-{T}(V3,V2,V0)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #56: input, references = 3, size of lhs = 1:
% 5.16/5.32 pppp16-{F}(V0,V1,V2,V3) | sequential-{T}(V1,V3)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #57: input, references = 6, size of lhs = 2:
% 5.16/5.32 P_empty-{F}(V0), shortest_path-{F}(V1,V2,V3) | pppp6-{T}(V1,V2,V3)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #58: input, references = 3, size of lhs = 2:
% 5.16/5.32 P_empty-{F}(V0), pppp6-{F}(V1,V2,V3) | shortest_path-{T}(V1,V2,V3)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #59: input, references = 6, size of lhs = 3:
% 5.16/5.32 P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V1,V2,V3) | path-{T}(V1,V2,V3)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #60: input, references = 3, size of lhs = 3:
% 5.16/5.32 P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V2,V2,V3) | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #61: input, references = 3, size of lhs = 5:
% 5.16/5.32 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)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #62: input, references = 3, size of lhs = 4:
% 5.16/5.32 P_empty-{F}(V0), P_length_of-{F}(V3,V4), path-{F}(V1,V2,V3), V1 == V2 | pppp6-{T}(V1,V2,V3), pppp27-{T}(V1,V2,V4)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #63: input, references = 3, size of lhs = 1:
% 5.16/5.32 pppp27-{F}(V0,V1,V2) | EXISTS V3: pppp17-{T}(V0,V1,V3,V2)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #64: input, references = 3, size of lhs = 3:
% 5.16/5.32 pppp17-{F}(V0,V1,V2,V3), P_length_of-{F}(V2,V4), less_or_equal-{F}(V3,V4) | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #65: input, references = 3, size of lhs = 2:
% 5.16/5.32 pppp17-{F}(V0,V1,V2,V3), P_length_of-{F}(V2,V4) | path-{T}(V0,V1,V2)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #66: input, references = 4, size of lhs = 7:
% 5.16/5.32 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
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #67: input, references = 4, size of lhs = 6:
% 5.16/5.32 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
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #68: input, references = 3, size of lhs = 2:
% 5.16/5.32 P_empty-{F}(V0), triangle-{F}(V1,V2,V3) | pppp7-{T}(V1,V2,V3)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #69: input, references = 4, size of lhs = 2:
% 5.16/5.32 P_empty-{F}(V0), pppp7-{F}(V1,V2,V3) | triangle-{T}(V1,V2,V3)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #70: input, references = 3, size of lhs = 2:
% 5.16/5.32 P_empty-{F}(V0), pppp7-{F}(V1,V2,V3) | pppp18-{T}(V1,V2,V3)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #71: input, references = 4, size of lhs = 7:
% 5.16/5.32 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)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #72: input, references = 3, size of lhs = 1:
% 5.16/5.32 pppp18-{F}(V0,V1,V2) | sequential-{T}(V2,V0)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #73: input, references = 3, size of lhs = 1:
% 5.16/5.32 pppp18-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #74: input, references = 3, size of lhs = 1:
% 5.16/5.32 pppp18-{F}(V0,V1,V2) | sequential-{T}(V0,V1)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #75: input, references = 3, size of lhs = 1:
% 5.16/5.32 pppp18-{F}(V0,V1,V2) | edge-{T}(V2)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #76: input, references = 3, size of lhs = 1:
% 5.16/5.32 pppp18-{F}(V0,V1,V2) | edge-{T}(V1)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #77: input, references = 3, size of lhs = 1:
% 5.16/5.32 pppp18-{F}(V0,V1,V2) | edge-{T}(V0)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #78: input, references = 6, size of lhs = 6:
% 5.16/5.32 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
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #79: input, references = 7, size of lhs = 9:
% 5.16/5.32 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
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #80: input, references = 3, size of lhs = 9:
% 5.16/5.32 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)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #81: input, references = 3, size of lhs = 1:
% 5.16/5.32 pppp20-{F}(V0,V1) | EXISTS V2: pppp19-{T}(V0,V2,V1)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #82: input, references = 3, size of lhs = 1:
% 5.16/5.32 pppp20-{F}(V0,V1) | on_path-{T}(V1,V0)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #83: input, references = 3, size of lhs = 2:
% 5.16/5.32 pppp19-{F}(V0,V1,V2), triangle-{F}(V1,V2,V3) | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #84: input, references = 3, size of lhs = 1:
% 5.16/5.32 pppp19-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #85: input, references = 3, size of lhs = 1:
% 5.16/5.32 pppp19-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #86: input, references = 3, size of lhs = 8:
% 5.16/5.32 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)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #87: input, references = 3, size of lhs = 11:
% 5.16/5.32 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-{F}(), shortest_path-{F}(V8,V7,V6), P_head_of-{F}(V9,V11), P_tail_of-{F}(V10,V12), precedes-{F}(V10,V9,V6) | EXISTS V13: pppp21-{T}(V13,V11,V12)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #88: input, references = 3, size of lhs = 4:
% 5.16/5.32 pppp21-{F}(V0,V1,V2), P_tail_of-{F}(V0,V3), P_head_of-{F}(V0,V4), V4 == V2 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #89: input, references = 3, size of lhs = 4:
% 5.16/5.32 pppp21-{F}(V0,V1,V2), P_tail_of-{F}(V0,V3), P_head_of-{F}(V0,V4), V3 == V1 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #90: input, references = 3, size of lhs = 3:
% 5.16/5.32 pppp21-{F}(V0,V1,V2), P_tail_of-{F}(V0,V3), P_head_of-{F}(V0,V4) | edge-{T}(V0)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #91: input, references = 4, size of lhs = 6:
% 5.16/5.32 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}()
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #92: input, references = 4, size of lhs = 6:
% 5.16/5.32 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: pppp26-{T}(V6)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #93: input, references = 5, size of lhs = 1:
% 5.16/5.32 pppp26-{F}(V0) | EXISTS V1: pppp25-{T}(V0,V1)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #94: input, references = 5, size of lhs = 1:
% 5.16/5.32 pppp25-{F}(V0,V1) | EXISTS V2: pppp24-{T}(V2,V0,V1)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #95: input, references = 4, size of lhs = 2:
% 5.16/5.32 pppp25-{F}(V0,V1), triangle-{F}(V0,V1,V2) | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #96: input, references = 5, size of lhs = 1:
% 5.16/5.32 pppp25-{F}(V0,V1) | sequential-{T}(V0,V1)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #97: input, references = 6, size of lhs = 1:
% 5.16/5.32 pppp24-{F}(V0,V1,V2) | EXISTS V3: pppp23-{T}(V0,V3)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #98: input, references = 6, size of lhs = 1:
% 5.16/5.32 pppp24-{F}(V0,V1,V2) | precedes-{T}(V1,V2,V0)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #99: input, references = 6, size of lhs = 1:
% 5.16/5.32 pppp23-{F}(V0,V1) | EXISTS V2: pppp22-{T}(V1,V0,V2)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #100: input, references = 7, size of lhs = 1:
% 5.16/5.32 pppp22-{F}(V0,V1,V2) | shortest_path-{T}(V2,V0,V1)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #101: input, references = 11, size of lhs = 1:
% 5.16/5.32 #-{F} V0 | EXISTS V1: P_head_of-{T}(V0,V1)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #102: input, references = 13, size of lhs = 1:
% 5.16/5.32 #-{F} V0 | EXISTS V1: P_tail_of-{T}(V0,V1)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #103: input, references = 5, size of lhs = 2:
% 5.16/5.32 #-{F} V0, #-{F} V1 | EXISTS V2: P_path_cons-{T}(V0,V1,V2)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #104: input, references = 4, size of lhs = 0:
% 5.16/5.32 FALSE | EXISTS V0: P_empty-{T}(V0)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #105: input, references = 4, size of lhs = 1:
% 5.16/5.32 #-{F} V0 | EXISTS V1: P_length_of-{T}(V0,V1)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #106: input, references = 5, size of lhs = 2:
% 5.16/5.32 #-{F} V0, #-{F} V1 | EXISTS V2: P_number_of_in-{T}(V0,V1,V2)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #107: input, references = 4, size of lhs = 0:
% 5.16/5.32 FALSE | EXISTS V0: P_edges-{T}(V0)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #108: input, references = 4, size of lhs = 0:
% 5.16/5.32 FALSE | EXISTS V0: P_sequential_pairs-{T}(V0)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #109: input, references = 5, size of lhs = 2:
% 5.16/5.32 #-{F} V0, #-{F} V1 | EXISTS V2: P_minus-{T}(V0,V1,V2)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #110: input, references = 4, size of lhs = 0:
% 5.16/5.32 FALSE | EXISTS V0: P_n1-{T}(V0)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #111: input, references = 4, size of lhs = 0:
% 5.16/5.32 FALSE | EXISTS V0: P_triangles-{T}(V0)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #112: input, references = 4, size of lhs = 0:
% 5.16/5.32 FALSE | EXISTS V0: P_graph-{T}(V0)
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 number of initial rules = 113
% 5.16/5.32
% 5.16/5.32 Simplifiers:
% 5.16/5.32 #113: unsound, references = 3, size of lhs = 3:
% 5.16/5.32 P_head_of-{F}(V0,V1), P_head_of-{F}(V0,V3), V1 == V3 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #114: unsound, references = 3, size of lhs = 3:
% 5.16/5.32 P_tail_of-{F}(V0,V1), P_tail_of-{F}(V0,V3), V1 == V3 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #115: unsound, references = 3, size of lhs = 3:
% 5.16/5.32 P_path_cons-{F}(V0,V1,V2), P_path_cons-{F}(V0,V1,V5), V2 == V5 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #116: unsound, references = 3, size of lhs = 3:
% 5.16/5.32 P_empty-{F}(V0), P_empty-{F}(V1), V0 == V1 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #117: unsound, references = 3, size of lhs = 3:
% 5.16/5.32 P_length_of-{F}(V0,V1), P_length_of-{F}(V0,V3), V1 == V3 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #118: unsound, references = 3, size of lhs = 3:
% 5.16/5.32 P_number_of_in-{F}(V0,V1,V2), P_number_of_in-{F}(V0,V1,V5), V2 == V5 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #119: unsound, references = 3, size of lhs = 3:
% 5.16/5.32 P_edges-{F}(V0), P_edges-{F}(V1), V0 == V1 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #120: unsound, references = 3, size of lhs = 3:
% 5.16/5.32 P_sequential_pairs-{F}(V0), P_sequential_pairs-{F}(V1), V0 == V1 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #121: unsound, references = 3, size of lhs = 3:
% 5.16/5.32 P_minus-{F}(V0,V1,V2), P_minus-{F}(V0,V1,V5), V2 == V5 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #122: unsound, references = 3, size of lhs = 3:
% 5.16/5.32 P_n1-{F}(V0), P_n1-{F}(V1), V0 == V1 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #123: unsound, references = 3, size of lhs = 3:
% 5.16/5.32 P_triangles-{F}(V0), P_triangles-{F}(V1), V0 == V1 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #124: unsound, references = 3, size of lhs = 3:
% 5.16/5.32 P_graph-{F}(V0), P_graph-{F}(V1), V0 == V1 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #125: unsound, references = 3, size of lhs = 3:
% 5.16/5.32 pppp8-{F}(V0,V1,V2), pppp8-{F}(V3,V1,V2), V0 == V3 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #126: unsound, references = 3, size of lhs = 3:
% 5.16/5.32 pppp9-{F}(V0,V1,V2), pppp9-{F}(V0,V1,V5), V2 == V5 | FALSE
% 5.16/5.32 (used 0 times, uses = {})
% 5.16/5.32
% 5.16/5.32 #127: unsound, references = 3, size of lhs = 3:
% 5.16/5.32 pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V5,V1,V2,V3,V9), V0 == V5 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #128: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #129: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp11-{F}(V0,V1,V2,V3), pppp11-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #130: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V1,V2,V8,V4), V3 == V8 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #131: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #132: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp13-{F}(V0,V1,V2), pppp13-{F}(V3,V1,V2), V0 == V3 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #133: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp14-{F}(V0,V1,V2,V3), pppp14-{F}(V0,V5,V6,V7), V2 == V6 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #134: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp14-{F}(V0,V1,V2,V3), pppp14-{F}(V4,V1,V6,V7), V3 == V7 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #135: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp16-{F}(V0,V1,V2,V3), pppp16-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #136: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp17-{F}(V0,V1,V2,V3), pppp17-{F}(V0,V1,V6,V3), V2 == V6 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #137: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp19-{F}(V0,V1,V2), pppp19-{F}(V0,V4,V2), V1 == V4 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #138: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp19-{F}(V0,V1,V2), pppp19-{F}(V0,V4,V5), V2 == V5 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #139: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp20-{F}(V0,V1), pppp20-{F}(V0,V3), V1 == V3 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #140: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp21-{F}(V0,V1,V2), pppp21-{F}(V3,V1,V2), V0 == V3 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #141: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp22-{F}(V0,V1,V2), pppp22-{F}(V0,V1,V5), V2 == V5 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #142: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp22-{F}(V0,V1,V2), pppp22-{F}(V3,V1,V5), V0 == V3 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #143: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp23-{F}(V0,V1), pppp23-{F}(V0,V3), V1 == V3 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #144: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp24-{F}(V0,V1,V2), pppp24-{F}(V3,V1,V2), V0 == V3 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #145: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp24-{F}(V0,V1,V2), pppp24-{F}(V3,V1,V5), V2 == V5 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #146: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp24-{F}(V0,V1,V2), pppp24-{F}(V3,V4,V5), V1 == V4 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #147: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp25-{F}(V0,V1), pppp25-{F}(V0,V3), V1 == V3 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #148: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp25-{F}(V0,V1), pppp25-{F}(V2,V3), V0 == V2 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #149: unsound, references = 3, size of lhs = 3:
% 5.16/5.33 pppp26-{F}(V0), pppp26-{F}(V1), V0 == V1 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 number of simplifiers = 37
% 5.16/5.33
% 5.16/5.33 Learnt:
% 5.16/5.33 #154: exists( #102, #152 ), references = 4, size of lhs = 3:
% 5.16/5.33 P_empty-{F}(V0), P_head_of-{F}(V1,V2), pppp4-{F}(V1,V3) | P_tail_of-{T}(V3,V2)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #165: mergings( V5 == V6, V6 == V7, V2 == V3, V3 == V4; #160 ), references = 1, size of lhs = 4:
% 5.16/5.33 pppp26-{F}(V0), P_empty-{F}(V1), P_head_of-{F}(V0,V2), P_tail_of-{F}(V0,V2) | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #177: mergings( V11 == V13, V9 == V10, V10 == V12, V2 == V3, V3 == V4; #171 ), references = 1, size of lhs = 12:
% 5.16/5.33 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp4-{F}(V4,V5), P_tail_of-{F}(V5,V6), P_head_of-{F}(V5,V7), P_path_cons-{F}(V5,V0,V8), P_number_of_in-{F}(V2,V8,V9), P_length_of-{F}(V8,V10), P_minus-{F}(V10,V3,V11), V9 == V11 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #186: exists( #101, #182 ), references = 1, size of lhs = 3:
% 5.16/5.33 P_empty-{F}(V0), pppp4-{F}(V1,V2), P_tail_of-{F}(V2,V3) | P_head_of-{T}(V1,V3)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #187: exists( #101, #180 ), references = 1, size of lhs = 4:
% 5.16/5.33 P_empty-{F}(V0), pppp4-{F}(V1,V2), P_head_of-{F}(V2,V3), pppp1-{F}(V2,V4,V5) | P_head_of-{T}(V1,V4)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #188: exists( #101, #181 ), references = 1, size of lhs = 4:
% 5.16/5.33 P_empty-{F}(V0), pppp4-{F}(V1,V2), P_head_of-{F}(V2,V3), pppp0-{F}(V2,V4,V5) | P_head_of-{T}(V1,V5)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #201: exists( #106, #78 ), references = 1, size of lhs = 4:
% 5.16/5.33 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)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #206: exists( #109, #79 ), references = 1, size of lhs = 7:
% 5.16/5.33 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_number_of_in-{F}(V2,V4,V5), P_length_of-{F}(V4,V6), path-{F}(V7,V8,V4) | P_minus-{T}(V6,V3,V5)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #220: exists( #102, #36 ), references = 3, size of lhs = 3:
% 5.16/5.33 P_head_of-{F}(V0,V1), pppp13-{F}(V0,V2,V3), V3 == V1 | P_tail_of-{T}(V0,V3)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #239: exists( #99, #237 ), references = 3, size of lhs = 7:
% 5.16/5.33 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) | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #241: exists( #97, #238 ), references = 4, size of lhs = 7:
% 5.16/5.33 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), pppp24-{F}(V6,V7,V8) | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #262: exists( #101, #260 ), references = 1, size of lhs = 3:
% 5.16/5.33 pppp13-{F}(V0,V1,V2), pppp13-{F}(V0,V3,V4), V4 == V2 | P_head_of-{T}(V0,V2), P_head_of-{T}(V0,V4)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #280: mergings( V1 == V8; #277 ), references = 2, size of lhs = 12:
% 5.16/5.33 vertex-{F}(V0), vertex-{F}(V1), edge-{F}(V2), P_tail_of-{F}(V2,V1), P_head_of-{F}(V2,V3), path-{F}(V3,V0,V4), P_path_cons-{F}(V2,V4,V5), P_empty-{F}(V6), P_edges-{F}(V7), P_length_of-{F}(V5,V8), P_number_of_in-{F}(V7,V5,V9), V8 == V9 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #282: mergings( V1 == V8; #278 ), references = 1, size of lhs = 15:
% 5.16/5.33 vertex-{F}(V0), vertex-{F}(V1), edge-{F}(V2), P_tail_of-{F}(V2,V1), P_head_of-{F}(V2,V3), path-{F}(V3,V0,V4), P_path_cons-{F}(V2,V4,V5), P_empty-{F}(V6), P_edges-{F}(V7), P_sequential_pairs-{F}(V8), P_n1-{F}(V9), P_number_of_in-{F}(V8,V5,V10), P_length_of-{F}(V5,V11), P_minus-{F}(V11,V9,V12), V10 == V12 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #287: disj( #6, input ), references = 4, size of lhs = 4:
% 5.16/5.33 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), pppp8-{F}(V0,V3,V4), V4 == V1 | pppp0-{T}(V0,V3,V4)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #289: mergings( V2 == V3; #286 ), references = 3, size of lhs = 4:
% 5.16/5.33 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), pppp8-{F}(V0,V3,V1), V3 == V2 | pppp0-{T}(V0,V3,V1)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #318: exists( #101, #315 ), references = 1, size of lhs = 3:
% 5.16/5.33 pppp13-{F}(V0,V1,V2), pppp8-{F}(V0,V3,V4), V4 == V2 | P_head_of-{T}(V0,V2), P_head_of-{T}(V0,V4)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #325: disj( #317, #220+#289+#12 ), references = 1, size of lhs = 7:
% 5.16/5.33 pppp13-{F}(V0,V1,V2), pppp8-{F}(V0,V3,V4), V4 == V2, pppp8-{F}(V0,V5,V4), pppp13-{F}(V0,V6,V7), V5 == V7, V4 == V7 | P_head_of-{T}(V0,V2)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #326: disj( #317, #220+#289+#11 ), references = 1, size of lhs = 8:
% 5.16/5.33 pppp13-{F}(V0,V1,V2), pppp8-{F}(V0,V3,V4), V4 == V2, pppp8-{F}(V0,V5,V4), V5 == V4, pppp13-{F}(V0,V6,V7), V7 == V4, V5 == V7 | P_head_of-{T}(V0,V2)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #346: mergings( V2 == V3; #343 ), references = 2, size of lhs = 4:
% 5.16/5.33 P_head_of-{F}(V0,V1), pppp8-{F}(V0,V2,V3), V3 == V1, V2 == V1 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #349: mergings( V2 == V3, V4 == V3; #344 ), references = 10, size of lhs = 3:
% 5.16/5.33 P_head_of-{F}(V0,V1), pppp8-{F}(V0,V1,V2), V2 == V1 | P_tail_of-{T}(V0,V2)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #357: exists( #101, #346 ), references = 4, size of lhs = 1:
% 5.16/5.33 pppp8-{F}(V0,V1,V2) | P_head_of-{T}(V0,V2), P_head_of-{T}(V0,V1)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #391: disj( #357, #349+#11 ), references = 1, size of lhs = 5:
% 5.16/5.33 pppp8-{F}(V0,V1,V2), pppp8-{F}(V0,V2,V3), V3 == V2, pppp0-{F}(V0,V4,V5), V4 == V2 | P_head_of-{T}(V0,V1)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #393: mergings( V4 == V2; #390 ), references = 1, size of lhs = 5:
% 5.16/5.33 pppp8-{F}(V0,V1,V2), pppp8-{F}(V0,V2,V3), V3 == V2, pppp0-{F}(V0,V2,V4), V4 == V3 | P_head_of-{T}(V0,V1)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #403: disj( #6, #389+#349+#241 ), references = 1, size of lhs = 12:
% 5.16/5.33 P_empty-{F}(V0), P_tail_of-{F}(V1,V2), P_head_of-{F}(V3,V4), V2 == V4, pppp8-{F}(V5,V4,V2), pppp8-{F}(V5,V4,V6), pppp8-{F}(V5,V6,V7), V7 == V6, precedes-{F}(V1,V3,V8), pppp8-{F}(V5,V9,V10), V9 == V6, pppp24-{F}(V8,V11,V12) | pppp1-{T}(V5,V9,V10)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #404: disj( #6, #389+#349+#239 ), references = 1, size of lhs = 12:
% 5.16/5.33 P_empty-{F}(V0), P_tail_of-{F}(V1,V2), P_head_of-{F}(V3,V4), V2 == V4, pppp8-{F}(V5,V4,V2), pppp8-{F}(V5,V4,V6), pppp8-{F}(V5,V6,V7), V7 == V6, precedes-{F}(V1,V3,V8), pppp23-{F}(V8,V9), pppp8-{F}(V5,V10,V11), V10 == V6 | pppp1-{T}(V5,V10,V11)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #414: disj( #357, #349+#8 ), references = 1, size of lhs = 5:
% 5.16/5.33 pppp8-{F}(V0,V1,V2), pppp8-{F}(V0,V2,V3), V3 == V2, pppp1-{F}(V0,V4,V5), V5 == V2 | P_head_of-{T}(V0,V1)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #439: disj( #357, #349+#241 ), references = 5, size of lhs = 8:
% 5.16/5.33 P_empty-{F}(V0), P_tail_of-{F}(V1,V2), P_head_of-{F}(V3,V4), V2 == V4, pppp8-{F}(V5,V4,V2), pppp8-{F}(V5,V4,V6), precedes-{F}(V1,V3,V7), pppp24-{F}(V7,V8,V9) | P_head_of-{T}(V5,V6)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #440: disj( #357, #349+#239 ), references = 1, size of lhs = 8:
% 5.16/5.33 P_empty-{F}(V0), P_tail_of-{F}(V1,V2), P_head_of-{F}(V3,V4), V2 == V4, pppp8-{F}(V5,V4,V2), pppp8-{F}(V5,V4,V6), precedes-{F}(V1,V3,V7), pppp23-{F}(V7,V8) | P_head_of-{T}(V5,V6)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #460: exists( #102, #11 ), references = 3, size of lhs = 3:
% 5.16/5.33 P_head_of-{F}(V0,V1), pppp0-{F}(V0,V2,V3), V2 == V1 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #462: mergings( V3 == V2; #459 ), references = 1, size of lhs = 2:
% 5.16/5.33 P_head_of-{F}(V0,V1), pppp0-{F}(V0,V1,V2) | P_tail_of-{T}(V0,V2)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #465: mergings( V2 == V3; #463 ), references = 1, size of lhs = 3:
% 5.16/5.33 P_head_of-{F}(V0,V1), pppp8-{F}(V0,V2,V1), V2 == V1 | pppp1-{T}(V0,V2,V1)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #486: exists( #102, #9 ), references = 1, size of lhs = 2:
% 5.16/5.33 P_head_of-{F}(V0,V1), pppp1-{F}(V0,V2,V3) | P_tail_of-{T}(V0,V2)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #507: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V11; #500 ), references = 1, size of lhs = 15:
% 5.16/5.33 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V0 == V1, edge-{F}(V2), P_tail_of-{F}(V2,V0), edge-{F}(V3), sequential-{F}(V2,V3), pppp25-{F}(V2,V3), P_head_of-{F}(V3,V1), P_empty-{F}(V4), P_head_of-{F}(V5,V1), P_tail_of-{F}(V6,V0), precedes-{F}(V6,V5,V7), pppp24-{F}(V7,V8,V9) | pppp9-{T}(V1,V0,V2), pppp9-{T}(V1,V0,V3)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #527: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V10, V10 == V16, V14 == V20, V15 == V21, V13 == V19; #516 ), references = 1, size of lhs = 20:
% 5.16/5.33 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V0 == V1, edge-{F}(V2), P_tail_of-{F}(V2,V0), edge-{F}(V3), sequential-{F}(V2,V3), pppp25-{F}(V2,V3), P_head_of-{F}(V3,V1), P_head_of-{F}(V4,V1), P_tail_of-{F}(V5,V0), precedes-{F}(V5,V4,V6), P_empty-{F}(V7), P_tail_of-{F}(V8,V0), P_head_of-{F}(V9,V1), precedes-{F}(V8,V9,V6), pppp24-{F}(V6,V10,V11), pppp0-{F}(V2,V12,V13), V12 == V0 | pppp9-{T}(V1,V0,V3)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #561: mergings( V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V11, V11 == V14, V14 == V17, V20 == V22, V21 == V23, V13 == V16, V22 == V26, V23 == V27, V16 == V19; #544 ), references = 2, size of lhs = 18:
% 5.16/5.33 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_tail_of-{F}(V1,V0), sequential-{F}(V1,V2), pppp25-{F}(V1,V2), edge-{F}(V2), P_tail_of-{F}(V2,V3), P_tail_of-{F}(V4,V0), precedes-{F}(V4,V2,V5), P_tail_of-{F}(V6,V0), precedes-{F}(V6,V2,V5), P_empty-{F}(V7), P_tail_of-{F}(V8,V0), precedes-{F}(V8,V2,V5), pppp0-{F}(V1,V9,V10), V9 == V0, pppp24-{F}(V5,V11,V12) | P_head_of-{T}(V2,V0)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #577: mergings( V2 == V11, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V12, V12 == V15, V15 == V18, V21 == V23, V22 == V24, V14 == V17, V23 == V27, V24 == V28, V17 == V20; #545 ), references = 1, size of lhs = 18:
% 5.16/5.33 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_tail_of-{F}(V1,V0), edge-{F}(V2), sequential-{F}(V1,V2), pppp25-{F}(V1,V2), P_tail_of-{F}(V2,V3), P_tail_of-{F}(V4,V0), precedes-{F}(V4,V2,V5), P_tail_of-{F}(V6,V0), precedes-{F}(V6,V2,V5), P_empty-{F}(V7), P_tail_of-{F}(V8,V0), precedes-{F}(V8,V2,V5), pppp0-{F}(V1,V9,V10), V9 == V0, pppp24-{F}(V5,V11,V12) | P_head_of-{T}(V2,V0)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #593: mergings( V2 == V11, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V12, V12 == V15, V15 == V18, V21 == V23, V22 == V24, V14 == V17, V23 == V27, V24 == V28, V17 == V20; #546 ), references = 1, size of lhs = 18:
% 5.16/5.33 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_tail_of-{F}(V1,V0), edge-{F}(V2), sequential-{F}(V1,V2), pppp25-{F}(V1,V2), P_tail_of-{F}(V2,V3), P_tail_of-{F}(V4,V0), precedes-{F}(V4,V2,V5), P_tail_of-{F}(V6,V0), precedes-{F}(V6,V2,V5), P_empty-{F}(V7), P_tail_of-{F}(V8,V0), precedes-{F}(V8,V2,V5), pppp0-{F}(V1,V9,V10), V9 == V0, pppp24-{F}(V5,V11,V12) | P_head_of-{T}(V2,V0)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #609: mergings( V1 == V11; #607 ), references = 1, size of lhs = 17:
% 5.16/5.33 vertex-{F}(V0), edge-{F}(V1), P_tail_of-{F}(V1,V0), P_head_of-{F}(V1,V2), vertex-{F}(V3), path-{F}(V2,V3,V4), P_path_cons-{F}(V1,V4,V5), vertex-{F}(V6), edge-{F}(V7), P_tail_of-{F}(V7,V6), P_head_of-{F}(V7,V0), P_path_cons-{F}(V7,V5,V8), P_empty-{F}(V9), P_edges-{F}(V10), P_length_of-{F}(V8,V11), P_number_of_in-{F}(V10,V8,V12), V11 == V12 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #620: exists( #102, #618 ), references = 1, size of lhs = 1:
% 5.16/5.33 pppp11-{F}(V0,V1,V2,V3) | P_tail_of-{T}(V3,V0)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #645: mergings( V3 == V4, V4 == V5, V7 == V8; #640 ), references = 2, size of lhs = 6:
% 5.16/5.33 P_empty-{F}(V0), P_edges-{F}(V1), pppp23-{F}(V2,V3), P_length_of-{F}(V2,V4), P_number_of_in-{F}(V1,V2,V5), V4 == V5 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #649: mergings( V3 == V4, V4 == V5, V9 == V11; #641 ), references = 2, size of lhs = 9:
% 5.16/5.33 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp23-{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
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #655: mergings( V4 == V5, V5 == V6, V8 == V9; #650 ), references = 2, size of lhs = 6:
% 5.16/5.33 P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), P_number_of_in-{F}(V1,V2,V4), V3 == V4, pppp24-{F}(V2,V5,V6) | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #659: mergings( V4 == V5, V5 == V6, V10 == V12; #651 ), references = 3, size of lhs = 9:
% 5.16/5.33 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, pppp24-{F}(V4,V8,V9) | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #671: exists( #106, #655 ), references = 1, size of lhs = 4:
% 5.16/5.33 P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), pppp24-{F}(V2,V4,V5) | P_number_of_in-{T}(V1,V2,V3)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #672: exists( #106, #659 ), references = 1, size of lhs = 7:
% 5.16/5.33 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), pppp24-{F}(V4,V7,V8) | P_number_of_in-{T}(V2,V4,V6)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #673: exists( #106, #645 ), references = 1, size of lhs = 4:
% 5.16/5.33 P_empty-{F}(V0), P_edges-{F}(V1), pppp23-{F}(V2,V3), P_length_of-{F}(V2,V4) | P_number_of_in-{T}(V1,V2,V4)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #702: exists( #109, #659 ), references = 1, size of lhs = 7:
% 5.16/5.33 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), pppp24-{F}(V4,V7,V8) | P_minus-{T}(V6,V3,V5)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #703: exists( #109, #649 ), references = 1, size of lhs = 7:
% 5.16/5.33 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp23-{F}(V4,V5), P_number_of_in-{F}(V2,V4,V6), P_length_of-{F}(V4,V7) | P_minus-{T}(V7,V3,V6)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #722: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7; #717 ), references = 1, size of lhs = 7:
% 5.16/5.33 P_empty-{F}(V0), sequential-{F}(V1,V2), precedes-{F}(V2,V1,V3), pppp23-{F}(V3,V4), P_length_of-{F}(V3,V5), P_tail_of-{F}(V2,V6), P_head_of-{F}(V1,V7) | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #728: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6; #723 ), references = 1, size of lhs = 6:
% 5.16/5.33 P_empty-{F}(V0), sequential-{F}(V1,V2), precedes-{F}(V2,V1,V3), pppp23-{F}(V3,V4), P_tail_of-{F}(V2,V5), P_head_of-{F}(V1,V6) | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #734: mergings( V4 == V5, V5 == V6, V6 == V7, V7 == V8; #729 ), references = 2, size of lhs = 6:
% 5.16/5.33 P_empty-{F}(V0), sequential-{F}(V1,V2), precedes-{F}(V2,V1,V3), P_tail_of-{F}(V2,V4), P_head_of-{F}(V1,V5), pppp24-{F}(V3,V6,V7) | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #750: mergings( V3 == V14, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V4 == V0; #740 ), references = 1, size of lhs = 12:
% 5.16/5.33 complete-{F}(), vertex-{F}(V0), edge-{F}(V1), P_tail_of-{F}(V1,V2), edge-{F}(V3), V1 == V3, sequential-{F}(V3,V1), pppp25-{F}(V3,V1), P_tail_of-{F}(V3,V0), P_empty-{F}(V4), pppp0-{F}(V3,V5,V6), V5 == V0 | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #762: mergings( V2 == V3, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13; #753 ), references = 1, size of lhs = 9:
% 5.16/5.33 complete-{F}(), edge-{F}(V0), P_tail_of-{F}(V0,V1), edge-{F}(V2), V0 == V2, sequential-{F}(V2,V0), pppp25-{F}(V2,V0), P_head_of-{F}(V2,V3), P_empty-{F}(V4) | P_tail_of-{T}(V2,V3)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #784: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11; #773 ), references = 1, size of lhs = 6:
% 5.16/5.33 complete-{F}(), P_empty-{F}(V0), sequential-{F}(V1,V2), V2 == V1, pppp25-{F}(V1,V2), pppp4-{F}(V1,V2) | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #801: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12; #789 ), references = 1, size of lhs = 3:
% 5.16/5.33 complete-{F}(), pppp26-{F}(V0), P_empty-{F}(V1) | pppp25-{T}(V0,V0)
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #804: exists( #102, #734 ), references = 1, size of lhs = 5:
% 5.16/5.33 P_empty-{F}(V0), sequential-{F}(V1,V2), precedes-{F}(V2,V1,V3), P_head_of-{F}(V1,V4), pppp24-{F}(V3,V5,V6) | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #805: exists( #102, #241 ), references = 1, size of lhs = 5:
% 5.16/5.33 P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_head_of-{F}(V3,V2), precedes-{F}(V1,V3,V4), pppp24-{F}(V4,V5,V6) | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #808: exists( #101, #803 ), references = 1, size of lhs = 3:
% 5.16/5.33 P_empty-{F}(V0), precedes-{F}(V1,V1,V2), pppp24-{F}(V2,V3,V4) | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #809: exists( #101, #802 ), references = 1, size of lhs = 4:
% 5.16/5.33 P_empty-{F}(V0), sequential-{F}(V1,V2), precedes-{F}(V2,V1,V3), pppp24-{F}(V3,V4,V5) | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #814: exists( #94, #810 ), references = 1, size of lhs = 2:
% 5.16/5.33 pppp25-{F}(V0,V0), P_empty-{F}(V1) | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #815: exists( #94, #811 ), references = 1, size of lhs = 3:
% 5.16/5.33 P_empty-{F}(V0), pppp25-{F}(V1,V2), sequential-{F}(V2,V1) | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #833: mergings( V0 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18; #819 ), references = 1, size of lhs = 7:
% 5.16/5.33 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
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #855: mergings( V1 == V6, V6 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V20, V20 == V21, V21 == V22, V2 == V7, V3 == V8, V4 == V9, V5 == V10; #836 ), references = 1, size of lhs = 5:
% 5.16/5.33 P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_empty-{F}(V4) | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #874: mergings( V1 == V5, V5 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V18 == V19, V19 == V20, V2 == V6, V3 == V7, V4 == V8; #856 ), references = 1, size of lhs = 4:
% 5.16/5.33 P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_empty-{F}(V3) | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #892: mergings( V1 == V4, V4 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V16 == V17, V17 == V18, V2 == V5, V3 == V6; #875 ), references = 1, size of lhs = 3:
% 5.16/5.33 P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_empty-{F}(V2) | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #909: mergings( V1 == V3, V3 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14, V14 == V15, V15 == V16, V2 == V4; #893 ), references = 1, size of lhs = 2:
% 5.16/5.33 P_edges-{F}(V0), P_empty-{F}(V1) | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #925: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12, V12 == V13, V13 == V14; #910 ), references = 1, size of lhs = 1:
% 5.16/5.33 P_empty-{F}(V0) | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 #928: exists( #104, #910 ), references = 1, size of lhs = 0:
% 5.16/5.33 FALSE | FALSE
% 5.16/5.33 (used 0 times, uses = {})
% 5.16/5.33
% 5.16/5.33 number of learnt formulas = 69
% 5.16/5.33
% 5.16/5.33
% 5.16/5.33 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.16/5.33
% 5.16/5.33 randbase = 1
%------------------------------------------------------------------------------