TSTP Solution File: GRA005+1 by Geo-III---2018C
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : GRA005+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n010.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 1.49s 1.65s
% Output : Refutation 1.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRA005+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.03/0.13 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jul 22 07:43:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.49/1.65 GeoParameters:
% 1.49/1.65
% 1.49/1.65 tptp_input = 1
% 1.49/1.65 tptp_output = 0
% 1.49/1.65 nonempty = 1
% 1.49/1.65 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.49/1.65 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 1.49/1.65
% 1.49/1.65
% 1.49/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.49/1.65 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.49/1.65
% 1.49/1.65 RuleSystem INPUT:
% 1.49/1.65
% 1.49/1.65 Initial Rules:
% 1.49/1.65 #0: input, references = 4, size of lhs = 3:
% 1.49/1.65 P_head_of-{F}(V0,V2), P_tail_of-{F}(V0,V2), edge-{F}(V0) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #1: input, references = 5, size of lhs = 3:
% 1.49/1.65 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), edge-{F}(V0) | vertex-{T}(V1)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #2: input, references = 7, size of lhs = 3:
% 1.49/1.65 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), edge-{F}(V0) | vertex-{T}(V2)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #3: input, references = 3, size of lhs = 4:
% 1.49/1.65 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0 | EXISTS V2: pppp9-{T}(V1,V0,V2)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #4: input, references = 3, size of lhs = 1:
% 1.49/1.65 pppp9-{F}(V0,V1,V2) | pppp8-{T}(V2,V0,V1)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #5: input, references = 3, size of lhs = 3:
% 1.49/1.65 pppp8-{F}(V0,V1,V2), pppp1-{F}(V0,V1,V2), pppp0-{F}(V0,V1,V2) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #6: input, references = 3, size of lhs = 1:
% 1.49/1.65 pppp8-{F}(V0,V1,V2) | pppp0-{T}(V0,V1,V2), pppp1-{T}(V0,V1,V2)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #7: input, references = 3, size of lhs = 1:
% 1.49/1.65 pppp8-{F}(V0,V1,V2) | edge-{T}(V0)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #8: input, references = 3, size of lhs = 4:
% 1.49/1.65 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp1-{F}(V0,V1,V2), V2 == V3 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #9: input, references = 3, size of lhs = 4:
% 1.49/1.65 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp1-{F}(V0,V1,V2), V1 == V4 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #10: input, references = 3, size of lhs = 2:
% 1.49/1.65 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | pppp1-{T}(V0,V4,V3)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #11: input, references = 3, size of lhs = 4:
% 1.49/1.65 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp0-{F}(V0,V1,V2), V1 == V3 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #12: input, references = 3, size of lhs = 4:
% 1.49/1.65 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp0-{F}(V0,V1,V2), V2 == V4 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #13: input, references = 3, size of lhs = 2:
% 1.49/1.65 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | pppp0-{T}(V0,V3,V4)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #14: input, references = 5, size of lhs = 7:
% 1.49/1.65 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)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #15: input, references = 7, size of lhs = 9:
% 1.49/1.65 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)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #16: input, references = 3, size of lhs = 2:
% 1.49/1.65 P_empty-{F}(V0), path-{F}(V1,V2,V3) | vertex-{T}(V1)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #17: input, references = 3, size of lhs = 2:
% 1.49/1.65 P_empty-{F}(V0), path-{F}(V1,V2,V3) | vertex-{T}(V2)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #18: input, references = 3, size of lhs = 2:
% 1.49/1.65 P_empty-{F}(V0), path-{F}(V1,V2,V3) | EXISTS V4: pppp11-{T}(V1,V2,V3,V4)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #19: input, references = 3, size of lhs = 2:
% 1.49/1.65 pppp11-{F}(V0,V1,V2,V3), P_tail_of-{F}(V3,V4) | pppp10-{T}(V3,V0,V1,V2,V4)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #20: input, references = 3, size of lhs = 3:
% 1.49/1.65 pppp10-{F}(V0,V1,V2,V3,V4), pppp3-{F}(V0,V2,V3), pppp2-{F}(V0,V2,V3) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #21: input, references = 3, size of lhs = 1:
% 1.49/1.65 pppp10-{F}(V0,V1,V2,V3,V4) | pppp2-{T}(V0,V2,V3), pppp3-{T}(V0,V2,V3)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #22: input, references = 3, size of lhs = 2:
% 1.49/1.65 pppp10-{F}(V0,V1,V2,V3,V4), V1 == V4 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #23: input, references = 3, size of lhs = 1:
% 1.49/1.65 pppp10-{F}(V0,V1,V2,V3,V4) | edge-{T}(V0)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #24: input, references = 3, size of lhs = 3:
% 1.49/1.65 P_empty-{F}(V0), P_head_of-{F}(V1,V4), pppp3-{F}(V1,V2,V3) | EXISTS V5: pppp12-{T}(V1,V2,V3,V5,V4)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #25: input, references = 3, size of lhs = 4:
% 1.49/1.65 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)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #26: input, references = 3, size of lhs = 3:
% 1.49/1.65 pppp12-{F}(V0,V1,V2,V3,V4), P_path_cons-{F}(V0,V3,V5), V2 == V5 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #27: input, references = 3, size of lhs = 2:
% 1.49/1.65 pppp12-{F}(V0,V1,V2,V3,V4), P_path_cons-{F}(V0,V3,V5) | path-{T}(V4,V1,V3)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #28: input, references = 3, size of lhs = 5:
% 1.49/1.65 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
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #29: input, references = 3, size of lhs = 5:
% 1.49/1.65 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
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #30: input, references = 3, size of lhs = 3:
% 1.49/1.65 P_empty-{F}(V0), P_head_of-{F}(V1,V4), P_path_cons-{F}(V1,V0,V5) | pppp2-{T}(V1,V4,V5)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #31: input, references = 9, size of lhs = 5:
% 1.49/1.65 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)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #32: input, references = 3, size of lhs = 5:
% 1.49/1.65 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)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #33: input, references = 3, size of lhs = 5:
% 1.49/1.65 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)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #34: input, references = 3, size of lhs = 3:
% 1.49/1.65 P_empty-{F}(V0), path-{F}(V3,V2,V1), in_path-{F}(V4,V1) | vertex-{T}(V4)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #35: input, references = 3, size of lhs = 3:
% 1.49/1.65 P_empty-{F}(V0), path-{F}(V3,V2,V1), in_path-{F}(V4,V1) | EXISTS V5: pppp13-{T}(V5,V1,V4)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #36: input, references = 4, size of lhs = 5:
% 1.49/1.65 pppp13-{F}(V0,V1,V2), P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), V2 == V3, V2 == V4 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #37: input, references = 3, size of lhs = 3:
% 1.49/1.65 pppp13-{F}(V0,V1,V2), P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | on_path-{T}(V0,V1)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #38: input, references = 3, size of lhs = 2:
% 1.49/1.65 P_empty-{F}(V0), sequential-{F}(V1,V2) | pppp4-{T}(V1,V2)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #39: input, references = 3, size of lhs = 2:
% 1.49/1.65 P_empty-{F}(V0), pppp4-{F}(V1,V2) | sequential-{T}(V1,V2)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #40: input, references = 3, size of lhs = 3:
% 1.49/1.65 P_empty-{F}(V0), P_head_of-{F}(V1,V3), P_tail_of-{F}(V2,V4) | pppp14-{T}(V1,V2,V3,V4)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #41: input, references = 3, size of lhs = 4:
% 1.49/1.65 pppp14-{F}(V0,V1,V3,V3), edge-{F}(V0), edge-{F}(V1), V0 == V1 | pppp4-{T}(V0,V1)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #42: input, references = 3, size of lhs = 3:
% 1.49/1.65 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1), V2 == V3 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #43: input, references = 3, size of lhs = 2:
% 1.49/1.65 pppp14-{F}(V1,V1,V2,V3), pppp4-{F}(V1,V1) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #44: input, references = 3, size of lhs = 2:
% 1.49/1.65 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1) | edge-{T}(V1)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #45: input, references = 3, size of lhs = 2:
% 1.49/1.65 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1) | edge-{T}(V0)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #46: input, references = 3, size of lhs = 5:
% 1.49/1.65 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)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #47: input, references = 3, size of lhs = 6:
% 1.49/1.65 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)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #48: input, references = 9, size of lhs = 3:
% 1.49/1.65 P_empty-{F}(V0), precedes-{F}(V2,V3,V1), path-{F}(V5,V4,V1) | pppp15-{T}(V1,V2,V3)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #49: input, references = 3, size of lhs = 3:
% 1.49/1.65 pppp15-{F}(V0,V1,V2), pppp5-{F}(V0,V1,V2), sequential-{F}(V1,V2) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #50: input, references = 3, size of lhs = 1:
% 1.49/1.65 pppp15-{F}(V0,V1,V2) | sequential-{T}(V1,V2), pppp5-{T}(V0,V1,V2)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #51: input, references = 8, size of lhs = 1:
% 1.49/1.65 pppp15-{F}(V0,V1,V2) | on_path-{T}(V2,V0)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #52: input, references = 4, size of lhs = 1:
% 1.49/1.65 pppp15-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #53: input, references = 3, size of lhs = 2:
% 1.49/1.65 P_empty-{F}(V0), pppp5-{F}(V1,V2,V3) | EXISTS V4: pppp16-{T}(V1,V2,V3,V4)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #54: input, references = 3, size of lhs = 3:
% 1.49/1.65 P_empty-{F}(V0), sequential-{F}(V2,V4), precedes-{F}(V4,V3,V1) | pppp5-{T}(V1,V2,V3)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #55: input, references = 3, size of lhs = 1:
% 1.49/1.65 pppp16-{F}(V0,V1,V2,V3) | precedes-{T}(V3,V2,V0)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #56: input, references = 3, size of lhs = 1:
% 1.49/1.65 pppp16-{F}(V0,V1,V2,V3) | sequential-{T}(V1,V3)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #57: input, references = 8, size of lhs = 2:
% 1.49/1.65 P_empty-{F}(V0), shortest_path-{F}(V1,V2,V3) | pppp6-{T}(V1,V2,V3)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #58: input, references = 3, size of lhs = 2:
% 1.49/1.65 P_empty-{F}(V0), pppp6-{F}(V1,V2,V3) | shortest_path-{T}(V1,V2,V3)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #59: input, references = 8, size of lhs = 3:
% 1.49/1.65 P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V1,V2,V3) | path-{T}(V1,V2,V3)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #60: input, references = 3, size of lhs = 3:
% 1.49/1.65 P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V2,V2,V3) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #61: input, references = 3, size of lhs = 5:
% 1.49/1.65 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)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #62: input, references = 3, size of lhs = 4:
% 1.49/1.65 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)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #63: input, references = 3, size of lhs = 1:
% 1.49/1.65 pppp27-{F}(V0,V1,V2) | EXISTS V3: pppp17-{T}(V0,V1,V3,V2)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #64: input, references = 3, size of lhs = 3:
% 1.49/1.65 pppp17-{F}(V0,V1,V2,V3), P_length_of-{F}(V2,V4), less_or_equal-{F}(V3,V4) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #65: input, references = 3, size of lhs = 2:
% 1.49/1.65 pppp17-{F}(V0,V1,V2,V3), P_length_of-{F}(V2,V4) | path-{T}(V0,V1,V2)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #66: input, references = 6, size of lhs = 7:
% 1.49/1.65 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
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #67: input, references = 4, size of lhs = 6:
% 1.49/1.65 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
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #68: input, references = 3, size of lhs = 2:
% 1.49/1.65 P_empty-{F}(V0), triangle-{F}(V1,V2,V3) | pppp7-{T}(V1,V2,V3)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #69: input, references = 3, size of lhs = 2:
% 1.49/1.65 P_empty-{F}(V0), pppp7-{F}(V1,V2,V3) | triangle-{T}(V1,V2,V3)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #70: input, references = 3, size of lhs = 2:
% 1.49/1.65 P_empty-{F}(V0), pppp7-{F}(V1,V2,V3) | pppp18-{T}(V1,V2,V3)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #71: input, references = 3, size of lhs = 7:
% 1.49/1.65 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)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #72: input, references = 3, size of lhs = 1:
% 1.49/1.65 pppp18-{F}(V0,V1,V2) | sequential-{T}(V2,V0)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #73: input, references = 3, size of lhs = 1:
% 1.49/1.65 pppp18-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #74: input, references = 3, size of lhs = 1:
% 1.49/1.65 pppp18-{F}(V0,V1,V2) | sequential-{T}(V0,V1)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #75: input, references = 3, size of lhs = 1:
% 1.49/1.65 pppp18-{F}(V0,V1,V2) | edge-{T}(V2)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #76: input, references = 3, size of lhs = 1:
% 1.49/1.65 pppp18-{F}(V0,V1,V2) | edge-{T}(V1)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #77: input, references = 3, size of lhs = 1:
% 1.49/1.65 pppp18-{F}(V0,V1,V2) | edge-{T}(V0)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #78: input, references = 6, size of lhs = 6:
% 1.49/1.65 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
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #79: input, references = 8, size of lhs = 9:
% 1.49/1.65 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
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #80: input, references = 3, size of lhs = 9:
% 1.49/1.65 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)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #81: input, references = 3, size of lhs = 1:
% 1.49/1.65 pppp20-{F}(V0,V1) | EXISTS V2: pppp19-{T}(V0,V2,V1)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #82: input, references = 3, size of lhs = 1:
% 1.49/1.65 pppp20-{F}(V0,V1) | on_path-{T}(V1,V0)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #83: input, references = 3, size of lhs = 2:
% 1.49/1.65 pppp19-{F}(V0,V1,V2), triangle-{F}(V1,V2,V3) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #84: input, references = 3, size of lhs = 1:
% 1.49/1.65 pppp19-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #85: input, references = 3, size of lhs = 1:
% 1.49/1.65 pppp19-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #86: input, references = 3, size of lhs = 8:
% 1.49/1.65 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)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #87: input, references = 4, size of lhs = 6:
% 1.49/1.65 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)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #88: input, references = 4, size of lhs = 1:
% 1.49/1.65 pppp26-{F}(V0) | EXISTS V1: pppp25-{T}(V0,V1)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #89: input, references = 7, size of lhs = 1:
% 1.49/1.65 pppp26-{F}(V0) | EXISTS V1: pppp22-{T}(V0,V1)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #90: input, references = 5, size of lhs = 1:
% 1.49/1.65 pppp25-{F}(V0,V1) | EXISTS V2: pppp24-{T}(V0,V2,V1)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #91: input, references = 4, size of lhs = 3:
% 1.49/1.65 pppp24-{F}(V0,V1,V2), P_tail_of-{F}(V1,V3), P_head_of-{F}(V2,V4) | EXISTS V5: pppp23-{T}(V5,V3,V4)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #92: input, references = 13, size of lhs = 3:
% 1.49/1.65 pppp24-{F}(V0,V1,V2), P_tail_of-{F}(V1,V3), P_head_of-{F}(V2,V4) | precedes-{T}(V1,V2,V0)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #93: input, references = 4, size of lhs = 4:
% 1.49/1.65 pppp23-{F}(V0,V1,V2), P_tail_of-{F}(V0,V3), P_head_of-{F}(V0,V4), V4 == V2 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #94: input, references = 4, size of lhs = 4:
% 1.49/1.65 pppp23-{F}(V0,V1,V2), P_tail_of-{F}(V0,V3), P_head_of-{F}(V0,V4), V3 == V1 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #95: input, references = 3, size of lhs = 3:
% 1.49/1.65 pppp23-{F}(V0,V1,V2), P_tail_of-{F}(V0,V3), P_head_of-{F}(V0,V4) | edge-{T}(V0)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #96: input, references = 9, size of lhs = 1:
% 1.49/1.65 pppp22-{F}(V0,V1) | EXISTS V2: pppp21-{T}(V1,V0,V2)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #97: input, references = 10, size of lhs = 1:
% 1.49/1.65 pppp21-{F}(V0,V1,V2) | shortest_path-{T}(V2,V0,V1)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #98: input, references = 6, size of lhs = 1:
% 1.49/1.65 #-{F} V0 | EXISTS V1: P_head_of-{T}(V0,V1)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #99: input, references = 10, size of lhs = 1:
% 1.49/1.65 #-{F} V0 | EXISTS V1: P_tail_of-{T}(V0,V1)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #100: input, references = 4, size of lhs = 2:
% 1.49/1.65 #-{F} V0, #-{F} V1 | EXISTS V2: P_path_cons-{T}(V0,V1,V2)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #101: input, references = 4, size of lhs = 0:
% 1.49/1.65 FALSE | EXISTS V0: P_empty-{T}(V0)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #102: input, references = 4, size of lhs = 1:
% 1.49/1.65 #-{F} V0 | EXISTS V1: P_length_of-{T}(V0,V1)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #103: input, references = 5, size of lhs = 2:
% 1.49/1.65 #-{F} V0, #-{F} V1 | EXISTS V2: P_number_of_in-{T}(V0,V1,V2)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #104: input, references = 4, size of lhs = 0:
% 1.49/1.65 FALSE | EXISTS V0: P_edges-{T}(V0)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #105: input, references = 4, size of lhs = 0:
% 1.49/1.65 FALSE | EXISTS V0: P_sequential_pairs-{T}(V0)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #106: input, references = 5, size of lhs = 2:
% 1.49/1.65 #-{F} V0, #-{F} V1 | EXISTS V2: P_minus-{T}(V0,V1,V2)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #107: input, references = 4, size of lhs = 0:
% 1.49/1.65 FALSE | EXISTS V0: P_n1-{T}(V0)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #108: input, references = 4, size of lhs = 0:
% 1.49/1.65 FALSE | EXISTS V0: P_triangles-{T}(V0)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #109: input, references = 4, size of lhs = 0:
% 1.49/1.65 FALSE | EXISTS V0: P_graph-{T}(V0)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 number of initial rules = 110
% 1.49/1.65
% 1.49/1.65 Simplifiers:
% 1.49/1.65 #110: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp0-{F}(V0,V1,V2), pppp0-{F}(V0,V4,V5), V1 == V4 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #111: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp0-{F}(V0,V1,V2), pppp0-{F}(V0,V4,V5), V2 == V5 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #112: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp1-{F}(V0,V1,V2), pppp1-{F}(V0,V4,V5), V2 == V5 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #113: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp1-{F}(V0,V1,V2), pppp1-{F}(V0,V4,V5), V1 == V4 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #114: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 P_head_of-{F}(V0,V1), P_head_of-{F}(V0,V3), V1 == V3 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #115: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 P_tail_of-{F}(V0,V1), P_tail_of-{F}(V0,V3), V1 == V3 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #116: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 P_path_cons-{F}(V0,V1,V2), P_path_cons-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #117: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 P_empty-{F}(V0), P_empty-{F}(V1), V0 == V1 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #118: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 P_length_of-{F}(V0,V1), P_length_of-{F}(V0,V3), V1 == V3 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #119: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 P_number_of_in-{F}(V0,V1,V2), P_number_of_in-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #120: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 P_edges-{F}(V0), P_edges-{F}(V1), V0 == V1 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #121: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 P_sequential_pairs-{F}(V0), P_sequential_pairs-{F}(V1), V0 == V1 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #122: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 P_minus-{F}(V0,V1,V2), P_minus-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #123: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 P_n1-{F}(V0), P_n1-{F}(V1), V0 == V1 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #124: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 P_triangles-{F}(V0), P_triangles-{F}(V1), V0 == V1 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #125: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 P_graph-{F}(V0), P_graph-{F}(V1), V0 == V1 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #126: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V5,V1,V2,V3,V9), V0 == V5 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #127: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #128: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp11-{F}(V0,V1,V2,V3), pppp11-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #129: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V1,V2,V8,V4), V3 == V8 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #130: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #131: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp13-{F}(V0,V1,V2), pppp13-{F}(V3,V1,V2), V0 == V3 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #132: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp14-{F}(V0,V1,V2,V3), pppp14-{F}(V0,V5,V6,V7), V2 == V6 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #133: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp14-{F}(V0,V1,V2,V3), pppp14-{F}(V4,V1,V6,V7), V3 == V7 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #134: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp16-{F}(V0,V1,V2,V3), pppp16-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #135: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp17-{F}(V0,V1,V2,V3), pppp17-{F}(V0,V1,V6,V3), V2 == V6 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #136: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp19-{F}(V0,V1,V2), pppp19-{F}(V0,V4,V2), V1 == V4 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #137: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp19-{F}(V0,V1,V2), pppp19-{F}(V0,V4,V5), V2 == V5 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #138: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp20-{F}(V0,V1), pppp20-{F}(V0,V3), V1 == V3 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #139: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp21-{F}(V0,V1,V2), pppp21-{F}(V0,V1,V5), V2 == V5 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #140: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp21-{F}(V0,V1,V2), pppp21-{F}(V3,V1,V5), V0 == V3 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #141: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp21-{F}(V0,V1,V2), pppp21-{F}(V3,V4,V5), V1 == V4 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #142: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp22-{F}(V0,V1), pppp22-{F}(V0,V3), V1 == V3 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #143: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp22-{F}(V0,V1), pppp22-{F}(V2,V3), V0 == V2 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #144: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp23-{F}(V0,V1,V2), pppp23-{F}(V3,V1,V2), V0 == V3 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #145: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp24-{F}(V0,V1,V2), pppp24-{F}(V0,V4,V2), V1 == V4 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #146: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp24-{F}(V0,V1,V2), pppp24-{F}(V0,V4,V5), V2 == V5 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #147: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp24-{F}(V0,V1,V2), pppp24-{F}(V3,V4,V5), V0 == V3 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #148: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp25-{F}(V0,V1), pppp25-{F}(V0,V3), V1 == V3 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #149: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp25-{F}(V0,V1), pppp25-{F}(V2,V3), V0 == V2 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #150: unsound, references = 3, size of lhs = 3:
% 1.49/1.65 pppp26-{F}(V0), pppp26-{F}(V1), V0 == V1 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 number of simplifiers = 41
% 1.49/1.65
% 1.49/1.65 Learnt:
% 1.49/1.65 #155: exists( #96, #151 ), references = 1, size of lhs = 6:
% 1.49/1.65 P_empty-{F}(V0), P_tail_of-{F}(V1,V2), P_head_of-{F}(V3,V4), precedes-{F}(V1,V3,V5), precedes-{F}(V3,V1,V5), pppp22-{F}(V5,V6) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #156: exists( #96, #152 ), references = 3, size of lhs = 7:
% 1.49/1.65 P_empty-{F}(V0), P_tail_of-{F}(V1,V2), P_tail_of-{F}(V3,V2), P_head_of-{F}(V3,V4), P_head_of-{F}(V5,V4), precedes-{F}(V1,V5,V6), pppp22-{F}(V6,V7) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #168: mergings( V3 == V4, V4 == V5, V9 == V11; #164 ), references = 2, size of lhs = 9:
% 1.49/1.65 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp22-{F}(V4,V5), P_number_of_in-{F}(V2,V4,V6), P_length_of-{F}(V4,V7), P_minus-{F}(V7,V3,V8), V6 == V8 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #173: mergings( V2 == V3, V3 == V4, V8 == V10; #169 ), references = 2, size of lhs = 9:
% 1.49/1.65 pppp26-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), P_number_of_in-{F}(V3,V0,V5), P_length_of-{F}(V0,V6), P_minus-{F}(V6,V4,V7), V5 == V7 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #178: mergings( V3 == V4, V4 == V5, V8 == V9; #174 ), references = 1, size of lhs = 7:
% 1.49/1.65 pppp26-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), P_length_of-{F}(V0,V5), P_minus-{F}(V5,V4,V6) | P_number_of_in-{T}(V3,V0,V6)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #189: mergings( V3 == V4, V4 == V5, V7 == V8; #185 ), references = 2, size of lhs = 6:
% 1.49/1.65 P_empty-{F}(V0), P_edges-{F}(V1), pppp22-{F}(V2,V3), P_length_of-{F}(V2,V4), P_number_of_in-{F}(V1,V2,V5), V4 == V5 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #194: mergings( V2 == V3, V3 == V4, V6 == V7; #190 ), references = 2, size of lhs = 6:
% 1.49/1.65 pppp26-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_length_of-{F}(V0,V3), P_number_of_in-{F}(V2,V0,V4), V3 == V4 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #200: exists( #103, #194 ), references = 1, size of lhs = 4:
% 1.49/1.65 pppp26-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_length_of-{F}(V0,V3) | P_number_of_in-{T}(V2,V0,V3)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #201: exists( #103, #189 ), references = 1, size of lhs = 4:
% 1.49/1.65 P_empty-{F}(V0), P_edges-{F}(V1), pppp22-{F}(V2,V3), P_length_of-{F}(V2,V4) | P_number_of_in-{T}(V1,V2,V4)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #204: exists( #106, #173 ), references = 1, size of lhs = 7:
% 1.49/1.65 pppp26-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), P_number_of_in-{F}(V3,V0,V5), P_length_of-{F}(V0,V6) | P_minus-{T}(V6,V4,V5)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #205: exists( #106, #168 ), references = 1, size of lhs = 7:
% 1.49/1.65 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp22-{F}(V4,V5), P_number_of_in-{F}(V2,V4,V6), P_length_of-{F}(V4,V7) | P_minus-{T}(V7,V3,V6)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #212: mergings( V3 == V6; #209 ), references = 1, size of lhs = 5:
% 1.49/1.65 P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_head_of-{F}(V3,V2), pppp24-{F}(V4,V1,V3), pppp22-{F}(V4,V5) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #214: mergings( V3 == V5; #210 ), references = 1, size of lhs = 5:
% 1.49/1.65 P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_head_of-{F}(V3,V2), pppp24-{F}(V4,V1,V3), shortest_path-{F}(V5,V6,V4) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #229: mergings( V11 == V12, V12 == V15, V5 == V13, V13 == V14, V2 == V3, V3 == V4, V4 == V6; #221 ), references = 2, size of lhs = 15:
% 1.49/1.65 vertex-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), P_tail_of-{F}(V5,V0), P_head_of-{F}(V5,V6), P_path_cons-{F}(V5,V1,V7), P_number_of_in-{F}(V3,V7,V8), P_length_of-{F}(V7,V9), P_minus-{F}(V9,V4,V10), V8 == V10, pppp24-{F}(V11,V12,V5), path-{F}(V13,V14,V11), path-{F}(V15,V16,V11) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #251: mergings( V9 == V10, V10 == V12, V11 == V13, V2 == V3, V3 == V4, V20 == V25, V8 == V14, V12 == V15, V0 == V26; #241 ), references = 1, size of lhs = 16:
% 1.49/1.65 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, pppp24-{F}(V11,V12,V4), path-{F}(V13,V14,V11), path-{F}(V15,V16,V11), path-{F}(V17,V18,V11), path-{F}(V19,V20,V11) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #266: mergings( V14 == V15, V15 == V17, V16 == V18, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V13 == V19, V17 == V20, V12 == V25; #255 ), references = 1, size of lhs = 14:
% 1.49/1.65 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp22-{F}(V4,V5), P_length_of-{F}(V4,V6), pppp24-{F}(V4,V7,V8), P_tail_of-{F}(V8,V9), P_head_of-{F}(V8,V10), P_path_cons-{F}(V8,V0,V11), P_number_of_in-{F}(V2,V11,V12), P_length_of-{F}(V11,V13), P_minus-{F}(V13,V3,V14), V12 == V14 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #276: mergings( V13 == V14, V14 == V16, V16 == V18, V15 == V17, V3 == V4, V4 == V5, V5 == V6, V6 == V7; #267 ), references = 2, size of lhs = 14:
% 1.49/1.65 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp25-{F}(V4,V5), pppp22-{F}(V4,V6), P_length_of-{F}(V4,V7), P_tail_of-{F}(V5,V8), P_head_of-{F}(V5,V9), P_path_cons-{F}(V5,V0,V10), P_number_of_in-{F}(V2,V10,V11), P_length_of-{F}(V10,V12), P_minus-{F}(V12,V3,V13), V11 == V13 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #286: mergings( V12 == V13, V13 == V15, V15 == V17, V14 == V16, V2 == V3, V3 == V4, V4 == V5, V5 == V6; #277 ), references = 2, size of lhs = 13:
% 1.49/1.65 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp25-{F}(V4,V5), pppp22-{F}(V4,V6), P_tail_of-{F}(V5,V7), P_head_of-{F}(V5,V8), P_path_cons-{F}(V5,V0,V9), P_number_of_in-{F}(V2,V9,V10), P_length_of-{F}(V9,V11), P_minus-{F}(V11,V3,V12), V10 == V12 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #296: mergings( V11 == V12, V12 == V14, V14 == V16, V13 == V15, V2 == V3, V3 == V4, V4 == V5, V5 == V6; #287 ), references = 2, size of lhs = 13:
% 1.49/1.65 pppp26-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), pppp25-{F}(V0,V5), P_tail_of-{F}(V5,V6), P_head_of-{F}(V5,V7), P_path_cons-{F}(V5,V1,V8), P_number_of_in-{F}(V3,V8,V9), P_length_of-{F}(V8,V10), P_minus-{F}(V10,V4,V11), V9 == V11 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #311: mergings( V8 == V10, V9 == V10, V3 == V4, V4 == V5, V5 == V6; #305 ), references = 2, size of lhs = 6:
% 1.49/1.65 P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_tail_of-{F}(V1,V2), precedes-{F}(V3,V1,V4), pppp22-{F}(V4,V5), P_length_of-{F}(V4,V6) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #342: mergings( V13 == V16, V16 == V18, V14 == V15, V15 == V17, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8; #332 ), references = 1, size of lhs = 14:
% 1.49/1.65 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_tail_of-{F}(V4,V5), P_head_of-{F}(V4,V6), P_path_cons-{F}(V4,V0,V7), P_number_of_in-{F}(V2,V7,V8), P_length_of-{F}(V7,V9), P_minus-{F}(V9,V3,V10), V8 == V10, precedes-{F}(V4,V11,V12), pppp22-{F}(V12,V13), P_length_of-{F}(V12,V14) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #355: mergings( V13 == V16, V16 == V18, V12 == V14, V14 == V15, V15 == V17, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7; #344 ), references = 1, size of lhs = 14:
% 1.49/1.65 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, pppp24-{F}(V11,V4,V12), pppp22-{F}(V11,V13), P_length_of-{F}(V11,V14) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #359: mergings( V5 == V6; #357 ), references = 1, size of lhs = 6:
% 1.49/1.65 P_empty-{F}(V0), pppp22-{F}(V1,V2), P_length_of-{F}(V1,V3), pppp24-{F}(V1,V4,V5), P_head_of-{F}(V5,V6), P_tail_of-{F}(V5,V6) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #363: exists( #106, #296 ), references = 1, size of lhs = 11:
% 1.49/1.65 pppp26-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), pppp25-{F}(V0,V5), P_tail_of-{F}(V5,V6), P_head_of-{F}(V5,V7), P_path_cons-{F}(V5,V1,V8), P_number_of_in-{F}(V3,V8,V9), P_length_of-{F}(V8,V10) | P_minus-{T}(V10,V4,V9)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #364: exists( #106, #286 ), references = 1, size of lhs = 11:
% 1.49/1.65 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp25-{F}(V4,V5), pppp22-{F}(V4,V6), P_tail_of-{F}(V5,V7), P_head_of-{F}(V5,V8), P_path_cons-{F}(V5,V0,V9), P_number_of_in-{F}(V2,V9,V10), P_length_of-{F}(V9,V11) | P_minus-{T}(V11,V3,V10)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #365: exists( #106, #276 ), references = 1, size of lhs = 12:
% 1.49/1.65 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp25-{F}(V4,V5), pppp22-{F}(V4,V6), P_length_of-{F}(V4,V7), P_tail_of-{F}(V5,V8), P_head_of-{F}(V5,V9), P_path_cons-{F}(V5,V0,V10), P_number_of_in-{F}(V2,V10,V11), P_length_of-{F}(V10,V12) | P_minus-{T}(V12,V3,V11)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #387: mergings( V9 == V10, V10 == V12, V12 == V14, V11 == V13, V2 == V3, V3 == V4, V4 == V6; #378 ), references = 1, size of lhs = 14:
% 1.49/1.65 vertex-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_tail_of-{F}(V3,V4), P_head_of-{F}(V3,V5), P_path_cons-{F}(V3,V1,V6), path-{F}(V5,V0,V7), P_path_cons-{F}(V3,V7,V8), P_length_of-{F}(V8,V9), P_number_of_in-{F}(V2,V8,V10), V9 == V10, pppp24-{F}(V11,V12,V3), path-{F}(V13,V14,V11), path-{F}(V15,V16,V11) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #395: mergings( V11 == V12, V12 == V14, V14 == V16, V13 == V15, V2 == V3, V3 == V4, V4 == V6; #379 ), references = 1, size of lhs = 17:
% 1.49/1.65 vertex-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), P_tail_of-{F}(V5,V6), P_head_of-{F}(V5,V7), P_path_cons-{F}(V5,V1,V8), path-{F}(V7,V0,V9), P_path_cons-{F}(V5,V9,V10), P_number_of_in-{F}(V3,V10,V11), P_length_of-{F}(V10,V12), P_minus-{F}(V12,V4,V13), V11 == V13, pppp24-{F}(V14,V15,V5), path-{F}(V16,V17,V14), path-{F}(V18,V19,V14) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #409: mergings( V1 == V8; #406 ), references = 1, size of lhs = 12:
% 1.49/1.65 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
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #411: mergings( V1 == V8; #407 ), references = 1, size of lhs = 15:
% 1.49/1.65 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
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #428: exists( #99, #93 ), references = 1, size of lhs = 3:
% 1.49/1.65 P_head_of-{F}(V0,V1), pppp23-{F}(V0,V2,V3), V1 == V3 | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #430: mergings( V4 == V3; #426 ), references = 3, size of lhs = 2:
% 1.49/1.65 P_head_of-{F}(V0,V1), pppp23-{F}(V0,V2,V1) | P_tail_of-{T}(V0,V2)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #431: exists( #99, #36 ), references = 1, size of lhs = 3:
% 1.49/1.65 P_head_of-{F}(V0,V1), pppp13-{F}(V0,V2,V3), V3 == V1 | P_tail_of-{T}(V0,V3)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #433: exists( #98, #425 ), references = 1, size of lhs = 1:
% 1.49/1.65 pppp23-{F}(V0,V1,V2) | P_head_of-{T}(V0,V2)
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #440: exists( #91, #436 ), references = 1, size of lhs = 8:
% 1.49/1.65 P_empty-{F}(V0), P_tail_of-{F}(V1,V2), P_tail_of-{F}(V3,V2), pppp24-{F}(V4,V1,V5), P_head_of-{F}(V5,V6), P_head_of-{F}(V7,V6), precedes-{F}(V3,V7,V8), pppp22-{F}(V8,V9) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #441: exists( #91, #437 ), references = 1, size of lhs = 8:
% 1.49/1.65 P_empty-{F}(V0), P_tail_of-{F}(V1,V2), P_tail_of-{F}(V3,V2), pppp24-{F}(V4,V1,V5), P_head_of-{F}(V5,V6), P_head_of-{F}(V7,V6), precedes-{F}(V3,V7,V8), shortest_path-{F}(V9,V10,V8) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #449: mergings( V5 == V6, V3 == V9, V4 == V8; #444 ), references = 1, size of lhs = 4:
% 1.49/1.65 P_empty-{F}(V0), pppp22-{F}(V1,V2), pppp24-{F}(V1,V3,V4), P_head_of-{F}(V4,V5) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #453: mergings( V5 == V7, V3 == V8, V4 == V6; #445 ), references = 1, size of lhs = 4:
% 1.49/1.65 P_empty-{F}(V0), P_head_of-{F}(V1,V2), pppp24-{F}(V3,V4,V1), shortest_path-{F}(V5,V6,V3) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #456: mergings( V3 == V6; #454 ), references = 1, size of lhs = 3:
% 1.49/1.65 P_empty-{F}(V0), pppp22-{F}(V1,V2), pppp24-{F}(V1,V3,V4) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #458: exists( #90, #454 ), references = 1, size of lhs = 3:
% 1.49/1.65 P_empty-{F}(V0), pppp25-{F}(V1,V2), pppp22-{F}(V1,V3) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #460: exists( #89, #457 ), references = 1, size of lhs = 3:
% 1.49/1.65 pppp26-{F}(V0), P_empty-{F}(V1), pppp25-{F}(V0,V2) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #462: exists( #88, #459 ), references = 1, size of lhs = 2:
% 1.49/1.65 pppp26-{F}(V0), P_empty-{F}(V1) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #465: mergings( V0 == V7; #463 ), references = 1, size of lhs = 6:
% 1.49/1.65 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
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #468: mergings( V1 == V6; #466 ), references = 1, size of lhs = 5:
% 1.49/1.65 P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_empty-{F}(V4) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #471: mergings( V1 == V5; #469 ), references = 1, size of lhs = 4:
% 1.49/1.65 P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_n1-{F}(V2), P_empty-{F}(V3) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #474: mergings( V1 == V4; #472 ), references = 1, size of lhs = 3:
% 1.49/1.65 P_edges-{F}(V0), P_sequential_pairs-{F}(V1), P_empty-{F}(V2) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #477: mergings( V1 == V3; #475 ), references = 1, size of lhs = 2:
% 1.49/1.65 P_edges-{F}(V0), P_empty-{F}(V1) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #480: mergings( V1 == V2; #478 ), references = 1, size of lhs = 1:
% 1.49/1.65 P_empty-{F}(V0) | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 #482: exists( #101, #478 ), references = 1, size of lhs = 0:
% 1.49/1.65 FALSE | FALSE
% 1.49/1.65 (used 0 times, uses = {})
% 1.49/1.65
% 1.49/1.65 number of learnt formulas = 49
% 1.49/1.65
% 1.49/1.65
% 1.49/1.65 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.49/1.65
% 1.49/1.65 randbase = 1
%------------------------------------------------------------------------------