TSTP Solution File: GRA010+2 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : GRA010+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n016.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 06:02:48 EDT 2022
% Result : Theorem 2.86s 3.04s
% Output : Refutation 2.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRA010+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.07/0.13 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n016.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 08:10:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.86/3.04 GeoParameters:
% 2.86/3.04
% 2.86/3.04 tptp_input = 1
% 2.86/3.04 tptp_output = 0
% 2.86/3.04 nonempty = 1
% 2.86/3.04 inputfile = /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.86/3.04 includepath = /export/starexec/sandbox/solver/bin/../../benchmark/
% 2.86/3.04
% 2.86/3.04
% 2.86/3.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.86/3.04 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.86/3.04
% 2.86/3.04 RuleSystem INPUT:
% 2.86/3.04
% 2.86/3.04 Initial Rules:
% 2.86/3.04 #0: input, references = 3, size of lhs = 3:
% 2.86/3.04 P_head_of-{F}(V0,V2), P_tail_of-{F}(V0,V2), edge-{F}(V0) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #1: input, references = 3, size of lhs = 3:
% 2.86/3.04 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), edge-{F}(V0) | vertex-{T}(V1)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #2: input, references = 3, size of lhs = 3:
% 2.86/3.04 P_head_of-{F}(V0,V1), P_tail_of-{F}(V0,V2), edge-{F}(V0) | vertex-{T}(V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #3: input, references = 3, size of lhs = 4:
% 2.86/3.04 complete-{F}(), vertex-{F}(V0), vertex-{F}(V1), V1 == V0 | EXISTS V2: pppp9-{T}(V1,V0,V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #4: input, references = 3, size of lhs = 1:
% 2.86/3.04 pppp9-{F}(V0,V1,V2) | pppp8-{T}(V2,V0,V1)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #5: input, references = 3, size of lhs = 3:
% 2.86/3.04 pppp8-{F}(V0,V1,V2), pppp1-{F}(V0,V1,V2), pppp0-{F}(V0,V1,V2) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #6: input, references = 3, size of lhs = 1:
% 2.86/3.04 pppp8-{F}(V0,V1,V2) | pppp0-{T}(V0,V1,V2), pppp1-{T}(V0,V1,V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #7: input, references = 3, size of lhs = 1:
% 2.86/3.04 pppp8-{F}(V0,V1,V2) | edge-{T}(V0)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #8: input, references = 3, size of lhs = 4:
% 2.86/3.04 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp1-{F}(V0,V1,V2), V2 == V3 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #9: input, references = 3, size of lhs = 4:
% 2.86/3.04 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp1-{F}(V0,V1,V2), V1 == V4 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #10: input, references = 3, size of lhs = 2:
% 2.86/3.04 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | pppp1-{T}(V0,V4,V3)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #11: input, references = 4, size of lhs = 4:
% 2.86/3.04 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp0-{F}(V0,V1,V2), V1 == V3 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #12: input, references = 3, size of lhs = 4:
% 2.86/3.04 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), pppp0-{F}(V0,V1,V2), V2 == V4 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #13: input, references = 3, size of lhs = 2:
% 2.86/3.04 P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | pppp0-{T}(V0,V3,V4)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #14: input, references = 3, size of lhs = 7:
% 2.86/3.04 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)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #15: input, references = 4, size of lhs = 9:
% 2.86/3.04 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)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #16: input, references = 3, size of lhs = 2:
% 2.86/3.04 P_empty-{F}(V0), path-{F}(V1,V2,V3) | vertex-{T}(V1)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #17: input, references = 3, size of lhs = 2:
% 2.86/3.04 P_empty-{F}(V0), path-{F}(V1,V2,V3) | vertex-{T}(V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #18: input, references = 3, size of lhs = 2:
% 2.86/3.04 P_empty-{F}(V0), path-{F}(V1,V2,V3) | EXISTS V4: pppp11-{T}(V1,V2,V3,V4)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #19: input, references = 5, size of lhs = 2:
% 2.86/3.04 pppp11-{F}(V0,V1,V2,V3), P_tail_of-{F}(V3,V4) | pppp10-{T}(V3,V0,V1,V2,V4)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #20: input, references = 3, size of lhs = 3:
% 2.86/3.04 pppp10-{F}(V0,V1,V2,V3,V4), pppp3-{F}(V0,V2,V3), pppp2-{F}(V0,V2,V3) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #21: input, references = 4, size of lhs = 1:
% 2.86/3.04 pppp10-{F}(V0,V1,V2,V3,V4) | pppp2-{T}(V0,V2,V3), pppp3-{T}(V0,V2,V3)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #22: input, references = 5, size of lhs = 2:
% 2.86/3.04 pppp10-{F}(V0,V1,V2,V3,V4), V1 == V4 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #23: input, references = 3, size of lhs = 1:
% 2.86/3.04 pppp10-{F}(V0,V1,V2,V3,V4) | edge-{T}(V0)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #24: input, references = 3, size of lhs = 3:
% 2.86/3.04 P_empty-{F}(V0), P_head_of-{F}(V1,V4), pppp3-{F}(V1,V2,V3) | EXISTS V5: pppp12-{T}(V1,V2,V3,V5,V4)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #25: input, references = 3, size of lhs = 4:
% 2.86/3.04 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)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #26: input, references = 4, size of lhs = 3:
% 2.86/3.04 pppp12-{F}(V0,V1,V2,V3,V4), P_path_cons-{F}(V0,V3,V5), V2 == V5 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #27: input, references = 3, size of lhs = 2:
% 2.86/3.04 pppp12-{F}(V0,V1,V2,V3,V4), P_path_cons-{F}(V0,V3,V5) | path-{T}(V4,V1,V3)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #28: input, references = 3, size of lhs = 5:
% 2.86/3.04 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
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #29: input, references = 3, size of lhs = 5:
% 2.86/3.04 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
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #30: input, references = 3, size of lhs = 3:
% 2.86/3.04 P_empty-{F}(V0), P_head_of-{F}(V1,V4), P_path_cons-{F}(V1,V0,V5) | pppp2-{T}(V1,V4,V5)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #31: input, references = 3, size of lhs = 5:
% 2.86/3.04 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)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #32: input, references = 3, size of lhs = 5:
% 2.86/3.04 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)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #33: input, references = 3, size of lhs = 5:
% 2.86/3.04 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)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #34: input, references = 3, size of lhs = 3:
% 2.86/3.04 P_empty-{F}(V0), path-{F}(V3,V2,V1), in_path-{F}(V4,V1) | vertex-{T}(V4)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #35: input, references = 3, size of lhs = 3:
% 2.86/3.04 P_empty-{F}(V0), path-{F}(V3,V2,V1), in_path-{F}(V4,V1) | EXISTS V5: pppp13-{T}(V5,V1,V4)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #36: input, references = 5, size of lhs = 5:
% 2.86/3.04 pppp13-{F}(V0,V1,V2), P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4), V2 == V3, V2 == V4 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #37: input, references = 3, size of lhs = 3:
% 2.86/3.04 pppp13-{F}(V0,V1,V2), P_head_of-{F}(V0,V3), P_tail_of-{F}(V0,V4) | on_path-{T}(V0,V1)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #38: input, references = 3, size of lhs = 2:
% 2.86/3.04 P_empty-{F}(V0), sequential-{F}(V1,V2) | pppp4-{T}(V1,V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #39: input, references = 3, size of lhs = 2:
% 2.86/3.04 P_empty-{F}(V0), pppp4-{F}(V1,V2) | sequential-{T}(V1,V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #40: input, references = 4, size of lhs = 3:
% 2.86/3.04 P_empty-{F}(V0), P_head_of-{F}(V1,V3), P_tail_of-{F}(V2,V4) | pppp14-{T}(V1,V2,V3,V4)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #41: input, references = 3, size of lhs = 4:
% 2.86/3.04 pppp14-{F}(V0,V1,V3,V3), edge-{F}(V0), edge-{F}(V1), V0 == V1 | pppp4-{T}(V0,V1)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #42: input, references = 4, size of lhs = 3:
% 2.86/3.04 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1), V2 == V3 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #43: input, references = 3, size of lhs = 2:
% 2.86/3.04 pppp14-{F}(V1,V1,V2,V3), pppp4-{F}(V1,V1) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #44: input, references = 3, size of lhs = 2:
% 2.86/3.04 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1) | edge-{T}(V1)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #45: input, references = 3, size of lhs = 2:
% 2.86/3.04 pppp14-{F}(V0,V1,V2,V3), pppp4-{F}(V0,V1) | edge-{T}(V0)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #46: input, references = 3, size of lhs = 5:
% 2.86/3.04 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)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #47: input, references = 3, size of lhs = 6:
% 2.86/3.04 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)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #48: input, references = 3, size of lhs = 3:
% 2.86/3.04 P_empty-{F}(V0), precedes-{F}(V2,V3,V1), path-{F}(V5,V4,V1) | pppp15-{T}(V1,V2,V3)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #49: input, references = 3, size of lhs = 3:
% 2.86/3.04 pppp15-{F}(V0,V1,V2), pppp5-{F}(V0,V1,V2), sequential-{F}(V1,V2) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #50: input, references = 3, size of lhs = 1:
% 2.86/3.04 pppp15-{F}(V0,V1,V2) | sequential-{T}(V1,V2), pppp5-{T}(V0,V1,V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #51: input, references = 3, size of lhs = 1:
% 2.86/3.04 pppp15-{F}(V0,V1,V2) | on_path-{T}(V2,V0)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #52: input, references = 3, size of lhs = 1:
% 2.86/3.04 pppp15-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #53: input, references = 3, size of lhs = 2:
% 2.86/3.04 P_empty-{F}(V0), pppp5-{F}(V1,V2,V3) | EXISTS V4: pppp16-{T}(V1,V2,V3,V4)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #54: input, references = 3, size of lhs = 3:
% 2.86/3.04 P_empty-{F}(V0), sequential-{F}(V2,V4), precedes-{F}(V4,V3,V1) | pppp5-{T}(V1,V2,V3)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #55: input, references = 3, size of lhs = 1:
% 2.86/3.04 pppp16-{F}(V0,V1,V2,V3) | precedes-{T}(V3,V2,V0)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #56: input, references = 3, size of lhs = 1:
% 2.86/3.04 pppp16-{F}(V0,V1,V2,V3) | sequential-{T}(V1,V3)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #57: input, references = 3, size of lhs = 2:
% 2.86/3.04 P_empty-{F}(V0), shortest_path-{F}(V1,V2,V3) | pppp6-{T}(V1,V2,V3)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #58: input, references = 4, size of lhs = 2:
% 2.86/3.04 P_empty-{F}(V0), pppp6-{F}(V1,V2,V3) | shortest_path-{T}(V1,V2,V3)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #59: input, references = 3, size of lhs = 3:
% 2.86/3.04 P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V1,V2,V3) | path-{T}(V1,V2,V3)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #60: input, references = 3, size of lhs = 3:
% 2.86/3.04 P_empty-{F}(V0), P_length_of-{F}(V3,V4), pppp6-{F}(V2,V2,V3) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #61: input, references = 3, size of lhs = 5:
% 2.86/3.04 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)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #62: input, references = 4, size of lhs = 4:
% 2.86/3.04 P_empty-{F}(V0), P_length_of-{F}(V3,V4), path-{F}(V1,V2,V3), V1 == V2 | pppp6-{T}(V1,V2,V3), pppp26-{T}(V1,V2,V4)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #63: input, references = 3, size of lhs = 1:
% 2.86/3.04 pppp26-{F}(V0,V1,V2) | EXISTS V3: pppp17-{T}(V0,V1,V3,V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #64: input, references = 3, size of lhs = 3:
% 2.86/3.04 pppp17-{F}(V0,V1,V2,V3), P_length_of-{F}(V2,V4), less_or_equal-{F}(V3,V4) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #65: input, references = 3, size of lhs = 2:
% 2.86/3.04 pppp17-{F}(V0,V1,V2,V3), P_length_of-{F}(V2,V4) | path-{T}(V0,V1,V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #66: input, references = 5, size of lhs = 7:
% 2.86/3.04 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
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #67: input, references = 3, size of lhs = 6:
% 2.86/3.04 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
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #68: input, references = 3, size of lhs = 2:
% 2.86/3.04 P_empty-{F}(V0), triangle-{F}(V1,V2,V3) | pppp7-{T}(V1,V2,V3)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #69: input, references = 3, size of lhs = 2:
% 2.86/3.04 P_empty-{F}(V0), pppp7-{F}(V1,V2,V3) | triangle-{T}(V1,V2,V3)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #70: input, references = 3, size of lhs = 2:
% 2.86/3.04 P_empty-{F}(V0), pppp7-{F}(V1,V2,V3) | pppp18-{T}(V1,V2,V3)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #71: input, references = 3, size of lhs = 7:
% 2.86/3.04 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)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #72: input, references = 3, size of lhs = 1:
% 2.86/3.04 pppp18-{F}(V0,V1,V2) | sequential-{T}(V2,V0)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #73: input, references = 3, size of lhs = 1:
% 2.86/3.04 pppp18-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #74: input, references = 3, size of lhs = 1:
% 2.86/3.04 pppp18-{F}(V0,V1,V2) | sequential-{T}(V0,V1)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #75: input, references = 3, size of lhs = 1:
% 2.86/3.04 pppp18-{F}(V0,V1,V2) | edge-{T}(V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #76: input, references = 3, size of lhs = 1:
% 2.86/3.04 pppp18-{F}(V0,V1,V2) | edge-{T}(V1)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #77: input, references = 3, size of lhs = 1:
% 2.86/3.04 pppp18-{F}(V0,V1,V2) | edge-{T}(V0)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #78: input, references = 6, size of lhs = 6:
% 2.86/3.04 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
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #79: input, references = 6, size of lhs = 9:
% 2.86/3.04 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
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #80: input, references = 4, size of lhs = 9:
% 2.86/3.04 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)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #81: input, references = 4, size of lhs = 1:
% 2.86/3.04 pppp20-{F}(V0,V1) | EXISTS V2: pppp19-{T}(V0,V2,V1)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #82: input, references = 4, size of lhs = 1:
% 2.86/3.04 pppp20-{F}(V0,V1) | on_path-{T}(V1,V0)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #83: input, references = 4, size of lhs = 2:
% 2.86/3.04 pppp19-{F}(V0,V1,V2), triangle-{F}(V1,V2,V3) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #84: input, references = 4, size of lhs = 1:
% 2.86/3.04 pppp19-{F}(V0,V1,V2) | sequential-{T}(V1,V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #85: input, references = 4, size of lhs = 1:
% 2.86/3.04 pppp19-{F}(V0,V1,V2) | on_path-{T}(V1,V0)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #86: input, references = 3, size of lhs = 8:
% 2.86/3.04 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)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #87: input, references = 3, size of lhs = 10:
% 2.86/3.04 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}(), sequential-{F}(V6,V7), precedes-{F}(V6,V7,V9), shortest_path-{F}(V11,V10,V9) | EXISTS V8: pppp21-{T}(V6,V7,V8)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #88: input, references = 3, size of lhs = 1:
% 2.86/3.04 pppp21-{F}(V0,V1,V2) | triangle-{T}(V0,V1,V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #89: input, references = 3, size of lhs = 6:
% 2.86/3.04 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}()
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #90: input, references = 5, size of lhs = 6:
% 2.86/3.04 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), P_graph-{F}(V5) | EXISTS V6: pppp25-{T}(V6,V2,V4)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #91: input, references = 6, size of lhs = 3:
% 2.86/3.04 pppp25-{F}(V0,V1,V2), P_number_of_in-{F}(V1,V0,V3), P_number_of_in-{F}(V2,V0,V4) | EXISTS V5: pppp24-{T}(V0,V5)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #92: input, references = 5, size of lhs = 3:
% 2.86/3.04 pppp25-{F}(V0,V1,V2), P_number_of_in-{F}(V1,V0,V4), P_number_of_in-{F}(V2,V0,V4) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #93: input, references = 4, size of lhs = 6:
% 2.86/3.04 pppp25-{F}(V0,V1,V2), P_number_of_in-{F}(V1,V0,V3), P_number_of_in-{F}(V2,V0,V4), on_path-{F}(V5,V0), on_path-{F}(V6,V0), sequential-{F}(V6,V5) | EXISTS V7: pppp22-{T}(V6,V5,V7)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #94: input, references = 6, size of lhs = 1:
% 2.86/3.04 pppp24-{F}(V0,V1) | EXISTS V2: pppp23-{T}(V1,V0,V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #95: input, references = 6, size of lhs = 1:
% 2.86/3.04 pppp23-{F}(V0,V1,V2) | path-{T}(V2,V0,V1)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #96: input, references = 4, size of lhs = 1:
% 2.86/3.04 pppp22-{F}(V0,V1,V2) | triangle-{T}(V0,V1,V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #97: input, references = 7, size of lhs = 1:
% 2.86/3.04 #-{F} V0 | EXISTS V1: P_head_of-{T}(V0,V1)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #98: input, references = 7, size of lhs = 1:
% 2.86/3.04 #-{F} V0 | EXISTS V1: P_tail_of-{T}(V0,V1)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #99: input, references = 5, size of lhs = 2:
% 2.86/3.04 #-{F} V0, #-{F} V1 | EXISTS V2: P_path_cons-{T}(V0,V1,V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #100: input, references = 4, size of lhs = 0:
% 2.86/3.04 FALSE | EXISTS V0: P_empty-{T}(V0)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #101: input, references = 4, size of lhs = 1:
% 2.86/3.04 #-{F} V0 | EXISTS V1: P_length_of-{T}(V0,V1)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #102: input, references = 13, size of lhs = 2:
% 2.86/3.04 #-{F} V0, #-{F} V1 | EXISTS V2: P_number_of_in-{T}(V0,V1,V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #103: input, references = 4, size of lhs = 0:
% 2.86/3.04 FALSE | EXISTS V0: P_edges-{T}(V0)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #104: input, references = 4, size of lhs = 0:
% 2.86/3.04 FALSE | EXISTS V0: P_sequential_pairs-{T}(V0)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #105: input, references = 5, size of lhs = 2:
% 2.86/3.04 #-{F} V0, #-{F} V1 | EXISTS V2: P_minus-{T}(V0,V1,V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #106: input, references = 5, size of lhs = 0:
% 2.86/3.04 FALSE | EXISTS V0: P_n1-{T}(V0)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #107: input, references = 5, size of lhs = 0:
% 2.86/3.04 FALSE | EXISTS V0: P_triangles-{T}(V0)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #108: input, references = 5, size of lhs = 0:
% 2.86/3.04 FALSE | EXISTS V0: P_graph-{T}(V0)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 number of initial rules = 109
% 2.86/3.04
% 2.86/3.04 Simplifiers:
% 2.86/3.04 #109: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 P_head_of-{F}(V0,V1), P_head_of-{F}(V0,V3), V1 == V3 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #110: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 P_tail_of-{F}(V0,V1), P_tail_of-{F}(V0,V3), V1 == V3 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #111: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 P_path_cons-{F}(V0,V1,V2), P_path_cons-{F}(V0,V1,V5), V2 == V5 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #112: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 P_empty-{F}(V0), P_empty-{F}(V1), V0 == V1 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #113: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 P_length_of-{F}(V0,V1), P_length_of-{F}(V0,V3), V1 == V3 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #114: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 P_number_of_in-{F}(V0,V1,V2), P_number_of_in-{F}(V0,V1,V5), V2 == V5 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #115: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 P_edges-{F}(V0), P_edges-{F}(V1), V0 == V1 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #116: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 P_sequential_pairs-{F}(V0), P_sequential_pairs-{F}(V1), V0 == V1 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #117: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 P_minus-{F}(V0,V1,V2), P_minus-{F}(V0,V1,V5), V2 == V5 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #118: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 P_n1-{F}(V0), P_n1-{F}(V1), V0 == V1 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #119: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 P_triangles-{F}(V0), P_triangles-{F}(V1), V0 == V1 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #120: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 P_graph-{F}(V0), P_graph-{F}(V1), V0 == V1 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #121: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp8-{F}(V0,V1,V2), pppp8-{F}(V3,V1,V2), V0 == V3 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #122: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp9-{F}(V0,V1,V2), pppp9-{F}(V0,V1,V5), V2 == V5 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #123: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V5,V1,V2,V3,V9), V0 == V5 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #124: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp10-{F}(V0,V1,V2,V3,V4), pppp10-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #125: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp11-{F}(V0,V1,V2,V3), pppp11-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #126: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V1,V2,V8,V4), V3 == V8 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #127: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp12-{F}(V0,V1,V2,V3,V4), pppp12-{F}(V0,V6,V7,V8,V9), V4 == V9 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #128: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp13-{F}(V0,V1,V2), pppp13-{F}(V3,V1,V2), V0 == V3 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #129: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp14-{F}(V0,V1,V2,V3), pppp14-{F}(V0,V5,V6,V7), V2 == V6 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #130: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp14-{F}(V0,V1,V2,V3), pppp14-{F}(V4,V1,V6,V7), V3 == V7 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #131: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp16-{F}(V0,V1,V2,V3), pppp16-{F}(V0,V1,V2,V7), V3 == V7 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #132: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp17-{F}(V0,V1,V2,V3), pppp17-{F}(V0,V1,V6,V3), V2 == V6 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #133: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp19-{F}(V0,V1,V2), pppp19-{F}(V0,V4,V2), V1 == V4 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #134: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp19-{F}(V0,V1,V2), pppp19-{F}(V0,V4,V5), V2 == V5 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #135: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp20-{F}(V0,V1), pppp20-{F}(V0,V3), V1 == V3 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #136: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp21-{F}(V0,V1,V2), pppp21-{F}(V0,V1,V5), V2 == V5 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #137: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp22-{F}(V0,V1,V2), pppp22-{F}(V0,V1,V5), V2 == V5 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #138: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp23-{F}(V0,V1,V2), pppp23-{F}(V0,V1,V5), V2 == V5 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #139: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp23-{F}(V0,V1,V2), pppp23-{F}(V3,V1,V5), V0 == V3 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #140: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp24-{F}(V0,V1), pppp24-{F}(V0,V3), V1 == V3 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #141: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp25-{F}(V0,V1,V2), pppp25-{F}(V3,V1,V2), V0 == V3 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #142: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp25-{F}(V0,V1,V2), pppp25-{F}(V3,V4,V5), V1 == V4 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #143: unsound, references = 3, size of lhs = 3:
% 2.86/3.04 pppp25-{F}(V0,V1,V2), pppp25-{F}(V3,V4,V5), V2 == V5 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 number of simplifiers = 35
% 2.86/3.04
% 2.86/3.04 Learnt:
% 2.86/3.04 #146: exists( #94, #144 ), references = 1, size of lhs = 9:
% 2.86/3.04 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), pppp24-{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
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #148: exists( #91, #145 ), references = 1, size of lhs = 11:
% 2.86/3.04 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, pppp25-{F}(V4,V8,V9), P_number_of_in-{F}(V8,V4,V10), P_number_of_in-{F}(V9,V4,V11) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #150: exists( #102, #147 ), references = 3, size of lhs = 8:
% 2.86/3.04 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), pppp25-{F}(V4,V2,V7), P_number_of_in-{F}(V7,V4,V8) | P_number_of_in-{T}(V2,V4,V6)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #154: exists( #94, #152 ), references = 1, size of lhs = 6:
% 2.86/3.04 P_empty-{F}(V0), P_edges-{F}(V1), pppp24-{F}(V2,V3), P_length_of-{F}(V2,V4), P_number_of_in-{F}(V1,V2,V5), V4 == V5 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #156: exists( #91, #153 ), references = 3, size of lhs = 8:
% 2.86/3.04 P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), P_number_of_in-{F}(V1,V2,V4), V3 == V4, pppp25-{F}(V2,V5,V6), P_number_of_in-{F}(V5,V2,V7), P_number_of_in-{F}(V6,V2,V8) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #162: mergings( V3 == V7, V8 == V10, V4 == V5; #158 ), references = 2, size of lhs = 8:
% 2.86/3.04 P_sequential_pairs-{F}(V0), P_edges-{F}(V0), P_n1-{F}(V1), P_empty-{F}(V2), P_length_of-{F}(V3,V4), P_minus-{F}(V4,V1,V5), V4 == V5, pppp25-{F}(V3,V0,V6) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #164: exists( #102, #156 ), references = 3, size of lhs = 5:
% 2.86/3.04 P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), pppp25-{F}(V2,V1,V4), P_number_of_in-{F}(V4,V2,V5) | P_number_of_in-{T}(V1,V2,V3)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #168: exists( #105, #162 ), references = 1, size of lhs = 6:
% 2.86/3.04 P_sequential_pairs-{F}(V0), P_edges-{F}(V0), P_n1-{F}(V1), P_empty-{F}(V2), P_length_of-{F}(V3,V4), pppp25-{F}(V3,V0,V5) | P_minus-{T}(V4,V1,V4)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #199: mergings( V1 == V8; #197 ), references = 1, size of lhs = 12:
% 2.86/3.04 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
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #204: exists( #102, #78 ), references = 1, size of lhs = 4:
% 2.86/3.04 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)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #205: exists( #102, #79 ), references = 1, size of lhs = 7:
% 2.86/3.04 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_length_of-{F}(V4,V5), P_minus-{F}(V5,V3,V6), path-{F}(V7,V8,V4) | P_number_of_in-{T}(V2,V4,V6)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #215: disj( #21, input ), references = 1, size of lhs = 5:
% 2.86/3.04 P_empty-{F}(V0), P_head_of-{F}(V1,V2), P_path_cons-{F}(V1,V0,V3), pppp10-{F}(V1,V4,V5,V6,V7), V5 == V2 | pppp3-{T}(V1,V5,V6)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #217: exists( #98, #11 ), references = 1, size of lhs = 3:
% 2.86/3.04 P_head_of-{F}(V0,V1), pppp0-{F}(V0,V2,V3), V2 == V1 | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #219: exists( #97, #216 ), references = 1, size of lhs = 1:
% 2.86/3.04 pppp0-{F}(V0,V1,V2) | P_head_of-{T}(V0,V1)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #222: exists( #105, #79 ), references = 1, size of lhs = 7:
% 2.86/3.04 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)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #248: exists( #98, #36 ), references = 1, size of lhs = 3:
% 2.86/3.04 P_head_of-{F}(V0,V1), pppp13-{F}(V0,V2,V3), V3 == V1 | P_tail_of-{T}(V0,V3)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #252: exists( #97, #250 ), references = 1, size of lhs = 3:
% 2.86/3.04 pppp13-{F}(V0,V1,V2), pppp11-{F}(V3,V4,V5,V0), V3 == V2 | P_head_of-{T}(V0,V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #265: exists( #97, #263 ), references = 1, size of lhs = 7:
% 2.86/3.04 P_empty-{F}(V0), P_tail_of-{F}(V1,V2), P_head_of-{F}(V1,V3), P_head_of-{F}(V4,V3), pppp13-{F}(V5,V6,V2), precedes-{F}(V5,V4,V7), shortest_path-{F}(V8,V9,V7) | P_head_of-{T}(V5,V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #274: exists( #98, #272 ), references = 1, size of lhs = 1:
% 2.86/3.04 pppp11-{F}(V0,V1,V2,V3) | P_tail_of-{T}(V3,V0)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #279: mergings( V0 == V5, V5 == V6; #276 ), references = 1, size of lhs = 9:
% 2.86/3.04 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), P_length_of-{F}(V6,V7), path-{F}(V8,V9,V6), V8 == V9 | pppp26-{T}(V8,V9,V7)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #291: exists( #97, #289 ), references = 1, size of lhs = 3:
% 2.86/3.04 P_empty-{F}(V0), pppp4-{F}(V1,V2), P_tail_of-{F}(V2,V3) | P_head_of-{T}(V1,V3)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #341: exists( #99, #26 ), references = 1, size of lhs = 1:
% 2.86/3.04 pppp12-{F}(V0,V1,V2,V3,V4) | P_path_cons-{T}(V0,V3,V2)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #349: exists( #93, #347 ), references = 1, size of lhs = 7:
% 2.86/3.04 on_path-{F}(V0,V1), sequential-{F}(V0,V2), on_path-{F}(V2,V1), pppp19-{F}(V3,V0,V2), pppp25-{F}(V1,V4,V5), P_number_of_in-{F}(V4,V1,V6), P_number_of_in-{F}(V5,V1,V7) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #353: exists( #81, #351 ), references = 1, size of lhs = 5:
% 2.86/3.04 pppp20-{F}(V0,V1), on_path-{F}(V1,V0), pppp25-{F}(V0,V2,V3), P_number_of_in-{F}(V2,V0,V4), P_number_of_in-{F}(V3,V0,V5) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #356: exists( #80, #354 ), references = 1, size of lhs = 12:
% 2.86/3.04 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), V6 == V7, path-{F}(V8,V9,V5), pppp25-{F}(V5,V10,V11), P_number_of_in-{F}(V10,V5,V12), P_number_of_in-{F}(V11,V5,V13) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #359: exists( #94, #357 ), references = 1, size of lhs = 12:
% 2.86/3.04 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), pppp24-{F}(V5,V6), P_number_of_in-{F}(V2,V5,V7), P_number_of_in-{F}(V4,V5,V8), V7 == V8, pppp25-{F}(V5,V9,V10), P_number_of_in-{F}(V9,V5,V11), P_number_of_in-{F}(V10,V5,V12) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #365: mergings( V1 == V13, V3 == V15, V2 == V14, V4 == V16; #360 ), references = 3, size of lhs = 11:
% 2.86/3.04 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), V6 == V7, pppp25-{F}(V5,V8,V9), P_number_of_in-{F}(V8,V5,V10), P_number_of_in-{F}(V9,V5,V11) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #370: mergings( V3 == V5, V4 == V6; #367 ), references = 1, size of lhs = 7:
% 2.86/3.04 P_sequential_pairs-{F}(V0), P_edges-{F}(V0), P_empty-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), pppp25-{F}(V4,V0,V3), P_length_of-{F}(V4,V5) | P_number_of_in-{T}(V3,V4,V5)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #378: mergings( V2 == V4, V4 == V8, V3 == V5, V5 == V9; #373 ), references = 1, size of lhs = 6:
% 2.86/3.04 P_sequential_pairs-{F}(V0), P_edges-{F}(V0), P_n1-{F}(V1), P_triangles-{F}(V2), P_empty-{F}(V3), pppp25-{F}(V4,V0,V2) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #386: mergings( V0 == V7, V7 == V8, V8 == V11, V1 == V2, V2 == V9, V3 == V10; #379 ), references = 1, size of lhs = 6:
% 2.86/3.04 P_graph-{F}(V0), P_sequential_pairs-{F}(V1), P_edges-{F}(V1), P_n1-{F}(V2), P_triangles-{F}(V3), P_empty-{F}(V4) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #394: mergings( V1 == V4, V4 == V6, V6 == V10, V2 == V5, V5 == V7, V3 == V8; #387 ), references = 1, size of lhs = 5:
% 2.86/3.04 P_sequential_pairs-{F}(V0), P_edges-{F}(V0), P_n1-{F}(V1), P_triangles-{F}(V2), P_empty-{F}(V3) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #402: mergings( V1 == V4, V4 == V6, V6 == V9, V2 == V5, V5 == V7, V3 == V8; #395 ), references = 1, size of lhs = 4:
% 2.86/3.04 P_sequential_pairs-{F}(V0), P_edges-{F}(V0), P_n1-{F}(V1), P_empty-{F}(V2) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #409: mergings( V1 == V3, V3 == V5, V5 == V7, V2 == V4, V4 == V6; #403 ), references = 1, size of lhs = 3:
% 2.86/3.04 P_sequential_pairs-{F}(V0), P_edges-{F}(V0), P_empty-{F}(V1) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #416: mergings( V3 == V6, V4 == V7, V5 == V9; #412 ), references = 1, size of lhs = 8:
% 2.86/3.04 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), pppp25-{F}(V5,V2,V4), P_length_of-{F}(V5,V6), P_minus-{F}(V6,V3,V7) | P_number_of_in-{T}(V4,V5,V7)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #420: exists( #102, #156 ), references = 1, size of lhs = 7:
% 2.86/3.04 P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), P_number_of_in-{F}(V1,V2,V4), V3 == V4, pppp25-{F}(V2,V5,V6), P_number_of_in-{F}(V6,V2,V7) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #422: exists( #102, #419 ), references = 1, size of lhs = 5:
% 2.86/3.04 P_empty-{F}(V0), P_edges-{F}(V1), P_length_of-{F}(V2,V3), pppp25-{F}(V2,V4,V5), P_number_of_in-{F}(V5,V2,V6) | P_number_of_in-{T}(V1,V2,V3)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #424: exists( #102, #365 ), references = 1, size of lhs = 8:
% 2.86/3.04 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}(V4,V5,V6), pppp25-{F}(V5,V2,V7), P_number_of_in-{F}(V7,V5,V8) | P_number_of_in-{T}(V2,V5,V6)
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #427: exists( #102, #425 ), references = 1, size of lhs = 6:
% 2.86/3.04 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4), pppp25-{F}(V5,V2,V4) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #432: mergings( V0 == V7, V1 == V8, V3 == V9; #428 ), references = 1, size of lhs = 6:
% 2.86/3.04 P_graph-{F}(V0), P_empty-{F}(V1), P_edges-{F}(V2), P_sequential_pairs-{F}(V3), P_n1-{F}(V4), P_triangles-{F}(V5) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #437: mergings( V1 == V4, V2 == V5, V3 == V7; #433 ), references = 1, size of lhs = 5:
% 2.86/3.04 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3), P_triangles-{F}(V4) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #442: mergings( V1 == V4, V2 == V5, V3 == V7; #438 ), references = 1, size of lhs = 4:
% 2.86/3.04 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2), P_n1-{F}(V3) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #446: mergings( V1 == V3, V2 == V4; #443 ), references = 1, size of lhs = 3:
% 2.86/3.04 P_empty-{F}(V0), P_edges-{F}(V1), P_sequential_pairs-{F}(V2) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #450: mergings( V1 == V3, V2 == V4; #447 ), references = 1, size of lhs = 2:
% 2.86/3.04 P_empty-{F}(V0), P_edges-{F}(V1) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #453: mergings( V1 == V2; #451 ), references = 1, size of lhs = 1:
% 2.86/3.04 P_empty-{F}(V0) | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 #455: exists( #100, #451 ), references = 1, size of lhs = 0:
% 2.86/3.04 FALSE | FALSE
% 2.86/3.04 (used 0 times, uses = {})
% 2.86/3.04
% 2.86/3.04 number of learnt formulas = 45
% 2.86/3.04
% 2.86/3.04
% 2.86/3.04 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.86/3.04
% 2.86/3.04 randbase = 1
%------------------------------------------------------------------------------