TSTP Solution File: GEO069-3 by Geo-III---2018C
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%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : GEO069-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n013.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 06:01:38 EDT 2022
% Result : Unsatisfiable 2.58s 2.75s
% Output : Refutation 2.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO069-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.12/0.33 % Computer : n013.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 18:14:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.58/2.75 GeoParameters:
% 2.58/2.75
% 2.58/2.75 tptp_input = 1
% 2.58/2.75 tptp_output = 0
% 2.58/2.75 nonempty = 1
% 2.58/2.75 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.58/2.75 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 2.58/2.75
% 2.58/2.75
% 2.58/2.75 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.58/2.75 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.58/2.75
% 2.58/2.75 RuleSystem INPUT:
% 2.58/2.75
% 2.58/2.75 Initial Rules:
% 2.58/2.75 #0: input, references = 3, size of lhs = 2:
% 2.58/2.75 #-{F} V0, #-{F} V1 | equidistant-{T}(V0,V1,V1,V0)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #1: input, references = 3, size of lhs = 2:
% 2.58/2.75 equidistant-{F}(V5,V4,V0,V1), equidistant-{F}(V5,V4,V2,V3) | equidistant-{T}(V0,V1,V2,V3)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #2: input, references = 3, size of lhs = 2:
% 2.58/2.75 equidistant-{F}(V0,V1,V2,V2), V0 == V1 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #3: input, references = 3, size of lhs = 1:
% 2.58/2.75 P_extension-{F}(V0,V1,V3,V2,V4) | between-{T}(V0,V1,V4)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #4: input, references = 3, size of lhs = 1:
% 2.58/2.75 P_extension-{F}(V0,V1,V3,V2,V4) | equidistant-{T}(V1,V4,V3,V2)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #5: input, references = 3, size of lhs = 7:
% 2.58/2.75 equidistant-{F}(V0,V1,V3,V2), equidistant-{F}(V0,V5,V3,V4), equidistant-{F}(V1,V5,V2,V4), between-{F}(V3,V2,V6), equidistant-{F}(V1,V7,V2,V6), between-{F}(V0,V1,V7), V0 == V1 | equidistant-{T}(V7,V5,V6,V4)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #6: input, references = 3, size of lhs = 2:
% 2.58/2.75 between-{F}(V0,V1,V0), V0 == V1 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #7: input, references = 3, size of lhs = 3:
% 2.58/2.75 between-{F}(V2,V0,V1), P_inner_pasch-{F}(V2,V0,V1,V4,V3,V5), between-{F}(V3,V4,V1) | between-{T}(V0,V5,V3)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #8: input, references = 3, size of lhs = 3:
% 2.58/2.75 between-{F}(V2,V0,V1), P_inner_pasch-{F}(V2,V0,V1,V4,V3,V5), between-{F}(V3,V4,V1) | between-{T}(V4,V5,V2)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #9: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V0,V1,V2) | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #10: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V1,V2,V0) | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #11: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V2,V0,V1) | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #12: input, references = 3, size of lhs = 7:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), equidistant-{F}(V5,V4,V5,V3), equidistant-{F}(V6,V4,V6,V3), equidistant-{F}(V7,V4,V7,V3), V4 == V3 | between-{T}(V7,V6,V5), between-{T}(V6,V5,V7), between-{T}(V5,V7,V6)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #13: input, references = 3, size of lhs = 7:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V4,V3,V5), P_euclid1-{F}(V4,V6,V3,V7,V5,V8), between-{F}(V6,V3,V7), V4 == V3 | between-{T}(V4,V6,V8)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #14: input, references = 3, size of lhs = 7:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V4,V3,V5), P_euclid2-{F}(V4,V6,V3,V7,V5,V8), between-{F}(V6,V3,V7), V4 == V3 | between-{T}(V4,V7,V8)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #15: input, references = 3, size of lhs = 8:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V4,V3,V5), P_euclid1-{F}(V4,V6,V3,V7,V5,V8), P_euclid2-{F}(V4,V6,V3,V7,V5,V9), between-{F}(V6,V3,V7), V4 == V3 | between-{T}(V8,V5,V9)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #16: input, references = 3, size of lhs = 8:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), equidistant-{F}(V5,V3,V5,V4), between-{F}(V5,V3,V6), equidistant-{F}(V5,V6,V5,V7), P_continuous-{F}(V5,V3,V4,V8,V6,V7,V9), between-{F}(V3,V8,V6) | between-{T}(V4,V9,V7)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #17: input, references = 3, size of lhs = 8:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), equidistant-{F}(V5,V3,V5,V4), between-{F}(V5,V3,V6), equidistant-{F}(V5,V6,V5,V7), P_continuous-{F}(V5,V3,V4,V8,V6,V7,V9), between-{F}(V3,V8,V6) | equidistant-{T}(V5,V8,V5,V9)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #18: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V3,V4,V5) | colinear-{T}(V3,V4,V5)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #19: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V4,V5,V3) | colinear-{T}(V3,V4,V5)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #20: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V5,V3,V4) | colinear-{T}(V3,V4,V5)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #21: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), colinear-{F}(V3,V4,V5) | between-{T}(V3,V4,V5), between-{T}(V4,V5,V3), between-{T}(V5,V3,V4)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #22: input, references = 3, size of lhs = 6:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_reflection-{F}(V4,V3,V5), P_extension-{F}(V4,V3,V4,V3,V6), V5 == V6 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #23: input, references = 3, size of lhs = 7:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_insertion-{F}(V5,V6,V4,V3,V7), P_extension-{F}(V6,V5,V0,V1,V8), P_extension-{F}(V8,V5,V4,V3,V9), V7 == V9 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #24: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), #-{F} V3, #-{F} V4 | equidistant-{T}(V4,V3,V4,V3)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #25: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), equidistant-{F}(V6,V4,V5,V3) | equidistant-{T}(V5,V3,V6,V4)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #26: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), equidistant-{F}(V6,V4,V5,V3) | equidistant-{T}(V4,V6,V5,V3)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #27: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), equidistant-{F}(V6,V4,V5,V3) | equidistant-{T}(V6,V4,V3,V5)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #28: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), equidistant-{F}(V6,V4,V5,V3) | equidistant-{T}(V4,V6,V3,V5)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #29: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), equidistant-{F}(V6,V4,V5,V3) | equidistant-{T}(V5,V3,V4,V6)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #30: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), equidistant-{F}(V6,V4,V5,V3) | equidistant-{T}(V3,V5,V6,V4)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #31: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), equidistant-{F}(V6,V4,V5,V3) | equidistant-{T}(V3,V5,V4,V6)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #32: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), equidistant-{F}(V6,V5,V7,V8), equidistant-{F}(V7,V8,V3,V4) | equidistant-{T}(V6,V5,V3,V4)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #33: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_extension-{F}(V5,V3,V4,V4,V6), V3 == V6 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #34: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_extension-{F}(V5,V4,V6,V7,V8) | between-{T}(V5,V4,V8)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #35: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_reflection-{F}(V4,V3,V5) | between-{T}(V4,V3,V5)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #36: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_reflection-{F}(V4,V3,V5) | equidistant-{T}(V3,V5,V4,V3)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #37: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_reflection-{F}(V3,V3,V5), V3 == V5 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #38: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_reflection-{F}(V3,V3,V4), V3 == V4 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #39: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_reflection-{F}(V4,V5,V5), V4 == V5 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #40: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), #-{F} V3, #-{F} V4 | equidistant-{T}(V4,V4,V3,V3)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #41: input, references = 3, size of lhs = 7:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V4,V3,V5), equidistant-{F}(V6,V8,V4,V3), equidistant-{F}(V8,V7,V3,V5), between-{F}(V6,V8,V7) | equidistant-{T}(V6,V7,V4,V5)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #42: input, references = 3, size of lhs = 8:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V4,V3,V5), between-{F}(V4,V3,V6), equidistant-{F}(V3,V5,V3,V6), V4 == V3, V5 == V6 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #43: input, references = 3, size of lhs = 7:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_extension-{F}(V4,V3,V3,V5,V6), between-{F}(V4,V3,V5), V4 == V3, V5 == V6 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #44: input, references = 3, size of lhs = 8:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_extension-{F}(V4,V3,V5,V8,V9), P_extension-{F}(V4,V3,V7,V6,V10), equidistant-{F}(V5,V8,V7,V6), V4 == V3, V9 == V10 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #45: input, references = 3, size of lhs = 7:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_extension-{F}(V4,V3,V4,V3,V5), P_extension-{F}(V4,V3,V3,V4,V6), V5 == V6, V4 == V3 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #46: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_reflection-{F}(V4,V3,V5), P_reflection-{F}(V5,V3,V6) | equidistant-{T}(V3,V4,V3,V6)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #47: input, references = 3, size of lhs = 6:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_reflection-{F}(V4,V3,V5), P_reflection-{F}(V5,V3,V6), V4 == V6 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #48: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), #-{F} V3, #-{F} V4 | between-{T}(V4,V3,V3)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #49: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V3,V5,V3), #-{F} V6 | between-{T}(V6,V5,V3)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #50: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V5,V3,V4) | between-{T}(V4,V3,V5)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #51: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), #-{F} V3, #-{F} V4 | between-{T}(V4,V4,V3)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #52: input, references = 3, size of lhs = 6:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V4,V3,V5), between-{F}(V3,V4,V5), V4 == V3 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #53: input, references = 3, size of lhs = 6:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V5,V3,V4), between-{F}(V5,V4,V3), V3 == V4 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #54: input, references = 3, size of lhs = 7:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V4,V3,V5), between-{F}(V3,V4,V5), V4 == V3, V3 == V5 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #55: input, references = 3, size of lhs = 7:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V4,V3,V5), between-{F}(V4,V5,V3), V4 == V3, V3 == V5 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #56: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V5,V3,V4), between-{F}(V5,V4,V6) | between-{T}(V3,V4,V6)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #57: input, references = 3, size of lhs = 6:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V5,V3,V4), between-{F}(V3,V4,V6), V3 == V4 | between-{T}(V5,V4,V6)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #58: input, references = 3, size of lhs = 6:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V5,V3,V4), between-{F}(V3,V4,V6), V3 == V4 | between-{T}(V5,V3,V6)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #59: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V5,V6,V3), between-{F}(V6,V4,V3) | between-{T}(V5,V4,V3)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #60: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V5,V3,V4), between-{F}(V5,V4,V6) | between-{T}(V5,V3,V6)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #61: input, references = 4, size of lhs = 3:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V1), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2) | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #62: input, references = 3, size of lhs = 3:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V2), P_lower_dimension_point_3-{F}(V2) | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #63: input, references = 3, size of lhs = 3:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V2), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2) | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #64: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_extension-{F}(V4,V5,V0,V1,V5) | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #65: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_extension-{F}(V6,V4,V0,V1,V7), P_extension-{F}(V5,V3,V0,V1,V8) | equidistant-{T}(V4,V7,V3,V8)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #66: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_extension-{F}(V4,V3,V0,V1,V5) | between-{T}(V4,V3,V5)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #67: input, references = 3, size of lhs = 8:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V5,V4,V3), between-{F}(V6,V7,V3), P_inner_pasch-{F}(V6,V8,V5,V4,V3,V9), P_inner_pasch-{F}(V4,V9,V6,V7,V3,V10), between-{F}(V6,V8,V5) | between-{T}(V8,V10,V3), between-{T}(V7,V10,V4)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #68: input, references = 3, size of lhs = 8:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), equidistant-{F}(V5,V3,V5,V4), between-{F}(V5,V6,V3), equidistant-{F}(V6,V3,V6,V4), V3 == V4, V5 == V6 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #69: input, references = 3, size of lhs = 9:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V4,V3,V5), equidistant-{F}(V6,V7,V4,V5), equidistant-{F}(V6,V8,V4,V3), between-{F}(V6,V8,V7), equidistant-{F}(V6,V10,V4,V9), equidistant-{F}(V7,V10,V5,V9) | equidistant-{T}(V8,V10,V3,V9)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #70: input, references = 3, size of lhs = 7:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V4,V3,V5), equidistant-{F}(V6,V7,V4,V5), between-{F}(V6,V8,V7), equidistant-{F}(V6,V8,V4,V3) | equidistant-{T}(V8,V7,V3,V5)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #71: input, references = 3, size of lhs = 9:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V4,V3,V5), equidistant-{F}(V6,V7,V4,V3), equidistant-{F}(V7,V8,V3,V5), between-{F}(V6,V7,V8), equidistant-{F}(V6,V10,V4,V9), equidistant-{F}(V8,V10,V5,V9) | equidistant-{T}(V7,V10,V3,V9)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #72: input, references = 3, size of lhs = 7:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), equidistant-{F}(V5,V4,V5,V3), between-{F}(V5,V4,V6), equidistant-{F}(V6,V4,V6,V3), V4 == V3 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #73: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_insertion-{F}(V5,V6,V4,V3,V7) | equidistant-{T}(V4,V3,V5,V7)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #74: input, references = 3, size of lhs = 6:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), equidistant-{F}(V4,V3,V5,V6), P_insertion-{F}(V5,V6,V4,V7,V8), between-{F}(V4,V7,V3) | between-{T}(V5,V8,V6)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #75: input, references = 3, size of lhs = 6:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), equidistant-{F}(V4,V3,V5,V6), P_insertion-{F}(V5,V6,V4,V7,V8), between-{F}(V4,V7,V3) | equidistant-{T}(V7,V3,V8,V6)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #76: input, references = 3, size of lhs = 6:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_insertion-{F}(V5,V4,V5,V3,V6), between-{F}(V5,V3,V4), V3 == V6 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #77: input, references = 3, size of lhs = 7:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), equidistant-{F}(V6,V3,V4,V5), P_insertion-{F}(V7,V8,V6,V3,V9), P_insertion-{F}(V7,V8,V4,V5,V10), V9 == V10 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #78: input, references = 3, size of lhs = 7:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), equidistant-{F}(V6,V7,V4,V5), equidistant-{F}(V6,V8,V4,V3), equidistant-{F}(V8,V7,V3,V5), between-{F}(V6,V8,V7) | between-{T}(V4,V3,V5)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #79: input, references = 3, size of lhs = 6:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V4,V3,V5), between-{F}(V4,V3,V6), V4 == V3 | between-{T}(V4,V5,V6), between-{T}(V4,V6,V5)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #80: input, references = 3, size of lhs = 6:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V4,V3,V5), between-{F}(V4,V3,V6), V4 == V3 | between-{T}(V3,V5,V6), between-{T}(V3,V6,V5)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #81: input, references = 3, size of lhs = 6:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V5,V4,V6), between-{F}(V3,V4,V6), V4 == V6 | between-{T}(V5,V3,V4), between-{T}(V3,V5,V4)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #82: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V5,V3,V6), between-{F}(V5,V4,V6) | between-{T}(V5,V3,V4), between-{T}(V5,V4,V3)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #83: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V6,V4,V3), between-{F}(V6,V5,V3) | between-{T}(V4,V5,V3), between-{T}(V5,V4,V3)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #84: input, references = 3, size of lhs = 6:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V5,V6,V3), between-{F}(V6,V4,V7), between-{F}(V5,V7,V3) | between-{T}(V5,V4,V3)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #85: input, references = 3, size of lhs = 6:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V5,V3,V4), equidistant-{F}(V5,V3,V5,V4), V3 == V4 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #86: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V4,V3,V5) | colinear-{T}(V5,V3,V4)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #87: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V5,V4,V3) | colinear-{T}(V5,V3,V4)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #88: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), between-{F}(V3,V5,V4) | colinear-{T}(V5,V3,V4)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #89: input, references = 5, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), colinear-{F}(V5,V3,V4) | colinear-{T}(V4,V3,V5)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #90: input, references = 6, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), colinear-{F}(V5,V3,V4) | colinear-{T}(V3,V4,V5)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #91: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), colinear-{F}(V5,V3,V4) | colinear-{T}(V5,V4,V3)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #92: input, references = 4, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), colinear-{F}(V5,V3,V4) | colinear-{T}(V4,V5,V3)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #93: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), colinear-{F}(V5,V3,V4) | colinear-{T}(V3,V5,V4)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #94: input, references = 3, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), colinear-{F}(V0,V1,V2) | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #95: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), #-{F} V3, #-{F} V4 | colinear-{T}(V3,V3,V4)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #96: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), #-{F} V3, #-{F} V4 | colinear-{T}(V3,V4,V3)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #97: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), #-{F} V3, #-{F} V4 | colinear-{T}(V4,V3,V3)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #98: input, references = 3, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), #-{F} V4, #-{F} V5 | colinear-{T}(V4,V5,V4)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #99: input, references = 3, size of lhs = 7:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), equidistant-{F}(V6,V7,V4,V5), equidistant-{F}(V6,V8,V4,V3), equidistant-{F}(V8,V7,V3,V5), colinear-{F}(V6,V8,V7) | colinear-{T}(V4,V3,V5)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #100: input, references = 4, size of lhs = 6:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), colinear-{F}(V4,V3,V5), colinear-{F}(V4,V3,V6), V4 == V3 | colinear-{T}(V4,V5,V6)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #101: input, references = 4, size of lhs = 6:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), colinear-{F}(V4,V3,V5), colinear-{F}(V4,V3,V6), V4 == V3 | colinear-{T}(V3,V5,V6)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #102: input, references = 4, size of lhs = 5:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_u-{F}(V4), P_v-{F}(V4) | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #103: input, references = 4, size of lhs = 6:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_u-{F}(V3), P_v-{F}(V4), P_w-{F}(V5) | colinear-{T}(V5,V4,V3)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #104: input, references = 4, size of lhs = 7:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_u-{F}(V3), P_v-{F}(V4), P_w-{F}(V5), P_x-{F}(V6) | colinear-{T}(V6,V4,V3)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #105: input, references = 4, size of lhs = 9:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_u-{F}(V3), P_v-{F}(V4), P_w-{F}(V5), P_x-{F}(V6), colinear-{F}(V6,V5,V3), colinear-{F}(V6,V5,V4) | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #106: input, references = 3, size of lhs = 4:
% 2.58/2.75 #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3 | EXISTS V4: P_extension-{T}(V0,V1,V2,V3,V4)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #107: input, references = 3, size of lhs = 5:
% 2.58/2.75 #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3, #-{F} V4 | EXISTS V5: P_inner_pasch-{T}(V0,V1,V2,V3,V4,V5)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #108: input, references = 4, size of lhs = 0:
% 2.58/2.75 FALSE | EXISTS V0: P_lower_dimension_point_1-{T}(V0)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #109: input, references = 4, size of lhs = 0:
% 2.58/2.75 FALSE | EXISTS V0: P_lower_dimension_point_2-{T}(V0)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #110: input, references = 5, size of lhs = 0:
% 2.58/2.75 FALSE | EXISTS V0: P_lower_dimension_point_3-{T}(V0)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #111: input, references = 3, size of lhs = 5:
% 2.58/2.75 #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3, #-{F} V4 | EXISTS V5: P_euclid1-{T}(V0,V1,V2,V3,V4,V5)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #112: input, references = 3, size of lhs = 5:
% 2.58/2.75 #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3, #-{F} V4 | EXISTS V5: P_euclid2-{T}(V0,V1,V2,V3,V4,V5)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #113: input, references = 3, size of lhs = 6:
% 2.58/2.75 #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3, #-{F} V4, #-{F} V5 | EXISTS V6: P_continuous-{T}(V0,V1,V2,V3,V4,V5,V6)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #114: input, references = 3, size of lhs = 2:
% 2.58/2.75 #-{F} V0, #-{F} V1 | EXISTS V2: P_reflection-{T}(V0,V1,V2)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #115: input, references = 3, size of lhs = 4:
% 2.58/2.75 #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3 | EXISTS V4: P_insertion-{T}(V0,V1,V2,V3,V4)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #116: input, references = 4, size of lhs = 0:
% 2.58/2.75 FALSE | EXISTS V0: P_u-{T}(V0)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #117: input, references = 4, size of lhs = 0:
% 2.58/2.75 FALSE | EXISTS V0: P_v-{T}(V0)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #118: input, references = 4, size of lhs = 0:
% 2.58/2.75 FALSE | EXISTS V0: P_w-{T}(V0)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #119: input, references = 4, size of lhs = 0:
% 2.58/2.75 FALSE | EXISTS V0: P_x-{T}(V0)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 number of initial rules = 120
% 2.58/2.75
% 2.58/2.75 Simplifiers:
% 2.58/2.75 #120: unsound, references = 3, size of lhs = 3:
% 2.58/2.75 P_extension-{F}(V0,V1,V2,V3,V4), P_extension-{F}(V0,V1,V2,V3,V9), V4 == V9 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #121: unsound, references = 3, size of lhs = 3:
% 2.58/2.75 P_inner_pasch-{F}(V0,V1,V2,V3,V4,V5), P_inner_pasch-{F}(V0,V1,V2,V3,V4,V11), V5 == V11 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #122: unsound, references = 3, size of lhs = 3:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_1-{F}(V1), V0 == V1 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #123: unsound, references = 3, size of lhs = 3:
% 2.58/2.75 P_lower_dimension_point_2-{F}(V0), P_lower_dimension_point_2-{F}(V1), V0 == V1 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #124: unsound, references = 3, size of lhs = 3:
% 2.58/2.75 P_lower_dimension_point_3-{F}(V0), P_lower_dimension_point_3-{F}(V1), V0 == V1 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #125: unsound, references = 3, size of lhs = 3:
% 2.58/2.75 P_euclid1-{F}(V0,V1,V2,V3,V4,V5), P_euclid1-{F}(V0,V1,V2,V3,V4,V11), V5 == V11 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #126: unsound, references = 3, size of lhs = 3:
% 2.58/2.75 P_euclid2-{F}(V0,V1,V2,V3,V4,V5), P_euclid2-{F}(V0,V1,V2,V3,V4,V11), V5 == V11 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #127: unsound, references = 3, size of lhs = 3:
% 2.58/2.75 P_continuous-{F}(V0,V1,V2,V3,V4,V5,V6), P_continuous-{F}(V0,V1,V2,V3,V4,V5,V13), V6 == V13 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #128: unsound, references = 3, size of lhs = 3:
% 2.58/2.75 P_reflection-{F}(V0,V1,V2), P_reflection-{F}(V0,V1,V5), V2 == V5 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #129: unsound, references = 3, size of lhs = 3:
% 2.58/2.75 P_insertion-{F}(V0,V1,V2,V3,V4), P_insertion-{F}(V0,V1,V2,V3,V9), V4 == V9 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #130: unsound, references = 3, size of lhs = 3:
% 2.58/2.75 P_u-{F}(V0), P_u-{F}(V1), V0 == V1 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #131: unsound, references = 3, size of lhs = 3:
% 2.58/2.75 P_v-{F}(V0), P_v-{F}(V1), V0 == V1 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #132: unsound, references = 3, size of lhs = 3:
% 2.58/2.75 P_w-{F}(V0), P_w-{F}(V1), V0 == V1 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #133: unsound, references = 3, size of lhs = 3:
% 2.58/2.75 P_x-{F}(V0), P_x-{F}(V1), V0 == V1 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 number of simplifiers = 14
% 2.58/2.75
% 2.58/2.75 Learnt:
% 2.58/2.75 #135: exists( #110, #61 ), references = 1, size of lhs = 2:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V0) | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #170: mergings( V1 == V5, V5 == V8, V8 == V11, V11 == V14, V14 == V17, V17 == V20, V20 == V23, V23 == V26, V2 == V6, V6 == V9, V9 == V12, V12 == V15, V15 == V18, V18 == V21, V21 == V24, V24 == V27, V3 == V7, V7 == V10, V10 == V13, V13 == V16, V16 == V19, V19 == V22, V22 == V25, V25 == V28, V4 == V31; #144 ), references = 1, size of lhs = 8:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_u-{F}(V3), P_v-{F}(V4), V4 == V3, P_w-{F}(V5), colinear-{F}(V4,V3,V5) | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #204: mergings( V1 == V4, V4 == V7, V7 == V10, V10 == V13, V13 == V16, V16 == V19, V19 == V22, V22 == V25, V25 == V28, V28 == V31, V2 == V5, V5 == V8, V8 == V11, V11 == V14, V14 == V17, V17 == V20, V20 == V23, V23 == V26, V26 == V29, V29 == V32, V3 == V6, V6 == V9, V9 == V12, V12 == V15, V15 == V18, V18 == V21, V21 == V24, V24 == V27, V27 == V30, V30 == V33; #173 ), references = 1, size of lhs = 6:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_u-{F}(V3), P_v-{F}(V4), V4 == V3 | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #236: mergings( V1 == V4, V4 == V7, V7 == V10, V10 == V13, V13 == V16, V16 == V19, V19 == V22, V22 == V25, V25 == V28, V28 == V31, V2 == V5, V5 == V8, V8 == V11, V11 == V14, V14 == V17, V17 == V20, V20 == V23, V23 == V26, V26 == V29, V29 == V32, V3 == V6, V6 == V9, V9 == V12, V12 == V15, V15 == V18, V18 == V21, V21 == V24, V24 == V27, V27 == V30, V30 == V33; #205 ), references = 1, size of lhs = 4:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_u-{F}(V3) | P_v-{T}(V3)
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #272: mergings( V1 == V4, V4 == V7, V7 == V10, V10 == V13, V13 == V16, V16 == V19, V19 == V22, V22 == V25, V25 == V28, V28 == V31, V31 == V34, V2 == V5, V5 == V8, V8 == V11, V11 == V14, V14 == V17, V17 == V20, V20 == V23, V23 == V26, V26 == V29, V29 == V32, V32 == V35, V3 == V6, V6 == V9, V9 == V12, V12 == V15, V15 == V18, V18 == V21, V21 == V24, V24 == V27, V27 == V30, V30 == V33, V33 == V36; #238 ), references = 1, size of lhs = 3:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2) | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #296: mergings( V1 == V3, V3 == V5, V5 == V7, V7 == V9, V9 == V11, V11 == V13, V13 == V15, V15 == V17, V17 == V19, V19 == V21, V21 == V23, V2 == V4, V4 == V6, V6 == V8, V8 == V10, V10 == V12, V12 == V14, V14 == V16, V16 == V18, V18 == V20, V20 == V22, V22 == V24; #273 ), references = 1, size of lhs = 2:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1) | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #309: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V8 == V9, V9 == V10, V10 == V11, V11 == V12; #297 ), references = 1, size of lhs = 1:
% 2.58/2.75 P_lower_dimension_point_1-{F}(V0) | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 #311: exists( #108, #297 ), references = 1, size of lhs = 0:
% 2.58/2.75 FALSE | FALSE
% 2.58/2.75 (used 0 times, uses = {})
% 2.58/2.75
% 2.58/2.75 number of learnt formulas = 8
% 2.58/2.75
% 2.58/2.75
% 2.58/2.75 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.58/2.75
% 2.58/2.75 randbase = 1
%------------------------------------------------------------------------------