TSTP Solution File: GEO030-3 by Geo-III---2018C

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Geo-III---2018C
% Problem  : GEO030-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : geo -tptp_input -nonempty -inputfile %s

% Computer : n009.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 06:01:30 EDT 2022

% Result   : Unsatisfiable 2.35s 2.57s
% Output   : Refutation 2.35s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GEO030-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : geo -tptp_input -nonempty -inputfile %s
% 0.14/0.34  % Computer : n009.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Fri Jul 22 18:03:51 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 2.35/2.57  GeoParameters:
% 2.35/2.57  
% 2.35/2.57  tptp_input =     1
% 2.35/2.57  tptp_output =    0
% 2.35/2.57  nonempty =       1
% 2.35/2.57  inputfile =      /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.35/2.57  includepath =    /export/starexec/sandbox2/solver/bin/../../benchmark/
% 2.35/2.57  
% 2.35/2.57  
% 2.35/2.57  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.35/2.57  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.35/2.57  
% 2.35/2.57  RuleSystem INPUT:
% 2.35/2.57  
% 2.35/2.57  Initial Rules:
% 2.35/2.57  #0: input, references = 5, size of lhs = 2:
% 2.35/2.57     #-{F} V0, #-{F} V1 | equidistant-{T}(V0,V1,V1,V0)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #1: input, references = 5, size of lhs = 2:
% 2.35/2.57     equidistant-{F}(V5,V4,V0,V1), equidistant-{F}(V5,V4,V2,V3) | equidistant-{T}(V0,V1,V2,V3)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #2: input, references = 5, size of lhs = 2:
% 2.35/2.57     equidistant-{F}(V0,V1,V2,V2), V0 == V1 | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #3: input, references = 3, size of lhs = 1:
% 2.35/2.57     P_extension-{F}(V0,V1,V3,V2,V4) | between-{T}(V0,V1,V4)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #4: input, references = 3, size of lhs = 1:
% 2.35/2.57     P_extension-{F}(V0,V1,V3,V2,V4) | equidistant-{T}(V1,V4,V3,V2)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #5: input, references = 4, size of lhs = 7:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #6: input, references = 3, size of lhs = 2:
% 2.35/2.57     between-{F}(V0,V1,V0), V0 == V1 | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #7: input, references = 3, size of lhs = 3:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #8: input, references = 3, size of lhs = 3:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #9: input, references = 3, size of lhs = 4:
% 2.35/2.57     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
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #10: input, references = 3, size of lhs = 4:
% 2.35/2.57     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
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #11: input, references = 3, size of lhs = 4:
% 2.35/2.57     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
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #12: input, references = 3, size of lhs = 7:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #13: input, references = 3, size of lhs = 7:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #14: input, references = 3, size of lhs = 7:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #15: input, references = 3, size of lhs = 8:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #16: input, references = 3, size of lhs = 8:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #17: input, references = 3, size of lhs = 8:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #18: input, references = 5, size of lhs = 6:
% 2.35/2.57     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
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #19: input, references = 3, size of lhs = 5:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #20: input, references = 5, size of lhs = 4:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #21: input, references = 3, size of lhs = 4:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #22: input, references = 3, size of lhs = 4:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #23: input, references = 3, size of lhs = 4:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #24: input, references = 3, size of lhs = 4:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #25: input, references = 3, size of lhs = 4:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #26: input, references = 3, size of lhs = 4:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #27: input, references = 3, size of lhs = 5:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #28: input, references = 4, size of lhs = 5:
% 2.35/2.57     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
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #29: input, references = 3, size of lhs = 4:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #30: input, references = 3, size of lhs = 4:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #31: input, references = 3, size of lhs = 4:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #32: input, references = 4, size of lhs = 5:
% 2.35/2.57     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
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #33: input, references = 3, size of lhs = 5:
% 2.35/2.57     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
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #34: input, references = 3, size of lhs = 5:
% 2.35/2.57     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
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #35: input, references = 3, size of lhs = 5:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #36: input, references = 3, size of lhs = 7:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #37: input, references = 3, size of lhs = 8:
% 2.35/2.57     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
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #38: input, references = 3, size of lhs = 7:
% 2.35/2.57     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
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #39: input, references = 3, size of lhs = 8:
% 2.35/2.57     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
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #40: input, references = 3, size of lhs = 7:
% 2.35/2.57     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
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #41: input, references = 3, size of lhs = 5:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #42: input, references = 3, size of lhs = 6:
% 2.35/2.57     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
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #43: input, references = 3, size of lhs = 5:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #44: input, references = 3, size of lhs = 5:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #45: input, references = 3, size of lhs = 4:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #46: input, references = 3, size of lhs = 5:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #47: input, references = 3, size of lhs = 6:
% 2.35/2.57     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
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #48: input, references = 3, size of lhs = 6:
% 2.35/2.57     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
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #49: input, references = 3, size of lhs = 7:
% 2.35/2.57     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
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #50: input, references = 3, size of lhs = 7:
% 2.35/2.57     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
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #51: input, references = 3, size of lhs = 5:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #52: input, references = 3, size of lhs = 6:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #53: input, references = 3, size of lhs = 6:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #54: input, references = 3, size of lhs = 5:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #55: input, references = 3, size of lhs = 5:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #56: input, references = 4, size of lhs = 3:
% 2.35/2.57     P_lower_dimension_point_1-{F}(V1), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2) | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #57: input, references = 3, size of lhs = 3:
% 2.35/2.57     P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V2), P_lower_dimension_point_3-{F}(V2) | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #58: input, references = 3, size of lhs = 3:
% 2.35/2.57     P_lower_dimension_point_1-{F}(V2), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2) | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #59: input, references = 3, size of lhs = 4:
% 2.35/2.57     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
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #60: input, references = 3, size of lhs = 5:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #61: input, references = 3, size of lhs = 4:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #62: input, references = 3, size of lhs = 8:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #63: input, references = 4, size of lhs = 6:
% 2.35/2.57     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) | between-{T}(V3,V4,V5)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #64: input, references = 4, size of lhs = 7:
% 2.35/2.57     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_w1-{F}(V6) | equidistant-{T}(V3,V5,V3,V6)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #65: input, references = 5, size of lhs = 7:
% 2.35/2.57     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_w1-{F}(V6) | equidistant-{T}(V4,V5,V4,V6)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #66: input, references = 4, size of lhs = 7:
% 2.35/2.57     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), P_w-{F}(V5), P_w1-{F}(V6) | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #67: input, references = 4, size of lhs = 7:
% 2.35/2.57     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}(V6), P_w1-{F}(V6) | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #68: input, references = 4, size of lhs = 4:
% 2.35/2.57     #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3 | EXISTS V4: P_extension-{T}(V0,V1,V2,V3,V4)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #69: input, references = 3, size of lhs = 5:
% 2.35/2.57     #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3, #-{F} V4 | EXISTS V5: P_inner_pasch-{T}(V0,V1,V2,V3,V4,V5)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #70: input, references = 4, size of lhs = 0:
% 2.35/2.57     FALSE | EXISTS V0: P_lower_dimension_point_1-{T}(V0)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #71: input, references = 4, size of lhs = 0:
% 2.35/2.57     FALSE | EXISTS V0: P_lower_dimension_point_2-{T}(V0)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #72: input, references = 5, size of lhs = 0:
% 2.35/2.57     FALSE | EXISTS V0: P_lower_dimension_point_3-{T}(V0)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #73: input, references = 3, size of lhs = 5:
% 2.35/2.57     #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3, #-{F} V4 | EXISTS V5: P_euclid1-{T}(V0,V1,V2,V3,V4,V5)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #74: input, references = 3, size of lhs = 5:
% 2.35/2.57     #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3, #-{F} V4 | EXISTS V5: P_euclid2-{T}(V0,V1,V2,V3,V4,V5)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #75: input, references = 3, size of lhs = 6:
% 2.35/2.57     #-{F} V0, #-{F} V1, #-{F} V2, #-{F} V3, #-{F} V4, #-{F} V5 | EXISTS V6: P_continuous-{T}(V0,V1,V2,V3,V4,V5,V6)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #76: input, references = 4, size of lhs = 2:
% 2.35/2.57     #-{F} V0, #-{F} V1 | EXISTS V2: P_reflection-{T}(V0,V1,V2)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #77: input, references = 4, size of lhs = 0:
% 2.35/2.57     FALSE | EXISTS V0: P_u-{T}(V0)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #78: input, references = 4, size of lhs = 0:
% 2.35/2.57     FALSE | EXISTS V0: P_v-{T}(V0)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #79: input, references = 5, size of lhs = 0:
% 2.35/2.57     FALSE | EXISTS V0: P_w-{T}(V0)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #80: input, references = 6, size of lhs = 0:
% 2.35/2.57     FALSE | EXISTS V0: P_w1-{T}(V0)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  number of initial rules = 81
% 2.35/2.57  
% 2.35/2.57  Simplifiers:
% 2.35/2.57  #81: unsound, references = 3, size of lhs = 3:
% 2.35/2.57     P_extension-{F}(V0,V1,V2,V3,V4), P_extension-{F}(V0,V1,V2,V3,V9), V4 == V9 | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #82: unsound, references = 3, size of lhs = 3:
% 2.35/2.57     P_inner_pasch-{F}(V0,V1,V2,V3,V4,V5), P_inner_pasch-{F}(V0,V1,V2,V3,V4,V11), V5 == V11 | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #83: unsound, references = 3, size of lhs = 3:
% 2.35/2.57     P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_1-{F}(V1), V0 == V1 | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #84: unsound, references = 3, size of lhs = 3:
% 2.35/2.57     P_lower_dimension_point_2-{F}(V0), P_lower_dimension_point_2-{F}(V1), V0 == V1 | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #85: unsound, references = 3, size of lhs = 3:
% 2.35/2.57     P_lower_dimension_point_3-{F}(V0), P_lower_dimension_point_3-{F}(V1), V0 == V1 | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #86: unsound, references = 3, size of lhs = 3:
% 2.35/2.57     P_euclid1-{F}(V0,V1,V2,V3,V4,V5), P_euclid1-{F}(V0,V1,V2,V3,V4,V11), V5 == V11 | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #87: unsound, references = 3, size of lhs = 3:
% 2.35/2.57     P_euclid2-{F}(V0,V1,V2,V3,V4,V5), P_euclid2-{F}(V0,V1,V2,V3,V4,V11), V5 == V11 | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #88: unsound, references = 3, size of lhs = 3:
% 2.35/2.57     P_continuous-{F}(V0,V1,V2,V3,V4,V5,V6), P_continuous-{F}(V0,V1,V2,V3,V4,V5,V13), V6 == V13 | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #89: unsound, references = 3, size of lhs = 3:
% 2.35/2.57     P_reflection-{F}(V0,V1,V2), P_reflection-{F}(V0,V1,V5), V2 == V5 | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #90: unsound, references = 3, size of lhs = 3:
% 2.35/2.57     P_u-{F}(V0), P_u-{F}(V1), V0 == V1 | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #91: unsound, references = 3, size of lhs = 3:
% 2.35/2.57     P_v-{F}(V0), P_v-{F}(V1), V0 == V1 | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #92: unsound, references = 3, size of lhs = 3:
% 2.35/2.57     P_w-{F}(V0), P_w-{F}(V1), V0 == V1 | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #93: unsound, references = 3, size of lhs = 3:
% 2.35/2.57     P_w1-{F}(V0), P_w1-{F}(V1), V0 == V1 | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  number of simplifiers = 13
% 2.35/2.57  
% 2.35/2.57  Learnt:
% 2.35/2.57  #95: exists( #72, #56 ), references = 1, size of lhs = 2:
% 2.35/2.57     P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V0) | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #98: exists( #68, #28 ), references = 1, size of lhs = 6:
% 2.35/2.57     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, #-{F} V5 | P_extension-{T}(V3,V4,V5,V5,V4)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #99: exists( #68, #18 ), references = 1, size of lhs = 4:
% 2.35/2.57     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,V4,V5) | P_extension-{T}(V3,V4,V3,V4,V5)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #101: exists( #80, #66 ), references = 1, size of lhs = 6:
% 2.35/2.57     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}(V3), P_w-{F}(V4) | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #103: exists( #79, #100 ), references = 2, size of lhs = 5:
% 2.35/2.57     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}(V3) | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #107: exists( #76, #32 ), references = 1, size of lhs = 4:
% 2.35/2.57     P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), #-{F} V3 | P_reflection-{T}(V3,V3,V3)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #108: exists( #76, #18 ), references = 1, size of lhs = 4:
% 2.35/2.57     P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2), P_extension-{F}(V3,V4,V3,V4,V5) | P_reflection-{T}(V3,V4,V5)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #118: mergings( V1 == V6, V2 == V7, V3 == V8; #114 ), references = 1, size of lhs = 6:
% 2.35/2.57     P_u-{F}(V0), P_v-{F}(V1), P_w-{F}(V1), P_lower_dimension_point_1-{F}(V2), P_lower_dimension_point_2-{F}(V3), P_lower_dimension_point_3-{F}(V4) | P_w1-{T}(V1)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #133: mergings( V1 == V6, V6 == V12, V2 == V7, V7 == V13, V3 == V8, V8 == V14, V4 == V9, V5 == V10; #124 ), references = 2, size of lhs = 11:
% 2.35/2.57     P_u-{F}(V0), P_v-{F}(V1), V0 == V1, equidistant-{F}(V0,V1,V0,V1), P_w-{F}(V2), between-{F}(V0,V1,V2), P_lower_dimension_point_1-{F}(V3), P_lower_dimension_point_2-{F}(V4), P_lower_dimension_point_3-{F}(V5), between-{F}(V0,V1,V6), equidistant-{F}(V1,V2,V1,V6) | P_w1-{T}(V6)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #149: mergings( V1 == V6, V6 == V9, V2 == V7, V7 == V10, V3 == V8, V8 == V11, V4 == V12, V5 == V13; #140 ), references = 2, size of lhs = 7:
% 2.35/2.57     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), V3 == V4, equidistant-{F}(V3,V4,V3,V4) | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #153: exists( #78, #151 ), references = 1, size of lhs = 4:
% 2.35/2.57     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)
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #159: mergings( V1 == V4, V2 == V5, V3 == V6; #155 ), references = 1, size of lhs = 3:
% 2.35/2.57     P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1), P_lower_dimension_point_3-{F}(V2) | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #163: mergings( V1 == V3, V2 == V4; #160 ), references = 1, size of lhs = 2:
% 2.35/2.57     P_lower_dimension_point_1-{F}(V0), P_lower_dimension_point_2-{F}(V1) | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #166: mergings( V1 == V2; #164 ), references = 1, size of lhs = 1:
% 2.35/2.57     P_lower_dimension_point_1-{F}(V0) | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  #168: exists( #70, #164 ), references = 1, size of lhs = 0:
% 2.35/2.57     FALSE | FALSE
% 2.35/2.57        (used 0 times, uses = {})
% 2.35/2.57  
% 2.35/2.57  number of learnt formulas = 15
% 2.35/2.57  
% 2.35/2.57  
% 2.35/2.57  % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.35/2.57  
% 2.35/2.57  randbase = 1
%------------------------------------------------------------------------------