%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO021-3 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n014.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 : Tue May 5 04:19:02 PM UTC 2026
% Result : Unsatisfiable 0.35s 1.61s
% Output : CNFRefutation 0.75s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 72)
% Comments :
%------------------------------------------------------------------------------
cnf(continuity2,axiom,
( equidistant(X1,X6,X1,continuous(X1,X2,X3,X6,X4,X5))
| ~ equidistant(X1,X2,X1,X3)
| ~ equidistant(X1,X4,X1,X5)
| ~ between(X1,X2,X4)
| ~ between(X2,X6,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',continuity2) ).
cnf(continuity1,axiom,
( between(X3,continuous(X1,X2,X3,X6,X4,X5),X5)
| ~ equidistant(X1,X2,X1,X3)
| ~ equidistant(X1,X4,X1,X5)
| ~ between(X1,X2,X4)
| ~ between(X2,X6,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',continuity1) ).
cnf(euclid3,axiom,
( X1 = X2
| between(euclid1(X1,X4,X2,X5,X3),X3,euclid2(X1,X4,X2,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X2,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',euclid3) ).
cnf(euclid1,axiom,
( X1 = X2
| between(X1,X4,euclid1(X1,X4,X2,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X2,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',euclid1) ).
cnf(euclid2,axiom,
( X1 = X2
| between(X1,X5,euclid2(X1,X4,X2,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X2,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',euclid2) ).
cnf(inner_pasch1,axiom,
( between(X2,inner_pasch(X1,X2,X3,X5,X4),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',inner_pasch1) ).
cnf(inner_pasch2,axiom,
( between(X5,inner_pasch(X1,X2,X3,X5,X4),X1)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',inner_pasch2) ).
cnf(outer_five_segment,axiom,
( X1 = X2
| equidistant(X5,X7,X6,X8)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X7,X3,X8)
| ~ equidistant(X2,X7,X4,X8)
| ~ between(X1,X2,X5)
| ~ between(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',outer_five_segment) ).
cnf(upper_dimension,axiom,
( between(X1,X4,X5)
| between(X4,X5,X1)
| between(X5,X1,X4)
| X2 = X3
| ~ equidistant(X1,X2,X1,X3)
| ~ equidistant(X4,X2,X4,X3)
| ~ equidistant(X5,X2,X5,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',upper_dimension) ).
cnf(transitivity_for_equidistance,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
cnf(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
cnf(d3,axiom,
( equidistant(X2,X1,X3,X4)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3) ).
cnf(d2,axiom,
( equidistant(X3,X4,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
cnf(identity_for_equidistance,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
cnf(prove_symmetry,negated_conjecture,
~ equidistant(x,w,v,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_symmetry) ).
cnf(d1,axiom,
equidistant(X1,X2,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
cnf(reflexivity_for_equidistance,axiom,
equidistant(X1,X2,X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).
cnf(u_to_v_equals_w_to_x,hypothesis,
equidistant(u,v,w,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_v_equals_w_to_x) ).
cnf(identity_for_betweeness,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).
cnf(lower_dimension3,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',lower_dimension3) ).
cnf(lower_dimension2,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',lower_dimension2) ).
cnf(lower_dimension1,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',lower_dimension1) ).
cnf(i_0_23,axiom,
( equidistant(X1,X6,X1,continuous(X1,X2,X3,X6,X4,X5))
| ~ equidistant(X1,X2,X1,X3)
| ~ equidistant(X1,X4,X1,X5)
| ~ between(X1,X2,X4)
| ~ between(X2,X6,X4) ),
continuity2,
[final] ).
cnf(i_0_24,axiom,
( between(X3,continuous(X1,X2,X3,X6,X4,X5),X5)
| ~ equidistant(X1,X2,X1,X3)
| ~ equidistant(X1,X4,X1,X5)
| ~ between(X1,X2,X4)
| ~ between(X2,X6,X4) ),
continuity1,
[final] ).
cnf(i_0_25,axiom,
( X1 = X2
| between(euclid1(X1,X4,X2,X5,X3),X3,euclid2(X1,X4,X2,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X2,X5) ),
euclid3,
[final] ).
cnf(i_0_26,axiom,
( X1 = X2
| between(X1,X4,euclid1(X1,X4,X2,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X2,X5) ),
euclid1,
[final] ).
cnf(i_0_27,axiom,
( X1 = X2
| between(X1,X5,euclid2(X1,X4,X2,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X2,X5) ),
euclid2,
[final] ).
cnf(i_0_28,axiom,
( between(X2,inner_pasch(X1,X2,X3,X5,X4),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
inner_pasch1,
[final] ).
cnf(i_0_29,axiom,
( between(X5,inner_pasch(X1,X2,X3,X5,X4),X1)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
inner_pasch2,
[final] ).
cnf(i_0_30,axiom,
( X1 = X2
| equidistant(X5,X7,X6,X8)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X7,X3,X8)
| ~ equidistant(X2,X7,X4,X8)
| ~ between(X1,X2,X5)
| ~ between(X3,X4,X6) ),
outer_five_segment,
[final] ).
cnf(i_0_31,axiom,
( between(X1,X4,X5)
| between(X4,X5,X1)
| between(X5,X1,X4)
| X2 = X3
| ~ equidistant(X1,X2,X1,X3)
| ~ equidistant(X4,X2,X4,X3)
| ~ equidistant(X5,X2,X5,X3) ),
upper_dimension,
[final] ).
cnf(i_0_32,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
transitivity_for_equidistance,
[final] ).
cnf(i_0_33,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2,
[final] ).
cnf(i_0_34,axiom,
( equidistant(X2,X1,X3,X4)
| ~ equidistant(X1,X2,X3,X4) ),
d3,
[final] ).
cnf(i_0_35,axiom,
( equidistant(X3,X4,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
d2,
[final] ).
cnf(i_0_36,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1,
[final] ).
cnf(i_0_37,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
identity_for_equidistance,
[final] ).
cnf(i_0_38,negated_conjecture,
~ equidistant(x,w,v,u),
prove_symmetry,
[final] ).
cnf(i_0_39,axiom,
equidistant(X1,X2,X1,X2),
d1,
[final] ).
cnf(i_0_40,axiom,
equidistant(X1,X2,X2,X1),
reflexivity_for_equidistance,
[final] ).
cnf(i_0_41,hypothesis,
equidistant(u,v,w,x),
u_to_v_equals_w_to_x,
[final] ).
cnf(i_0_42,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
identity_for_betweeness,
[final] ).
cnf(i_0_43,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
lower_dimension3,
[final] ).
cnf(i_0_44,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
lower_dimension2,
[final] ).
cnf(i_0_45,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
lower_dimension1,
[final] ).
cnf(i_0_46,axiom,
X1 = X1 ).
cnf(i_0_47,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_48,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_49,axiom,
( X1 != X2
| ~ equidistant(X1,X3,X4,X5)
| equidistant(X2,X3,X4,X5) ) ).
cnf(i_0_50,axiom,
( X1 != X2
| ~ equidistant(X3,X1,X4,X5)
| equidistant(X3,X2,X4,X5) ) ).
cnf(i_0_51,axiom,
( X1 != X2
| ~ equidistant(X3,X4,X1,X5)
| equidistant(X3,X4,X2,X5) ) ).
cnf(i_0_52,axiom,
( X1 != X2
| ~ equidistant(X3,X4,X5,X1)
| equidistant(X3,X4,X5,X2) ) ).
cnf(i_0_53,axiom,
( X1 != X2
| ~ between(X1,X3,X4)
| between(X2,X3,X4) ) ).
cnf(i_0_54,axiom,
( X1 != X2
| ~ between(X3,X1,X4)
| between(X3,X2,X4) ) ).
cnf(i_0_55,axiom,
( X1 != X2
| ~ between(X3,X4,X1)
| between(X3,X4,X2) ) ).
cnf(i_0_46_001,axiom,
X1 = X1 ).
cnf(i_0_47_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_48_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_49_004,axiom,
( X1 != X2
| ~ equidistant(X1,X3,X4,X5)
| equidistant(X2,X3,X4,X5) ) ).
cnf(i_0_50_005,axiom,
( X1 != X2
| ~ equidistant(X3,X1,X4,X5)
| equidistant(X3,X2,X4,X5) ) ).
cnf(i_0_51_006,axiom,
( X1 != X2
| ~ equidistant(X3,X4,X1,X5)
| equidistant(X3,X4,X2,X5) ) ).
cnf(i_0_52_007,axiom,
( X1 != X2
| ~ equidistant(X3,X4,X5,X1)
| equidistant(X3,X4,X5,X2) ) ).
cnf(i_0_53_008,axiom,
( X1 != X2
| ~ between(X1,X3,X4)
| between(X2,X3,X4) ) ).
cnf(i_0_54_009,axiom,
( X1 != X2
| ~ between(X3,X1,X4)
| between(X3,X2,X4) ) ).
cnf(i_0_55_010,axiom,
( X1 != X2
| ~ between(X3,X4,X1)
| between(X3,X4,X2) ) ).
cnf(i_0_56,plain,
equidistant(extension(X1,X2,X3,X4),X2,X3,X4),
inference(scs_inference,[],[i_0_33,i_0_34]) ).
cnf(i_0_57,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X2,X1,X3,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_58,plain,
equidistant(X1,X2,X3,extension(X4,X3,X1,X2)),
inference(scs_inference,[],[i_0_33,i_0_34,i_0_35]) ).
cnf(i_0_59,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X1,X2) ),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_60,plain,
X1 = extension(X2,X1,X3,X3),
inference(scs_inference,[],[i_0_33,i_0_34,i_0_35,i_0_37]) ).
cnf(i_0_61,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_62,plain,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
inference(rename_variables,[],[i_0_37]) ).
cnf(i_0_63,plain,
~ equidistant(v,u,x,w),
inference(scs_inference,[],[i_0_38,i_0_39,i_0_33,i_0_34,i_0_35,i_0_37,i_0_32]) ).
cnf(i_0_64,plain,
equidistant(X1,X2,X1,X2),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_65,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X5,X6,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_66,plain,
extension(X1,x,v,u) != w,
inference(scs_inference,[],[i_0_38,i_0_39,i_0_33,i_0_61,i_0_34,i_0_35,i_0_37,i_0_32,i_0_50]) ).
cnf(i_0_67,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_68,plain,
extension(lower_dimension_point_3,lower_dimension_point_1,X1,X2) != lower_dimension_point_2,
inference(scs_inference,[],[i_0_38,i_0_39,i_0_33,i_0_61,i_0_36,i_0_43,i_0_34,i_0_35,i_0_37,i_0_32,i_0_50,i_0_55]) ).
cnf(i_0_69,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_70,plain,
extension(X1,X2,X3,X3) = X2,
inference(scs_inference,[],[i_0_38,i_0_39,i_0_33,i_0_61,i_0_36,i_0_43,i_0_34,i_0_35,i_0_37,i_0_32,i_0_50,i_0_55,i_0_47]) ).
cnf(i_0_71,plain,
~ equidistant(extension(X1,x,X2,X2),w,v,u),
inference(scs_inference,[],[i_0_38,i_0_39,i_0_33,i_0_61,i_0_36,i_0_43,i_0_34,i_0_35,i_0_37,i_0_32,i_0_50,i_0_55,i_0_47,i_0_49]) ).
cnf(i_0_72,plain,
( X1 != v
| ~ equidistant(x,w,X1,u) ),
inference(scs_inference,[],[i_0_38,i_0_39,i_0_33,i_0_61,i_0_36,i_0_43,i_0_34,i_0_35,i_0_37,i_0_32,i_0_50,i_0_55,i_0_47,i_0_49,i_0_51]) ).
cnf(i_0_73,plain,
( w != u
| x != v ),
inference(scs_inference,[],[i_0_38,i_0_39,i_0_64,i_0_33,i_0_61,i_0_36,i_0_43,i_0_34,i_0_35,i_0_37,i_0_32,i_0_50,i_0_55,i_0_47,i_0_49,i_0_51,i_0_52]) ).
cnf(i_0_74,plain,
equidistant(X1,X2,X1,X2),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_75,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_76,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_77,plain,
( between(X1,inner_pasch(X2,X1,X3,X4,X5),X5)
| ~ between(X2,X1,X3)
| ~ between(X5,X4,X3) ),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_78,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_79,plain,
( x != v
| inner_pasch(lower_dimension_point_2,lower_dimension_point_3,extension(lower_dimension_point_2,lower_dimension_point_3,X1,X2),lower_dimension_point_3,lower_dimension_point_2) != lower_dimension_point_1 ),
inference(scs_inference,[],[i_0_38,i_0_39,i_0_64,i_0_33,i_0_61,i_0_36,i_0_69,i_0_76,i_0_43,i_0_34,i_0_35,i_0_37,i_0_32,i_0_50,i_0_55,i_0_47,i_0_49,i_0_51,i_0_52,i_0_54,i_0_28,i_0_29]) ).
cnf(i_0_80,plain,
~ equidistant(x,w,v,u),
inference(equality_inference,[],[72]) ).
cnf(i_0_81,plain,
equidistant(X1,X2,extension(X3,X4,X1,X2),X4),
inference(scs_inference,[],[i_0_56,i_0_35]) ).
cnf(i_0_82,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X1,X2) ),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_83,plain,
equidistant(X1,X2,X3,extension(X4,X3,X2,X1)),
inference(scs_inference,[],[i_0_56,i_0_58,i_0_35,i_0_34]) ).
cnf(i_0_84,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X2,X1,X3,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_85,plain,
extension(X1,x,v,u) != extension(X2,w,X3,X3),
inference(scs_inference,[],[i_0_56,i_0_58,i_0_70,i_0_66,i_0_35,i_0_34,i_0_48]) ).
cnf(i_0_86,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_87,plain,
~ equidistant(extension(X1,X2,v,u),X2,x,w),
inference(scs_inference,[],[i_0_38,i_0_56,i_0_58,i_0_70,i_0_66,i_0_35,i_0_34,i_0_48,i_0_32]) ).
cnf(i_0_88,plain,
equidistant(extension(X1,X2,X3,X4),X2,X3,X4),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_89,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X5,X6,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_90,plain,
~ equidistant(extension(X1,extension(X2,x,X3,X3),X4,X4),w,v,u),
inference(scs_inference,[],[i_0_38,i_0_56,i_0_58,i_0_70,i_0_86,i_0_66,i_0_71,i_0_35,i_0_34,i_0_48,i_0_32,i_0_49]) ).
cnf(i_0_91,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_92,plain,
~ equidistant(x,extension(X1,w,X2,X2),v,u),
inference(scs_inference,[],[i_0_38,i_0_56,i_0_58,i_0_70,i_0_86,i_0_91,i_0_66,i_0_71,i_0_35,i_0_34,i_0_48,i_0_32,i_0_49,i_0_50]) ).
cnf(i_0_93,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_94,plain,
~ equidistant(x,w,extension(X1,v,X2,X2),u),
inference(scs_inference,[],[i_0_38,i_0_56,i_0_58,i_0_70,i_0_86,i_0_91,i_0_93,i_0_66,i_0_71,i_0_35,i_0_34,i_0_48,i_0_32,i_0_49,i_0_50,i_0_51]) ).
cnf(i_0_95,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_96,plain,
~ equidistant(x,w,v,extension(X1,u,X2,X2)),
inference(scs_inference,[],[i_0_38,i_0_56,i_0_58,i_0_70,i_0_86,i_0_91,i_0_93,i_0_95,i_0_66,i_0_71,i_0_35,i_0_34,i_0_48,i_0_32,i_0_49,i_0_50,i_0_51,i_0_52]) ).
cnf(i_0_97,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_98,plain,
~ between(extension(X1,lower_dimension_point_2,X2,X2),lower_dimension_point_3,lower_dimension_point_1),
inference(scs_inference,[],[i_0_38,i_0_56,i_0_58,i_0_70,i_0_86,i_0_91,i_0_93,i_0_95,i_0_97,i_0_66,i_0_71,i_0_44,i_0_35,i_0_34,i_0_48,i_0_32,i_0_49,i_0_50,i_0_51,i_0_52,i_0_53]) ).
cnf(i_0_99,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_100,plain,
~ between(lower_dimension_point_2,extension(X1,lower_dimension_point_3,X2,X2),lower_dimension_point_1),
inference(scs_inference,[],[i_0_38,i_0_56,i_0_58,i_0_70,i_0_86,i_0_91,i_0_93,i_0_95,i_0_97,i_0_99,i_0_66,i_0_71,i_0_44,i_0_35,i_0_34,i_0_48,i_0_32,i_0_49,i_0_50,i_0_51,i_0_52,i_0_53,i_0_54]) ).
cnf(i_0_101,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_102,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,extension(X1,lower_dimension_point_1,X2,X2)),
inference(scs_inference,[],[i_0_38,i_0_56,i_0_58,i_0_70,i_0_86,i_0_91,i_0_93,i_0_95,i_0_97,i_0_99,i_0_101,i_0_66,i_0_71,i_0_44,i_0_35,i_0_34,i_0_48,i_0_32,i_0_49,i_0_50,i_0_51,i_0_52,i_0_53,i_0_54,i_0_55]) ).
cnf(i_0_103,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_104,plain,
equidistant(X1,X2,X3,extension(X4,X3,X1,X2)),
inference(rename_variables,[],[i_0_58]) ).
cnf(i_0_105,plain,
( between(X1,X2,X3)
| between(X2,X3,X1)
| ~ equidistant(X3,X4,X3,X5)
| ~ equidistant(X1,X4,X1,X5)
| ~ equidistant(X2,X4,X2,X5)
| between(X3,X1,X2)
| X4 = X5 ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_106,plain,
equidistant(X1,X2,X1,X2),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_107,plain,
equidistant(extension(X1,X2,X3,X4),X2,X3,X4),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_108,plain,
equidistant(X1,X2,X3,extension(X4,X3,X1,X2)),
inference(rename_variables,[],[i_0_58]) ).
cnf(i_0_109,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_110,plain,
extension(lower_dimension_point_3,lower_dimension_point_1,X1,X2) != lower_dimension_point_2,
inference(rename_variables,[],[i_0_68]) ).
cnf(i_0_111,plain,
( ~ between(X1,lower_dimension_point_2,extension(extension(lower_dimension_point_3,lower_dimension_point_1,X1,extension(X2,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_1)),lower_dimension_point_2,X3,X4))
| equidistant(extension(extension(lower_dimension_point_3,lower_dimension_point_1,X1,extension(X2,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_1)),lower_dimension_point_2,X3,X4),lower_dimension_point_1,extension(extension(lower_dimension_point_3,lower_dimension_point_1,X1,extension(X2,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_1)),lower_dimension_point_2,X3,X4),extension(X2,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_1))
| ~ equidistant(extension(lower_dimension_point_3,lower_dimension_point_1,X1,extension(X2,lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_1)),lower_dimension_point_2,X1,lower_dimension_point_2) ),
inference(scs_inference,[],[i_0_38,i_0_56,i_0_88,i_0_58,i_0_104,i_0_70,i_0_86,i_0_91,i_0_93,i_0_95,i_0_97,i_0_99,i_0_101,i_0_66,i_0_71,i_0_68,i_0_44,i_0_45,i_0_39,i_0_36,i_0_43,i_0_35,i_0_34,i_0_48,i_0_32,i_0_49,i_0_50,i_0_51,i_0_52,i_0_53,i_0_54,i_0_55,i_0_30]) ).
cnf(i_0_112,plain,
extension(X1,u,x,w) != v,
inference(scs_inference,[],[i_0_81,i_0_72]) ).
cnf(i_0_113,plain,
equidistant(X1,X2,extension(X3,X4,X1,X2),X4),
inference(rename_variables,[],[i_0_81]) ).
cnf(i_0_114,plain,
equidistant(X1,extension(X2,X1,X3,X4),X4,X3),
inference(scs_inference,[],[i_0_81,i_0_83,i_0_72,i_0_35]) ).
cnf(i_0_115,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X1,X2) ),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_116,plain,
equidistant(X1,X2,extension(X3,X4,X2,X1),X4),
inference(scs_inference,[],[i_0_81,i_0_113,i_0_83,i_0_72,i_0_35,i_0_34]) ).
cnf(i_0_117,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X2,X1,X3,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_118,plain,
equidistant(extension(X1,X2,X3,X4),X2,X5,extension(X6,X5,X4,X3)),
inference(scs_inference,[],[i_0_81,i_0_113,i_0_83,i_0_72,i_0_35,i_0_34,i_0_32]) ).
cnf(i_0_119,plain,
equidistant(X1,X2,X3,extension(X4,X3,X2,X1)),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_120,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X5,X6,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_121,plain,
~ equidistant(extension(X1,X2,v,u),extension(X3,X2,X4,X4),x,w),
inference(scs_inference,[],[i_0_81,i_0_113,i_0_83,i_0_87,i_0_70,i_0_72,i_0_35,i_0_34,i_0_32,i_0_50]) ).
cnf(i_0_122,plain,
~ equidistant(extension(X1,X2,v,u),X2,x,w),
inference(rename_variables,[],[i_0_87]) ).
cnf(i_0_123,plain,
~ equidistant(extension(X1,X2,v,u),X2,extension(X3,x,X4,X4),w),
inference(scs_inference,[],[i_0_81,i_0_113,i_0_83,i_0_87,i_0_122,i_0_70,i_0_72,i_0_35,i_0_34,i_0_32,i_0_50,i_0_51]) ).
cnf(i_0_124,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_125,plain,
~ equidistant(extension(X1,X2,v,u),X2,x,extension(X3,w,X4,X4)),
inference(scs_inference,[],[i_0_81,i_0_113,i_0_83,i_0_87,i_0_122,i_0_70,i_0_124,i_0_72,i_0_35,i_0_34,i_0_32,i_0_50,i_0_51,i_0_52]) ).
cnf(i_0_126,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_127,plain,
~ between(extension(X1,extension(X2,lower_dimension_point_2,X3,X3),X4,X4),lower_dimension_point_3,lower_dimension_point_1),
inference(scs_inference,[],[i_0_81,i_0_113,i_0_83,i_0_87,i_0_122,i_0_70,i_0_124,i_0_126,i_0_98,i_0_72,i_0_35,i_0_34,i_0_32,i_0_50,i_0_51,i_0_52,i_0_53]) ).
cnf(i_0_128,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_129,plain,
~ between(extension(X1,lower_dimension_point_2,X2,X2),extension(X3,lower_dimension_point_3,X4,X4),lower_dimension_point_1),
inference(scs_inference,[],[i_0_81,i_0_113,i_0_83,i_0_87,i_0_122,i_0_70,i_0_124,i_0_126,i_0_128,i_0_98,i_0_72,i_0_35,i_0_34,i_0_32,i_0_50,i_0_51,i_0_52,i_0_53,i_0_54]) ).
cnf(i_0_130,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_131,plain,
~ between(extension(X1,lower_dimension_point_2,X2,X2),lower_dimension_point_3,extension(X3,lower_dimension_point_1,X4,X4)),
inference(scs_inference,[],[i_0_81,i_0_113,i_0_83,i_0_87,i_0_122,i_0_70,i_0_124,i_0_126,i_0_128,i_0_130,i_0_98,i_0_72,i_0_35,i_0_34,i_0_32,i_0_50,i_0_51,i_0_52,i_0_53,i_0_54,i_0_55]) ).
cnf(i_0_132,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_133,plain,
~ equidistant(extension(X1,extension(X2,X3,v,u),X4,X4),X3,x,w),
inference(scs_inference,[],[i_0_81,i_0_113,i_0_83,i_0_87,i_0_122,i_0_70,i_0_124,i_0_126,i_0_128,i_0_130,i_0_132,i_0_98,i_0_72,i_0_35,i_0_34,i_0_32,i_0_50,i_0_51,i_0_52,i_0_53,i_0_54,i_0_55,i_0_49]) ).
cnf(i_0_134,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_135,plain,
equidistant(X1,X2,X3,extension(X4,X3,X2,X1)),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_136,plain,
( between(X1,X2,X3)
| between(X2,X3,X1)
| ~ equidistant(X3,X4,X3,X5)
| ~ equidistant(X1,X4,X1,X5)
| ~ equidistant(X2,X4,X2,X5)
| between(X3,X1,X2)
| X4 = X5 ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_137,plain,
equidistant(X1,X2,X1,X2),
inference(rename_variables,[],[i_0_39]) ).
cnf(i_0_138,plain,
equidistant(X1,X2,extension(X3,X4,X1,X2),X4),
inference(rename_variables,[],[i_0_81]) ).
cnf(i_0_139,plain,
equidistant(X1,X2,X3,extension(X4,X3,X2,X1)),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_140,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_141,plain,
( ~ between(extension(X1,extension(X2,w,X3,w),extension(X4,x,v,u),X3),w,extension(extension(X4,x,v,u),w,X5,X6))
| equidistant(extension(extension(X4,x,v,u),w,X5,X6),X3,extension(extension(X4,x,v,u),w,X5,X6),extension(X2,w,X3,w))
| ~ equidistant(extension(X4,x,v,u),w,extension(X1,extension(X2,w,X3,w),extension(X4,x,v,u),X3),w) ),
inference(scs_inference,[],[i_0_81,i_0_113,i_0_83,i_0_119,i_0_135,i_0_87,i_0_122,i_0_70,i_0_124,i_0_126,i_0_128,i_0_130,i_0_132,i_0_66,i_0_98,i_0_39,i_0_36,i_0_72,i_0_35,i_0_34,i_0_32,i_0_50,i_0_51,i_0_52,i_0_53,i_0_54,i_0_55,i_0_49,i_0_30]) ).
cnf(i_0_142,plain,
extension(X1,u,w,x) != v,
inference(scs_inference,[],[i_0_116,i_0_72]) ).
cnf(i_0_143,plain,
equidistant(X1,X2,extension(X3,X4,X2,X1),X4),
inference(rename_variables,[],[i_0_116]) ).
cnf(i_0_144,plain,
equidistant(extension(X1,X2,X3,X4),X2,X4,X3),
inference(scs_inference,[],[i_0_116,i_0_143,i_0_72,i_0_35]) ).
cnf(i_0_145,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X1,X2) ),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_146,plain,
equidistant(X1,extension(X2,X1,X3,X4),X5,extension(X6,X5,X4,X3)),
inference(scs_inference,[],[i_0_116,i_0_143,i_0_118,i_0_72,i_0_35,i_0_34]) ).
cnf(i_0_147,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X2,X1,X3,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_148,plain,
~ equidistant(X1,extension(X2,X1,u,v),x,w),
inference(scs_inference,[],[i_0_38,i_0_114,i_0_116,i_0_143,i_0_118,i_0_72,i_0_35,i_0_34,i_0_32]) ).
cnf(i_0_149,plain,
equidistant(X1,extension(X2,X1,X3,X4),X4,X3),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_150,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X5,X6,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_151,plain,
extension(X1,u,x,w) != extension(X2,v,X3,X3),
inference(scs_inference,[],[i_0_38,i_0_114,i_0_116,i_0_143,i_0_118,i_0_112,i_0_70,i_0_72,i_0_35,i_0_34,i_0_32,i_0_48]) ).
cnf(i_0_152,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_153,plain,
~ between(extension(X1,extension(X2,lower_dimension_point_2,X3,X3),X4,X4),extension(X5,lower_dimension_point_3,X6,X6),lower_dimension_point_1),
inference(scs_inference,[],[i_0_38,i_0_114,i_0_116,i_0_143,i_0_118,i_0_112,i_0_70,i_0_152,i_0_129,i_0_72,i_0_35,i_0_34,i_0_32,i_0_48,i_0_53]) ).
cnf(i_0_154,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_155,plain,
~ between(extension(X1,lower_dimension_point_2,X2,X2),extension(X3,extension(X4,lower_dimension_point_3,X5,X5),X6,X6),lower_dimension_point_1),
inference(scs_inference,[],[i_0_38,i_0_114,i_0_116,i_0_143,i_0_118,i_0_112,i_0_70,i_0_152,i_0_154,i_0_129,i_0_72,i_0_35,i_0_34,i_0_32,i_0_48,i_0_53,i_0_54]) ).
cnf(i_0_156,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_157,plain,
~ between(extension(X1,extension(X2,lower_dimension_point_2,X3,X3),X4,X4),lower_dimension_point_3,extension(X5,lower_dimension_point_1,X6,X6)),
inference(scs_inference,[],[i_0_38,i_0_114,i_0_116,i_0_143,i_0_118,i_0_112,i_0_70,i_0_152,i_0_154,i_0_156,i_0_127,i_0_129,i_0_72,i_0_35,i_0_34,i_0_32,i_0_48,i_0_53,i_0_54,i_0_55]) ).
cnf(i_0_158,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_159,plain,
~ equidistant(extension(X1,X2,v,u),extension(X3,X2,X4,X4),extension(X5,x,X6,X6),w),
inference(scs_inference,[],[i_0_38,i_0_114,i_0_116,i_0_143,i_0_118,i_0_123,i_0_112,i_0_70,i_0_152,i_0_154,i_0_156,i_0_158,i_0_127,i_0_129,i_0_72,i_0_35,i_0_34,i_0_32,i_0_48,i_0_53,i_0_54,i_0_55,i_0_50]) ).
cnf(i_0_160,plain,
~ equidistant(extension(X1,X2,v,u),X2,extension(X3,x,X4,X4),w),
inference(rename_variables,[],[i_0_123]) ).
cnf(i_0_161,plain,
~ equidistant(extension(X1,X2,v,u),X2,extension(X3,extension(X4,x,X5,X5),X6,X6),w),
inference(scs_inference,[],[i_0_38,i_0_114,i_0_116,i_0_143,i_0_118,i_0_123,i_0_160,i_0_112,i_0_70,i_0_152,i_0_154,i_0_156,i_0_158,i_0_127,i_0_129,i_0_72,i_0_35,i_0_34,i_0_32,i_0_48,i_0_53,i_0_54,i_0_55,i_0_50,i_0_51]) ).
cnf(i_0_162,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_163,plain,
~ equidistant(extension(X1,X2,v,u),X2,extension(X3,x,X4,X4),extension(X5,w,X6,X6)),
inference(scs_inference,[],[i_0_38,i_0_114,i_0_116,i_0_143,i_0_118,i_0_123,i_0_160,i_0_112,i_0_70,i_0_152,i_0_154,i_0_156,i_0_158,i_0_162,i_0_127,i_0_129,i_0_72,i_0_35,i_0_34,i_0_32,i_0_48,i_0_53,i_0_54,i_0_55,i_0_50,i_0_51,i_0_52]) ).
cnf(i_0_164,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_165,plain,
~ equidistant(extension(X1,extension(X2,X3,v,u),X4,X4),X3,extension(X5,x,X6,X6),w),
inference(scs_inference,[],[i_0_38,i_0_114,i_0_116,i_0_143,i_0_118,i_0_123,i_0_160,i_0_112,i_0_70,i_0_152,i_0_154,i_0_156,i_0_158,i_0_162,i_0_164,i_0_127,i_0_129,i_0_72,i_0_35,i_0_34,i_0_32,i_0_48,i_0_53,i_0_54,i_0_55,i_0_50,i_0_51,i_0_52,i_0_49]) ).
cnf(i_0_166,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_167,plain,
( ~ equidistant(lower_dimension_point_2,extension(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_1),lower_dimension_point_2,lower_dimension_point_2)
| ~ equidistant(lower_dimension_point_3,extension(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_1),lower_dimension_point_3,lower_dimension_point_2) ),
inference(scs_inference,[],[i_0_38,i_0_114,i_0_149,i_0_116,i_0_143,i_0_118,i_0_123,i_0_160,i_0_112,i_0_70,i_0_152,i_0_154,i_0_156,i_0_158,i_0_162,i_0_164,i_0_127,i_0_129,i_0_68,i_0_45,i_0_43,i_0_44,i_0_72,i_0_35,i_0_34,i_0_32,i_0_48,i_0_53,i_0_54,i_0_55,i_0_50,i_0_51,i_0_52,i_0_49,i_0_31]) ).
cnf(i_0_168,plain,
equidistant(X1,extension(X2,X1,X3,X4),X4,X3),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_169,plain,
extension(lower_dimension_point_3,lower_dimension_point_1,X1,X2) != lower_dimension_point_2,
inference(rename_variables,[],[i_0_68]) ).
cnf(i_0_170,plain,
( between(X1,X2,X3)
| between(X2,X3,X1)
| ~ equidistant(X3,X4,X3,X5)
| ~ equidistant(X1,X4,X1,X5)
| ~ equidistant(X2,X4,X2,X5)
| between(X3,X1,X2)
| X4 = X5 ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_172,plain,
equidistant(X1,extension(X2,X1,X3,X4),extension(X5,X6,X4,X3),X6),
inference(scs_inference,[],[i_0_118,i_0_35]) ).
cnf(i_0_173,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X1,X2) ),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_174,plain,
equidistant(v,u,w,x),
inference(scs_inference,[],[i_0_118,i_0_41,i_0_35,i_0_34]) ).
cnf(i_0_175,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X2,X1,X3,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_176,plain,
~ equidistant(extension(X1,X2,u,v),X2,x,w),
inference(scs_inference,[],[i_0_38,i_0_144,i_0_118,i_0_41,i_0_35,i_0_34,i_0_32]) ).
cnf(i_0_177,plain,
equidistant(extension(X1,X2,X3,X4),X2,X4,X3),
inference(rename_variables,[],[i_0_144]) ).
cnf(i_0_178,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X5,X6,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_179,plain,
extension(X1,u,w,x) != extension(X2,v,X3,X3),
inference(scs_inference,[],[i_0_38,i_0_144,i_0_142,i_0_118,i_0_70,i_0_41,i_0_35,i_0_34,i_0_32,i_0_48]) ).
cnf(i_0_180,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_181,plain,
~ between(extension(X1,extension(X2,lower_dimension_point_2,X3,X3),X4,X4),extension(X5,lower_dimension_point_3,X6,X6),extension(X7,lower_dimension_point_1,X8,X8)),
inference(scs_inference,[],[i_0_38,i_0_144,i_0_142,i_0_118,i_0_70,i_0_180,i_0_153,i_0_41,i_0_35,i_0_34,i_0_32,i_0_48,i_0_55]) ).
cnf(i_0_182,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_183,plain,
~ between(extension(X1,lower_dimension_point_1,X2,X2),lower_dimension_point_2,lower_dimension_point_3),
inference(scs_inference,[],[i_0_38,i_0_144,i_0_142,i_0_118,i_0_70,i_0_180,i_0_182,i_0_153,i_0_41,i_0_45,i_0_35,i_0_34,i_0_32,i_0_48,i_0_55,i_0_53]) ).
cnf(i_0_184,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_185,plain,
~ equidistant(extension(X1,X2,v,u),extension(X3,X2,X4,X4),extension(X5,x,X6,X6),extension(X7,w,X8,X8)),
inference(scs_inference,[],[i_0_38,i_0_144,i_0_163,i_0_142,i_0_118,i_0_70,i_0_180,i_0_182,i_0_184,i_0_153,i_0_41,i_0_45,i_0_35,i_0_34,i_0_32,i_0_48,i_0_55,i_0_53,i_0_50]) ).
cnf(i_0_186,plain,
~ equidistant(extension(X1,X2,v,u),X2,extension(X3,x,X4,X4),extension(X5,w,X6,X6)),
inference(rename_variables,[],[i_0_163]) ).
cnf(i_0_187,plain,
~ equidistant(extension(X1,X2,v,u),X2,extension(X3,extension(X4,x,X5,X5),X6,X6),extension(X7,w,X8,X8)),
inference(scs_inference,[],[i_0_38,i_0_144,i_0_163,i_0_186,i_0_142,i_0_118,i_0_70,i_0_180,i_0_182,i_0_184,i_0_153,i_0_41,i_0_45,i_0_35,i_0_34,i_0_32,i_0_48,i_0_55,i_0_53,i_0_50,i_0_51]) ).
cnf(i_0_188,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_189,plain,
~ equidistant(extension(X1,X2,v,u),X2,extension(X3,x,X4,X4),extension(X5,extension(X6,w,X7,X7),X8,X8)),
inference(scs_inference,[],[i_0_38,i_0_144,i_0_163,i_0_186,i_0_142,i_0_118,i_0_70,i_0_180,i_0_182,i_0_184,i_0_188,i_0_153,i_0_41,i_0_45,i_0_35,i_0_34,i_0_32,i_0_48,i_0_55,i_0_53,i_0_50,i_0_51,i_0_52]) ).
cnf(i_0_190,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_191,plain,
~ between(extension(X1,lower_dimension_point_2,X2,X2),extension(X3,lower_dimension_point_3,X4,X4),extension(X5,lower_dimension_point_1,X6,X6)),
inference(scs_inference,[],[i_0_38,i_0_144,i_0_163,i_0_186,i_0_142,i_0_118,i_0_70,i_0_180,i_0_182,i_0_184,i_0_188,i_0_190,i_0_153,i_0_131,i_0_41,i_0_45,i_0_35,i_0_34,i_0_32,i_0_48,i_0_55,i_0_53,i_0_50,i_0_51,i_0_52,i_0_54]) ).
cnf(i_0_192,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_193,plain,
~ equidistant(extension(X1,extension(X2,X3,v,u),X4,X4),X3,extension(X5,x,X6,X6),extension(X7,w,X8,X8)),
inference(scs_inference,[],[i_0_38,i_0_144,i_0_163,i_0_186,i_0_142,i_0_118,i_0_70,i_0_180,i_0_182,i_0_184,i_0_188,i_0_190,i_0_192,i_0_153,i_0_131,i_0_41,i_0_45,i_0_35,i_0_34,i_0_32,i_0_48,i_0_55,i_0_53,i_0_50,i_0_51,i_0_52,i_0_54,i_0_49]) ).
cnf(i_0_194,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_195,plain,
equidistant(X1,X2,extension(X3,X4,X1,X2),X4),
inference(rename_variables,[],[i_0_81]) ).
cnf(i_0_196,plain,
equidistant(extension(X1,X2,X3,X4),X2,X3,X4),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_197,plain,
equidistant(X1,extension(X2,X1,X3,X4),X5,extension(X6,X5,X4,X3)),
inference(rename_variables,[],[i_0_146]) ).
cnf(i_0_198,plain,
( ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X5,X6,X7,X8)
| ~ equidistant(X1,X6,X3,X8)
| ~ between(X5,X1,X2)
| ~ between(X7,X3,X4)
| X5 = X1
| equidistant(X2,X6,X4,X8)
| ~ equidistant(X5,X1,X7,X3) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_199,plain,
( ~ between(X1,extension(X2,X3,X4,X5),X3)
| ~ between(extension(X6,extension(X7,X4,X8,X9),X1,extension(X10,extension(X2,X3,X4,X5),X9,X8)),X4,X5)
| extension(X6,extension(X7,X4,X8,X9),X1,extension(X10,extension(X2,X3,X4,X5),X9,X8)) = X4
| equidistant(X5,extension(X7,X4,X8,X9),X3,extension(X10,extension(X2,X3,X4,X5),X9,X8))
| ~ equidistant(extension(X6,extension(X7,X4,X8,X9),X1,extension(X10,extension(X2,X3,X4,X5),X9,X8)),X4,X1,extension(X2,X3,X4,X5)) ),
inference(scs_inference,[],[i_0_38,i_0_56,i_0_144,i_0_146,i_0_163,i_0_186,i_0_142,i_0_81,i_0_118,i_0_70,i_0_180,i_0_182,i_0_184,i_0_188,i_0_190,i_0_192,i_0_153,i_0_131,i_0_41,i_0_45,i_0_35,i_0_34,i_0_32,i_0_48,i_0_55,i_0_53,i_0_50,i_0_51,i_0_52,i_0_54,i_0_49,i_0_30]) ).
cnf(i_0_200,plain,
equidistant(w,x,v,u),
inference(scs_inference,[],[i_0_174,i_0_35]) ).
cnf(i_0_201,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X1,X2) ),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_202,plain,
equidistant(extension(X1,X2,X3,X4),X2,extension(X5,X6,X4,X3),X6),
inference(scs_inference,[],[i_0_172,i_0_174,i_0_35,i_0_34]) ).
cnf(i_0_203,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X2,X1,X3,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_204,plain,
equidistant(X1,X2,extension(X3,X4,X5,extension(X6,X5,X1,X2)),X4),
inference(scs_inference,[],[i_0_56,i_0_172,i_0_174,i_0_116,i_0_35,i_0_34,i_0_32]) ).
cnf(i_0_205,plain,
equidistant(X1,X2,extension(X3,X4,X2,X1),X4),
inference(rename_variables,[],[i_0_116]) ).
cnf(i_0_206,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X5,X6,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_207,plain,
~ between(extension(X1,lower_dimension_point_1,X2,X2),lower_dimension_point_2,extension(X3,lower_dimension_point_3,X4,X4)),
inference(scs_inference,[],[i_0_56,i_0_172,i_0_174,i_0_116,i_0_70,i_0_183,i_0_35,i_0_34,i_0_32,i_0_55]) ).
cnf(i_0_208,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_209,plain,
~ equidistant(extension(X1,extension(X2,X3,v,u),X4,X4),extension(X5,X3,X6,X6),extension(X7,x,X8,X8),extension(X9,w,X10,X10)),
inference(scs_inference,[],[i_0_56,i_0_172,i_0_193,i_0_174,i_0_116,i_0_70,i_0_208,i_0_183,i_0_35,i_0_34,i_0_32,i_0_55,i_0_50]) ).
cnf(i_0_210,plain,
~ equidistant(extension(X1,extension(X2,X3,v,u),X4,X4),X3,extension(X5,x,X6,X6),extension(X7,w,X8,X8)),
inference(rename_variables,[],[i_0_193]) ).
cnf(i_0_211,plain,
~ equidistant(extension(X1,X2,v,u),extension(X3,X2,X4,X4),extension(X5,extension(X6,x,X7,X7),X8,X8),extension(X9,w,X10,X10)),
inference(scs_inference,[],[i_0_56,i_0_172,i_0_193,i_0_185,i_0_174,i_0_116,i_0_70,i_0_208,i_0_183,i_0_35,i_0_34,i_0_32,i_0_55,i_0_50,i_0_51]) ).
cnf(i_0_212,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_213,plain,
~ equidistant(extension(X1,X2,v,u),extension(X3,X2,X4,X4),extension(X5,x,X6,X6),extension(X7,extension(X8,w,X9,X9),X10,X10)),
inference(scs_inference,[],[i_0_56,i_0_172,i_0_193,i_0_185,i_0_174,i_0_116,i_0_70,i_0_208,i_0_212,i_0_183,i_0_35,i_0_34,i_0_32,i_0_55,i_0_50,i_0_51,i_0_52]) ).
cnf(i_0_214,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_215,plain,
~ equidistant(extension(X1,extension(X2,X3,v,u),X4,X4),X3,x,extension(X5,w,X6,X6)),
inference(scs_inference,[],[i_0_56,i_0_172,i_0_193,i_0_185,i_0_125,i_0_174,i_0_116,i_0_70,i_0_208,i_0_212,i_0_214,i_0_183,i_0_35,i_0_34,i_0_32,i_0_55,i_0_50,i_0_51,i_0_52,i_0_49]) ).
cnf(i_0_216,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_217,plain,
~ between(extension(X1,lower_dimension_point_1,X2,X2),extension(X3,lower_dimension_point_2,X4,X4),lower_dimension_point_3),
inference(scs_inference,[],[i_0_56,i_0_172,i_0_193,i_0_185,i_0_125,i_0_174,i_0_116,i_0_70,i_0_208,i_0_212,i_0_214,i_0_216,i_0_183,i_0_35,i_0_34,i_0_32,i_0_55,i_0_50,i_0_51,i_0_52,i_0_49,i_0_54]) ).
cnf(i_0_218,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_219,plain,
~ between(extension(X1,extension(X2,lower_dimension_point_1,X3,X3),X4,X4),lower_dimension_point_2,lower_dimension_point_3),
inference(scs_inference,[],[i_0_56,i_0_172,i_0_193,i_0_185,i_0_125,i_0_174,i_0_116,i_0_70,i_0_208,i_0_212,i_0_214,i_0_216,i_0_218,i_0_183,i_0_35,i_0_34,i_0_32,i_0_55,i_0_50,i_0_51,i_0_52,i_0_49,i_0_54,i_0_53]) ).
cnf(i_0_220,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_221,plain,
extension(X1,u,X2,extension(X3,X2,x,w)) != v,
inference(scs_inference,[],[i_0_56,i_0_172,i_0_193,i_0_185,i_0_125,i_0_174,i_0_116,i_0_70,i_0_208,i_0_212,i_0_214,i_0_216,i_0_218,i_0_183,i_0_35,i_0_34,i_0_32,i_0_55,i_0_50,i_0_51,i_0_52,i_0_49,i_0_54,i_0_53,i_0_72]) ).
cnf(i_0_222,plain,
~ between(extension(X1,lower_dimension_point_1,X2,X2),lower_dimension_point_2,lower_dimension_point_3),
inference(rename_variables,[],[i_0_183]) ).
cnf(i_0_223,plain,
equidistant(X1,extension(X2,X1,X3,X4),X4,X3),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_224,plain,
( between(X1,X2,X3)
| between(X2,X3,X1)
| ~ equidistant(X3,X4,X3,X5)
| ~ equidistant(X1,X4,X1,X5)
| ~ equidistant(X2,X4,X2,X5)
| between(X3,X1,X2)
| X4 = X5 ),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_225,plain,
equidistant(extension(X1,X2,X3,X4),X2,X4,X3),
inference(rename_variables,[],[i_0_144]) ).
cnf(i_0_226,plain,
equidistant(extension(X1,X2,X3,X4),X2,X3,X4),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_227,plain,
equidistant(X1,extension(X2,X1,X3,X4),extension(X5,X6,X4,X3),X6),
inference(rename_variables,[],[i_0_172]) ).
cnf(i_0_228,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_229,plain,
( ~ between(extension(X1,extension(X2,extension(X3,X4,extension(x,extension(X5,w,X6,X7),X8,X9),extension(X5,w,X6,X7)),X7,X6),x,w),extension(X3,X4,extension(x,extension(X5,w,X6,X7),X8,X9),extension(X5,w,X6,X7)),X4)
| extension(X1,extension(X2,extension(X3,X4,extension(x,extension(X5,w,X6,X7),X8,X9),extension(X5,w,X6,X7)),X7,X6),x,w) = extension(X3,X4,extension(x,extension(X5,w,X6,X7),X8,X9),extension(X5,w,X6,X7))
| equidistant(X4,extension(X2,extension(X3,X4,extension(x,extension(X5,w,X6,X7),X8,X9),extension(X5,w,X6,X7)),X7,X6),extension(x,extension(X5,w,X6,X7),X8,X9),w)
| ~ equidistant(extension(X1,extension(X2,extension(X3,X4,extension(x,extension(X5,w,X6,X7),X8,X9),extension(X5,w,X6,X7)),X7,X6),x,w),extension(X3,X4,extension(x,extension(X5,w,X6,X7),X8,X9),extension(X5,w,X6,X7)),x,extension(X5,w,X6,X7)) ),
inference(scs_inference,[],[i_0_56,i_0_172,i_0_193,i_0_185,i_0_125,i_0_174,i_0_114,i_0_116,i_0_144,i_0_70,i_0_208,i_0_212,i_0_214,i_0_216,i_0_218,i_0_183,i_0_102,i_0_36,i_0_35,i_0_34,i_0_32,i_0_55,i_0_50,i_0_51,i_0_52,i_0_49,i_0_54,i_0_53,i_0_72,i_0_30]) ).
cnf(i_0_230,plain,
equidistant(extension(X1,X2,X3,extension(X4,X3,X5,X6)),X2,X5,X6),
inference(scs_inference,[],[i_0_204,i_0_35]) ).
cnf(i_0_231,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X3,X4,X1,X2) ),
inference(rename_variables,[],[i_0_35]) ).
cnf(i_0_232,plain,
equidistant(X1,X2,extension(X3,X4,X5,extension(X6,X5,X2,X1)),X4),
inference(scs_inference,[],[i_0_204,i_0_35,i_0_34]) ).
cnf(i_0_233,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X2,X1,X3,X4) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_234,plain,
extension(X1,u,X2,extension(X3,X2,w,x)) != v,
inference(scs_inference,[],[i_0_204,i_0_35,i_0_34,i_0_72]) ).
cnf(i_0_235,plain,
$false,
inference(scs_inference,[],[i_0_38,i_0_204,i_0_200,i_0_40,i_0_35,i_0_34,i_0_72,i_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO021-3 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n014.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 17:39:36 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 0.35/1.61 % Version : CSE_E---1.7
% 0.35/1.61 % Problem : theBenchmark.p
% 0.35/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 0.35/1.61 % SZS output start CNFRefutation
% See solution above
% 0.75/2.03 % Total time : 1.272s
%------------------------------------------------------------------------------