%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO015-2 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n007.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 04:19:00 PM UTC 2026
% Result : Unsatisfiable 0.26s 1.62s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 62)
% 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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
cnf(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
cnf(identity_for_equidistance,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
cnf(prove_symmetry,negated_conjecture,
~ equidistant(w,x,u,v),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_symmetry) ).
cnf(reflexivity_for_equidistance,axiom,
equidistant(X1,X2,X2,X1),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',u_to_v_equals_w_to_x) ).
cnf(identity_for_betweeness,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/GEO002-0.ax',lower_dimension1) ).
cnf(i_0_20,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_21,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_22,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_23,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_24,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_25,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_26,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_27,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_28,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_29,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
transitivity_for_equidistance,
[final] ).
cnf(i_0_30,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2,
[final] ).
cnf(i_0_31,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1,
[final] ).
cnf(i_0_32,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
identity_for_equidistance,
[final] ).
cnf(i_0_33,negated_conjecture,
~ equidistant(w,x,u,v),
prove_symmetry,
[final] ).
cnf(i_0_34,axiom,
equidistant(X1,X2,X2,X1),
reflexivity_for_equidistance,
[final] ).
cnf(i_0_35,hypothesis,
equidistant(u,v,w,x),
u_to_v_equals_w_to_x,
[final] ).
cnf(i_0_36,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
identity_for_betweeness,
[final] ).
cnf(i_0_37,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
lower_dimension3,
[final] ).
cnf(i_0_38,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
lower_dimension2,
[final] ).
cnf(i_0_39,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
lower_dimension1,
[final] ).
cnf(i_0_40,axiom,
X1 = X1 ).
cnf(i_0_41,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_42,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_43,axiom,
( X1 != X2
| ~ equidistant(X1,X3,X4,X5)
| equidistant(X2,X3,X4,X5) ) ).
cnf(i_0_44,axiom,
( X1 != X2
| ~ equidistant(X3,X1,X4,X5)
| equidistant(X3,X2,X4,X5) ) ).
cnf(i_0_45,axiom,
( X1 != X2
| ~ equidistant(X3,X4,X1,X5)
| equidistant(X3,X4,X2,X5) ) ).
cnf(i_0_46,axiom,
( X1 != X2
| ~ equidistant(X3,X4,X5,X1)
| equidistant(X3,X4,X5,X2) ) ).
cnf(i_0_47,axiom,
( X1 != X2
| ~ between(X1,X3,X4)
| between(X2,X3,X4) ) ).
cnf(i_0_48,axiom,
( X1 != X2
| ~ between(X3,X1,X4)
| between(X3,X2,X4) ) ).
cnf(i_0_49,axiom,
( X1 != X2
| ~ between(X3,X4,X1)
| between(X3,X4,X2) ) ).
cnf(i_0_40_001,axiom,
X1 = X1 ).
cnf(i_0_41_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_42_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_43_004,axiom,
( X1 != X2
| ~ equidistant(X1,X3,X4,X5)
| equidistant(X2,X3,X4,X5) ) ).
cnf(i_0_44_005,axiom,
( X1 != X2
| ~ equidistant(X3,X1,X4,X5)
| equidistant(X3,X2,X4,X5) ) ).
cnf(i_0_45_006,axiom,
( X1 != X2
| ~ equidistant(X3,X4,X1,X5)
| equidistant(X3,X4,X2,X5) ) ).
cnf(i_0_46_007,axiom,
( X1 != X2
| ~ equidistant(X3,X4,X5,X1)
| equidistant(X3,X4,X5,X2) ) ).
cnf(i_0_47_008,axiom,
( X1 != X2
| ~ between(X1,X3,X4)
| between(X2,X3,X4) ) ).
cnf(i_0_48_009,axiom,
( X1 != X2
| ~ between(X3,X1,X4)
| between(X3,X2,X4) ) ).
cnf(i_0_49_010,axiom,
( X1 != X2
| ~ between(X3,X4,X1)
| between(X3,X4,X2) ) ).
cnf(i_0_50,plain,
X1 = extension(X2,X1,X3,X3),
inference(scs_inference,[],[i_0_30,i_0_32]) ).
cnf(i_0_51,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_52,plain,
( ~ equidistant(X1,X2,X3,X3)
| X1 = X2 ),
inference(rename_variables,[],[i_0_32]) ).
cnf(i_0_53,plain,
~ equidistant(v,u,w,x),
inference(scs_inference,[],[i_0_33,i_0_34,i_0_30,i_0_32,i_0_29]) ).
cnf(i_0_54,plain,
equidistant(X1,X2,X2,X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_55,plain,
( ~ equidistant(X1,X2,X3,X4)
| equidistant(X5,X6,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
inference(rename_variables,[],[i_0_29]) ).
cnf(i_0_56,plain,
extension(X1,w,u,v) != x,
inference(scs_inference,[],[i_0_33,i_0_34,i_0_30,i_0_51,i_0_32,i_0_29,i_0_44]) ).
cnf(i_0_57,plain,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_58,plain,
extension(lower_dimension_point_3,lower_dimension_point_1,X1,X2) != lower_dimension_point_2,
inference(scs_inference,[],[i_0_33,i_0_34,i_0_30,i_0_51,i_0_31,i_0_37,i_0_32,i_0_29,i_0_44,i_0_49]) ).
cnf(i_0_59,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_60,plain,
extension(X1,X2,X3,X3) = X2,
inference(scs_inference,[],[i_0_33,i_0_34,i_0_30,i_0_51,i_0_31,i_0_37,i_0_32,i_0_29,i_0_44,i_0_49,i_0_41]) ).
cnf(i_0_61,plain,
~ equidistant(extension(X1,w,X2,X2),x,u,v),
inference(scs_inference,[],[i_0_33,i_0_34,i_0_30,i_0_51,i_0_31,i_0_37,i_0_32,i_0_29,i_0_44,i_0_49,i_0_41,i_0_43]) ).
cnf(i_0_62,plain,
( X1 != u
| ~ equidistant(w,x,X1,v) ),
inference(scs_inference,[],[i_0_33,i_0_34,i_0_30,i_0_51,i_0_31,i_0_37,i_0_32,i_0_29,i_0_44,i_0_49,i_0_41,i_0_43,i_0_45]) ).
cnf(i_0_63,plain,
( w != v
| x != u ),
inference(scs_inference,[],[i_0_33,i_0_34,i_0_54,i_0_30,i_0_51,i_0_31,i_0_37,i_0_32,i_0_29,i_0_44,i_0_49,i_0_41,i_0_43,i_0_45,i_0_46]) ).
cnf(i_0_64,plain,
equidistant(X1,X2,X2,X1),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_65,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_66,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_67,plain,
( between(X1,inner_pasch(X2,X1,X3,X4,X5),X5)
| ~ between(X2,X1,X3)
| ~ between(X5,X4,X3) ),
inference(rename_variables,[],[i_0_25]) ).
cnf(i_0_68,plain,
between(X1,X2,extension(X1,X2,X3,X4)),
inference(rename_variables,[],[i_0_31]) ).
cnf(i_0_69,plain,
( x != u
| 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_33,i_0_34,i_0_54,i_0_30,i_0_51,i_0_31,i_0_59,i_0_66,i_0_37,i_0_32,i_0_29,i_0_44,i_0_49,i_0_41,i_0_43,i_0_45,i_0_46,i_0_48,i_0_25,i_0_26]) ).
cnf(i_0_70,plain,
~ equidistant(w,x,u,v),
inference(equality_inference,[],[62]) ).
cnf(i_0_71,plain,
extension(X1,w,u,v) != extension(X2,x,X3,X3),
inference(scs_inference,[],[i_0_60,i_0_56,i_0_42]) ).
cnf(i_0_72,plain,
extension(X1,X2,X3,X3) = X2,
inference(rename_variables,[],[i_0_60]) ).
cnf(i_0_73,plain,
$false,
inference(scs_inference,[],[i_0_60,i_0_56,i_0_53,i_0_35,i_0_34,i_0_42,i_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO015-2 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n007.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 17:35:39 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.26/1.62 % Version : CSE_E---1.7
% 0.26/1.62 % Problem : theBenchmark.p
% 0.26/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 0.26/1.62 % SZS output start CNFRefutation
% See solution above
% 0.26/1.69 % Total time : 1.271s
%------------------------------------------------------------------------------