%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO049-3 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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 : n017.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 04:19:09 PM UTC 2026
% Result : Unsatisfiable 216.20s 108.30s
% Output : CNFRefutation 216.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 22
% Syntax : Number of clauses : 88 ( 42 unt; 5 nHn; 64 RR)
% Number of literals : 153 ( 29 equ; 65 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-4 aty)
% Number of variables : 224 ( 20 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d4_4,axiom,
( equidistant(X4,X3,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_4) ).
cnf(u_to_v_equals_u1_to_v1,hypothesis,
equidistant(u,v,u1,v1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_u1_to_v1) ).
cnf(i3,axiom,
( X2 = insertion(X1,X3,X1,X2)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i3) ).
cnf(insertion,axiom,
insertion(X1,X2,X3,X4) = extension(extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),X1,X3,X4),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-3.ax',insertion) ).
cnf(d10_2,axiom,
( extension(X5,X6,X1,X2) = extension(X5,X6,X3,X4)
| X5 = X6
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_2) ).
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(e3_1,axiom,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_1) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
cnf(d4_1,axiom,
( equidistant(X1,X2,X4,X3)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_1) ).
cnf(d4_5,axiom,
( equidistant(X4,X3,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_5) ).
cnf(u_to_w_equals_u1_to_w1,hypothesis,
equidistant(u,w,u1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_w_equals_u1_to_w1) ).
cnf(v_to_w_equals_v1_to_w1,hypothesis,
equidistant(v,w,v1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_to_w_equals_v1_to_w1) ).
cnf(i4,axiom,
( insertion(X5,X6,X1,X2) = insertion(X5,X6,X3,X4)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i4) ).
cnf(i2_2,axiom,
( between(X4,insertion(X4,X5,X1,X2),X5)
| ~ between(X1,X2,X3)
| ~ equidistant(X1,X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i2_2) ).
cnf(d2,axiom,
( equidistant(X3,X4,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
cnf(i2_3,axiom,
( equidistant(X2,X3,insertion(X4,X5,X1,X2),X5)
| ~ between(X1,X2,X3)
| ~ equidistant(X1,X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i2_3) ).
cnf(d4_3,axiom,
( equidistant(X3,X4,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_3) ).
cnf(t1,axiom,
( between(X3,X2,X1)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
cnf(d15,axiom,
( X2 = X4
| ~ between(X1,X2,X3)
| ~ equidistant(X1,X2,X1,X4)
| ~ equidistant(X3,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15) ).
cnf(prove_v1_between_u1_and_w1,negated_conjecture,
~ between(u1,v1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v1_between_u1_and_w1) ).
cnf(c_0_22,axiom,
( equidistant(X4,X3,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
d4_4 ).
cnf(c_0_23,hypothesis,
equidistant(u,v,u1,v1),
u_to_v_equals_u1_to_v1 ).
cnf(c_0_24,axiom,
( X2 = insertion(X1,X3,X1,X2)
| ~ between(X1,X2,X3) ),
i3 ).
cnf(c_0_25,axiom,
insertion(X1,X2,X3,X4) = extension(extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),X1,X3,X4),
insertion ).
cnf(c_0_26,axiom,
( extension(X5,X6,X1,X2) = extension(X5,X6,X3,X4)
| X5 = X6
| ~ equidistant(X1,X2,X3,X4) ),
d10_2 ).
cnf(c_0_27,hypothesis,
equidistant(v1,u1,u,v),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
transitivity_for_equidistance ).
cnf(c_0_29,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_30,plain,
( X2 = extension(extension(X3,X1,lower_dimension_point_1,lower_dimension_point_2),X1,X1,X2)
| ~ between(X1,X2,X3) ),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,hypothesis,
( extension(X1,X2,u,v) = extension(X1,X2,v1,u1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,axiom,
X1 != extension(X2,X1,lower_dimension_point_1,lower_dimension_point_2),
e3_1 ).
cnf(c_0_33,plain,
( equidistant(X1,X2,X3,X4)
| ~ equidistant(X5,extension(X6,X5,X3,X4),X1,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,hypothesis,
( extension(extension(X1,u,lower_dimension_point_1,lower_dimension_point_2),u,v1,u1) = v
| ~ between(u,v,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_35,hypothesis,
( equidistant(X1,X2,v1,u1)
| ~ between(u,v,X3)
| ~ equidistant(u,v,X1,X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_36,plain,
equidistant(X1,X2,X3,extension(X4,X3,X2,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_29]) ).
cnf(c_0_37,hypothesis,
( equidistant(X1,extension(X2,X1,v,u),v1,u1)
| ~ between(u,v,X3) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_39,axiom,
( equidistant(X1,X2,X4,X3)
| ~ equidistant(X1,X2,X3,X4) ),
d4_1 ).
cnf(c_0_40,hypothesis,
equidistant(X1,extension(X2,X1,v,u),v1,u1),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,hypothesis,
equidistant(X1,extension(X2,X1,v,u),u1,v1),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_42,axiom,
( equidistant(X4,X3,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
d4_5 ).
cnf(c_0_43,hypothesis,
equidistant(u,w,u1,w1),
u_to_w_equals_u1_to_w1 ).
cnf(c_0_44,hypothesis,
( equidistant(X1,X2,u1,v1)
| ~ equidistant(X3,extension(X4,X3,v,u),X1,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_41]) ).
cnf(c_0_45,hypothesis,
equidistant(v,w,v1,w1),
v_to_w_equals_v1_to_w1 ).
cnf(c_0_46,axiom,
( insertion(X5,X6,X1,X2) = insertion(X5,X6,X3,X4)
| ~ equidistant(X1,X2,X3,X4) ),
i4 ).
cnf(c_0_47,axiom,
( between(X4,insertion(X4,X5,X1,X2),X5)
| ~ between(X1,X2,X3)
| ~ equidistant(X1,X3,X4,X5) ),
i2_2 ).
cnf(c_0_48,axiom,
( equidistant(X3,X4,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
d2 ).
cnf(c_0_49,hypothesis,
equidistant(w1,u1,w,u),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,hypothesis,
( equidistant(X1,X2,u1,v1)
| ~ between(v,u,X3)
| ~ equidistant(v,u,X1,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_30]) ).
cnf(c_0_51,hypothesis,
equidistant(w1,v1,w,v),
inference(spm,[status(thm)],[c_0_42,c_0_45]) ).
cnf(c_0_52,axiom,
( equidistant(X2,X3,insertion(X4,X5,X1,X2),X5)
| ~ between(X1,X2,X3)
| ~ equidistant(X1,X3,X4,X5) ),
i2_3 ).
cnf(c_0_53,axiom,
( equidistant(X3,X4,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
d4_3 ).
cnf(c_0_54,plain,
( extension(extension(X6,X5,lower_dimension_point_1,lower_dimension_point_2),X5,X1,X2) = extension(extension(X6,X5,lower_dimension_point_1,lower_dimension_point_2),X5,X3,X4)
| ~ equidistant(X1,X2,X3,X4) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_25]),c_0_25]) ).
cnf(c_0_55,hypothesis,
equidistant(v1,u1,v,u),
inference(spm,[status(thm)],[c_0_42,c_0_23]) ).
cnf(c_0_56,plain,
( between(X4,extension(extension(X5,X4,lower_dimension_point_1,lower_dimension_point_2),X4,X1,X2),X5)
| ~ between(X1,X2,X3)
| ~ equidistant(X1,X3,X4,X5) ),
inference(rw,[status(thm)],[c_0_47,c_0_25]) ).
cnf(c_0_57,hypothesis,
equidistant(u1,v1,u,v),
inference(spm,[status(thm)],[c_0_48,c_0_23]) ).
cnf(c_0_58,hypothesis,
equidistant(w,u,w1,u1),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_59,axiom,
( between(X3,X2,X1)
| ~ between(X1,X2,X3) ),
t1 ).
cnf(c_0_60,hypothesis,
between(u,v,w),
v_between_u_and_w ).
cnf(c_0_61,hypothesis,
( equidistant(X1,extension(X2,X1,u,v),u1,v1)
| ~ between(v,u,X3) ),
inference(spm,[status(thm)],[c_0_50,c_0_36]) ).
cnf(c_0_62,hypothesis,
equidistant(v,w,w1,v1),
inference(spm,[status(thm)],[c_0_22,c_0_51]) ).
cnf(c_0_63,plain,
( equidistant(X2,X3,extension(extension(X5,X4,lower_dimension_point_1,lower_dimension_point_2),X4,X1,X2),X5)
| ~ between(X1,X2,X3)
| ~ equidistant(X1,X3,X4,X5) ),
inference(rw,[status(thm)],[c_0_52,c_0_25]) ).
cnf(c_0_64,hypothesis,
equidistant(u1,v1,v,u),
inference(spm,[status(thm)],[c_0_53,c_0_23]) ).
cnf(c_0_65,hypothesis,
extension(extension(X1,X2,lower_dimension_point_1,lower_dimension_point_2),X2,v,u) = extension(extension(X1,X2,lower_dimension_point_1,lower_dimension_point_2),X2,v1,u1),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_66,hypothesis,
( between(u1,extension(extension(w1,u1,lower_dimension_point_1,lower_dimension_point_2),u1,u,X1),w1)
| ~ between(u,X1,w) ),
inference(spm,[status(thm)],[c_0_56,c_0_43]) ).
cnf(c_0_67,hypothesis,
( extension(X1,X2,u,v) = extension(X1,X2,u1,v1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_26,c_0_57]) ).
cnf(c_0_68,hypothesis,
( between(w1,extension(extension(u1,w1,lower_dimension_point_1,lower_dimension_point_2),w1,w,X1),u1)
| ~ between(w,X1,u) ),
inference(spm,[status(thm)],[c_0_56,c_0_58]) ).
cnf(c_0_69,hypothesis,
( extension(X1,X2,w,v) = extension(X1,X2,w1,v1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_26,c_0_51]) ).
cnf(c_0_70,hypothesis,
between(w,v,u),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_71,axiom,
( X2 = X4
| ~ between(X1,X2,X3)
| ~ equidistant(X1,X2,X1,X4)
| ~ equidistant(X3,X2,X3,X4) ),
d15 ).
cnf(c_0_72,hypothesis,
equidistant(X1,extension(X2,X1,u,v),u1,v1),
inference(spm,[status(thm)],[c_0_61,c_0_38]) ).
cnf(c_0_73,hypothesis,
( equidistant(X1,X2,w1,v1)
| ~ equidistant(v,w,X1,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_62]) ).
cnf(c_0_74,plain,
( equidistant(X1,X2,X3,extension(extension(X3,X4,lower_dimension_point_1,lower_dimension_point_2),X4,X5,X1))
| ~ between(X5,X1,X2)
| ~ equidistant(X5,X2,X4,X3) ),
inference(spm,[status(thm)],[c_0_39,c_0_63]) ).
cnf(c_0_75,hypothesis,
extension(extension(X1,X2,lower_dimension_point_1,lower_dimension_point_2),X2,u,v) = extension(extension(X1,X2,lower_dimension_point_1,lower_dimension_point_2),X2,v1,u1),
inference(spm,[status(thm)],[c_0_54,c_0_27]) ).
cnf(c_0_76,hypothesis,
extension(extension(X1,X2,lower_dimension_point_1,lower_dimension_point_2),X2,v1,u1) = extension(extension(X1,X2,lower_dimension_point_1,lower_dimension_point_2),X2,u1,v1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_64]),c_0_65]) ).
cnf(c_0_77,hypothesis,
between(u1,extension(extension(w1,u1,lower_dimension_point_1,lower_dimension_point_2),u1,u1,v1),w1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_60])]),c_0_32]) ).
cnf(c_0_78,hypothesis,
between(w1,extension(extension(u1,w1,lower_dimension_point_1,lower_dimension_point_2),w1,w1,v1),u1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70])]),c_0_32]) ).
cnf(c_0_79,hypothesis,
( extension(X1,u1,u,v) = v1
| ~ between(X2,extension(X1,u1,u,v),u1)
| ~ equidistant(X2,extension(X1,u1,u,v),X2,v1) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_80,hypothesis,
( equidistant(X1,extension(extension(X1,X2,lower_dimension_point_1,lower_dimension_point_2),X2,X3,v),w1,v1)
| ~ between(X3,v,w)
| ~ equidistant(X3,w,X2,X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,hypothesis,
extension(extension(X1,X2,lower_dimension_point_1,lower_dimension_point_2),X2,u,v) = extension(extension(X1,X2,lower_dimension_point_1,lower_dimension_point_2),X2,u1,v1),
inference(rw,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_82,hypothesis,
between(w1,extension(extension(w1,u1,lower_dimension_point_1,lower_dimension_point_2),u1,u1,v1),u1),
inference(spm,[status(thm)],[c_0_59,c_0_77]) ).
cnf(c_0_83,hypothesis,
between(u1,extension(extension(u1,w1,lower_dimension_point_1,lower_dimension_point_2),w1,w1,v1),w1),
inference(spm,[status(thm)],[c_0_59,c_0_78]) ).
cnf(c_0_84,negated_conjecture,
~ between(u1,v1,w1),
prove_v1_between_u1_and_w1 ).
cnf(c_0_85,hypothesis,
extension(extension(w1,u1,lower_dimension_point_1,lower_dimension_point_2),u1,u1,v1) = v1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_81]),c_0_82]),c_0_60]),c_0_43])]) ).
cnf(c_0_86,hypothesis,
~ between(w1,v1,u1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_30]),c_0_84]) ).
cnf(c_0_87,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_85]),c_0_86]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO049-3 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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
% 0.16/0.33 % Computer : n017.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 17:37:27 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 216.20/108.30 % Version : CSE_E---1.7
% 216.20/108.30 % Problem : theBenchmark.p
% 216.20/108.30 % SZS status Unsatisfiable for theBenchmark.p
% 216.20/108.30 % SZS output start CNFRefutation
% See solution above
% 216.80/108.97 % Total time : 81.420s
%------------------------------------------------------------------------------