%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO037-3 : 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 : n024.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 04:19:06 PM UTC 2026
% Result : Unsatisfiable 1.43s 1.86s
% Output : CNFRefutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 24 ( 12 unt; 0 nHn; 16 RR)
% Number of literals : 40 ( 8 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-4 aty)
% Number of variables : 70 ( 11 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(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
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(prove_lengthen,negated_conjecture,
( v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2)
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lengthen) ).
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_5,axiom,
( equidistant(X4,X3,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_5) ).
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(e2_1,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_1) ).
cnf(c_0_8,axiom,
( equidistant(X4,X3,X1,X2)
| ~ equidistant(X1,X2,X3,X4) ),
d4_4 ).
cnf(c_0_9,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_10,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
transitivity_for_equidistance ).
cnf(c_0_11,plain,
equidistant(X1,X2,X3,extension(X4,X3,X2,X1)),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
( v = extension(u,v,lower_dimension_point_1,lower_dimension_point_2)
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2))
| ~ between(u,v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2)) ),
prove_lengthen ).
cnf(c_0_13,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_14,plain,
( equidistant(X1,X2,X3,extension(X4,X3,X5,X6))
| ~ equidistant(X6,X5,X1,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,axiom,
( equidistant(X4,X3,X2,X1)
| ~ equidistant(X1,X2,X3,X4) ),
d4_5 ).
cnf(c_0_16,negated_conjecture,
( extension(u,v,lower_dimension_point_1,lower_dimension_point_2) = v
| ~ equidistant(v,extension(u,v,lower_dimension_point_1,lower_dimension_point_2),x,extension(w,x,lower_dimension_point_1,lower_dimension_point_2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13])]) ).
cnf(c_0_17,plain,
equidistant(X1,extension(X2,X1,X3,X4),X5,extension(X6,X5,X3,X4)),
inference(spm,[status(thm)],[c_0_14,c_0_11]) ).
cnf(c_0_18,plain,
equidistant(X1,X2,extension(X3,X4,X2,X1),X4),
inference(spm,[status(thm)],[c_0_15,c_0_9]) ).
cnf(c_0_19,negated_conjecture,
extension(u,v,lower_dimension_point_1,lower_dimension_point_2) = v,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).
cnf(c_0_20,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
identity_for_equidistance ).
cnf(c_0_21,negated_conjecture,
equidistant(lower_dimension_point_2,lower_dimension_point_1,v,v),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
e2_1 ).
cnf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.15 % Problem : GEO037-3 : TPTP v9.2.1. Released v1.0.0.
% 0.03/0.15 % 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
% 0.07/0.34 % Computer : n024.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8042.1875MB
% 0.07/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon May 4 12:36:56 EDT 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % start to proof: theBenchmark
% 1.43/1.86 % Version : CSE_E---1.7
% 1.43/1.86 % Problem : theBenchmark.p
% 1.43/1.86 % SZS status Unsatisfiable for theBenchmark.p
% 1.43/1.86 % SZS output start CNFRefutation
% See solution above
% 1.43/1.87 % Total time : 1.374s
%------------------------------------------------------------------------------