%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO059-2 : 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 : n018.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 04:19:11 PM UTC 2026
% Result : Unsatisfiable 1.23s 2.01s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of clauses : 20 ( 15 unt; 0 nHn; 8 RR)
% Number of literals : 27 ( 2 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-4 aty)
% Number of variables : 62 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
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(reflexivity_for_equidistance,axiom,
equidistant(X1,X2,X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',reflexivity_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(prove_congruence,negated_conjecture,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_congruence) ).
cnf(reflection,axiom,
reflection(X1,X2) = extension(X1,X2,X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-2.ax',reflection) ).
cnf(c_0_5,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
transitivity_for_equidistance ).
cnf(c_0_6,axiom,
equidistant(X1,X2,X2,X1),
reflexivity_for_equidistance ).
cnf(c_0_7,plain,
( equidistant(X1,X2,X3,X4)
| ~ equidistant(X4,X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
equidistant(X1,X2,X1,X2),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_9,plain,
( equidistant(X1,X2,X3,X4)
| ~ equidistant(X3,X4,X1,X2) ),
inference(spm,[status(thm)],[c_0_5,c_0_8]) ).
cnf(c_0_10,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_11,plain,
equidistant(X1,X2,X3,extension(X4,X3,X1,X2)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
equidistant(X1,X2,extension(X3,X4,X1,X2),X4),
inference(spm,[status(thm)],[c_0_7,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
prove_congruence ).
cnf(c_0_14,axiom,
reflection(X1,X2) = extension(X1,X2,X1,X2),
reflection ).
cnf(c_0_15,plain,
( equidistant(X1,X2,X3,extension(X4,X3,X5,X6))
| ~ equidistant(X5,X6,X1,X2) ),
inference(spm,[status(thm)],[c_0_5,c_0_11]) ).
cnf(c_0_16,plain,
equidistant(extension(X1,X2,X3,X4),X2,X4,X3),
inference(spm,[status(thm)],[c_0_7,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
~ equidistant(v,u,v,extension(extension(u,v,u,v),v,extension(u,v,u,v),v)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_14]) ).
cnf(c_0_18,plain,
equidistant(X1,X2,X3,extension(X4,X3,extension(X5,X6,X2,X1),X6)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.29 % Problem : GEO059-2 : TPTP v9.2.1. Released v1.0.0.
% 0.07/0.29 % 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
% 0.12/0.54 % Computer : n018.cluster.edu
% 0.12/0.54 % Model : x86_64 x86_64
% 0.12/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.54 % Memory : 8042.1875MB
% 0.12/0.54 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.55 % CPULimit : 300
% 0.12/0.55 % WCLimit : 300
% 0.12/0.55 % DateTime : Mon May 4 17:38:17 EDT 2026
% 0.12/0.55 % CPUTime :
% 0.12/0.56 % start to proof: theBenchmark
% 1.23/2.01 % Version : CSE_E---1.7
% 1.23/2.01 % Problem : theBenchmark.p
% 1.23/2.01 % SZS status Unsatisfiable for theBenchmark.p
% 1.23/2.01 % SZS output start CNFRefutation
% See solution above
% 1.23/2.01 % Total time : 1.382s
%------------------------------------------------------------------------------