%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO059-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:14:03 AM UTC 2026
% Result : Unsatisfiable 15.21s 2.58s
% Output : CNFRefutation 15.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 15 ( 7 unt; 0 nHn; 12 RR)
% Number of literals : 25 ( 0 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d3,axiom,
( equidistant(X1,X0,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(d4_4,axiom,
( equidistant(X3,X2,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(d5,axiom,
( equidistant(X0,X1,X4,X5)
| ~ equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(r2_2,axiom,
equidistant(X0,reflection(X1,X0),X1,X0) ).
cnf(prove_congruence,negated_conjecture,
~ equidistant(v,u,v,reflection(reflection(u,v),v)) ).
cnf(c2,plain,
( equidistant(X1,X0,X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[d3]) ).
cnf(c6,plain,
( equidistant(X3,X2,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[d4_4]) ).
cnf(c8,plain,
( equidistant(X0,X1,X4,X5)
| ~ equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[d5]) ).
cnf(c12,plain,
equidistant(X0,reflection(X1,X0),X1,X0),
inference(clausification,[status(esa)],[r2_2]) ).
cnf(c22,plain,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
inference(clausification,[status(esa)],[prove_congruence]) ).
cnf(d_0,plain,
( equidistant(X1,reflection(X0,X1),X2,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c12,c8]) ).
cnf(d_1,plain,
( equidistant(X3,X2,X1,reflection(X0,X1))
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d_0,c6]) ).
cnf(d_2,plain,
~ equidistant(reflection(u,v),v,u,v),
inference(resolution,[status(thm)],[d_1,c22]) ).
cnf(d_3,plain,
equidistant(reflection(X0,X1),X1,X0,X1),
inference(resolution,[status(thm)],[c12,c2]) ).
cnf(d_4,plain,
$false,
inference(resolution,[status(thm)],[d_3,d_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO059-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n010.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Fri Sep 25 12:37:45 UTC 2026
% 0.09/0.56 % CPUTime :
% 0.09/0.56 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.21/2.58 % SZS status Unsatisfiable for theBenchmark.p
% 15.21/2.58 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------