%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO058-3 : 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 : n014.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 11.83s 3.53s
% Output : CNFRefutation 11.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 10 unt; 0 nHn; 12 RR)
% Number of literals : 18 ( 7 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d4_3,axiom,
( equidistant(X2,X3,X1,X0)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(r2_2,axiom,
equidistant(X0,reflection(X1,X0),X1,X0) ).
cnf(v_equals_reflection,hypothesis,
v = reflection(u,v) ).
cnf(prove_u_equals_v,negated_conjecture,
u != v ).
cnf(identity_for_equidistance,axiom,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ) ).
cnf(c5,plain,
( equidistant(X2,X3,X1,X0)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[d4_3]) ).
cnf(c12,plain,
equidistant(X0,reflection(X1,X0),X1,X0),
inference(clausification,[status(esa)],[r2_2]) ).
cnf(c15,plain,
v = reflection(u,v),
inference(clausification,[status(esa)],[v_equals_reflection]) ).
cnf(c16,plain,
u != v,
inference(clausification,[status(esa)],[prove_u_equals_v]) ).
cnf(c19,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[identity_for_equidistance]) ).
cnf(d_0,plain,
equidistant(v,v,u,v),
inference(superposition,[status(thm)],[c15,c12]) ).
cnf(d_1,plain,
equidistant(u,v,v,v),
inference(resolution,[status(thm)],[d_0,c5]) ).
cnf(d_2,plain,
u = v,
inference(resolution,[status(thm)],[d_1,c19]) ).
cnf(d_3,plain,
$false,
inference(resolution,[status(thm)],[c16,d_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO058-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 12:37:19 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.83/3.53 % SZS status Unsatisfiable for theBenchmark.p
% 11.83/3.53 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------