%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO022-3 : 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 : n006.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 07:13:55 AM UTC 2026
% Result : Unsatisfiable 13.73s 2.21s
% Output : CNFRefutation 13.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 9 unt; 0 nHn; 14 RR)
% Number of literals : 21 ( 0 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d2,axiom,
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(u_to_v_equals_w_to_x,hypothesis,
equidistant(u,v,w,x) ).
cnf(w_to_x_equals_y_to_z,hypothesis,
equidistant(w,x,y,z) ).
cnf(prove_transitivity,negated_conjecture,
~ equidistant(u,v,y,z) ).
cnf(transitivity_for_equidistance,axiom,
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(c1,plain,
( equidistant(X2,X3,X0,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[d2]) ).
cnf(c8,plain,
equidistant(u,v,w,x),
inference(clausification,[status(esa)],[u_to_v_equals_w_to_x]) ).
cnf(c9,plain,
equidistant(w,x,y,z),
inference(clausification,[status(esa)],[w_to_x_equals_y_to_z]) ).
cnf(c10,plain,
~ equidistant(u,v,y,z),
inference(clausification,[status(esa)],[prove_transitivity]) ).
cnf(c12,plain,
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[transitivity_for_equidistance]) ).
cnf(d_0,plain,
equidistant(w,x,u,v),
inference(resolution,[status(thm)],[c8,c1]) ).
cnf(d_1,plain,
( ~ equidistant(w,x,X0,X1)
| equidistant(X0,X1,y,z) ),
inference(resolution,[status(thm)],[c12,c9]) ).
cnf(d_2,plain,
equidistant(u,v,y,z),
inference(resolution,[status(thm)],[d_1,d_0]) ).
cnf(d_3,plain,
$false,
inference(resolution,[status(thm)],[c10,d_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO022-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n006.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 : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 12:32:55 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.73/2.21 % SZS status Unsatisfiable for theBenchmark.p
% 13.73/2.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------