%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO021-2 : 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 : n017.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 11.90s 3.43s
% Output : CNFRefutation 11.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of clauses : 15 ( 11 unt; 0 nHn; 13 RR)
% Number of literals : 21 ( 0 equ; 8 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(u_to_v_equals_w_to_x,hypothesis,
equidistant(u,v,w,x) ).
cnf(prove_symmetry,negated_conjecture,
~ equidistant(x,w,v,u) ).
cnf(reflexivity_for_equidistance,axiom,
equidistant(X0,X1,X1,X0) ).
cnf(transitivity_for_equidistance,axiom,
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(c0,plain,
equidistant(u,v,w,x),
inference(clausification,[status(esa)],[u_to_v_equals_w_to_x]) ).
cnf(c1,plain,
~ equidistant(x,w,v,u),
inference(clausification,[status(esa)],[prove_symmetry]) ).
cnf(c2,plain,
equidistant(X0,X1,X1,X0),
inference(clausification,[status(esa)],[reflexivity_for_equidistance]) ).
cnf(c3,plain,
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[transitivity_for_equidistance]) ).
cnf(d0,plain,
( ~ equidistant(X3,X2,X0,X1)
| equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c3,c2]) ).
cnf(d1,plain,
( ~ equidistant(u,v,X0,X1)
| equidistant(X0,X1,w,x) ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d2,plain,
equidistant(v,u,w,x),
inference(resolution,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
equidistant(w,x,u,v),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
equidistant(u,v,x,w),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
equidistant(x,w,v,u),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c1,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO021-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.40 % Computer : n017.cluster.edu
% 0.08/0.40 % Model : x86_64 x86_64
% 0.08/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.40 % Memory : 8046.5625MB
% 0.08/0.40 % OS : Linux 6.8.0-71-generic
% 0.08/0.40 % CPULimit : 300
% 0.08/0.40 % WCLimit : 300
% 0.08/0.40 % DateTime : Fri Sep 25 12:28:02 UTC 2026
% 0.08/0.41 % CPUTime :
% 0.08/0.41 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.90/3.43 % SZS status Unsatisfiable for theBenchmark.p
% 11.90/3.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------