%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO058-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/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 07:14:02 AM UTC 2026
% Result : Unsatisfiable 12.77s 3.50s
% Output : CNFRefutation 12.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 20 ( 15 unt; 0 nHn; 13 RR)
% Number of literals : 27 ( 9 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 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 : 40 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(v_equals_reflection,hypothesis,
v = reflection(u,v) ).
cnf(prove_u_equals_v,negated_conjecture,
u != v ).
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(identity_for_equidistance,axiom,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ) ).
cnf(segment_construction2,axiom,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3) ).
cnf(reflection,axiom,
reflection(X0,X1) = extension(X0,X1,X0,X1) ).
cnf(c0,plain,
v = reflection(u,v),
inference(clausification,[status(esa)],[v_equals_reflection]) ).
cnf(c1,plain,
u != v,
inference(clausification,[status(esa)],[prove_u_equals_v]) ).
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(c4,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[identity_for_equidistance]) ).
cnf(c6,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(clausification,[status(esa)],[segment_construction2]) ).
cnf(c20,plain,
reflection(X0,X1) = extension(X0,X1,X0,X1),
inference(clausification,[status(esa)],[reflection]) ).
cnf(d0,plain,
( ~ equidistant(X3,X2,X0,X1)
| equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c3,c2]) ).
cnf(d1,plain,
equidistant(X1,reflection(X0,X1),X0,X1),
inference(superposition,[status(thm)],[c20,c6]) ).
cnf(d2,plain,
equidistant(v,v,u,v),
inference(superposition,[status(thm)],[c0,d1]) ).
cnf(d3,plain,
equidistant(u,v,v,v),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
u = v,
inference(resolution,[status(thm)],[d3,c4]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c1,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO058-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/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
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.77/3.50 % SZS status Unsatisfiable for theBenchmark.p
% 12.77/3.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------