%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO059-2 : 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 : n026.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 12.27s 3.94s
% Output : CNFRefutation 12.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of clauses : 22 ( 17 unt; 0 nHn; 9 RR)
% Number of literals : 29 ( 2 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 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 : 54 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_congruence,negated_conjecture,
~ equidistant(v,u,v,reflection(reflection(u,v),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(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,
~ equidistant(v,u,v,reflection(reflection(u,v),v)),
inference(clausification,[status(esa)],[prove_congruence]) ).
cnf(c1,plain,
equidistant(X0,X1,X1,X0),
inference(clausification,[status(esa)],[reflexivity_for_equidistance]) ).
cnf(c2,plain,
( equidistant(X2,X3,X4,X5)
| ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[transitivity_for_equidistance]) ).
cnf(c5,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(clausification,[status(esa)],[segment_construction2]) ).
cnf(c19,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)],[c2,c1]) ).
cnf(d1,plain,
equidistant(X1,reflection(X0,X1),X0,X1),
inference(superposition,[status(thm)],[c19,c5]) ).
cnf(d2,plain,
equidistant(X0,X1,reflection(X0,X1),X1),
inference(resolution,[status(thm)],[d0,d1]) ).
cnf(d3,plain,
equidistant(reflection(X0,X1),X1,X1,X0),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
equidistant(X0,X1,X0,reflection(X1,X0)),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( ~ equidistant(X2,X3,X0,X1)
| equidistant(X0,X1,X2,reflection(X3,X2)) ),
inference(resolution,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
~ equidistant(v,reflection(u,v),v,u),
inference(resolution,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
( ~ equidistant(X3,reflection(X2,X3),X0,X1)
| equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[d1,c2]) ).
cnf(d8,plain,
equidistant(reflection(X0,X1),X1,X0,X1),
inference(resolution,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
equidistant(X0,X1,X1,reflection(X0,X1)),
inference(resolution,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
equidistant(X0,reflection(X1,X0),X0,X1),
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO059-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 12:40:11 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.27/3.94 % SZS status Unsatisfiable for theBenchmark.p
% 12.27/3.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------