%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO011-2 : 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 : n016.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 07:13:52 AM UTC 2026
% Result : Unsatisfiable 12.59s 2.00s
% Output : CNFRefutation 12.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 10 unt; 4 nHn; 14 RR)
% Number of literals : 23 ( 0 equ; 8 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 6 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_lower_dimension_points_not_colinear,negated_conjecture,
colinear('lower$udimension$upoint$u1','lower$udimension$upoint$u2','lower$udimension$upoint$u3') ).
cnf(lower_dimension1,axiom,
~ between('lower$udimension$upoint$u1','lower$udimension$upoint$u2','lower$udimension$upoint$u3') ).
cnf(lower_dimension2,axiom,
~ between('lower$udimension$upoint$u2','lower$udimension$upoint$u3','lower$udimension$upoint$u1') ).
cnf(lower_dimension3,axiom,
~ between('lower$udimension$upoint$u3','lower$udimension$upoint$u1','lower$udimension$upoint$u2') ).
cnf(colinearity4,axiom,
( between(X2,X0,X1)
| between(X1,X2,X0)
| between(X0,X1,X2)
| ~ colinear(X0,X1,X2) ) ).
cnf(c0,plain,
colinear('lower$udimension$upoint$u1','lower$udimension$upoint$u2','lower$udimension$upoint$u3'),
inference(clausification,[status(esa)],[prove_lower_dimension_points_not_colinear]) ).
cnf(c10,plain,
~ between('lower$udimension$upoint$u1','lower$udimension$upoint$u2','lower$udimension$upoint$u3'),
inference(clausification,[status(esa)],[lower_dimension1]) ).
cnf(c11,plain,
~ between('lower$udimension$upoint$u2','lower$udimension$upoint$u3','lower$udimension$upoint$u1'),
inference(clausification,[status(esa)],[lower_dimension2]) ).
cnf(c12,plain,
~ between('lower$udimension$upoint$u3','lower$udimension$upoint$u1','lower$udimension$upoint$u2'),
inference(clausification,[status(esa)],[lower_dimension3]) ).
cnf(c22,plain,
( between(X2,X0,X1)
| between(X1,X2,X0)
| between(X0,X1,X2)
| ~ colinear(X0,X1,X2) ),
inference(clausification,[status(esa)],[colinearity4]) ).
cnf(d0,plain,
( between('lower$udimension$upoint$u1','lower$udimension$upoint$u2','lower$udimension$upoint$u3')
| between('lower$udimension$upoint$u2','lower$udimension$upoint$u3','lower$udimension$upoint$u1')
| between('lower$udimension$upoint$u3','lower$udimension$upoint$u1','lower$udimension$upoint$u2') ),
inference(resolution,[status(thm)],[c22,c0]) ).
cnf(d1,plain,
( between('lower$udimension$upoint$u3','lower$udimension$upoint$u1','lower$udimension$upoint$u2')
| between('lower$udimension$upoint$u2','lower$udimension$upoint$u3','lower$udimension$upoint$u1') ),
inference(resolution,[status(thm)],[c10,d0]) ).
cnf(d2,plain,
between('lower$udimension$upoint$u3','lower$udimension$upoint$u1','lower$udimension$upoint$u2'),
inference(resolution,[status(thm)],[c11,d1]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[c12,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO011-2 : 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 : n016.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 12:36:45 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.59/2.00 % SZS status Unsatisfiable for theBenchmark.p
% 12.59/2.00 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------