%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO011-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 07:13:52 AM UTC 2026
% Result : Unsatisfiable 28.17s 4.30s
% Output : CNFRefutation 28.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 17 ( 11 unt; 4 nHn; 17 RR)
% Number of literals : 28 ( 0 equ; 10 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 : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t10_2,axiom,
( colinear(X1,X2,X0)
| ~ colinear(X0,X1,X2) ) ).
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(c67,plain,
( colinear(X1,X2,X0)
| ~ colinear(X0,X1,X2) ),
inference(clausification,[status(esa)],[t10_2]) ).
cnf(c71,plain,
colinear('lower$udimension$upoint$u1','lower$udimension$upoint$u2','lower$udimension$upoint$u3'),
inference(clausification,[status(esa)],[prove_lower_dimension_points_not_colinear]) ).
cnf(c81,plain,
~ between('lower$udimension$upoint$u1','lower$udimension$upoint$u2','lower$udimension$upoint$u3'),
inference(clausification,[status(esa)],[lower_dimension1]) ).
cnf(c82,plain,
~ between('lower$udimension$upoint$u2','lower$udimension$upoint$u3','lower$udimension$upoint$u1'),
inference(clausification,[status(esa)],[lower_dimension2]) ).
cnf(c83,plain,
~ between('lower$udimension$upoint$u3','lower$udimension$upoint$u1','lower$udimension$upoint$u2'),
inference(clausification,[status(esa)],[lower_dimension3]) ).
cnf(c93,plain,
( between(X2,X0,X1)
| between(X1,X2,X0)
| between(X0,X1,X2)
| ~ colinear(X0,X1,X2) ),
inference(clausification,[status(esa)],[colinearity4]) ).
cnf(d_0,plain,
colinear('lower$udimension$upoint$u2','lower$udimension$upoint$u3','lower$udimension$upoint$u1'),
inference(resolution,[status(thm)],[c67,c71]) ).
cnf(d_1,plain,
( between('lower$udimension$upoint$u2','lower$udimension$upoint$u3','lower$udimension$upoint$u1')
| between('lower$udimension$upoint$u3','lower$udimension$upoint$u1','lower$udimension$upoint$u2')
| between('lower$udimension$upoint$u1','lower$udimension$upoint$u2','lower$udimension$upoint$u3') ),
inference(resolution,[status(thm)],[c93,d_0]) ).
cnf(d_2,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)],[c81,d_1]) ).
cnf(d_3,plain,
between('lower$udimension$upoint$u3','lower$udimension$upoint$u1','lower$udimension$upoint$u2'),
inference(resolution,[status(thm)],[c82,d_2]) ).
cnf(d_4,plain,
$false,
inference(resolution,[status(thm)],[c83,d_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO011-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.54 % Computer : n017.cluster.edu
% 0.09/0.54 % Model : x86_64 x86_64
% 0.09/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.54 % Memory : 8046.5625MB
% 0.09/0.54 % OS : Linux 6.8.0-71-generic
% 0.09/0.54 % CPULimit : 300
% 0.09/0.54 % WCLimit : 300
% 0.09/0.54 % DateTime : Fri Sep 25 12:27:03 UTC 2026
% 0.09/0.54 % CPUTime :
% 0.09/0.54 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.17/4.30 % SZS status Unsatisfiable for theBenchmark.p
% 28.17/4.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------