%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO036-2 : 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 : n010.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 07:13:57 AM UTC 2026
% Result : Unsatisfiable 9.77s 3.44s
% Output : CNFRefutation 9.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 22 ( 15 unt; 4 nHn; 16 RR)
% Number of literals : 32 ( 15 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 27 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_axioms_points_are_distinct,negated_conjecture,
( 'lower$udimension$upoint$u1' = 'lower$udimension$upoint$u3'
| 'lower$udimension$upoint$u2' = 'lower$udimension$upoint$u3'
| 'lower$udimension$upoint$u1' = 'lower$udimension$upoint$u2' ) ).
cnf(identity_for_equidistance,axiom,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ) ).
cnf(segment_construction1,axiom,
between(X0,X1,extension(X0,X1,X2,X3)) ).
cnf(segment_construction2,axiom,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3) ).
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$u2') ).
cnf(c0,plain,
( 'lower$udimension$upoint$u1' = 'lower$udimension$upoint$u3'
| 'lower$udimension$upoint$u2' = 'lower$udimension$upoint$u3'
| 'lower$udimension$upoint$u1' = 'lower$udimension$upoint$u2' ),
inference(clausification,[status(esa)],[prove_axioms_points_are_distinct]) ).
cnf(c3,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[identity_for_equidistance]) ).
cnf(c4,plain,
between(X0,X1,extension(X0,X1,X2,X3)),
inference(clausification,[status(esa)],[segment_construction1]) ).
cnf(c5,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(clausification,[status(esa)],[segment_construction2]) ).
cnf(c10,plain,
~ between('lower$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(d0,plain,
( 'lower$udimension$upoint$u1' = 'lower$udimension$upoint$u3'
| 'lower$udimension$upoint$u1' = 'lower$udimension$upoint$u2'
| ~ between('lower$udimension$upoint$u1','lower$udimension$upoint$u2','lower$udimension$upoint$u2') ),
inference(superposition,[status(thm)],[c0,c10]) ).
cnf(d1,plain,
X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[c5,c3]) ).
cnf(d2,plain,
between(X0,X1,X1),
inference(superposition,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
( 'lower$udimension$upoint$u1' = 'lower$udimension$upoint$u3'
| 'lower$udimension$upoint$u1' = 'lower$udimension$upoint$u2' ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( 'lower$udimension$upoint$u1' = 'lower$udimension$upoint$u2'
| ~ between('lower$udimension$upoint$u2','lower$udimension$upoint$u1','lower$udimension$upoint$u1') ),
inference(superposition,[status(thm)],[d3,c11]) ).
cnf(d5,plain,
'lower$udimension$upoint$u1' = 'lower$udimension$upoint$u2',
inference(resolution,[status(thm)],[d2,d4]) ).
cnf(d6,plain,
~ between('lower$udimension$upoint$u3','lower$udimension$upoint$u1','lower$udimension$upoint$u1'),
inference(demodulation,[status(thm)],[c12,d5]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d2,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO036-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n010.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 12:34:59 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.77/3.44 % SZS status Unsatisfiable for theBenchmark.p
% 9.77/3.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------