%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO002-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 07:13:49 AM UTC 2026
% Result : Unsatisfiable 6.67s 2.72s
% Output : CNFRefutation 6.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 28 ( 11 unt; 0 nHn; 20 RR)
% Number of literals : 59 ( 0 equ; 33 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-5 aty)
% Number of variables : 99 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_for_betweeness,axiom,
( between(X0,X1,X3)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ) ).
cnf(identity_for_equidistance,axiom,
( equalish(X0,X1)
| ~ equidistant(X0,X1,X2,X2) ) ).
cnf(outer_pasch1,axiom,
( between(X0,'outer$upasch'(X1,X0,X3,X4,X2),X3)
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ) ).
cnf(outer_pasch2,axiom,
( between(X4,X1,'outer$upasch'(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,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(between_substitution3,axiom,
( between(X2,X3,X1)
| ~ between(X2,X3,X0)
| ~ equalish(X0,X1) ) ).
cnf(prove_a_between_a_and_b,negated_conjecture,
~ between(a,a,b) ).
cnf(c0,plain,
( between(X0,X1,X3)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[transitivity_for_betweeness]) ).
cnf(c1,plain,
( equalish(X0,X1)
| ~ equidistant(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[identity_for_equidistance]) ).
cnf(c2,plain,
( between(X0,'outer$upasch'(X1,X0,X3,X4,X2),X3)
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[outer_pasch1]) ).
cnf(c3,plain,
( between(X4,X1,'outer$upasch'(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[outer_pasch2]) ).
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(c6,plain,
( between(X2,X3,X1)
| ~ between(X2,X3,X0)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[between_substitution3]) ).
cnf(c7,plain,
~ between(a,a,b),
inference(clausification,[status(esa)],[prove_a_between_a_and_b]) ).
cnf(d0,plain,
equalish(X0,extension(X1,X0,X2,X2)),
inference(resolution,[status(thm)],[c5,c1]) ).
cnf(d1,plain,
( between(X2,X0,X1)
| ~ between(X0,X1,extension(X2,X0,X3,X4)) ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(d2,plain,
between(X0,X0,X0),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
( ~ equalish(X0,X1)
| between(X0,X0,X1) ),
inference(resolution,[status(thm)],[d2,c6]) ).
cnf(d4,plain,
( between(X1,X0,X0)
| ~ equalish(X0,extension(X1,X0,X2,X3)) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
between(X0,X1,X1),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
( between(X2,X4,X5)
| ~ between(X4,X5,'outer$upasch'(X4,X3,X0,X2,X1))
| ~ between(X3,X4,X1)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d7,plain,
( ~ between(extension(X0,X1,X3,X4),X6,X5)
| ~ between(X1,X2,X6)
| between(X0,X1,'outer$upasch'(X2,X1,extension(X0,X1,X3,X4),X5,X6)) ),
inference(resolution,[status(thm)],[d1,c2]) ).
cnf(d8,plain,
( ~ between(extension(X1,X0,X3,X4),X2,X5)
| between(X5,X1,X0)
| ~ between(X0,X1,X2)
| ~ between(extension(X1,X0,X3,X4),X2,X5)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( ~ between(X2,X1,X0)
| between(X0,X1,X2) ),
inference(resolution,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
between(X0,X0,X1),
inference(resolution,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,c7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO002-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n015.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 12:32:27 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.67/2.72 % SZS status Unsatisfiable for theBenchmark.p
% 6.67/2.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------