%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO008-3 : 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 : n019.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 07:13:51 AM UTC 2026
% Result : Unsatisfiable 54.83s 8.41s
% Output : CNFRefutation 54.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of clauses : 33 ( 16 unt; 7 nHn; 33 RR)
% Number of literals : 59 ( 0 equ; 21 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 35 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t1,axiom,
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ) ).
cnf(b8,axiom,
( between(X0,X3,X2)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ) ).
cnf(b9,axiom,
( between(X0,X1,X3)
| ~ between(X0,X2,X3)
| ~ between(X0,X1,X2) ) ).
cnf(t9,axiom,
( between(X0,X3,X1)
| between(X0,X1,X3)
| ~ between(X0,X3,X2)
| ~ between(X0,X1,X2) ) ).
cnf(c_between_a_and_e,hypothesis,
between(a,c,e) ).
cnf(d_between_a_and_e,hypothesis,
between(a,d,e) ).
cnf(b_between_c_and_d,hypothesis,
between(c,b,d) ).
cnf(prove_betweenness,negated_conjecture,
~ between(a,b,e) ).
cnf(c26,plain,
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[t1]) ).
cnf(c35,plain,
( between(X3,X1,X2)
| ~ between(X3,X0,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[b8]) ).
cnf(c36,plain,
( between(X0,X3,X2)
| ~ between(X0,X3,X1)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[b9]) ).
cnf(c58,plain,
( between(X0,X2,X1)
| ~ between(X0,X2,X3)
| ~ between(X0,X1,X3)
| between(X0,X1,X2) ),
inference(clausification,[status(esa)],[t9]) ).
cnf(c60,plain,
between(a,c,e),
inference(clausification,[status(esa)],[c_between_a_and_e]) ).
cnf(c61,plain,
between(a,d,e),
inference(clausification,[status(esa)],[d_between_a_and_e]) ).
cnf(c62,plain,
between(c,b,d),
inference(clausification,[status(esa)],[b_between_c_and_d]) ).
cnf(c63,plain,
~ between(a,b,e),
inference(clausification,[status(esa)],[prove_betweenness]) ).
cnf(d_0,plain,
between(e,d,a),
inference(resolution,[status(thm)],[c26,c61]) ).
cnf(d_1,plain,
( ~ between(e,X0,d)
| between(e,X0,a) ),
inference(resolution,[status(thm)],[c36,d_0]) ).
cnf(d_2,plain,
( ~ between(X0,c,d)
| between(X0,b,d) ),
inference(resolution,[status(thm)],[c35,c62]) ).
cnf(d_3,plain,
between(e,c,a),
inference(resolution,[status(thm)],[c26,c60]) ).
cnf(d_4,plain,
( ~ between(e,X0,c)
| between(e,X0,a) ),
inference(resolution,[status(thm)],[c36,d_3]) ).
cnf(d_5,plain,
between(d,b,c),
inference(resolution,[status(thm)],[c26,c62]) ).
cnf(d_6,plain,
( ~ between(X0,d,c)
| between(X0,b,c) ),
inference(resolution,[status(thm)],[c35,d_5]) ).
cnf(d_7,plain,
( between(e,d,X0)
| between(e,X0,d)
| ~ between(e,X0,a) ),
inference(resolution,[status(thm)],[c58,d_0]) ).
cnf(d_8,plain,
( between(e,d,c)
| between(e,c,d) ),
inference(resolution,[status(thm)],[d_7,d_3]) ).
cnf(d_9,plain,
( between(e,b,c)
| between(e,c,d) ),
inference(resolution,[status(thm)],[d_8,d_6]) ).
cnf(d_10,plain,
( between(e,b,a)
| between(e,c,d) ),
inference(resolution,[status(thm)],[d_9,d_4]) ).
cnf(d_11,plain,
( between(a,b,e)
| between(e,c,d) ),
inference(resolution,[status(thm)],[d_10,c26]) ).
cnf(d_12,plain,
between(e,c,d),
inference(resolution,[status(thm)],[c63,d_11]) ).
cnf(d_13,plain,
between(e,b,d),
inference(resolution,[status(thm)],[d_12,d_2]) ).
cnf(d_14,plain,
between(e,b,a),
inference(resolution,[status(thm)],[d_13,d_1]) ).
cnf(d_15,plain,
between(a,b,e),
inference(resolution,[status(thm)],[d_14,c26]) ).
cnf(d_16,plain,
$false,
inference(resolution,[status(thm)],[c63,d_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO008-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.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 12:31:20 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 54.83/8.41 % SZS status Unsatisfiable for theBenchmark.p
% 54.83/8.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------