%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO001-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 07:13:48 AM UTC 2026
% Result : Unsatisfiable 14.12s 2.35s
% Output : CNFRefutation 14.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 25 ( 12 unt; 0 nHn; 17 RR)
% Number of literals : 50 ( 3 equ; 27 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-5 aty)
% Number of variables : 76 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_between_a_and_c,hypothesis,
between(a,b,c) ).
cnf(prove_b_between_c_and_a,negated_conjecture,
~ between(c,b,a) ).
cnf(transitivity_for_betweeness,axiom,
( between(X0,X1,X3)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ) ).
cnf(identity_for_equidistance,axiom,
( 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(c0,plain,
between(a,b,c),
inference(clausification,[status(esa)],[b_between_a_and_c]) ).
cnf(c1,plain,
~ between(c,b,a),
inference(clausification,[status(esa)],[prove_b_between_c_and_a]) ).
cnf(c3,plain,
( between(X0,X1,X3)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[transitivity_for_betweeness]) ).
cnf(c6,plain,
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
inference(clausification,[status(esa)],[identity_for_equidistance]) ).
cnf(c8,plain,
( between(X0,'outer$upasch'(X1,X0,X3,X4,X2),X3)
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[outer_pasch1]) ).
cnf(c9,plain,
( between(X4,X1,'outer$upasch'(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[outer_pasch2]) ).
cnf(c14,plain,
between(X0,X1,extension(X0,X1,X2,X3)),
inference(clausification,[status(esa)],[segment_construction1]) ).
cnf(c15,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(clausification,[status(esa)],[segment_construction2]) ).
cnf(d0,plain,
X0 = extension(X1,X0,X2,X2),
inference(resolution,[status(thm)],[c15,c6]) ).
cnf(d1,plain,
between(X0,X1,X1),
inference(superposition,[status(thm)],[d0,c14]) ).
cnf(d2,plain,
( between(X4,X1,X5)
| ~ between(X1,X5,'outer$upasch'(X1,X0,X3,X4,X2))
| ~ between(X3,X2,X4)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c9,c3]) ).
cnf(d3,plain,
( between(X2,X0,X1)
| ~ between(X0,X1,X0) ),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d4,plain,
( ~ between(X1,X2,X4)
| ~ between(X1,X4,X3)
| between(X0,X1,'outer$upasch'(X2,X1,X1,X3,X4)) ),
inference(resolution,[status(thm)],[d3,c8]) ).
cnf(d5,plain,
( ~ between(X0,X3,X1)
| ~ between(X0,X1,X2)
| between(X2,X3,X0)
| ~ between(X0,X3,X1)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( ~ between(X2,X1,X0)
| between(X0,X1,X2) ),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
between(c,b,a),
inference(resolution,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c1,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO001-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.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 12:30:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.12/2.35 % SZS status Unsatisfiable for theBenchmark.p
% 14.12/2.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------