%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO001-3 : 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 : n012.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 20.85s 4.59s
% Output : CNFRefutation 20.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 17 ( 8 unt; 0 nHn; 15 RR)
% Number of literals : 34 ( 3 equ; 19 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-5 aty)
% Number of variables : 37 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t3,axiom,
between(X0,X1,X1) ).
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(identity_for_betweeness,axiom,
( X0 = X1
| ~ between(X0,X1,X0) ) ).
cnf(inner_pasch1,axiom,
( between(X1,'inner$upasch'(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ) ).
cnf(inner_pasch2,axiom,
( between(X4,'inner$upasch'(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ) ).
cnf(c24,plain,
between(X0,X1,X1),
inference(clausification,[status(esa)],[t3]) ).
cnf(c26,plain,
between(a,b,c),
inference(clausification,[status(esa)],[b_between_a_and_c]) ).
cnf(c27,plain,
~ between(c,b,a),
inference(clausification,[status(esa)],[prove_b_between_c_and_a]) ).
cnf(c34,plain,
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(clausification,[status(esa)],[identity_for_betweeness]) ).
cnf(c35,plain,
( between(X1,'inner$upasch'(X0,X1,X2,X4,X3),X3)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[inner_pasch1]) ).
cnf(c36,plain,
( between(X4,'inner$upasch'(X0,X1,X2,X4,X3),X0)
| ~ between(X3,X4,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[inner_pasch2]) ).
cnf(d_0,plain,
( X0 = 'inner$upasch'(X3,X0,X2,X1,X0)
| ~ between(X3,X0,X2)
| ~ between(X0,X1,X2) ),
inference(resolution,[status(thm)],[c35,c34]) ).
cnf(d_1,plain,
( ~ between(X1,X3,X2)
| ~ between(X0,X1,X2)
| ~ between(X1,X3,X2)
| ~ between(X0,X1,X2)
| between(X3,X1,X0) ),
inference(superposition,[status(thm)],[d_0,c36]) ).
cnf(d_2,plain,
( ~ between(b,X0,c)
| between(X0,b,a) ),
inference(resolution,[status(thm)],[d_1,c26]) ).
cnf(d_3,plain,
between(c,b,a),
inference(resolution,[status(thm)],[d_2,c24]) ).
cnf(d_4,plain,
$false,
inference(resolution,[status(thm)],[c27,d_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO001-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Fri Sep 25 12:29:35 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.29 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.85/4.59 % SZS status Unsatisfiable for theBenchmark.p
% 20.85/4.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------