%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO039-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 07:13:58 AM UTC 2026
% Result : Unsatisfiable 12.07s 1.98s
% Output : CNFRefutation 12.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 12 unt; 0 nHn; 12 RR)
% Number of literals : 16 ( 5 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 8 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t3,axiom,
between(X0,X1,X1) ).
cnf(w_between_u_and_x,hypothesis,
between(u,w,x) ).
cnf(u_is_x,hypothesis,
u = x ).
cnf(prove_corollary,negated_conjecture,
~ between(v,w,x) ).
cnf(identity_for_betweeness,axiom,
( X0 = X1
| ~ between(X0,X1,X0) ) ).
cnf(c24,plain,
between(X0,X1,X1),
inference(clausification,[status(esa)],[t3]) ).
cnf(c25,plain,
between(u,w,x),
inference(clausification,[status(esa)],[w_between_u_and_x]) ).
cnf(c26,plain,
u = x,
inference(clausification,[status(esa)],[u_is_x]) ).
cnf(c27,plain,
~ between(v,w,x),
inference(clausification,[status(esa)],[prove_corollary]) ).
cnf(c34,plain,
( X0 = X1
| ~ between(X0,X1,X0) ),
inference(clausification,[status(esa)],[identity_for_betweeness]) ).
cnf(d_0,plain,
between(x,w,x),
inference(demodulation,[status(thm)],[c25,c26]) ).
cnf(d_1,plain,
x = w,
inference(resolution,[status(thm)],[c34,d_0]) ).
cnf(d_2,plain,
~ between(v,x,x),
inference(demodulation,[status(thm)],[c27,d_1]) ).
cnf(d_3,plain,
$false,
inference(resolution,[status(thm)],[c24,d_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO039-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 12:37:55 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.07/1.98 % SZS status Unsatisfiable for theBenchmark.p
% 12.07/1.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------