%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO051-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 07:14:01 AM UTC 2026
% Result : Unsatisfiable 40.40s 8.05s
% Output : CNFRefutation 40.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 23 ( 13 unt; 6 nHn; 23 RR)
% Number of literals : 44 ( 5 equ; 18 neg)
% Maximal clause size : 5 ( 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 : 20 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b5,axiom,
( between(X1,X2,X3)
| ~ between(X0,X2,X3)
| ~ between(X0,X1,X2) ) ).
cnf(b12,axiom,
( between(X0,X3,X2)
| between(X0,X2,X3)
| X0 = X1
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2) ) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w) ).
cnf(v_between_u_and_x,hypothesis,
between(u,v,x) ).
cnf(u_not_v,hypothesis,
u != v ).
cnf(w_not_between_v_and_x,hypothesis,
~ between(v,w,x) ).
cnf(prove_x_between_v_and_w,negated_conjecture,
~ between(v,x,w) ).
cnf(c32,plain,
( between(X3,X1,X2)
| ~ between(X0,X3,X1)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[b5]) ).
cnf(c55,plain,
( X1 = X0
| between(X0,X3,X2)
| ~ between(X0,X1,X3)
| between(X0,X2,X3)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[b12]) ).
cnf(c56,plain,
between(u,v,w),
inference(clausification,[status(esa)],[v_between_u_and_w]) ).
cnf(c57,plain,
between(u,v,x),
inference(clausification,[status(esa)],[v_between_u_and_x]) ).
cnf(c58,plain,
v != u,
inference(clausification,[status(esa)],[u_not_v]) ).
cnf(c59,plain,
~ between(v,w,x),
inference(clausification,[status(esa)],[w_not_between_v_and_x]) ).
cnf(c60,plain,
~ between(v,x,w),
inference(clausification,[status(esa)],[prove_x_between_v_and_w]) ).
cnf(d_0,plain,
( ~ between(u,w,X0)
| between(v,w,X0) ),
inference(resolution,[status(thm)],[c32,c56]) ).
cnf(d_1,plain,
( ~ between(u,x,X0)
| between(v,x,X0) ),
inference(resolution,[status(thm)],[c32,c57]) ).
cnf(d_2,plain,
( ~ between(u,v,X0)
| between(u,x,X0)
| between(u,X0,x)
| v = u ),
inference(resolution,[status(thm)],[c55,c57]) ).
cnf(d_3,plain,
( between(u,x,X0)
| ~ between(u,v,X0)
| between(u,X0,x) ),
inference(resolution,[status(thm)],[c58,d_2]) ).
cnf(d_4,plain,
( between(u,x,w)
| between(u,w,x) ),
inference(resolution,[status(thm)],[d_3,c56]) ).
cnf(d_5,plain,
( between(v,x,w)
| between(u,w,x) ),
inference(resolution,[status(thm)],[d_4,d_1]) ).
cnf(d_6,plain,
between(u,w,x),
inference(resolution,[status(thm)],[c60,d_5]) ).
cnf(d_7,plain,
between(v,w,x),
inference(resolution,[status(thm)],[d_6,d_0]) ).
cnf(d_8,plain,
$false,
inference(resolution,[status(thm)],[c59,d_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO051-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 12:41:15 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 40.40/8.05 % SZS status Unsatisfiable for theBenchmark.p
% 40.40/8.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------