%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO045-3 : 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 : n015.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 07:14:00 AM UTC 2026
% Result : Unsatisfiable 17.99s 2.83s
% Output : CNFRefutation 17.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of clauses : 20 ( 13 unt; 5 nHn; 20 RR)
% Number of literals : 32 ( 9 equ; 12 neg)
% Maximal clause size : 4 ( 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 : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t1,axiom,
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ) ).
cnf(b6,axiom,
( X1 = X2
| between(X0,X2,X3)
| ~ between(X1,X2,X3)
| ~ between(X0,X1,X2) ) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w) ).
cnf(w_between_v_and_x,hypothesis,
between(v,w,x) ).
cnf(v_not_w,hypothesis,
v != w ).
cnf(prove_v_between_u_and_x,negated_conjecture,
~ between(u,v,x) ).
cnf(c26,plain,
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[t1]) ).
cnf(c34,plain,
( X1 = X2
| between(X0,X2,X3)
| ~ between(X1,X2,X3)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[b6]) ).
cnf(c35,plain,
between(u,v,w),
inference(clausification,[status(esa)],[v_between_u_and_w]) ).
cnf(c36,plain,
between(v,w,x),
inference(clausification,[status(esa)],[w_between_v_and_x]) ).
cnf(c37,plain,
v != w,
inference(clausification,[status(esa)],[v_not_w]) ).
cnf(c38,plain,
~ between(u,v,x),
inference(clausification,[status(esa)],[prove_v_between_u_and_x]) ).
cnf(d_0,plain,
between(w,v,u),
inference(resolution,[status(thm)],[c26,c35]) ).
cnf(d_1,plain,
between(x,w,v),
inference(resolution,[status(thm)],[c26,c36]) ).
cnf(d_2,plain,
( between(x,v,X0)
| ~ between(w,v,X0)
| w = v ),
inference(resolution,[status(thm)],[c34,d_1]) ).
cnf(d_3,plain,
( between(x,v,u)
| w = v ),
inference(resolution,[status(thm)],[d_2,d_0]) ).
cnf(d_4,plain,
( between(u,v,x)
| w = v ),
inference(resolution,[status(thm)],[d_3,c26]) ).
cnf(d_5,plain,
w = v,
inference(resolution,[status(thm)],[c38,d_4]) ).
cnf(d_6,plain,
v != v,
inference(demodulation,[status(thm)],[c37,d_5]) ).
cnf(d_7,plain,
$false,
inference(equality_resolution,[status(thm)],[d_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO045-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.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 12:39:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.99/2.83 % SZS status Unsatisfiable for theBenchmark.p
% 17.99/2.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------