%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO041-3 : 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 : 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 07:13:59 AM UTC 2026
% Result : Unsatisfiable 13.88s 2.15s
% Output : CNFRefutation 13.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 15 ( 10 unt; 0 nHn; 15 RR)
% Number of literals : 22 ( 5 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t1,axiom,
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ) ).
cnf(b2,axiom,
( X0 = X1
| ~ between(X1,X0,X2)
| ~ between(X0,X1,X2) ) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w) ).
cnf(w_between_u_and_v,hypothesis,
between(u,w,v) ).
cnf(prove_v_is_w,negated_conjecture,
v != w ).
cnf(c26,plain,
( between(X2,X1,X0)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[t1]) ).
cnf(c28,plain,
( X0 = X1
| ~ between(X1,X0,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[b2]) ).
cnf(c29,plain,
between(u,v,w),
inference(clausification,[status(esa)],[v_between_u_and_w]) ).
cnf(c30,plain,
between(u,w,v),
inference(clausification,[status(esa)],[w_between_u_and_v]) ).
cnf(c31,plain,
v != w,
inference(clausification,[status(esa)],[prove_v_is_w]) ).
cnf(d_0,plain,
between(v,w,u),
inference(resolution,[status(thm)],[c26,c30]) ).
cnf(d_1,plain,
( ~ between(w,v,u)
| v = w ),
inference(resolution,[status(thm)],[c28,d_0]) ).
cnf(d_2,plain,
~ between(w,v,u),
inference(resolution,[status(thm)],[c31,d_1]) ).
cnf(d_3,plain,
between(w,v,u),
inference(resolution,[status(thm)],[c26,c29]) ).
cnf(d_4,plain,
$false,
inference(resolution,[status(thm)],[d_3,d_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO041-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Fri Sep 25 12:35:20 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.88/2.15 % SZS status Unsatisfiable for theBenchmark.p
% 13.88/2.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------