%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO032-3 : 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 : n020.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 07:13:57 AM UTC 2026
% Result : Unsatisfiable 114.82s 18.02s
% Output : CNFRefutation 114.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 14 unt; 0 nHn; 19 RR)
% Number of literals : 48 ( 0 equ; 29 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 30 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d7,axiom,
equidistant(X0,X0,X1,X1) ).
cnf(d12,axiom,
( equidistant(X1,X6,X3,X7)
| ~ between(X2,X3,X5)
| ~ between(X0,X1,X4)
| ~ equidistant(X4,X6,X5,X7)
| ~ equidistant(X0,X6,X2,X7)
| ~ equidistant(X0,X4,X2,X5)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w) ).
cnf(v1_between_u1_and_w1,hypothesis,
between(u1,v1,w1) ).
cnf(u_to_v_equals_u1_to_v1,hypothesis,
equidistant(u,v,u1,v1) ).
cnf(u_to_w_equals_u1_to_w1,hypothesis,
equidistant(u,w,u1,w1) ).
cnf(v_to_w_equals_v1_to_w1,negated_conjecture,
~ equidistant(v,w,v1,w1) ).
cnf(c16,plain,
equidistant(X0,X0,X1,X1),
inference(clausification,[status(esa)],[d7]) ).
cnf(c46,plain,
( ~ equidistant(X4,X6,X2,X7)
| ~ equidistant(X3,X6,X0,X7)
| equidistant(X5,X6,X1,X7)
| ~ equidistant(X3,X5,X0,X1)
| ~ between(X3,X5,X4)
| ~ equidistant(X3,X4,X0,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[d12]) ).
cnf(c47,plain,
between(u,v,w),
inference(clausification,[status(esa)],[v_between_u_and_w]) ).
cnf(c48,plain,
between(u1,v1,w1),
inference(clausification,[status(esa)],[v1_between_u1_and_w1]) ).
cnf(c49,plain,
equidistant(u,v,u1,v1),
inference(clausification,[status(esa)],[u_to_v_equals_u1_to_v1]) ).
cnf(c50,plain,
equidistant(u,w,u1,w1),
inference(clausification,[status(esa)],[u_to_w_equals_u1_to_w1]) ).
cnf(c51,plain,
~ equidistant(v,w,v1,w1),
inference(clausification,[status(esa)],[v_to_w_equals_v1_to_w1]) ).
cnf(d_0,plain,
( ~ between(u,v,X0)
| ~ between(u1,v1,X2)
| ~ equidistant(u,X0,u1,X2)
| ~ equidistant(u,X1,u1,X3)
| equidistant(v,X1,v1,X3)
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c46,c49]) ).
cnf(d_1,plain,
( ~ between(u1,v1,w1)
| ~ between(u,v,w)
| equidistant(v,X0,v1,X1)
| ~ equidistant(u,X0,u1,X1)
| ~ equidistant(w,X0,w1,X1) ),
inference(resolution,[status(thm)],[d_0,c50]) ).
cnf(d_2,plain,
( ~ between(u1,v1,w1)
| ~ equidistant(w,X0,w1,X1)
| equidistant(v,X0,v1,X1)
| ~ equidistant(u,X0,u1,X1) ),
inference(resolution,[status(thm)],[c47,d_1]) ).
cnf(d_3,plain,
( ~ equidistant(w,X0,w1,X1)
| equidistant(v,X0,v1,X1)
| ~ equidistant(u,X0,u1,X1) ),
inference(resolution,[status(thm)],[c48,d_2]) ).
cnf(d_4,plain,
( equidistant(v,w,v1,w1)
| ~ equidistant(u,w,u1,w1) ),
inference(resolution,[status(thm)],[d_3,c16]) ).
cnf(d_5,plain,
equidistant(v,w,v1,w1),
inference(resolution,[status(thm)],[c50,d_4]) ).
cnf(d_6,plain,
$false,
inference(resolution,[status(thm)],[c51,d_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO032-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.01/0.36 % Computer : n020.cluster.edu
% 0.01/0.36 % Model : x86_64 x86_64
% 0.01/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.01/0.36 % Memory : 8046.5625MB
% 0.01/0.36 % OS : Linux 6.8.0-71-generic
% 0.01/0.36 % CPULimit : 300
% 0.01/0.36 % WCLimit : 300
% 0.01/0.36 % DateTime : Fri Sep 25 12:35:04 UTC 2026
% 0.01/0.36 % CPUTime :
% 0.01/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 114.82/18.02 % SZS status Unsatisfiable for theBenchmark.p
% 114.82/18.02 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------