%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO027-3 : 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 : n011.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 07:13:56 AM UTC 2026
% Result : Unsatisfiable 17.07s 3.27s
% Output : CNFRefutation 17.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 18 ( 13 unt; 5 nHn; 14 RR)
% Number of literals : 32 ( 16 equ; 14 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 31 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d9,axiom,
( X2 = X3
| X0 = X1
| ~ equidistant(X1,X2,X1,X3)
| ~ between(X0,X1,X3)
| ~ between(X0,X1,X2) ) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w) ).
cnf(u_not_v,hypothesis,
u != v ).
cnf(prove_w_is_an_extension,negated_conjecture,
w != extension(u,v,v,w) ).
cnf(segment_construction1,axiom,
between(X0,X1,extension(X0,X1,X2,X3)) ).
cnf(segment_construction2,axiom,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3) ).
cnf(c18,plain,
( ~ equidistant(X1,X3,X1,X2)
| ~ between(X0,X1,X3)
| X3 = X2
| X0 = X1
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[d9]) ).
cnf(c19,plain,
between(u,v,w),
inference(clausification,[status(esa)],[v_between_u_and_w]) ).
cnf(c20,plain,
u != v,
inference(clausification,[status(esa)],[u_not_v]) ).
cnf(c21,plain,
w != extension(u,v,v,w),
inference(clausification,[status(esa)],[prove_w_is_an_extension]) ).
cnf(c25,plain,
between(X0,X1,extension(X0,X1,X2,X3)),
inference(clausification,[status(esa)],[segment_construction1]) ).
cnf(c26,plain,
equidistant(X0,extension(X1,X0,X2,X3),X2,X3),
inference(clausification,[status(esa)],[segment_construction2]) ).
cnf(d_0,plain,
( ~ between(X3,X1,extension(X0,X1,X1,X2))
| ~ between(X3,X1,X2)
| X3 = X1
| extension(X0,X1,X1,X2) = X2 ),
inference(resolution,[status(thm)],[c26,c18]) ).
cnf(d_1,plain,
( ~ between(X0,X1,X2)
| extension(X0,X1,X1,X2) = X2
| X0 = X1 ),
inference(resolution,[status(thm)],[d_0,c25]) ).
cnf(d_2,plain,
( extension(u,v,v,w) = w
| u = v ),
inference(resolution,[status(thm)],[d_1,c19]) ).
cnf(d_3,plain,
extension(u,v,v,w) = w,
inference(resolution,[status(thm)],[c20,d_2]) ).
cnf(d_4,plain,
w != w,
inference(demodulation,[status(thm)],[c21,d_3]) ).
cnf(d_5,plain,
$false,
inference(equality_resolution,[status(thm)],[d_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO027-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 12:33:28 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.07/3.27 % SZS status Unsatisfiable for theBenchmark.p
% 17.07/3.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------