%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO062-3 : 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 : n019.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 07:14:03 AM UTC 2026
% Result : Unsatisfiable 57.62s 12.77s
% Output : CNFRefutation 57.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 20 ( 10 unt; 0 nHn; 16 RR)
% Number of literals : 40 ( 8 equ; 22 neg)
% Maximal clause size : 4 ( 2 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 : 53 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d1,axiom,
equidistant(X0,X1,X0,X1) ).
cnf(d4_2,axiom,
( equidistant(X1,X0,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ) ).
cnf(d15,axiom,
( X1 = X3
| ~ equidistant(X2,X1,X2,X3)
| ~ equidistant(X0,X1,X0,X3)
| ~ between(X0,X1,X2) ) ).
cnf(i2_1,axiom,
equidistant(X0,X1,X2,insertion(X2,X3,X0,X1)) ).
cnf(i2_3,axiom,
( equidistant(X1,X2,insertion(X3,X4,X0,X1),X4)
| ~ equidistant(X0,X2,X3,X4)
| ~ between(X0,X1,X2) ) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w) ).
cnf(prove_v_equals_insertion,negated_conjecture,
v != insertion(u,w,u,v) ).
cnf(c0,plain,
equidistant(X0,X1,X0,X1),
inference(clausification,[status(esa)],[d1]) ).
cnf(c4,plain,
( equidistant(X1,X0,X3,X2)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[d4_2]) ).
cnf(c48,plain,
( X2 = X1
| ~ equidistant(X3,X1,X3,X2)
| ~ between(X3,X1,X0)
| ~ equidistant(X0,X1,X0,X2) ),
inference(clausification,[status(esa)],[d15]) ).
cnf(c49,plain,
equidistant(X0,X1,X2,insertion(X2,X3,X0,X1)),
inference(clausification,[status(esa)],[i2_1]) ).
cnf(c51,plain,
( equidistant(X4,X1,insertion(X2,X3,X0,X4),X3)
| ~ between(X0,X4,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(clausification,[status(esa)],[i2_3]) ).
cnf(c52,plain,
between(u,v,w),
inference(clausification,[status(esa)],[v_between_u_and_w]) ).
cnf(c53,plain,
insertion(u,w,u,v) != v,
inference(clausification,[status(esa)],[prove_v_equals_insertion]) ).
cnf(d_0,plain,
( ~ between(X0,X2,X3)
| ~ equidistant(X3,X2,X3,insertion(X0,X1,X0,X2))
| insertion(X0,X1,X0,X2) = X2 ),
inference(resolution,[status(thm)],[c49,c48]) ).
cnf(d_1,plain,
( equidistant(X1,X4,X3,insertion(X2,X3,X0,X4))
| ~ between(X0,X4,X1)
| ~ equidistant(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[c51,c4]) ).
cnf(d_2,plain,
( ~ between(X0,X2,X1)
| insertion(X0,X1,X0,X2) = X2
| ~ between(X0,X2,X1)
| ~ equidistant(X0,X1,X0,X1) ),
inference(resolution,[status(thm)],[d_1,d_0]) ).
cnf(d_3,plain,
( ~ between(X0,X2,X1)
| insertion(X0,X1,X0,X2) = X2 ),
inference(resolution,[status(thm)],[c0,d_2]) ).
cnf(d_4,plain,
insertion(u,w,u,v) = v,
inference(resolution,[status(thm)],[d_3,c52]) ).
cnf(d_5,plain,
$false,
inference(resolution,[status(thm)],[c53,d_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO062-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 12:38:03 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 57.62/12.77 % SZS status Unsatisfiable for theBenchmark.p
% 57.62/12.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------