%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GEO006-3 : 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 : 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 07:13:50 AM UTC 2026
% Result : Unsatisfiable 14.43s 2.25s
% Output : CNFRefutation 14.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 19 ( 11 unt; 2 nHn; 19 RR)
% Number of literals : 31 ( 12 equ; 16 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(b2,axiom,
( X0 = X1
| ~ between(X1,X0,X2)
| ~ between(X0,X1,X2) ) ).
cnf(b3,axiom,
( X1 = X2
| ~ between(X0,X2,X1)
| ~ between(X0,X1,X2) ) ).
cnf(a_not_c,hypothesis,
a != c ).
cnf(c_not_d,hypothesis,
c != d ).
cnf(c_between_a_and_d,hypothesis,
between(a,c,d) ).
cnf(prove_not_between_others,negated_conjecture,
( between(a,d,c)
| between(c,a,d) ) ).
cnf(c28,plain,
( X0 = X1
| ~ between(X1,X0,X2)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[b2]) ).
cnf(c29,plain,
( X1 = X2
| ~ between(X0,X2,X1)
| ~ between(X0,X1,X2) ),
inference(clausification,[status(esa)],[b3]) ).
cnf(c30,plain,
a != c,
inference(clausification,[status(esa)],[a_not_c]) ).
cnf(c32,plain,
c != d,
inference(clausification,[status(esa)],[c_not_d]) ).
cnf(c33,plain,
between(a,c,d),
inference(clausification,[status(esa)],[c_between_a_and_d]) ).
cnf(c34,plain,
( between(a,d,c)
| between(c,a,d) ),
inference(clausification,[status(esa)],[prove_not_between_others]) ).
cnf(d_0,plain,
( ~ between(a,d,c)
| d = c ),
inference(resolution,[status(thm)],[c29,c33]) ).
cnf(d_1,plain,
( ~ between(c,a,d)
| a = c ),
inference(resolution,[status(thm)],[c28,c33]) ).
cnf(d_2,plain,
~ between(c,a,d),
inference(resolution,[status(thm)],[c30,d_1]) ).
cnf(d_3,plain,
between(a,d,c),
inference(resolution,[status(thm)],[d_2,c34]) ).
cnf(d_4,plain,
d = c,
inference(resolution,[status(thm)],[d_3,d_0]) ).
cnf(d_5,plain,
c != c,
inference(demodulation,[status(thm)],[c32,d_4]) ).
cnf(d_6,plain,
$false,
inference(equality_resolution,[status(thm)],[d_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 12:31:33 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.43/2.25 % SZS status Unsatisfiable for theBenchmark.p
% 14.43/2.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------