%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM020-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 08:10:39 AM UTC 2026
% Result : Unsatisfiable 10.34s 1.74s
% Output : CNFRefutation 10.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 8 unt; 0 nHn; 10 RR)
% Number of literals : 23 ( 0 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity,axiom,
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ) ).
cnf(deny_addition_lemma,negated_conjecture,
~ equalish(add(a,successor(n0)),successor(a)) ).
cnf(adding_zero,axiom,
equalish(add(X0,n0),X0) ).
cnf(addition,axiom,
equalish(add(X0,successor(X1)),successor(add(X0,X1))) ).
cnf(successor_substitution,axiom,
( equalish(successor(X0),successor(X1))
| ~ equalish(X0,X1) ) ).
cnf(c2,plain,
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[transitivity]) ).
cnf(c4,plain,
~ equalish(add(a,successor(n0)),successor(a)),
inference(clausification,[status(esa)],[deny_addition_lemma]) ).
cnf(c6,plain,
equalish(add(X0,n0),X0),
inference(clausification,[status(esa)],[adding_zero]) ).
cnf(c7,plain,
equalish(add(X0,successor(X1)),successor(add(X0,X1))),
inference(clausification,[status(esa)],[addition]) ).
cnf(c11,plain,
( equalish(successor(X0),successor(X1))
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[successor_substitution]) ).
cnf(d0,plain,
( ~ equalish(X2,successor(X0))
| equalish(X2,successor(X1))
| ~ equalish(X0,X1) ),
inference(resolution,[status(thm)],[c11,c2]) ).
cnf(d1,plain,
( ~ equalish(add(X0,X1),X2)
| equalish(add(X0,successor(X1)),successor(X2)) ),
inference(resolution,[status(thm)],[d0,c7]) ).
cnf(d2,plain,
~ equalish(add(a,n0),a),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[c6,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM020-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.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 : Sat Sep 26 01:54:00 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.34/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 10.34/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------