%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM021-1 : 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 : n001.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 21.49s 4.10s
% Output : CNFRefutation 21.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 25 ( 9 unt; 5 nHn; 25 RR)
% Number of literals : 48 ( 0 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity,axiom,
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ) ).
cnf(b_less_than_c,hypothesis,
less(b,c) ).
cnf(b_greater_equal_a,hypothesis,
~ less(b,a) ).
cnf(impossible_c_divides_a,negated_conjecture,
divides(c,a) ).
cnf(transitivity_of_less,axiom,
( less(X2,X1)
| ~ less(X2,X0)
| ~ less(X0,X1) ) ).
cnf(smaller_number,axiom,
( less(X1,X2)
| ~ equalish(add(successor(X0),X1),X2) ) ).
cnf(less_lemma,axiom,
( equalish(add(successor('predecessor$uof$u1st$uminus$u2nd'(X1,X0)),X0),X1)
| ~ less(X0,X1) ) ).
cnf(divides_only_less_or_equal,axiom,
( equalish(X0,X1)
| less(X0,X1)
| ~ divides(X0,X1) ) ).
cnf(c2,plain,
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[transitivity]) ).
cnf(c3,plain,
less(b,c),
inference(clausification,[status(esa)],[b_less_than_c]) ).
cnf(c4,plain,
~ less(b,a),
inference(clausification,[status(esa)],[b_greater_equal_a]) ).
cnf(c5,plain,
divides(c,a),
inference(clausification,[status(esa)],[impossible_c_divides_a]) ).
cnf(c13,plain,
( less(X2,X1)
| ~ less(X2,X0)
| ~ less(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_of_less]) ).
cnf(c14,plain,
( less(X1,X2)
| ~ equalish(add(successor(X0),X1),X2) ),
inference(clausification,[status(esa)],[smaller_number]) ).
cnf(c15,plain,
( equalish(add(successor('predecessor$uof$u1st$uminus$u2nd'(X1,X0)),X0),X1)
| ~ less(X0,X1) ),
inference(clausification,[status(esa)],[less_lemma]) ).
cnf(c16,plain,
( equalish(X0,X1)
| less(X0,X1)
| ~ divides(X0,X1) ),
inference(clausification,[status(esa)],[divides_only_less_or_equal]) ).
cnf(d0,plain,
( less(c,a)
| equalish(c,a) ),
inference(resolution,[status(thm)],[c16,c5]) ).
cnf(d1,plain,
( ~ less(X0,c)
| less(X0,a)
| equalish(c,a) ),
inference(resolution,[status(thm)],[d0,c13]) ).
cnf(d2,plain,
( less(b,a)
| equalish(c,a) ),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
equalish(c,a),
inference(resolution,[status(thm)],[c4,d2]) ).
cnf(d4,plain,
( ~ equalish(X0,c)
| equalish(X0,a) ),
inference(resolution,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
( ~ less(X0,c)
| equalish(add(successor('predecessor$uof$u1st$uminus$u2nd'(c,X0)),X0),a) ),
inference(resolution,[status(thm)],[d4,c15]) ).
cnf(d6,plain,
( less(X0,a)
| ~ less(X0,c) ),
inference(resolution,[status(thm)],[d5,c14]) ).
cnf(d7,plain,
less(b,a),
inference(resolution,[status(thm)],[d6,c3]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c4,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM021-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46 % Computer : n001.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Sat Sep 26 01:59:26 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.47 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.49/4.10 % SZS status Unsatisfiable for theBenchmark.p
% 21.49/4.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------