%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM022-1 : 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 : n008.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 9.55s 2.55s
% Output : CNFRefutation 9.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 25 ( 9 unt; 7 nHn; 25 RR)
% Number of literals : 50 ( 0 equ; 20 neg)
% Maximal clause size : 3 ( 2 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(X2,X1)
| ~ equalish(X2,X0)
| ~ equalish(X0,X1) ) ).
cnf(a_less_than_b,hypothesis,
less(a,b) ).
cnf(b_divides_d,hypothesis,
divides(b,d) ).
cnf(prove_a_less_than_d,negated_conjecture,
~ less(a,d) ).
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(c0,plain,
( equalish(X2,X1)
| ~ equalish(X2,X0)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[transitivity]) ).
cnf(c1,plain,
less(a,b),
inference(clausification,[status(esa)],[a_less_than_b]) ).
cnf(c2,plain,
divides(b,d),
inference(clausification,[status(esa)],[b_divides_d]) ).
cnf(c3,plain,
~ less(a,d),
inference(clausification,[status(esa)],[prove_a_less_than_d]) ).
cnf(c4,plain,
( less(X2,X1)
| ~ less(X2,X0)
| ~ less(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_of_less]) ).
cnf(c5,plain,
( less(X1,X2)
| ~ equalish(add(successor(X0),X1),X2) ),
inference(clausification,[status(esa)],[smaller_number]) ).
cnf(c6,plain,
( equalish(add(successor('predecessor$uof$u1st$uminus$u2nd'(X1,X0)),X0),X1)
| ~ less(X0,X1) ),
inference(clausification,[status(esa)],[less_lemma]) ).
cnf(c7,plain,
( equalish(X0,X1)
| less(X0,X1)
| ~ divides(X0,X1) ),
inference(clausification,[status(esa)],[divides_only_less_or_equal]) ).
cnf(d0,plain,
( less(b,d)
| equalish(b,d) ),
inference(resolution,[status(thm)],[c7,c2]) ).
cnf(d1,plain,
( ~ equalish(X0,b)
| equalish(X0,d)
| less(b,d) ),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
( ~ less(X0,b)
| less(b,d)
| equalish(add(successor('predecessor$uof$u1st$uminus$u2nd'(b,X0)),X0),d) ),
inference(resolution,[status(thm)],[d1,c6]) ).
cnf(d3,plain,
( less(X0,d)
| less(b,d)
| ~ less(X0,b) ),
inference(resolution,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
( less(b,d)
| less(a,d) ),
inference(resolution,[status(thm)],[d3,c1]) ).
cnf(d5,plain,
less(b,d),
inference(resolution,[status(thm)],[c3,d4]) ).
cnf(d6,plain,
( ~ less(X0,b)
| less(X0,d) ),
inference(resolution,[status(thm)],[d5,c4]) ).
cnf(d7,plain,
less(a,d),
inference(resolution,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c3,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM022-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 01:54:40 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.55/2.55 % SZS status Unsatisfiable for theBenchmark.p
% 9.55/2.55 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------