%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM024-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 08:10:40 AM UTC 2026
% Result : Unsatisfiable 16.57s 12.83s
% Output : CNFRefutation 16.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 28 ( 12 unt; 0 nHn; 23 RR)
% Number of literals : 46 ( 0 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(symmetry,axiom,
( equalish(X1,X0)
| ~ equalish(X0,X1) ) ).
cnf(transitivity,axiom,
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ) ).
cnf(plus_substitution,axiom,
( equalish(X0,X2)
| ~ equalish(add(X0,X1),add(X2,X1)) ) ).
cnf(commutativity_of_plus,axiom,
equalish(add(X0,X1),add(X1,X0)) ).
cnf(impossible_a_is_less_than_itself,hypothesis,
less(a,a) ).
cnf(prove_a_contradiction,negated_conjecture,
~ equalish(successor(X0),n0) ).
cnf(adding_zero,axiom,
equalish(add(X0,n0),X0) ).
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(c1,plain,
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[symmetry]) ).
cnf(c2,plain,
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(clausification,[status(esa)],[transitivity]) ).
cnf(c3,plain,
( equalish(X0,X2)
| ~ equalish(add(X0,X1),add(X2,X1)) ),
inference(clausification,[status(esa)],[plus_substitution]) ).
cnf(c4,plain,
equalish(add(X0,X1),add(X1,X0)),
inference(clausification,[status(esa)],[commutativity_of_plus]) ).
cnf(c5,plain,
less(a,a),
inference(clausification,[status(esa)],[impossible_a_is_less_than_itself]) ).
cnf(c6,plain,
~ equalish(successor(X0),n0),
inference(clausification,[status(esa)],[prove_a_contradiction]) ).
cnf(c7,plain,
equalish(add(X0,n0),X0),
inference(clausification,[status(esa)],[adding_zero]) ).
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(d0,plain,
( ~ equalish(X0,add(X2,X1))
| equalish(X0,add(X1,X2)) ),
inference(resolution,[status(thm)],[c4,c2]) ).
cnf(d1,plain,
( ~ less(X2,add(X0,X1))
| equalish(add(successor('predecessor$uof$u1st$uminus$u2nd'(add(X0,X1),X2)),X2),add(X1,X0)) ),
inference(resolution,[status(thm)],[d0,c15]) ).
cnf(d2,plain,
( equalish(successor('predecessor$uof$u1st$uminus$u2nd'(add(X0,X1),X0)),X1)
| ~ less(X0,add(X0,X1)) ),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
~ less(X0,add(X0,n0)),
inference(resolution,[status(thm)],[d2,c6]) ).
cnf(d4,plain,
equalish(X0,add(X0,n0)),
inference(resolution,[status(thm)],[c7,c1]) ).
cnf(d5,plain,
( ~ equalish(X0,X1)
| equalish(X0,add(X1,n0)) ),
inference(resolution,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
( less(X1,add(X2,n0))
| ~ equalish(add(successor(X0),X1),X2) ),
inference(resolution,[status(thm)],[d5,c14]) ).
cnf(d7,plain,
( ~ less(X0,X1)
| less(X0,add(X1,n0)) ),
inference(resolution,[status(thm)],[d6,c15]) ).
cnf(d8,plain,
~ less(X0,X0),
inference(resolution,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[d8,c5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM024-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.38 % Computer : n017.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Sat Sep 26 01:49:30 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.57/12.83 % SZS status Unsatisfiable for theBenchmark.p
% 16.57/12.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------