%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV008-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 20:29:48 EDT 2022
% Result : Unsatisfiable 1.23s 1.39s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of clauses : 38 ( 13 unt; 9 nHn; 37 RR)
% Number of literals : 84 ( 22 equ; 42 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(all_related,axiom,
( less_than(X,Y)
| less_than(Y,X)
| X = Y ) ).
cnf(x_not_less_than_x,axiom,
~ less_than(X,X) ).
cnf(clause_1,negated_conjecture,
~ less_than(n,l) ).
cnf(clause_2,negated_conjecture,
less_than(one,l) ).
cnf(clause_3,negated_conjecture,
less_than(a(l),a(predecessor(l))) ).
cnf(clause_4,negated_conjecture,
( less_than(X,n)
| less_than(n,X)
| ~ less_than(one,n)
| ~ less_than(a(X),a(predecessor(n))) ) ).
cnf(clause_5,negated_conjecture,
( ~ less_than(one,X)
| ~ less_than(X,n)
| ~ less_than(a(X),a(predecessor(X))) ) ).
cnf(refute_0_0,plain,
( less_than(l,n)
| less_than(n,l)
| n = l ),
inference(subst,[],[all_related:[bind(X,$fot(n)),bind(Y,$fot(l))]]) ).
cnf(refute_0_1,plain,
( less_than(l,n)
| n = l ),
inference(resolve,[$cnf( less_than(n,l) )],[refute_0_0,clause_1]) ).
cnf(refute_0_2,plain,
( ~ less_than(a(l),a(predecessor(l)))
| ~ less_than(l,n)
| ~ less_than(one,l) ),
inference(subst,[],[clause_5:[bind(X,$fot(l))]]) ).
cnf(refute_0_3,plain,
( ~ less_than(l,n)
| ~ less_than(one,l) ),
inference(resolve,[$cnf( less_than(a(l),a(predecessor(l))) )],[clause_3,refute_0_2]) ).
cnf(refute_0_4,plain,
~ less_than(l,n),
inference(resolve,[$cnf( less_than(one,l) )],[clause_2,refute_0_3]) ).
cnf(refute_0_5,plain,
n = l,
inference(resolve,[$cnf( less_than(l,n) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
predecessor(n) = predecessor(n),
introduced(tautology,[refl,[$fot(predecessor(n))]]) ).
cnf(refute_0_7,plain,
( n != l
| predecessor(n) != predecessor(n)
| predecessor(n) = predecessor(l) ),
introduced(tautology,[equality,[$cnf( $equal(predecessor(n),predecessor(n)) ),[1,0],$fot(l)]]) ).
cnf(refute_0_8,plain,
( n != l
| predecessor(n) = predecessor(l) ),
inference(resolve,[$cnf( $equal(predecessor(n),predecessor(n)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
predecessor(n) = predecessor(l),
inference(resolve,[$cnf( $equal(n,l) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
a(predecessor(n)) = a(predecessor(n)),
introduced(tautology,[refl,[$fot(a(predecessor(n)))]]) ).
cnf(refute_0_11,plain,
( a(predecessor(n)) != a(predecessor(n))
| predecessor(n) != predecessor(l)
| a(predecessor(n)) = a(predecessor(l)) ),
introduced(tautology,[equality,[$cnf( $equal(a(predecessor(n)),a(predecessor(n))) ),[1,0],$fot(predecessor(l))]]) ).
cnf(refute_0_12,plain,
( predecessor(n) != predecessor(l)
| a(predecessor(n)) = a(predecessor(l)) ),
inference(resolve,[$cnf( $equal(a(predecessor(n)),a(predecessor(n))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
a(predecessor(n)) = a(predecessor(l)),
inference(resolve,[$cnf( $equal(predecessor(n),predecessor(l)) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ less_than(a(X),a(predecessor(l)))
| a(predecessor(n)) != a(predecessor(l))
| less_than(a(X),a(predecessor(n))) ),
introduced(tautology,[equality,[$cnf( ~ less_than(a(X),a(predecessor(n))) ),[1],$fot(a(predecessor(l)))]]) ).
cnf(refute_0_15,plain,
( ~ less_than(a(X),a(predecessor(l)))
| less_than(a(X),a(predecessor(n))) ),
inference(resolve,[$cnf( $equal(a(predecessor(n)),a(predecessor(l))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ less_than(a(X),a(predecessor(l)))
| ~ less_than(one,n)
| less_than(X,n)
| less_than(n,X) ),
inference(resolve,[$cnf( less_than(a(X),a(predecessor(n))) )],[refute_0_15,clause_4]) ).
cnf(refute_0_17,plain,
( ~ less_than(one,l)
| n != l
| less_than(one,n) ),
introduced(tautology,[equality,[$cnf( ~ less_than(one,n) ),[1],$fot(l)]]) ).
cnf(refute_0_18,plain,
( ~ less_than(one,l)
| less_than(one,n) ),
inference(resolve,[$cnf( $equal(n,l) )],[refute_0_5,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ less_than(a(X),a(predecessor(l)))
| ~ less_than(one,l)
| less_than(X,n)
| less_than(n,X) ),
inference(resolve,[$cnf( less_than(one,n) )],[refute_0_18,refute_0_16]) ).
cnf(refute_0_20,plain,
( ~ less_than(X,n)
| n != l
| less_than(X,l) ),
introduced(tautology,[equality,[$cnf( less_than(X,n) ),[1],$fot(l)]]) ).
cnf(refute_0_21,plain,
( ~ less_than(X,n)
| less_than(X,l) ),
inference(resolve,[$cnf( $equal(n,l) )],[refute_0_5,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ less_than(a(X),a(predecessor(l)))
| ~ less_than(one,l)
| less_than(X,l)
| less_than(n,X) ),
inference(resolve,[$cnf( less_than(X,n) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ less_than(n,X)
| n != l
| less_than(l,X) ),
introduced(tautology,[equality,[$cnf( less_than(n,X) ),[0],$fot(l)]]) ).
cnf(refute_0_24,plain,
( ~ less_than(n,X)
| less_than(l,X) ),
inference(resolve,[$cnf( $equal(n,l) )],[refute_0_5,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ less_than(a(X),a(predecessor(l)))
| ~ less_than(one,l)
| less_than(X,l)
| less_than(l,X) ),
inference(resolve,[$cnf( less_than(n,X) )],[refute_0_22,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ less_than(a(X),a(predecessor(l)))
| less_than(X,l)
| less_than(l,X) ),
inference(resolve,[$cnf( less_than(one,l) )],[clause_2,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ less_than(a(l),a(predecessor(l)))
| less_than(l,l) ),
inference(subst,[],[refute_0_26:[bind(X,$fot(l))]]) ).
cnf(refute_0_28,plain,
less_than(l,l),
inference(resolve,[$cnf( less_than(a(l),a(predecessor(l))) )],[clause_3,refute_0_27]) ).
cnf(refute_0_29,plain,
~ less_than(l,l),
inference(subst,[],[x_not_less_than_x:[bind(X,$fot(l))]]) ).
cnf(refute_0_30,plain,
$false,
inference(resolve,[$cnf( less_than(l,l) )],[refute_0_28,refute_0_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWV008-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.15 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n026.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jun 14 21:47:52 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.23/1.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.23/1.39
% 1.23/1.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.23/1.39
%------------------------------------------------------------------------------