TSTP Solution File: NUM020-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM020-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 : Mon Jul 18 12:24:09 EDT 2022
% Result : Unsatisfiable 52.11s 52.27s
% Output : CNFRefutation 52.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of clauses : 24 ( 14 unt; 0 nHn; 13 RR)
% Number of literals : 36 ( 0 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 2 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 : 30 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(adding_zero,axiom,
equalish(add(A,n0),A) ).
cnf(addition,axiom,
equalish(add(A,successor(B)),successor(add(A,B))) ).
cnf(successor_substitution,axiom,
( ~ equalish(A,B)
| equalish(successor(A),successor(B)) ) ).
cnf(symmetry,axiom,
( ~ equalish(X,Y)
| equalish(Y,X) ) ).
cnf(transitivity,axiom,
( ~ equalish(X,Y)
| ~ equalish(Y,Z)
| equalish(X,Z) ) ).
cnf(deny_addition_lemma,negated_conjecture,
~ equalish(add(a,successor(n0)),successor(a)) ).
cnf(refute_0_0,plain,
( ~ equalish(successor(X_877),add(X_877,successor(n0)))
| equalish(add(X_877,successor(n0)),successor(X_877)) ),
inference(subst,[],[symmetry:[bind(X,$fot(successor(X_877))),bind(Y,$fot(add(X_877,successor(n0))))]]) ).
cnf(refute_0_1,plain,
( ~ equalish(add(A,successor(B)),successor(add(A,B)))
| equalish(successor(add(A,B)),add(A,successor(B))) ),
inference(subst,[],[symmetry:[bind(X,$fot(add(A,successor(B)))),bind(Y,$fot(successor(add(A,B))))]]) ).
cnf(refute_0_2,plain,
equalish(successor(add(A,B)),add(A,successor(B))),
inference(resolve,[$cnf( equalish(add(A,successor(B)),successor(add(A,B))) )],[addition,refute_0_1]) ).
cnf(refute_0_3,plain,
equalish(successor(add(X_875,n0)),add(X_875,successor(n0))),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_875)),bind(B,$fot(n0))]]) ).
cnf(refute_0_4,plain,
equalish(add(X_9,n0),X_9),
inference(subst,[],[adding_zero:[bind(A,$fot(X_9))]]) ).
cnf(refute_0_5,plain,
( ~ equalish(add(X_9,n0),X_9)
| equalish(X_9,add(X_9,n0)) ),
inference(subst,[],[symmetry:[bind(X,$fot(add(X_9,n0))),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_6,plain,
equalish(X_9,add(X_9,n0)),
inference(resolve,[$cnf( equalish(add(X_9,n0),X_9) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
equalish(X_16,add(X_16,n0)),
inference(subst,[],[refute_0_6:[bind(X_9,$fot(X_16))]]) ).
cnf(refute_0_8,plain,
( ~ equalish(X_16,add(X_16,n0))
| equalish(successor(X_16),successor(add(X_16,n0))) ),
inference(subst,[],[successor_substitution:[bind(A,$fot(X_16)),bind(B,$fot(add(X_16,n0)))]]) ).
cnf(refute_0_9,plain,
equalish(successor(X_16),successor(add(X_16,n0))),
inference(resolve,[$cnf( equalish(X_16,add(X_16,n0)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ equalish(successor(X_16),successor(add(X_16,n0)))
| ~ equalish(successor(add(X_16,n0)),X_74)
| equalish(successor(X_16),X_74) ),
inference(subst,[],[transitivity:[bind(X,$fot(successor(X_16))),bind(Y,$fot(successor(add(X_16,n0)))),bind(Z,$fot(X_74))]]) ).
cnf(refute_0_11,plain,
( ~ equalish(successor(add(X_16,n0)),X_74)
| equalish(successor(X_16),X_74) ),
inference(resolve,[$cnf( equalish(successor(X_16),successor(add(X_16,n0))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ equalish(successor(add(X_875,n0)),add(X_875,successor(n0)))
| equalish(successor(X_875),add(X_875,successor(n0))) ),
inference(subst,[],[refute_0_11:[bind(X_16,$fot(X_875)),bind(X_74,$fot(add(X_875,successor(n0))))]]) ).
cnf(refute_0_13,plain,
equalish(successor(X_875),add(X_875,successor(n0))),
inference(resolve,[$cnf( equalish(successor(add(X_875,n0)),add(X_875,successor(n0))) )],[refute_0_3,refute_0_12]) ).
cnf(refute_0_14,plain,
equalish(successor(X_877),add(X_877,successor(n0))),
inference(subst,[],[refute_0_13:[bind(X_875,$fot(X_877))]]) ).
cnf(refute_0_15,plain,
equalish(add(X_877,successor(n0)),successor(X_877)),
inference(resolve,[$cnf( equalish(successor(X_877),add(X_877,successor(n0))) )],[refute_0_14,refute_0_0]) ).
cnf(refute_0_16,plain,
equalish(add(a,successor(n0)),successor(a)),
inference(subst,[],[refute_0_15:[bind(X_877,$fot(a))]]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( equalish(add(a,successor(n0)),successor(a)) )],[refute_0_16,deny_addition_lemma]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUM020-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.08/0.15 % Command : metis --show proof --show saturation %s
% 0.15/0.37 % Computer : n013.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Thu Jul 7 21:31:44 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.15/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 52.11/52.27 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 52.11/52.27
% 52.11/52.27 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 52.11/52.27
%------------------------------------------------------------------------------