TSTP Solution File: SWV007-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV007-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 0.19s 0.58s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of clauses : 32 ( 12 unt; 5 nHn; 29 RR)
% Number of literals : 60 ( 15 equ; 25 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(less_than_successor,axiom,
less_than(X,successor(X)) ).
cnf(transitivity_of_less_than,axiom,
( less_than(X,Z)
| ~ less_than(X,Y)
| ~ less_than(Y,Z) ) ).
cnf(all_related,axiom,
( less_than(X,Y)
| less_than(Y,X)
| X = Y ) ).
cnf(anti_symmetry_of_less_than,axiom,
( ~ less_than(X,Y)
| ~ less_than(Y,X) ) ).
cnf(clause_4,negated_conjecture,
~ less_than(n,m) ).
cnf(clause_5,negated_conjecture,
less_than(i,m) ).
cnf(clause_8,negated_conjecture,
less_than(a(m),a(k)) ).
cnf(clause_11,negated_conjecture,
( less_than(X,i)
| ~ less_than(X,successor(n))
| ~ less_than(a(X),a(k)) ) ).
cnf(refute_0_0,plain,
( ~ less_than(i,m)
| ~ less_than(m,i) ),
inference(subst,[],[anti_symmetry_of_less_than:[bind(X,$fot(m)),bind(Y,$fot(i))]]) ).
cnf(refute_0_1,plain,
( ~ less_than(a(m),a(k))
| ~ less_than(m,successor(n))
| less_than(m,i) ),
inference(subst,[],[clause_11:[bind(X,$fot(m))]]) ).
cnf(refute_0_2,plain,
( ~ less_than(m,successor(n))
| less_than(m,i) ),
inference(resolve,[$cnf( less_than(a(m),a(k)) )],[clause_8,refute_0_1]) ).
cnf(refute_0_3,plain,
( less_than(m,n)
| less_than(n,m)
| n = m ),
inference(subst,[],[all_related:[bind(X,$fot(n)),bind(Y,$fot(m))]]) ).
cnf(refute_0_4,plain,
( less_than(m,n)
| n = m ),
inference(resolve,[$cnf( less_than(n,m) )],[refute_0_3,clause_4]) ).
cnf(refute_0_5,plain,
less_than(X_19,successor(X_19)),
inference(subst,[],[less_than_successor:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_6,plain,
( ~ less_than(X_18,X_19)
| ~ less_than(X_19,successor(X_19))
| less_than(X_18,successor(X_19)) ),
inference(subst,[],[transitivity_of_less_than:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(successor(X_19)))]]) ).
cnf(refute_0_7,plain,
( ~ less_than(X_18,X_19)
| less_than(X_18,successor(X_19)) ),
inference(resolve,[$cnf( less_than(X_19,successor(X_19)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ less_than(m,n)
| less_than(m,successor(n)) ),
inference(subst,[],[refute_0_7:[bind(X_18,$fot(m)),bind(X_19,$fot(n))]]) ).
cnf(refute_0_9,plain,
( less_than(m,successor(n))
| n = m ),
inference(resolve,[$cnf( less_than(m,n) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( less_than(m,i)
| n = m ),
inference(resolve,[$cnf( less_than(m,successor(n)) )],[refute_0_9,refute_0_2]) ).
cnf(refute_0_11,plain,
( ~ less_than(i,m)
| n = m ),
inference(resolve,[$cnf( less_than(m,i) )],[refute_0_10,refute_0_0]) ).
cnf(refute_0_12,plain,
n = m,
inference(resolve,[$cnf( less_than(i,m) )],[clause_5,refute_0_11]) ).
cnf(refute_0_13,plain,
successor(n) = successor(n),
introduced(tautology,[refl,[$fot(successor(n))]]) ).
cnf(refute_0_14,plain,
( n != m
| successor(n) != successor(n)
| successor(n) = successor(m) ),
introduced(tautology,[equality,[$cnf( $equal(successor(n),successor(n)) ),[1,0],$fot(m)]]) ).
cnf(refute_0_15,plain,
( n != m
| successor(n) = successor(m) ),
inference(resolve,[$cnf( $equal(successor(n),successor(n)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
successor(n) = successor(m),
inference(resolve,[$cnf( $equal(n,m) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ less_than(m,successor(m))
| successor(n) != successor(m)
| less_than(m,successor(n)) ),
introduced(tautology,[equality,[$cnf( ~ less_than(m,successor(n)) ),[1],$fot(successor(m))]]) ).
cnf(refute_0_18,plain,
( ~ less_than(m,successor(m))
| less_than(m,successor(n)) ),
inference(resolve,[$cnf( $equal(successor(n),successor(m)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ less_than(m,successor(m))
| less_than(m,i) ),
inference(resolve,[$cnf( less_than(m,successor(n)) )],[refute_0_18,refute_0_2]) ).
cnf(refute_0_20,plain,
less_than(m,successor(m)),
inference(subst,[],[less_than_successor:[bind(X,$fot(m))]]) ).
cnf(refute_0_21,plain,
less_than(m,i),
inference(resolve,[$cnf( less_than(m,successor(m)) )],[refute_0_20,refute_0_19]) ).
cnf(refute_0_22,plain,
~ less_than(i,m),
inference(resolve,[$cnf( less_than(m,i) )],[refute_0_21,refute_0_0]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( less_than(i,m) )],[clause_5,refute_0_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV007-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 15 09:58:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.58 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.58
% 0.19/0.58 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.58
%------------------------------------------------------------------------------