TSTP Solution File: SYN013-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN013-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 : Thu Jul 21 08:58:28 EDT 2022
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 24
% Syntax : Number of clauses : 93 ( 22 unt; 50 nHn; 90 RR)
% Number of literals : 245 ( 147 equ; 76 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 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 : 19 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_1,negated_conjecture,
m != n ).
cnf(c_2,negated_conjecture,
n != k ).
cnf(c_3,negated_conjecture,
k != m ).
cnf(c_4,negated_conjecture,
( Y = m
| ~ element(Y,m)
| f(Y) != m ) ).
cnf(c_5,negated_conjecture,
( Y = m
| ~ element(Y,m)
| f(Y) != Y ) ).
cnf(c_6,negated_conjecture,
( Y = m
| ~ element(Y,m)
| element(Y,f(Y)) ) ).
cnf(c_7,negated_conjecture,
( Y = m
| ~ element(Y,m)
| element(f(Y),Y) ) ).
cnf(c_8,negated_conjecture,
( Y = m
| element(Y,m)
| V = m
| V = Y
| ~ element(Y,V)
| ~ element(V,Y) ) ).
cnf(c_10,negated_conjecture,
( Y = n
| element(Y,n)
| g(Y) != Y ) ).
cnf(c_11,negated_conjecture,
( Y = n
| element(Y,n)
| element(Y,g(Y)) ) ).
cnf(c_12,negated_conjecture,
( Y = n
| element(Y,n)
| element(g(Y),Y) ) ).
cnf(c_13,negated_conjecture,
( Y = n
| ~ element(Y,n)
| V = n
| V = Y
| ~ element(Y,V)
| ~ element(V,Y) ) ).
cnf(c_14,negated_conjecture,
( Y = k
| Y != m
| element(Y,k) ) ).
cnf(c_15,negated_conjecture,
( Y = k
| Y != n
| element(Y,k) ) ).
cnf(c_16,negated_conjecture,
( Y = k
| Y = m
| Y = n
| ~ element(Y,k) ) ).
cnf(refute_0_0,plain,
( m != m
| m = k
| element(m,k) ),
inference(subst,[],[c_14:[bind(Y,$fot(m))]]) ).
cnf(refute_0_1,plain,
m = m,
introduced(tautology,[refl,[$fot(m)]]) ).
cnf(refute_0_2,plain,
( m = k
| element(m,k) ),
inference(resolve,[$cnf( $equal(m,m) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_4,plain,
( X != X
| X != Y0
| Y0 = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y0)]]) ).
cnf(refute_0_5,plain,
( X != Y0
| Y0 = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( m != k
| k = m ),
inference(subst,[],[refute_0_5:[bind(X,$fot(m)),bind(Y0,$fot(k))]]) ).
cnf(refute_0_7,plain,
m != k,
inference(resolve,[$cnf( $equal(k,m) )],[refute_0_6,c_3]) ).
cnf(refute_0_8,plain,
element(m,k),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ element(k,m)
| ~ element(k,n)
| ~ element(m,k)
| k = n
| m = k
| m = n ),
inference(subst,[],[c_13:[bind(V,$fot(m)),bind(Y,$fot(k))]]) ).
cnf(refute_0_10,plain,
( ~ element(k,m)
| ~ element(k,n)
| k = n
| m = k
| m = n ),
inference(resolve,[$cnf( element(m,k) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( k != n
| n = k ),
inference(subst,[],[refute_0_5:[bind(X,$fot(k)),bind(Y0,$fot(n))]]) ).
cnf(refute_0_12,plain,
k != n,
inference(resolve,[$cnf( $equal(n,k) )],[refute_0_11,c_2]) ).
cnf(refute_0_13,plain,
( ~ element(k,m)
| ~ element(k,n)
| m = k
| m = n ),
inference(resolve,[$cnf( $equal(k,n) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ element(k,m)
| ~ element(k,n)
| m = n ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_13,refute_0_7]) ).
cnf(refute_0_15,plain,
( ~ element(k,m)
| ~ element(k,n) ),
inference(resolve,[$cnf( $equal(m,n) )],[refute_0_14,c_1]) ).
cnf(refute_0_16,plain,
( ~ element(k,m)
| k = m
| element(k,f(k)) ),
inference(subst,[],[c_6:[bind(Y,$fot(k))]]) ).
cnf(refute_0_17,plain,
( n != n
| n = k
| element(n,k) ),
inference(subst,[],[c_15:[bind(Y,$fot(n))]]) ).
cnf(refute_0_18,plain,
n = n,
introduced(tautology,[refl,[$fot(n)]]) ).
cnf(refute_0_19,plain,
( n = k
| element(n,k) ),
inference(resolve,[$cnf( $equal(n,n) )],[refute_0_18,refute_0_17]) ).
cnf(refute_0_20,plain,
element(n,k),
inference(resolve,[$cnf( $equal(n,k) )],[refute_0_19,c_2]) ).
cnf(refute_0_21,plain,
( ~ element(k,n)
| ~ element(n,k)
| k = m
| n = k
| n = m
| element(k,m) ),
inference(subst,[],[c_8:[bind(V,$fot(n)),bind(Y,$fot(k))]]) ).
cnf(refute_0_22,plain,
( ~ element(k,n)
| k = m
| n = k
| n = m
| element(k,m) ),
inference(resolve,[$cnf( element(n,k) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ element(k,n)
| n = k
| n = m
| element(k,m) ),
inference(resolve,[$cnf( $equal(k,m) )],[refute_0_22,c_3]) ).
cnf(refute_0_24,plain,
( ~ element(k,n)
| n = m
| element(k,m) ),
inference(resolve,[$cnf( $equal(n,k) )],[refute_0_23,c_2]) ).
cnf(refute_0_25,plain,
( n != m
| m = n ),
inference(subst,[],[refute_0_5:[bind(X,$fot(n)),bind(Y0,$fot(m))]]) ).
cnf(refute_0_26,plain,
n != m,
inference(resolve,[$cnf( $equal(m,n) )],[refute_0_25,c_1]) ).
cnf(refute_0_27,plain,
( ~ element(k,n)
| element(k,m) ),
inference(resolve,[$cnf( $equal(n,m) )],[refute_0_24,refute_0_26]) ).
cnf(refute_0_28,plain,
( k = n
| element(k,g(k))
| element(k,n) ),
inference(subst,[],[c_11:[bind(Y,$fot(k))]]) ).
cnf(refute_0_29,plain,
( g(k) != k
| k = n
| element(k,n) ),
inference(subst,[],[c_10:[bind(Y,$fot(k))]]) ).
cnf(refute_0_30,plain,
( k = n
| element(g(k),k)
| element(k,n) ),
inference(subst,[],[c_12:[bind(Y,$fot(k))]]) ).
cnf(refute_0_31,plain,
( ~ element(g(k),k)
| g(k) = k
| g(k) = m
| g(k) = n ),
inference(subst,[],[c_16:[bind(Y,$fot(g(k)))]]) ).
cnf(refute_0_32,plain,
( g(k) = k
| g(k) = m
| g(k) = n
| k = n
| element(k,n) ),
inference(resolve,[$cnf( element(g(k),k) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( g(k) = k
| g(k) = m
| g(k) = n
| element(k,n) ),
inference(resolve,[$cnf( $equal(k,n) )],[refute_0_32,refute_0_12]) ).
cnf(refute_0_34,plain,
( g(k) = k
| g(k) = m
| g(k) = n
| element(k,m) ),
inference(resolve,[$cnf( element(k,n) )],[refute_0_33,refute_0_27]) ).
cnf(refute_0_35,plain,
( ~ element(k,m)
| g(k) = k
| g(k) = m
| g(k) = n ),
inference(resolve,[$cnf( element(k,n) )],[refute_0_33,refute_0_15]) ).
cnf(refute_0_36,plain,
( g(k) = k
| g(k) = m
| g(k) = n ),
inference(resolve,[$cnf( element(k,m) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( g(k) != k
| k != k
| g(k) = k ),
introduced(tautology,[equality,[$cnf( ~ $equal(g(k),k) ),[0],$fot(k)]]) ).
cnf(refute_0_38,plain,
( k != k
| g(k) = k
| g(k) = m
| g(k) = n ),
inference(resolve,[$cnf( $equal(g(k),k) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( k != k
| g(k) = m
| g(k) = n
| k = n
| element(k,n) ),
inference(resolve,[$cnf( $equal(g(k),k) )],[refute_0_38,refute_0_29]) ).
cnf(refute_0_40,plain,
k = k,
introduced(tautology,[refl,[$fot(k)]]) ).
cnf(refute_0_41,plain,
( g(k) = m
| g(k) = n
| k = n
| element(k,n) ),
inference(resolve,[$cnf( $equal(k,k) )],[refute_0_40,refute_0_39]) ).
cnf(refute_0_42,plain,
( g(k) = m
| g(k) = n
| element(k,n) ),
inference(resolve,[$cnf( $equal(k,n) )],[refute_0_41,refute_0_12]) ).
cnf(refute_0_43,plain,
( g(k) = m
| g(k) = n
| element(k,m) ),
inference(resolve,[$cnf( element(k,n) )],[refute_0_42,refute_0_27]) ).
cnf(refute_0_44,plain,
( ~ element(k,m)
| g(k) = m
| g(k) = n ),
inference(resolve,[$cnf( element(k,n) )],[refute_0_42,refute_0_15]) ).
cnf(refute_0_45,plain,
( g(k) = m
| g(k) = n ),
inference(resolve,[$cnf( element(k,m) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( g(k) != n
| ~ element(k,g(k))
| element(k,n) ),
introduced(tautology,[equality,[$cnf( element(k,g(k)) ),[1],$fot(n)]]) ).
cnf(refute_0_47,plain,
( ~ element(k,g(k))
| g(k) = m
| element(k,n) ),
inference(resolve,[$cnf( $equal(g(k),n) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( g(k) = m
| k = n
| element(k,n) ),
inference(resolve,[$cnf( element(k,g(k)) )],[refute_0_28,refute_0_47]) ).
cnf(refute_0_49,plain,
( g(k) = m
| element(k,n) ),
inference(resolve,[$cnf( $equal(k,n) )],[refute_0_48,refute_0_12]) ).
cnf(refute_0_50,plain,
( g(k) = m
| element(k,m) ),
inference(resolve,[$cnf( element(k,n) )],[refute_0_49,refute_0_27]) ).
cnf(refute_0_51,plain,
( ~ element(k,m)
| g(k) = m ),
inference(resolve,[$cnf( element(k,n) )],[refute_0_49,refute_0_15]) ).
cnf(refute_0_52,plain,
g(k) = m,
inference(resolve,[$cnf( element(k,m) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( g(k) != m
| ~ element(k,g(k))
| element(k,m) ),
introduced(tautology,[equality,[$cnf( element(k,g(k)) ),[1],$fot(m)]]) ).
cnf(refute_0_54,plain,
( ~ element(k,g(k))
| element(k,m) ),
inference(resolve,[$cnf( $equal(g(k),m) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( k = n
| element(k,m)
| element(k,n) ),
inference(resolve,[$cnf( element(k,g(k)) )],[refute_0_28,refute_0_54]) ).
cnf(refute_0_56,plain,
( element(k,m)
| element(k,n) ),
inference(resolve,[$cnf( $equal(k,n) )],[refute_0_55,refute_0_12]) ).
cnf(refute_0_57,plain,
element(k,m),
inference(resolve,[$cnf( element(k,n) )],[refute_0_56,refute_0_27]) ).
cnf(refute_0_58,plain,
( k = m
| element(k,f(k)) ),
inference(resolve,[$cnf( element(k,m) )],[refute_0_57,refute_0_16]) ).
cnf(refute_0_59,plain,
element(k,f(k)),
inference(resolve,[$cnf( $equal(k,m) )],[refute_0_58,c_3]) ).
cnf(refute_0_60,plain,
( ~ element(f(k),k)
| f(k) = k
| f(k) = m
| f(k) = n ),
inference(subst,[],[c_16:[bind(Y,$fot(f(k)))]]) ).
cnf(refute_0_61,plain,
( ~ element(k,m)
| k = m
| element(f(k),k) ),
inference(subst,[],[c_7:[bind(Y,$fot(k))]]) ).
cnf(refute_0_62,plain,
( k = m
| element(f(k),k) ),
inference(resolve,[$cnf( element(k,m) )],[refute_0_57,refute_0_61]) ).
cnf(refute_0_63,plain,
element(f(k),k),
inference(resolve,[$cnf( $equal(k,m) )],[refute_0_62,c_3]) ).
cnf(refute_0_64,plain,
( f(k) = k
| f(k) = m
| f(k) = n ),
inference(resolve,[$cnf( element(f(k),k) )],[refute_0_63,refute_0_60]) ).
cnf(refute_0_65,plain,
( f(k) != k
| ~ element(k,m)
| k = m ),
inference(subst,[],[c_5:[bind(Y,$fot(k))]]) ).
cnf(refute_0_66,plain,
( f(k) != k
| k = m ),
inference(resolve,[$cnf( element(k,m) )],[refute_0_57,refute_0_65]) ).
cnf(refute_0_67,plain,
f(k) != k,
inference(resolve,[$cnf( $equal(k,m) )],[refute_0_66,c_3]) ).
cnf(refute_0_68,plain,
( f(k) = m
| f(k) = n ),
inference(resolve,[$cnf( $equal(f(k),k) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
( f(k) != m
| ~ element(k,m)
| k = m ),
inference(subst,[],[c_4:[bind(Y,$fot(k))]]) ).
cnf(refute_0_70,plain,
( f(k) != m
| k = m ),
inference(resolve,[$cnf( element(k,m) )],[refute_0_57,refute_0_69]) ).
cnf(refute_0_71,plain,
f(k) != m,
inference(resolve,[$cnf( $equal(k,m) )],[refute_0_70,c_3]) ).
cnf(refute_0_72,plain,
f(k) = n,
inference(resolve,[$cnf( $equal(f(k),m) )],[refute_0_68,refute_0_71]) ).
cnf(refute_0_73,plain,
( f(k) != n
| ~ element(k,f(k))
| element(k,n) ),
introduced(tautology,[equality,[$cnf( element(k,f(k)) ),[1],$fot(n)]]) ).
cnf(refute_0_74,plain,
( ~ element(k,f(k))
| element(k,n) ),
inference(resolve,[$cnf( $equal(f(k),n) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
element(k,n),
inference(resolve,[$cnf( element(k,f(k)) )],[refute_0_59,refute_0_74]) ).
cnf(refute_0_76,plain,
~ element(k,m),
inference(resolve,[$cnf( element(k,n) )],[refute_0_75,refute_0_15]) ).
cnf(refute_0_77,plain,
$false,
inference(resolve,[$cnf( element(k,m) )],[refute_0_57,refute_0_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN013-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n020.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 : Mon Jul 11 17:13:42 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.38
%------------------------------------------------------------------------------