TSTP Solution File: SYN015-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN015-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 08:58:29 EDT 2022
% Result : Unsatisfiable 0.67s 0.86s
% Output : CNFRefutation 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 102
% Number of leaves : 49
% Syntax : Number of clauses : 236 ( 13 unt; 166 nHn; 233 RR)
% Number of literals : 830 ( 643 equ; 209 neg)
% Maximal clause size : 7 ( 3 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 : 36 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_1,negated_conjecture,
m != n ).
cnf(c_2,negated_conjecture,
( Y = j
| Y != k
| element(Y,j) ) ).
cnf(c_3,negated_conjecture,
( Y = j
| Y = k
| ~ element(Y,j) ) ).
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)
| V1 = m
| V1 = Y
| ~ element(Y,V1)
| ~ element(V1,Y) ) ).
cnf(c_9,negated_conjecture,
( Y = n
| element(Y,n)
| g(Y) != n ) ).
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( $equal(m,m) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
( k != k
| k = j
| element(k,j) ),
inference(subst,[],[c_2:[bind(Y,$fot(k))]]) ).
cnf(refute_0_4,plain,
k = k,
introduced(tautology,[refl,[$fot(k)]]) ).
cnf(refute_0_5,plain,
( k = j
| element(k,j) ),
inference(resolve,[$cnf( $equal(k,k) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ element(j,k)
| j = k
| j = m
| j = n ),
inference(subst,[],[c_16:[bind(Y,$fot(j))]]) ).
cnf(refute_0_7,plain,
( g(j) != j
| j = n
| element(j,n) ),
inference(subst,[],[c_10:[bind(Y,$fot(j))]]) ).
cnf(refute_0_8,plain,
( g(j) != n
| j = n
| element(j,n) ),
inference(subst,[],[c_9:[bind(Y,$fot(j))]]) ).
cnf(refute_0_9,plain,
( ~ element(g(j),j)
| g(j) = j
| g(j) = k ),
inference(subst,[],[c_3:[bind(Y,$fot(g(j)))]]) ).
cnf(refute_0_10,plain,
( j = n
| element(g(j),j)
| element(j,n) ),
inference(subst,[],[c_12:[bind(Y,$fot(j))]]) ).
cnf(refute_0_11,plain,
( g(j) = j
| g(j) = k
| j = n
| element(j,n) ),
inference(resolve,[$cnf( element(g(j),j) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
( n != n
| n = k
| element(n,k) ),
inference(subst,[],[c_15:[bind(Y,$fot(n))]]) ).
cnf(refute_0_13,plain,
n = n,
introduced(tautology,[refl,[$fot(n)]]) ).
cnf(refute_0_14,plain,
( n = k
| element(n,k) ),
inference(resolve,[$cnf( $equal(n,n) )],[refute_0_13,refute_0_12]) ).
cnf(refute_0_15,plain,
( ~ element(k,n)
| ~ element(n,k)
| k = m
| n = k
| n = m
| element(k,m) ),
inference(subst,[],[c_8:[bind(V1,$fot(n)),bind(Y,$fot(k))]]) ).
cnf(refute_0_16,plain,
( ~ element(k,n)
| k = m
| n = k
| n = m
| element(k,m) ),
inference(resolve,[$cnf( element(n,k) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_18,plain,
( X != X
| X != Y0
| Y0 = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y0)]]) ).
cnf(refute_0_19,plain,
( X != Y0
| Y0 = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( n != m
| m = n ),
inference(subst,[],[refute_0_19:[bind(X,$fot(n)),bind(Y0,$fot(m))]]) ).
cnf(refute_0_21,plain,
n != m,
inference(resolve,[$cnf( $equal(m,n) )],[refute_0_20,c_1]) ).
cnf(refute_0_22,plain,
( ~ element(k,n)
| k = m
| n = k
| element(k,m) ),
inference(resolve,[$cnf( $equal(n,m) )],[refute_0_16,refute_0_21]) ).
cnf(refute_0_23,plain,
( k = n
| element(k,g(k))
| element(k,n) ),
inference(subst,[],[c_11:[bind(Y,$fot(k))]]) ).
cnf(refute_0_24,plain,
( g(k) != k
| k = n
| element(k,n) ),
inference(subst,[],[c_10:[bind(Y,$fot(k))]]) ).
cnf(refute_0_25,plain,
( k = n
| element(g(k),k)
| element(k,n) ),
inference(subst,[],[c_12:[bind(Y,$fot(k))]]) ).
cnf(refute_0_26,plain,
( ~ element(g(k),k)
| g(k) = k
| g(k) = m
| g(k) = n ),
inference(subst,[],[c_16:[bind(Y,$fot(g(k)))]]) ).
cnf(refute_0_27,plain,
( g(k) = k
| g(k) = m
| g(k) = n
| k = n
| element(k,n) ),
inference(resolve,[$cnf( element(g(k),k) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( g(k) = k
| g(k) = m
| g(k) = n
| k = m
| k = n
| n = k
| element(k,m) ),
inference(resolve,[$cnf( element(k,n) )],[refute_0_27,refute_0_22]) ).
cnf(refute_0_29,plain,
( n != k
| k = n ),
inference(subst,[],[refute_0_19:[bind(X,$fot(n)),bind(Y0,$fot(k))]]) ).
cnf(refute_0_30,plain,
( g(k) = k
| g(k) = m
| g(k) = n
| k = m
| k = n
| element(k,m) ),
inference(resolve,[$cnf( $equal(n,k) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ element(k,m)
| ~ element(k,n)
| ~ element(m,k)
| k = n
| m = k
| m = n ),
inference(subst,[],[c_13:[bind(V,$fot(m)),bind(Y,$fot(k))]]) ).
cnf(refute_0_32,plain,
( ~ element(k,m)
| ~ element(k,n)
| k = n
| m = k
| m = n ),
inference(resolve,[$cnf( element(m,k) )],[refute_0_2,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ element(k,m)
| ~ element(k,n)
| k = n
| m = k ),
inference(resolve,[$cnf( $equal(m,n) )],[refute_0_32,c_1]) ).
cnf(refute_0_34,plain,
( ~ element(k,m)
| g(k) = k
| g(k) = m
| g(k) = n
| k = n
| m = k ),
inference(resolve,[$cnf( element(k,n) )],[refute_0_27,refute_0_33]) ).
cnf(refute_0_35,plain,
( g(k) = k
| g(k) = m
| g(k) = n
| k = m
| k = n
| m = k ),
inference(resolve,[$cnf( element(k,m) )],[refute_0_30,refute_0_34]) ).
cnf(refute_0_36,plain,
( m != k
| k = m ),
inference(subst,[],[refute_0_19:[bind(X,$fot(m)),bind(Y0,$fot(k))]]) ).
cnf(refute_0_37,plain,
( g(k) = k
| g(k) = m
| g(k) = n
| k = m
| k = n ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( g(k) != k
| k != k
| g(k) = k ),
introduced(tautology,[equality,[$cnf( ~ $equal(g(k),k) ),[0],$fot(k)]]) ).
cnf(refute_0_39,plain,
( k != k
| g(k) = k
| g(k) = m
| g(k) = n
| k = m
| k = n ),
inference(resolve,[$cnf( $equal(g(k),k) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( k != k
| g(k) = m
| g(k) = n
| k = m
| k = n
| element(k,n) ),
inference(resolve,[$cnf( $equal(g(k),k) )],[refute_0_39,refute_0_24]) ).
cnf(refute_0_41,plain,
( g(k) = m
| g(k) = n
| k = m
| k = n
| element(k,n) ),
inference(resolve,[$cnf( $equal(k,k) )],[refute_0_4,refute_0_40]) ).
cnf(refute_0_42,plain,
( g(k) = m
| g(k) = n
| k = m
| k = n
| n = k
| element(k,m) ),
inference(resolve,[$cnf( element(k,n) )],[refute_0_41,refute_0_22]) ).
cnf(refute_0_43,plain,
( g(k) = m
| g(k) = n
| k = m
| k = n
| element(k,m) ),
inference(resolve,[$cnf( $equal(n,k) )],[refute_0_42,refute_0_29]) ).
cnf(refute_0_44,plain,
( ~ element(k,m)
| g(k) = m
| g(k) = n
| k = m
| k = n
| m = k ),
inference(resolve,[$cnf( element(k,n) )],[refute_0_41,refute_0_33]) ).
cnf(refute_0_45,plain,
( ~ element(k,m)
| g(k) = m
| g(k) = n
| k = m
| k = n ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_44,refute_0_36]) ).
cnf(refute_0_46,plain,
( g(k) = m
| g(k) = n
| k = m
| k = n ),
inference(resolve,[$cnf( element(k,m) )],[refute_0_43,refute_0_45]) ).
cnf(refute_0_47,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_48,plain,
( ~ element(k,g(k))
| g(k) = m
| k = m
| k = n
| element(k,n) ),
inference(resolve,[$cnf( $equal(g(k),n) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( g(k) = m
| k = m
| k = n
| element(k,n) ),
inference(resolve,[$cnf( element(k,g(k)) )],[refute_0_23,refute_0_48]) ).
cnf(refute_0_50,plain,
( g(k) = m
| k = m
| k = n
| n = k
| element(k,m) ),
inference(resolve,[$cnf( element(k,n) )],[refute_0_49,refute_0_22]) ).
cnf(refute_0_51,plain,
( g(k) = m
| k = m
| k = n
| element(k,m) ),
inference(resolve,[$cnf( $equal(n,k) )],[refute_0_50,refute_0_29]) ).
cnf(refute_0_52,plain,
( ~ element(k,m)
| g(k) = m
| k = m
| k = n
| m = k ),
inference(resolve,[$cnf( element(k,n) )],[refute_0_49,refute_0_33]) ).
cnf(refute_0_53,plain,
( ~ element(k,m)
| g(k) = m
| k = m
| k = n ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_52,refute_0_36]) ).
cnf(refute_0_54,plain,
( g(k) = m
| k = m
| k = n ),
inference(resolve,[$cnf( element(k,m) )],[refute_0_51,refute_0_53]) ).
cnf(refute_0_55,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_56,plain,
( ~ element(k,g(k))
| k = m
| k = n
| element(k,m) ),
inference(resolve,[$cnf( $equal(g(k),m) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( k = m
| k = n
| element(k,m)
| element(k,n) ),
inference(resolve,[$cnf( element(k,g(k)) )],[refute_0_23,refute_0_56]) ).
cnf(refute_0_58,plain,
( k = m
| k = n
| n = k
| element(k,m) ),
inference(resolve,[$cnf( element(k,n) )],[refute_0_57,refute_0_22]) ).
cnf(refute_0_59,plain,
( k = m
| k = n
| element(k,m) ),
inference(resolve,[$cnf( $equal(n,k) )],[refute_0_58,refute_0_29]) ).
cnf(refute_0_60,plain,
( ~ element(k,m)
| k = m
| element(k,f(k)) ),
inference(subst,[],[c_6:[bind(Y,$fot(k))]]) ).
cnf(refute_0_61,plain,
( k = m
| k = n
| element(k,f(k)) ),
inference(resolve,[$cnf( element(k,m) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( f(k) != m
| ~ element(k,m)
| k = m ),
inference(subst,[],[c_4:[bind(Y,$fot(k))]]) ).
cnf(refute_0_63,plain,
( f(k) != m
| k = m
| k = n ),
inference(resolve,[$cnf( element(k,m) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
( f(k) != k
| ~ element(k,m)
| k = m ),
inference(subst,[],[c_5:[bind(Y,$fot(k))]]) ).
cnf(refute_0_65,plain,
( f(k) != k
| k = m
| k = n ),
inference(resolve,[$cnf( element(k,m) )],[refute_0_59,refute_0_64]) ).
cnf(refute_0_66,plain,
( ~ element(f(k),k)
| f(k) = k
| f(k) = m
| f(k) = n ),
inference(subst,[],[c_16:[bind(Y,$fot(f(k)))]]) ).
cnf(refute_0_67,plain,
( ~ element(k,m)
| k = m
| element(f(k),k) ),
inference(subst,[],[c_7:[bind(Y,$fot(k))]]) ).
cnf(refute_0_68,plain,
( k = m
| k = n
| element(f(k),k) ),
inference(resolve,[$cnf( element(k,m) )],[refute_0_59,refute_0_67]) ).
cnf(refute_0_69,plain,
( f(k) = k
| f(k) = m
| f(k) = n
| k = m
| k = n ),
inference(resolve,[$cnf( element(f(k),k) )],[refute_0_68,refute_0_66]) ).
cnf(refute_0_70,plain,
( f(k) != k
| k != k
| f(k) = k ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(k),k) ),[0],$fot(k)]]) ).
cnf(refute_0_71,plain,
( k != k
| f(k) = k
| f(k) = m
| f(k) = n
| k = m
| k = n ),
inference(resolve,[$cnf( $equal(f(k),k) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( k != k
| f(k) = m
| f(k) = n
| k = m
| k = n ),
inference(resolve,[$cnf( $equal(f(k),k) )],[refute_0_71,refute_0_65]) ).
cnf(refute_0_73,plain,
( f(k) = m
| f(k) = n
| k = m
| k = n ),
inference(resolve,[$cnf( $equal(k,k) )],[refute_0_4,refute_0_72]) ).
cnf(refute_0_74,plain,
( f(k) != m
| m != m
| f(k) = m ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(k),m) ),[0],$fot(m)]]) ).
cnf(refute_0_75,plain,
( m != m
| f(k) = m
| f(k) = n
| k = m
| k = n ),
inference(resolve,[$cnf( $equal(f(k),m) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
( m != m
| f(k) = n
| k = m
| k = n ),
inference(resolve,[$cnf( $equal(f(k),m) )],[refute_0_75,refute_0_63]) ).
cnf(refute_0_77,plain,
( f(k) = n
| k = m
| k = n ),
inference(resolve,[$cnf( $equal(m,m) )],[refute_0_1,refute_0_76]) ).
cnf(refute_0_78,plain,
( f(k) != n
| ~ element(k,f(k))
| element(k,n) ),
introduced(tautology,[equality,[$cnf( element(k,f(k)) ),[1],$fot(n)]]) ).
cnf(refute_0_79,plain,
( ~ element(k,f(k))
| k = m
| k = n
| element(k,n) ),
inference(resolve,[$cnf( $equal(f(k),n) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
( k = m
| k = n
| element(k,n) ),
inference(resolve,[$cnf( element(k,f(k)) )],[refute_0_61,refute_0_79]) ).
cnf(refute_0_81,plain,
( ~ element(k,m)
| k = m
| k = n
| m = k ),
inference(resolve,[$cnf( element(k,n) )],[refute_0_80,refute_0_33]) ).
cnf(refute_0_82,plain,
( ~ element(k,m)
| k = m
| k = n ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_81,refute_0_36]) ).
cnf(refute_0_83,plain,
( k = m
| k = n ),
inference(resolve,[$cnf( element(k,m) )],[refute_0_59,refute_0_82]) ).
cnf(refute_0_84,plain,
( k != n
| n = k ),
inference(subst,[],[refute_0_19:[bind(X,$fot(k)),bind(Y0,$fot(n))]]) ).
cnf(refute_0_85,plain,
( k = m
| n = k ),
inference(resolve,[$cnf( $equal(k,n) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
( n != k
| ~ element(j,n)
| element(j,k) ),
introduced(tautology,[equality,[$cnf( element(j,n) ),[1],$fot(k)]]) ).
cnf(refute_0_87,plain,
( ~ element(j,n)
| k = m
| element(j,k) ),
inference(resolve,[$cnf( $equal(n,k) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
( g(j) = j
| g(j) = k
| j = n
| k = m
| element(j,k) ),
inference(resolve,[$cnf( element(j,n) )],[refute_0_11,refute_0_87]) ).
cnf(refute_0_89,plain,
( g(j) = j
| g(j) = k
| j = k
| j = m
| j = n
| k = m ),
inference(resolve,[$cnf( element(j,k) )],[refute_0_88,refute_0_6]) ).
cnf(refute_0_90,plain,
( g(j) != k
| k != n
| g(j) = n ),
introduced(tautology,[equality,[$cnf( ~ $equal(g(j),n) ),[0],$fot(k)]]) ).
cnf(refute_0_91,plain,
( k != n
| g(j) = j
| g(j) = n
| j = k
| j = m
| j = n
| k = m ),
inference(resolve,[$cnf( $equal(g(j),k) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
( k != n
| g(j) = j
| j = k
| j = m
| j = n
| k = m
| element(j,n) ),
inference(resolve,[$cnf( $equal(g(j),n) )],[refute_0_91,refute_0_8]) ).
cnf(refute_0_93,plain,
( j != n
| n != k
| j = k ),
introduced(tautology,[equality,[$cnf( ~ $equal(j,k) ),[0],$fot(n)]]) ).
cnf(refute_0_94,plain,
( j != n
| k != n
| j = k ),
inference(resolve,[$cnf( $equal(n,k) )],[refute_0_84,refute_0_93]) ).
cnf(refute_0_95,plain,
( k != n
| g(j) = j
| j = k
| j = m
| k = m
| element(j,n) ),
inference(resolve,[$cnf( $equal(j,n) )],[refute_0_92,refute_0_94]) ).
cnf(refute_0_96,plain,
( k != n
| ~ element(j,n)
| element(j,k) ),
inference(resolve,[$cnf( $equal(n,k) )],[refute_0_84,refute_0_86]) ).
cnf(refute_0_97,plain,
( k != n
| g(j) = j
| j = k
| j = m
| k = m
| element(j,k) ),
inference(resolve,[$cnf( element(j,n) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
( k != k
| n != k
| k = n ),
introduced(tautology,[equality,[$cnf( ~ $equal(k,n) ),[1],$fot(k)]]) ).
cnf(refute_0_99,plain,
( k != k
| k = m
| k = n ),
inference(resolve,[$cnf( $equal(n,k) )],[refute_0_85,refute_0_98]) ).
cnf(refute_0_100,plain,
( k != k
| g(j) = j
| j = k
| j = m
| k = m
| element(j,k) ),
inference(resolve,[$cnf( $equal(k,n) )],[refute_0_99,refute_0_97]) ).
cnf(refute_0_101,plain,
( g(j) = j
| j = k
| j = m
| k = m
| element(j,k) ),
inference(resolve,[$cnf( $equal(k,k) )],[refute_0_4,refute_0_100]) ).
cnf(refute_0_102,plain,
( g(j) = j
| j = k
| j = m
| j = n
| k = m ),
inference(resolve,[$cnf( element(j,k) )],[refute_0_101,refute_0_6]) ).
cnf(refute_0_103,plain,
( g(j) != j
| j != j
| g(j) = j ),
introduced(tautology,[equality,[$cnf( ~ $equal(g(j),j) ),[0],$fot(j)]]) ).
cnf(refute_0_104,plain,
( j != j
| g(j) = j
| j = k
| j = m
| j = n
| k = m ),
inference(resolve,[$cnf( $equal(g(j),j) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
( j != j
| j = k
| j = m
| j = n
| k = m
| element(j,n) ),
inference(resolve,[$cnf( $equal(g(j),j) )],[refute_0_104,refute_0_7]) ).
cnf(refute_0_106,plain,
j = j,
introduced(tautology,[refl,[$fot(j)]]) ).
cnf(refute_0_107,plain,
( j = k
| j = m
| j = n
| k = m
| element(j,n) ),
inference(resolve,[$cnf( $equal(j,j) )],[refute_0_106,refute_0_105]) ).
cnf(refute_0_108,plain,
( j = k
| j = m
| j = n
| k = m
| element(j,k) ),
inference(resolve,[$cnf( element(j,n) )],[refute_0_107,refute_0_87]) ).
cnf(refute_0_109,plain,
( j = k
| j = m
| j = n
| k = m ),
inference(resolve,[$cnf( element(j,k) )],[refute_0_108,refute_0_6]) ).
cnf(refute_0_110,plain,
( j != n
| j = k
| k = m ),
inference(resolve,[$cnf( $equal(n,k) )],[refute_0_85,refute_0_93]) ).
cnf(refute_0_111,plain,
( j = k
| j = m
| k = m ),
inference(resolve,[$cnf( $equal(j,n) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
( j != m
| m = j ),
inference(subst,[],[refute_0_19:[bind(X,$fot(j)),bind(Y0,$fot(m))]]) ).
cnf(refute_0_113,plain,
( j = k
| k = m
| m = j ),
inference(resolve,[$cnf( $equal(j,m) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
( m != j
| ~ element(Y,j)
| element(Y,m) ),
introduced(tautology,[equality,[$cnf( ~ element(Y,m) ),[1],$fot(j)]]) ).
cnf(refute_0_115,plain,
( ~ element(Y,j)
| j = k
| k = m
| element(Y,m) ),
inference(resolve,[$cnf( $equal(m,j) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
( f(Y) != Y
| ~ element(Y,j)
| Y = m
| j = k
| k = m ),
inference(resolve,[$cnf( element(Y,m) )],[refute_0_115,c_5]) ).
cnf(refute_0_117,plain,
( f(k) != k
| ~ element(k,j)
| j = k
| k = m ),
inference(subst,[],[refute_0_116:[bind(Y,$fot(k))]]) ).
cnf(refute_0_118,plain,
( f(k) != k
| j = k
| k = j
| k = m ),
inference(resolve,[$cnf( element(k,j) )],[refute_0_5,refute_0_117]) ).
cnf(refute_0_119,plain,
( k != j
| j = k ),
inference(subst,[],[refute_0_19:[bind(X,$fot(k)),bind(Y0,$fot(j))]]) ).
cnf(refute_0_120,plain,
( f(k) != k
| j = k
| k = m ),
inference(resolve,[$cnf( $equal(k,j) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
( ~ element(Y,j)
| Y = m
| j = k
| k = m
| element(Y,f(Y)) ),
inference(resolve,[$cnf( element(Y,m) )],[refute_0_115,c_6]) ).
cnf(refute_0_122,plain,
( ~ element(k,j)
| j = k
| k = m
| element(k,f(k)) ),
inference(subst,[],[refute_0_121:[bind(Y,$fot(k))]]) ).
cnf(refute_0_123,plain,
( j = k
| k = j
| k = m
| element(k,f(k)) ),
inference(resolve,[$cnf( element(k,j) )],[refute_0_5,refute_0_122]) ).
cnf(refute_0_124,plain,
( j = k
| k = m
| element(k,f(k)) ),
inference(resolve,[$cnf( $equal(k,j) )],[refute_0_123,refute_0_119]) ).
cnf(refute_0_125,plain,
( ~ element(Y,j)
| Y = m
| j = k
| k = m
| element(f(Y),Y) ),
inference(resolve,[$cnf( element(Y,m) )],[refute_0_115,c_7]) ).
cnf(refute_0_126,plain,
( ~ element(k,j)
| j = k
| k = m
| element(f(k),k) ),
inference(subst,[],[refute_0_125:[bind(Y,$fot(k))]]) ).
cnf(refute_0_127,plain,
( j = k
| k = j
| k = m
| element(f(k),k) ),
inference(resolve,[$cnf( element(k,j) )],[refute_0_5,refute_0_126]) ).
cnf(refute_0_128,plain,
( j = k
| k = m
| element(f(k),k) ),
inference(resolve,[$cnf( $equal(k,j) )],[refute_0_127,refute_0_119]) ).
cnf(refute_0_129,plain,
( f(k) = k
| f(k) = m
| f(k) = n
| j = k
| k = m ),
inference(resolve,[$cnf( element(f(k),k) )],[refute_0_128,refute_0_66]) ).
cnf(refute_0_130,plain,
( f(k) != n
| n != k
| f(k) = k ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(k),k) ),[0],$fot(n)]]) ).
cnf(refute_0_131,plain,
( f(k) != n
| f(k) = k
| k = m ),
inference(resolve,[$cnf( $equal(n,k) )],[refute_0_85,refute_0_130]) ).
cnf(refute_0_132,plain,
( f(k) = k
| f(k) = m
| j = k
| k = m ),
inference(resolve,[$cnf( $equal(f(k),n) )],[refute_0_129,refute_0_131]) ).
cnf(refute_0_133,plain,
( f(k) != m
| ~ element(k,f(k))
| element(k,m) ),
introduced(tautology,[equality,[$cnf( element(k,f(k)) ),[1],$fot(m)]]) ).
cnf(refute_0_134,plain,
( ~ element(k,f(k))
| f(k) = k
| j = k
| k = m
| element(k,m) ),
inference(resolve,[$cnf( $equal(f(k),m) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
( f(k) = k
| j = k
| k = m
| element(k,m) ),
inference(resolve,[$cnf( element(k,f(k)) )],[refute_0_124,refute_0_134]) ).
cnf(refute_0_136,plain,
( f(k) != m
| f(k) = k
| j = k
| k = m ),
inference(resolve,[$cnf( element(k,m) )],[refute_0_135,refute_0_62]) ).
cnf(refute_0_137,plain,
( f(k) != k
| f(k) != m
| m = k ),
introduced(tautology,[equality,[$cnf( $equal(f(k),k) ),[0],$fot(m)]]) ).
cnf(refute_0_138,plain,
( f(k) != m
| j = k
| k = m
| m = k ),
inference(resolve,[$cnf( $equal(f(k),k) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
( f(k) != m
| j = k
| k = m ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_138,refute_0_36]) ).
cnf(refute_0_140,plain,
( m != m
| f(k) = k
| f(k) = m
| j = k
| k = m ),
inference(resolve,[$cnf( $equal(f(k),m) )],[refute_0_132,refute_0_74]) ).
cnf(refute_0_141,plain,
( m != m
| f(k) = k
| j = k
| k = m ),
inference(resolve,[$cnf( $equal(f(k),m) )],[refute_0_140,refute_0_139]) ).
cnf(refute_0_142,plain,
( f(k) = k
| j = k
| k = m ),
inference(resolve,[$cnf( $equal(m,m) )],[refute_0_1,refute_0_141]) ).
cnf(refute_0_143,plain,
( k != k
| f(k) = k
| j = k
| k = m ),
inference(resolve,[$cnf( $equal(f(k),k) )],[refute_0_142,refute_0_70]) ).
cnf(refute_0_144,plain,
( k != k
| j = k
| k = m ),
inference(resolve,[$cnf( $equal(f(k),k) )],[refute_0_143,refute_0_120]) ).
cnf(refute_0_145,plain,
( j = k
| k = m ),
inference(resolve,[$cnf( $equal(k,k) )],[refute_0_4,refute_0_144]) ).
cnf(refute_0_146,plain,
( k != m
| m = k ),
inference(subst,[],[refute_0_19:[bind(X,$fot(k)),bind(Y0,$fot(m))]]) ).
cnf(refute_0_147,plain,
( j = k
| m = k ),
inference(resolve,[$cnf( $equal(k,m) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
( k != n
| m != k
| m = n ),
introduced(tautology,[equality,[$cnf( $equal(m,k) ),[1],$fot(n)]]) ).
cnf(refute_0_149,plain,
( k != n
| j = k
| m = n ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
( k != n
| j = k ),
inference(resolve,[$cnf( $equal(m,n) )],[refute_0_149,c_1]) ).
cnf(refute_0_151,plain,
( m != k
| ~ element(Y,k)
| element(Y,m) ),
introduced(tautology,[equality,[$cnf( ~ element(Y,m) ),[1],$fot(k)]]) ).
cnf(refute_0_152,plain,
( ~ element(Y,k)
| j = k
| element(Y,m) ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_147,refute_0_151]) ).
cnf(refute_0_153,plain,
( f(Y) != Y
| ~ element(Y,k)
| Y = m
| j = k ),
inference(resolve,[$cnf( element(Y,m) )],[refute_0_152,c_5]) ).
cnf(refute_0_154,plain,
( f(n) != n
| ~ element(n,k)
| j = k
| n = m ),
inference(subst,[],[refute_0_153:[bind(Y,$fot(n))]]) ).
cnf(refute_0_155,plain,
( f(n) != n
| j = k
| n = k
| n = m ),
inference(resolve,[$cnf( element(n,k) )],[refute_0_14,refute_0_154]) ).
cnf(refute_0_156,plain,
( f(n) != n
| j = k
| n = k ),
inference(resolve,[$cnf( $equal(n,m) )],[refute_0_155,refute_0_21]) ).
cnf(refute_0_157,plain,
( f(Y) != m
| ~ element(Y,k)
| Y = m
| j = k ),
inference(resolve,[$cnf( element(Y,m) )],[refute_0_152,c_4]) ).
cnf(refute_0_158,plain,
( f(n) != m
| ~ element(n,k)
| j = k
| n = m ),
inference(subst,[],[refute_0_157:[bind(Y,$fot(n))]]) ).
cnf(refute_0_159,plain,
( f(n) != m
| j = k
| n = k
| n = m ),
inference(resolve,[$cnf( element(n,k) )],[refute_0_14,refute_0_158]) ).
cnf(refute_0_160,plain,
( f(n) != m
| j = k
| n = k ),
inference(resolve,[$cnf( $equal(n,m) )],[refute_0_159,refute_0_21]) ).
cnf(refute_0_161,plain,
( ~ element(f(n),k)
| f(n) = k
| f(n) = m
| f(n) = n ),
inference(subst,[],[c_16:[bind(Y,$fot(f(n)))]]) ).
cnf(refute_0_162,plain,
( ~ element(Y,k)
| Y = m
| j = k
| element(Y,f(Y)) ),
inference(resolve,[$cnf( element(Y,m) )],[refute_0_152,c_6]) ).
cnf(refute_0_163,plain,
( ~ element(n,k)
| j = k
| n = m
| element(n,f(n)) ),
inference(subst,[],[refute_0_162:[bind(Y,$fot(n))]]) ).
cnf(refute_0_164,plain,
( j = k
| n = k
| n = m
| element(n,f(n)) ),
inference(resolve,[$cnf( element(n,k) )],[refute_0_14,refute_0_163]) ).
cnf(refute_0_165,plain,
( j = k
| n = k
| element(n,f(n)) ),
inference(resolve,[$cnf( $equal(n,m) )],[refute_0_164,refute_0_21]) ).
cnf(refute_0_166,plain,
( ~ element(f(n),n)
| ~ element(n,f(n))
| f(n) = m
| n = f(n)
| n = m
| element(f(n),m) ),
inference(subst,[],[c_8:[bind(V1,$fot(n)),bind(Y,$fot(f(n)))]]) ).
cnf(refute_0_167,plain,
( ~ element(Y,k)
| Y = m
| j = k
| element(f(Y),Y) ),
inference(resolve,[$cnf( element(Y,m) )],[refute_0_152,c_7]) ).
cnf(refute_0_168,plain,
( ~ element(n,k)
| j = k
| n = m
| element(f(n),n) ),
inference(subst,[],[refute_0_167:[bind(Y,$fot(n))]]) ).
cnf(refute_0_169,plain,
( j = k
| n = k
| n = m
| element(f(n),n) ),
inference(resolve,[$cnf( element(n,k) )],[refute_0_14,refute_0_168]) ).
cnf(refute_0_170,plain,
( j = k
| n = k
| element(f(n),n) ),
inference(resolve,[$cnf( $equal(n,m) )],[refute_0_169,refute_0_21]) ).
cnf(refute_0_171,plain,
( ~ element(n,f(n))
| f(n) = m
| j = k
| n = f(n)
| n = k
| n = m
| element(f(n),m) ),
inference(resolve,[$cnf( element(f(n),n) )],[refute_0_170,refute_0_166]) ).
cnf(refute_0_172,plain,
( ~ element(n,f(n))
| f(n) = m
| j = k
| n = f(n)
| n = k
| element(f(n),m) ),
inference(resolve,[$cnf( $equal(n,m) )],[refute_0_171,refute_0_21]) ).
cnf(refute_0_173,plain,
( f(n) = m
| j = k
| n = f(n)
| n = k
| element(f(n),m) ),
inference(resolve,[$cnf( element(n,f(n)) )],[refute_0_165,refute_0_172]) ).
cnf(refute_0_174,plain,
( m != k
| ~ element(f(n),m)
| element(f(n),k) ),
introduced(tautology,[equality,[$cnf( element(f(n),m) ),[1],$fot(k)]]) ).
cnf(refute_0_175,plain,
( ~ element(f(n),m)
| j = k
| element(f(n),k) ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_147,refute_0_174]) ).
cnf(refute_0_176,plain,
( f(n) = m
| j = k
| n = f(n)
| n = k
| element(f(n),k) ),
inference(resolve,[$cnf( element(f(n),m) )],[refute_0_173,refute_0_175]) ).
cnf(refute_0_177,plain,
( f(n) = k
| f(n) = m
| f(n) = n
| j = k
| n = f(n)
| n = k ),
inference(resolve,[$cnf( element(f(n),k) )],[refute_0_176,refute_0_161]) ).
cnf(refute_0_178,plain,
( n != f(n)
| f(n) = n ),
inference(subst,[],[refute_0_19:[bind(X,$fot(n)),bind(Y0,$fot(f(n)))]]) ).
cnf(refute_0_179,plain,
( f(n) = k
| f(n) = m
| f(n) = n
| j = k
| n = k ),
inference(resolve,[$cnf( $equal(n,f(n)) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
( f(n) != k
| k != m
| f(n) = m ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(n),m) ),[0],$fot(k)]]) ).
cnf(refute_0_181,plain,
( k != m
| f(n) = m
| f(n) = n
| j = k
| n = k ),
inference(resolve,[$cnf( $equal(f(n),k) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
( k != m
| f(n) = n
| j = k
| n = k ),
inference(resolve,[$cnf( $equal(f(n),m) )],[refute_0_181,refute_0_160]) ).
cnf(refute_0_183,plain,
( k != k
| f(n) = n
| j = k
| n = k ),
inference(resolve,[$cnf( $equal(k,m) )],[refute_0_144,refute_0_182]) ).
cnf(refute_0_184,plain,
( f(n) = n
| j = k
| n = k ),
inference(resolve,[$cnf( $equal(k,k) )],[refute_0_4,refute_0_183]) ).
cnf(refute_0_185,plain,
( f(n) != n
| n != n
| f(n) = n ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(n),n) ),[0],$fot(n)]]) ).
cnf(refute_0_186,plain,
( n != n
| f(n) = n
| j = k
| n = k ),
inference(resolve,[$cnf( $equal(f(n),n) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
( n != n
| j = k
| n = k ),
inference(resolve,[$cnf( $equal(f(n),n) )],[refute_0_186,refute_0_156]) ).
cnf(refute_0_188,plain,
( j = k
| n = k ),
inference(resolve,[$cnf( $equal(n,n) )],[refute_0_13,refute_0_187]) ).
cnf(refute_0_189,plain,
( k != k
| j = k
| k = n ),
inference(resolve,[$cnf( $equal(n,k) )],[refute_0_188,refute_0_98]) ).
cnf(refute_0_190,plain,
( k != k
| j = k ),
inference(resolve,[$cnf( $equal(k,n) )],[refute_0_189,refute_0_150]) ).
cnf(refute_0_191,plain,
j = k,
inference(resolve,[$cnf( $equal(k,k) )],[refute_0_4,refute_0_190]) ).
cnf(refute_0_192,plain,
( j != k
| k = j ),
inference(subst,[],[refute_0_19:[bind(X,$fot(j)),bind(Y0,$fot(k))]]) ).
cnf(refute_0_193,plain,
k = j,
inference(resolve,[$cnf( $equal(j,k) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
( k != j
| m != k
| m = j ),
introduced(tautology,[equality,[$cnf( $equal(m,k) ),[1],$fot(j)]]) ).
cnf(refute_0_195,plain,
( m != k
| m = j ),
inference(resolve,[$cnf( $equal(k,j) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
( m = j
| element(m,k) ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_2,refute_0_195]) ).
cnf(refute_0_197,plain,
( k != j
| ~ element(m,k)
| element(m,j) ),
introduced(tautology,[equality,[$cnf( element(m,k) ),[1],$fot(j)]]) ).
cnf(refute_0_198,plain,
( ~ element(m,k)
| element(m,j) ),
inference(resolve,[$cnf( $equal(k,j) )],[refute_0_193,refute_0_197]) ).
cnf(refute_0_199,plain,
( m = j
| element(m,j) ),
inference(resolve,[$cnf( element(m,k) )],[refute_0_196,refute_0_198]) ).
cnf(refute_0_200,plain,
( Y != k
| k != j
| Y = j ),
introduced(tautology,[equality,[$cnf( ~ $equal(Y,j) ),[0],$fot(k)]]) ).
cnf(refute_0_201,plain,
( Y != k
| Y = j ),
inference(resolve,[$cnf( $equal(k,j) )],[refute_0_193,refute_0_200]) ).
cnf(refute_0_202,plain,
( ~ element(Y,j)
| Y = j ),
inference(resolve,[$cnf( $equal(Y,k) )],[c_3,refute_0_201]) ).
cnf(refute_0_203,plain,
( ~ element(m,j)
| m = j ),
inference(subst,[],[refute_0_202:[bind(Y,$fot(m))]]) ).
cnf(refute_0_204,plain,
m = j,
inference(resolve,[$cnf( element(m,j) )],[refute_0_199,refute_0_203]) ).
cnf(refute_0_205,plain,
( j != n
| m != j
| m = n ),
introduced(tautology,[equality,[$cnf( $equal(m,j) ),[1],$fot(n)]]) ).
cnf(refute_0_206,plain,
( j != n
| m = n ),
inference(resolve,[$cnf( $equal(m,j) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
( k != j
| n != k
| n = j ),
introduced(tautology,[equality,[$cnf( $equal(n,k) ),[1],$fot(j)]]) ).
cnf(refute_0_208,plain,
( n != k
| n = j ),
inference(resolve,[$cnf( $equal(k,j) )],[refute_0_193,refute_0_207]) ).
cnf(refute_0_209,plain,
( n = j
| element(n,k) ),
inference(resolve,[$cnf( $equal(n,k) )],[refute_0_14,refute_0_208]) ).
cnf(refute_0_210,plain,
( k != j
| ~ element(n,k)
| element(n,j) ),
introduced(tautology,[equality,[$cnf( element(n,k) ),[1],$fot(j)]]) ).
cnf(refute_0_211,plain,
( ~ element(n,k)
| element(n,j) ),
inference(resolve,[$cnf( $equal(k,j) )],[refute_0_193,refute_0_210]) ).
cnf(refute_0_212,plain,
( n = j
| element(n,j) ),
inference(resolve,[$cnf( element(n,k) )],[refute_0_209,refute_0_211]) ).
cnf(refute_0_213,plain,
( ~ element(n,j)
| n = j ),
inference(subst,[],[refute_0_202:[bind(Y,$fot(n))]]) ).
cnf(refute_0_214,plain,
n = j,
inference(resolve,[$cnf( element(n,j) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
( j != j
| n != j
| j = n ),
introduced(tautology,[equality,[$cnf( ~ $equal(j,n) ),[1],$fot(j)]]) ).
cnf(refute_0_216,plain,
( j != j
| j = n ),
inference(resolve,[$cnf( $equal(n,j) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
( j != j
| m = n ),
inference(resolve,[$cnf( $equal(j,n) )],[refute_0_216,refute_0_206]) ).
cnf(refute_0_218,plain,
j != j,
inference(resolve,[$cnf( $equal(m,n) )],[refute_0_217,c_1]) ).
cnf(refute_0_219,plain,
$false,
inference(resolve,[$cnf( $equal(j,j) )],[refute_0_106,refute_0_218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN015-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 23:15:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.67/0.86 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.67/0.86
% 0.67/0.86 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.67/0.87
%------------------------------------------------------------------------------