%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN014-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 65
% Number of leaves : 46
% Syntax : Number of clauses : 181 ( 13 unt; 114 nHn; 179 RR)
% Number of literals : 615 ( 501 equ; 172 neg)
% Maximal clause size : 8 ( 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 : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_1,negated_conjecture,
m != n ).
cnf(c_2,negated_conjecture,
( n = k
| m = k ) ).
cnf(c_3,negated_conjecture,
( Y = j
| Y != k
| element(Y,j) ) ).
cnf(c_4,negated_conjecture,
( Y = j
| Y = k
| ~ element(Y,j) ) ).
cnf(c_5,negated_conjecture,
( Y = m
| ~ element(Y,m)
| f(Y) != m ) ).
cnf(c_6,negated_conjecture,
( Y = m
| ~ element(Y,m)
| f(Y) != Y ) ).
cnf(c_7,negated_conjecture,
( Y = m
| ~ element(Y,m)
| element(Y,f(Y)) ) ).
cnf(c_8,negated_conjecture,
( Y = m
| ~ element(Y,m)
| element(f(Y),Y) ) ).
cnf(c_9,negated_conjecture,
( Y = m
| element(Y,m)
| V1 = m
| V1 = Y
| ~ element(Y,V1)
| ~ element(V1,Y) ) ).
cnf(c_10,negated_conjecture,
( Y = n
| element(Y,n)
| g(Y) != n ) ).
cnf(c_11,negated_conjecture,
( Y = n
| element(Y,n)
| g(Y) != Y ) ).
cnf(c_13,negated_conjecture,
( Y = n
| element(Y,n)
| element(g(Y),Y) ) ).
cnf(c_15,negated_conjecture,
( Y = k
| Y != m
| element(Y,k) ) ).
cnf(c_16,negated_conjecture,
( Y = k
| Y != n
| element(Y,k) ) ).
cnf(c_17,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_15:[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( $equal(m,m) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
( k != k
| k = j
| element(k,j) ),
inference(subst,[],[c_3:[bind(Y,$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( $equal(k,k) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ element(j,k)
| j = k
| j = m
| j = n ),
inference(subst,[],[c_17:[bind(Y,$fot(j))]]) ).
cnf(refute_0_7,plain,
( g(j) != j
| j = n
| element(j,n) ),
inference(subst,[],[c_11:[bind(Y,$fot(j))]]) ).
cnf(refute_0_8,plain,
( g(j) != n
| j = n
| element(j,n) ),
inference(subst,[],[c_10:[bind(Y,$fot(j))]]) ).
cnf(refute_0_9,plain,
( ~ element(g(j),j)
| g(j) = j
| g(j) = k ),
inference(subst,[],[c_4:[bind(Y,$fot(g(j)))]]) ).
cnf(refute_0_10,plain,
( j = n
| element(g(j),j)
| element(j,n) ),
inference(subst,[],[c_13:[bind(Y,$fot(j))]]) ).
cnf(refute_0_11,plain,
( g(j) = j
| g(j) = k
| j = n
| element(j,n) ),
inference(resolve,[$cnf( element(g(j),j) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
( n != k
| ~ element(j,n)
| element(j,k) ),
introduced(tautology,[equality,[$cnf( element(j,n) ),[1],$fot(k)]]) ).
cnf(refute_0_13,plain,
( ~ element(j,n)
| m = k
| element(j,k) ),
inference(resolve,[$cnf( $equal(n,k) )],[c_2,refute_0_12]) ).
cnf(refute_0_14,plain,
( g(j) = j
| g(j) = k
| j = n
| m = k
| element(j,k) ),
inference(resolve,[$cnf( element(j,n) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( g(j) = j
| g(j) = k
| j = k
| j = m
| j = n
| m = k ),
inference(resolve,[$cnf( element(j,k) )],[refute_0_14,refute_0_6]) ).
cnf(refute_0_16,plain,
( g(j) != k
| k != n
| g(j) = n ),
introduced(tautology,[equality,[$cnf( ~ $equal(g(j),n) ),[0],$fot(k)]]) ).
cnf(refute_0_17,plain,
( k != n
| g(j) = j
| g(j) = n
| j = k
| j = m
| j = n
| m = k ),
inference(resolve,[$cnf( $equal(g(j),k) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( k != n
| g(j) = j
| j = k
| j = m
| j = n
| m = k
| element(j,n) ),
inference(resolve,[$cnf( $equal(g(j),n) )],[refute_0_17,refute_0_8]) ).
cnf(refute_0_19,plain,
( k != k
| k != n
| n = k ),
introduced(tautology,[equality,[$cnf( $equal(k,k) ),[0],$fot(n)]]) ).
cnf(refute_0_20,plain,
( k != n
| n = k ),
inference(resolve,[$cnf( $equal(k,k) )],[refute_0_4,refute_0_19]) ).
cnf(refute_0_21,plain,
( j != n
| n != k
| j = k ),
introduced(tautology,[equality,[$cnf( ~ $equal(j,k) ),[0],$fot(n)]]) ).
cnf(refute_0_22,plain,
( j != n
| k != n
| j = k ),
inference(resolve,[$cnf( $equal(n,k) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( k != n
| g(j) = j
| j = k
| j = m
| m = k
| element(j,n) ),
inference(resolve,[$cnf( $equal(j,n) )],[refute_0_18,refute_0_22]) ).
cnf(refute_0_24,plain,
( k != n
| ~ element(j,n)
| element(j,k) ),
inference(resolve,[$cnf( $equal(n,k) )],[refute_0_20,refute_0_12]) ).
cnf(refute_0_25,plain,
( k != n
| g(j) = j
| j = k
| j = m
| m = k
| element(j,k) ),
inference(resolve,[$cnf( element(j,n) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( k != k
| n != k
| k = n ),
introduced(tautology,[equality,[$cnf( ~ $equal(k,n) ),[1],$fot(k)]]) ).
cnf(refute_0_27,plain,
( k != k
| k = n
| m = k ),
inference(resolve,[$cnf( $equal(n,k) )],[c_2,refute_0_26]) ).
cnf(refute_0_28,plain,
( k != k
| g(j) = j
| j = k
| j = m
| m = k
| element(j,k) ),
inference(resolve,[$cnf( $equal(k,n) )],[refute_0_27,refute_0_25]) ).
cnf(refute_0_29,plain,
( g(j) = j
| j = k
| j = m
| m = k
| element(j,k) ),
inference(resolve,[$cnf( $equal(k,k) )],[refute_0_4,refute_0_28]) ).
cnf(refute_0_30,plain,
( g(j) = j
| j = k
| j = m
| j = n
| m = k ),
inference(resolve,[$cnf( element(j,k) )],[refute_0_29,refute_0_6]) ).
cnf(refute_0_31,plain,
( g(j) != j
| j != j
| g(j) = j ),
introduced(tautology,[equality,[$cnf( ~ $equal(g(j),j) ),[0],$fot(j)]]) ).
cnf(refute_0_32,plain,
( j != j
| g(j) = j
| j = k
| j = m
| j = n
| m = k ),
inference(resolve,[$cnf( $equal(g(j),j) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( j != j
| j = k
| j = m
| j = n
| m = k
| element(j,n) ),
inference(resolve,[$cnf( $equal(g(j),j) )],[refute_0_32,refute_0_7]) ).
cnf(refute_0_34,plain,
j = j,
introduced(tautology,[refl,[$fot(j)]]) ).
cnf(refute_0_35,plain,
( j = k
| j = m
| j = n
| m = k
| element(j,n) ),
inference(resolve,[$cnf( $equal(j,j) )],[refute_0_34,refute_0_33]) ).
cnf(refute_0_36,plain,
( j = k
| j = m
| j = n
| m = k
| element(j,k) ),
inference(resolve,[$cnf( element(j,n) )],[refute_0_35,refute_0_13]) ).
cnf(refute_0_37,plain,
( j = k
| j = m
| j = n
| m = k ),
inference(resolve,[$cnf( element(j,k) )],[refute_0_36,refute_0_6]) ).
cnf(refute_0_38,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_39,plain,
( X != X
| X != Y0
| Y0 = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y0)]]) ).
cnf(refute_0_40,plain,
( X != Y0
| Y0 = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( j != n
| n = j ),
inference(subst,[],[refute_0_40:[bind(X,$fot(j)),bind(Y0,$fot(n))]]) ).
cnf(refute_0_42,plain,
( j = k
| j = m
| m = k
| n = j ),
inference(resolve,[$cnf( $equal(j,n) )],[refute_0_37,refute_0_41]) ).
cnf(refute_0_43,plain,
( n != j
| n != k
| j = k ),
introduced(tautology,[equality,[$cnf( $equal(n,k) ),[0],$fot(j)]]) ).
cnf(refute_0_44,plain,
( n != k
| j = k
| j = m
| m = k ),
inference(resolve,[$cnf( $equal(n,j) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( j = k
| j = m
| m = k ),
inference(resolve,[$cnf( $equal(n,k) )],[c_2,refute_0_44]) ).
cnf(refute_0_46,plain,
( j != m
| m = j ),
inference(subst,[],[refute_0_40:[bind(X,$fot(j)),bind(Y0,$fot(m))]]) ).
cnf(refute_0_47,plain,
( j = k
| m = j
| m = k ),
inference(resolve,[$cnf( $equal(j,m) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( m != j
| ~ element(Y,j)
| element(Y,m) ),
introduced(tautology,[equality,[$cnf( ~ element(Y,m) ),[1],$fot(j)]]) ).
cnf(refute_0_49,plain,
( ~ element(Y,j)
| j = k
| m = k
| element(Y,m) ),
inference(resolve,[$cnf( $equal(m,j) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( f(Y) != m
| ~ element(Y,j)
| Y = m
| j = k
| m = k ),
inference(resolve,[$cnf( element(Y,m) )],[refute_0_49,c_5]) ).
cnf(refute_0_51,plain,
( f(k) != m
| ~ element(k,j)
| j = k
| k = m
| m = k ),
inference(subst,[],[refute_0_50:[bind(Y,$fot(k))]]) ).
cnf(refute_0_52,plain,
( f(k) != m
| j = k
| k = j
| k = m
| m = k ),
inference(resolve,[$cnf( element(k,j) )],[refute_0_5,refute_0_51]) ).
cnf(refute_0_53,plain,
( k != j
| j = k ),
inference(subst,[],[refute_0_40:[bind(X,$fot(k)),bind(Y0,$fot(j))]]) ).
cnf(refute_0_54,plain,
( f(k) != m
| j = k
| k = m
| m = k ),
inference(resolve,[$cnf( $equal(k,j) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( m != k
| k = m ),
inference(subst,[],[refute_0_40:[bind(X,$fot(m)),bind(Y0,$fot(k))]]) ).
cnf(refute_0_56,plain,
( f(k) != m
| j = k
| k = m ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( f(Y) != Y
| ~ element(Y,j)
| Y = m
| j = k
| m = k ),
inference(resolve,[$cnf( element(Y,m) )],[refute_0_49,c_6]) ).
cnf(refute_0_58,plain,
( f(k) != k
| ~ element(k,j)
| j = k
| k = m
| m = k ),
inference(subst,[],[refute_0_57:[bind(Y,$fot(k))]]) ).
cnf(refute_0_59,plain,
( f(k) != k
| j = k
| k = j
| k = m
| m = k ),
inference(resolve,[$cnf( element(k,j) )],[refute_0_5,refute_0_58]) ).
cnf(refute_0_60,plain,
( f(k) != k
| j = k
| k = m
| m = k ),
inference(resolve,[$cnf( $equal(k,j) )],[refute_0_59,refute_0_53]) ).
cnf(refute_0_61,plain,
( f(k) != k
| j = k
| k = m ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_60,refute_0_55]) ).
cnf(refute_0_62,plain,
( ~ element(f(k),k)
| f(k) = k
| f(k) = m
| f(k) = n ),
inference(subst,[],[c_17:[bind(Y,$fot(f(k)))]]) ).
cnf(refute_0_63,plain,
( ~ element(Y,j)
| Y = m
| j = k
| m = k
| element(f(Y),Y) ),
inference(resolve,[$cnf( element(Y,m) )],[refute_0_49,c_8]) ).
cnf(refute_0_64,plain,
( ~ element(k,j)
| j = k
| k = m
| m = k
| element(f(k),k) ),
inference(subst,[],[refute_0_63:[bind(Y,$fot(k))]]) ).
cnf(refute_0_65,plain,
( j = k
| k = j
| k = m
| m = k
| element(f(k),k) ),
inference(resolve,[$cnf( element(k,j) )],[refute_0_5,refute_0_64]) ).
cnf(refute_0_66,plain,
( j = k
| k = m
| m = k
| element(f(k),k) ),
inference(resolve,[$cnf( $equal(k,j) )],[refute_0_65,refute_0_53]) ).
cnf(refute_0_67,plain,
( j = k
| k = m
| element(f(k),k) ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_66,refute_0_55]) ).
cnf(refute_0_68,plain,
( f(k) = k
| f(k) = m
| f(k) = n
| j = k
| k = m ),
inference(resolve,[$cnf( element(f(k),k) )],[refute_0_67,refute_0_62]) ).
cnf(refute_0_69,plain,
( f(k) != n
| n != k
| f(k) = k ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(k),k) ),[0],$fot(n)]]) ).
cnf(refute_0_70,plain,
( f(k) != n
| f(k) = k
| m = k ),
inference(resolve,[$cnf( $equal(n,k) )],[c_2,refute_0_69]) ).
cnf(refute_0_71,plain,
( f(k) = k
| f(k) = m
| j = k
| k = m
| m = k ),
inference(resolve,[$cnf( $equal(f(k),n) )],[refute_0_68,refute_0_70]) ).
cnf(refute_0_72,plain,
( f(k) = k
| f(k) = m
| j = k
| k = m ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_71,refute_0_55]) ).
cnf(refute_0_73,plain,
( f(k) != k
| k != k
| f(k) = k ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(k),k) ),[0],$fot(k)]]) ).
cnf(refute_0_74,plain,
( k != k
| f(k) = k
| f(k) = m
| j = k
| k = m ),
inference(resolve,[$cnf( $equal(f(k),k) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
( k != k
| f(k) = m
| j = k
| k = m ),
inference(resolve,[$cnf( $equal(f(k),k) )],[refute_0_74,refute_0_61]) ).
cnf(refute_0_76,plain,
( f(k) = m
| j = k
| k = m ),
inference(resolve,[$cnf( $equal(k,k) )],[refute_0_4,refute_0_75]) ).
cnf(refute_0_77,plain,
( f(k) != m
| m != m
| f(k) = m ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(k),m) ),[0],$fot(m)]]) ).
cnf(refute_0_78,plain,
( m != m
| f(k) = m
| j = k
| k = m ),
inference(resolve,[$cnf( $equal(f(k),m) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
( m != m
| j = k
| k = m ),
inference(resolve,[$cnf( $equal(f(k),m) )],[refute_0_78,refute_0_56]) ).
cnf(refute_0_80,plain,
( j = k
| k = m ),
inference(resolve,[$cnf( $equal(m,m) )],[refute_0_1,refute_0_79]) ).
cnf(refute_0_81,plain,
( k != m
| m = k ),
inference(subst,[],[refute_0_40:[bind(X,$fot(k)),bind(Y0,$fot(m))]]) ).
cnf(refute_0_82,plain,
( j = k
| m = k ),
inference(resolve,[$cnf( $equal(k,m) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
( k != n
| m != k
| m = n ),
introduced(tautology,[equality,[$cnf( $equal(m,k) ),[1],$fot(n)]]) ).
cnf(refute_0_84,plain,
( k != n
| j = k
| m = n ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
( k != n
| j = k ),
inference(resolve,[$cnf( $equal(m,n) )],[refute_0_84,c_1]) ).
cnf(refute_0_86,plain,
( n != n
| n = k
| element(n,k) ),
inference(subst,[],[c_16:[bind(Y,$fot(n))]]) ).
cnf(refute_0_87,plain,
n = n,
introduced(tautology,[refl,[$fot(n)]]) ).
cnf(refute_0_88,plain,
( n = k
| element(n,k) ),
inference(resolve,[$cnf( $equal(n,n) )],[refute_0_87,refute_0_86]) ).
cnf(refute_0_89,plain,
( m != k
| ~ element(Y,k)
| element(Y,m) ),
introduced(tautology,[equality,[$cnf( ~ element(Y,m) ),[1],$fot(k)]]) ).
cnf(refute_0_90,plain,
( ~ element(Y,k)
| j = k
| element(Y,m) ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_82,refute_0_89]) ).
cnf(refute_0_91,plain,
( f(Y) != m
| ~ element(Y,k)
| Y = m
| j = k ),
inference(resolve,[$cnf( element(Y,m) )],[refute_0_90,c_5]) ).
cnf(refute_0_92,plain,
( f(n) != m
| ~ element(n,k)
| j = k
| n = m ),
inference(subst,[],[refute_0_91:[bind(Y,$fot(n))]]) ).
cnf(refute_0_93,plain,
( f(n) != m
| j = k
| n = k
| n = m ),
inference(resolve,[$cnf( element(n,k) )],[refute_0_88,refute_0_92]) ).
cnf(refute_0_94,plain,
( n != m
| m = n ),
inference(subst,[],[refute_0_40:[bind(X,$fot(n)),bind(Y0,$fot(m))]]) ).
cnf(refute_0_95,plain,
n != m,
inference(resolve,[$cnf( $equal(m,n) )],[refute_0_94,c_1]) ).
cnf(refute_0_96,plain,
( f(n) != m
| j = k
| n = k ),
inference(resolve,[$cnf( $equal(n,m) )],[refute_0_93,refute_0_95]) ).
cnf(refute_0_97,plain,
( f(Y) != Y
| ~ element(Y,k)
| Y = m
| j = k ),
inference(resolve,[$cnf( element(Y,m) )],[refute_0_90,c_6]) ).
cnf(refute_0_98,plain,
( f(n) != n
| ~ element(n,k)
| j = k
| n = m ),
inference(subst,[],[refute_0_97:[bind(Y,$fot(n))]]) ).
cnf(refute_0_99,plain,
( f(n) != n
| j = k
| n = k
| n = m ),
inference(resolve,[$cnf( element(n,k) )],[refute_0_88,refute_0_98]) ).
cnf(refute_0_100,plain,
( f(n) != n
| j = k
| n = k ),
inference(resolve,[$cnf( $equal(n,m) )],[refute_0_99,refute_0_95]) ).
cnf(refute_0_101,plain,
( ~ element(f(n),k)
| f(n) = k
| f(n) = m
| f(n) = n ),
inference(subst,[],[c_17:[bind(Y,$fot(f(n)))]]) ).
cnf(refute_0_102,plain,
( ~ element(Y,k)
| Y = m
| j = k
| element(Y,f(Y)) ),
inference(resolve,[$cnf( element(Y,m) )],[refute_0_90,c_7]) ).
cnf(refute_0_103,plain,
( ~ element(n,k)
| j = k
| n = m
| element(n,f(n)) ),
inference(subst,[],[refute_0_102:[bind(Y,$fot(n))]]) ).
cnf(refute_0_104,plain,
( j = k
| n = k
| n = m
| element(n,f(n)) ),
inference(resolve,[$cnf( element(n,k) )],[refute_0_88,refute_0_103]) ).
cnf(refute_0_105,plain,
( j = k
| n = k
| element(n,f(n)) ),
inference(resolve,[$cnf( $equal(n,m) )],[refute_0_104,refute_0_95]) ).
cnf(refute_0_106,plain,
( ~ element(f(n),n)
| ~ element(n,f(n))
| f(n) = m
| n = f(n)
| n = m
| element(f(n),m) ),
inference(subst,[],[c_9:[bind(V1,$fot(n)),bind(Y,$fot(f(n)))]]) ).
cnf(refute_0_107,plain,
( ~ element(Y,k)
| j = k
| j = m
| element(Y,m) ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_45,refute_0_89]) ).
cnf(refute_0_108,plain,
( ~ element(Y,k)
| Y = m
| j = k
| j = m
| element(f(Y),Y) ),
inference(resolve,[$cnf( element(Y,m) )],[refute_0_107,c_8]) ).
cnf(refute_0_109,plain,
( ~ element(n,k)
| j = k
| j = m
| n = m
| element(f(n),n) ),
inference(subst,[],[refute_0_108:[bind(Y,$fot(n))]]) ).
cnf(refute_0_110,plain,
( j = k
| j = m
| n = k
| n = m
| element(f(n),n) ),
inference(resolve,[$cnf( element(n,k) )],[refute_0_88,refute_0_109]) ).
cnf(refute_0_111,plain,
( j = k
| j = m
| n = k
| element(f(n),n) ),
inference(resolve,[$cnf( $equal(n,m) )],[refute_0_110,refute_0_95]) ).
cnf(refute_0_112,plain,
( ~ element(n,f(n))
| f(n) = m
| j = k
| j = m
| n = f(n)
| n = k
| n = m
| element(f(n),m) ),
inference(resolve,[$cnf( element(f(n),n) )],[refute_0_111,refute_0_106]) ).
cnf(refute_0_113,plain,
( ~ element(n,f(n))
| f(n) = m
| j = k
| j = m
| n = f(n)
| n = k
| element(f(n),m) ),
inference(resolve,[$cnf( $equal(n,m) )],[refute_0_112,refute_0_95]) ).
cnf(refute_0_114,plain,
( f(n) = m
| j = k
| j = m
| n = f(n)
| n = k
| element(f(n),m) ),
inference(resolve,[$cnf( element(n,f(n)) )],[refute_0_105,refute_0_113]) ).
cnf(refute_0_115,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_116,plain,
( ~ element(f(n),m)
| j = k
| element(f(n),k) ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_82,refute_0_115]) ).
cnf(refute_0_117,plain,
( f(n) = m
| j = k
| j = m
| n = f(n)
| n = k
| element(f(n),k) ),
inference(resolve,[$cnf( element(f(n),m) )],[refute_0_114,refute_0_116]) ).
cnf(refute_0_118,plain,
( f(n) = k
| f(n) = m
| f(n) = n
| j = k
| j = m
| n = f(n)
| n = k ),
inference(resolve,[$cnf( element(f(n),k) )],[refute_0_117,refute_0_101]) ).
cnf(refute_0_119,plain,
( n != f(n)
| f(n) = n ),
inference(subst,[],[refute_0_40:[bind(X,$fot(n)),bind(Y0,$fot(f(n)))]]) ).
cnf(refute_0_120,plain,
( f(n) = k
| f(n) = m
| f(n) = n
| j = k
| j = m
| n = k ),
inference(resolve,[$cnf( $equal(n,f(n)) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
( f(n) != n
| n != n
| f(n) = n ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(n),n) ),[0],$fot(n)]]) ).
cnf(refute_0_122,plain,
( n != n
| f(n) = k
| f(n) = m
| f(n) = n
| j = k
| j = m
| n = k ),
inference(resolve,[$cnf( $equal(f(n),n) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
( n != n
| f(n) = k
| f(n) = m
| j = k
| j = m
| n = k ),
inference(resolve,[$cnf( $equal(f(n),n) )],[refute_0_122,refute_0_100]) ).
cnf(refute_0_124,plain,
( f(n) = k
| f(n) = m
| j = k
| j = m
| n = k ),
inference(resolve,[$cnf( $equal(n,n) )],[refute_0_87,refute_0_123]) ).
cnf(refute_0_125,plain,
( f(n) != k
| k != m
| f(n) = m ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(n),m) ),[0],$fot(k)]]) ).
cnf(refute_0_126,plain,
( k != m
| f(n) = m
| j = k
| j = m
| n = k ),
inference(resolve,[$cnf( $equal(f(n),k) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
( k != m
| j = k
| j = m
| n = k ),
inference(resolve,[$cnf( $equal(f(n),m) )],[refute_0_126,refute_0_96]) ).
cnf(refute_0_128,plain,
( j != m
| m != k
| j = k ),
introduced(tautology,[equality,[$cnf( ~ $equal(j,k) ),[0],$fot(m)]]) ).
cnf(refute_0_129,plain,
( j != m
| k != m
| j = k ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_81,refute_0_128]) ).
cnf(refute_0_130,plain,
( k != m
| j = k
| n = k ),
inference(resolve,[$cnf( $equal(j,m) )],[refute_0_127,refute_0_129]) ).
cnf(refute_0_131,plain,
( k != k
| m != k
| k = m ),
introduced(tautology,[equality,[$cnf( ~ $equal(k,m) ),[1],$fot(k)]]) ).
cnf(refute_0_132,plain,
( k != k
| j = k
| k = m ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_82,refute_0_131]) ).
cnf(refute_0_133,plain,
( k != k
| j = k
| n = k ),
inference(resolve,[$cnf( $equal(k,m) )],[refute_0_132,refute_0_130]) ).
cnf(refute_0_134,plain,
( j = k
| n = k ),
inference(resolve,[$cnf( $equal(k,k) )],[refute_0_4,refute_0_133]) ).
cnf(refute_0_135,plain,
( k != k
| j = k
| k = n ),
inference(resolve,[$cnf( $equal(n,k) )],[refute_0_134,refute_0_26]) ).
cnf(refute_0_136,plain,
( k != k
| j = k ),
inference(resolve,[$cnf( $equal(k,n) )],[refute_0_135,refute_0_85]) ).
cnf(refute_0_137,plain,
j = k,
inference(resolve,[$cnf( $equal(k,k) )],[refute_0_4,refute_0_136]) ).
cnf(refute_0_138,plain,
( j != k
| k = j ),
inference(subst,[],[refute_0_40:[bind(X,$fot(j)),bind(Y0,$fot(k))]]) ).
cnf(refute_0_139,plain,
k = j,
inference(resolve,[$cnf( $equal(j,k) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
( k != j
| m != k
| m = j ),
introduced(tautology,[equality,[$cnf( $equal(m,k) ),[1],$fot(j)]]) ).
cnf(refute_0_141,plain,
( m != k
| m = j ),
inference(resolve,[$cnf( $equal(k,j) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
( m = j
| element(m,k) ),
inference(resolve,[$cnf( $equal(m,k) )],[refute_0_2,refute_0_141]) ).
cnf(refute_0_143,plain,
( k != j
| ~ element(m,k)
| element(m,j) ),
introduced(tautology,[equality,[$cnf( element(m,k) ),[1],$fot(j)]]) ).
cnf(refute_0_144,plain,
( ~ element(m,k)
| element(m,j) ),
inference(resolve,[$cnf( $equal(k,j) )],[refute_0_139,refute_0_143]) ).
cnf(refute_0_145,plain,
( m = j
| element(m,j) ),
inference(resolve,[$cnf( element(m,k) )],[refute_0_142,refute_0_144]) ).
cnf(refute_0_146,plain,
( Y != k
| k != j
| Y = j ),
introduced(tautology,[equality,[$cnf( ~ $equal(Y,j) ),[0],$fot(k)]]) ).
cnf(refute_0_147,plain,
( Y != k
| Y = j ),
inference(resolve,[$cnf( $equal(k,j) )],[refute_0_139,refute_0_146]) ).
cnf(refute_0_148,plain,
( ~ element(Y,j)
| Y = j ),
inference(resolve,[$cnf( $equal(Y,k) )],[c_4,refute_0_147]) ).
cnf(refute_0_149,plain,
( ~ element(m,j)
| m = j ),
inference(subst,[],[refute_0_148:[bind(Y,$fot(m))]]) ).
cnf(refute_0_150,plain,
m = j,
inference(resolve,[$cnf( element(m,j) )],[refute_0_145,refute_0_149]) ).
cnf(refute_0_151,plain,
( j != n
| m != j
| m = n ),
introduced(tautology,[equality,[$cnf( $equal(m,j) ),[1],$fot(n)]]) ).
cnf(refute_0_152,plain,
( j != n
| m = n ),
inference(resolve,[$cnf( $equal(m,j) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
( k != j
| n != k
| n = j ),
introduced(tautology,[equality,[$cnf( $equal(n,k) ),[1],$fot(j)]]) ).
cnf(refute_0_154,plain,
( n != k
| n = j ),
inference(resolve,[$cnf( $equal(k,j) )],[refute_0_139,refute_0_153]) ).
cnf(refute_0_155,plain,
( n = j
| element(n,k) ),
inference(resolve,[$cnf( $equal(n,k) )],[refute_0_88,refute_0_154]) ).
cnf(refute_0_156,plain,
( k != j
| ~ element(n,k)
| element(n,j) ),
introduced(tautology,[equality,[$cnf( element(n,k) ),[1],$fot(j)]]) ).
cnf(refute_0_157,plain,
( ~ element(n,k)
| element(n,j) ),
inference(resolve,[$cnf( $equal(k,j) )],[refute_0_139,refute_0_156]) ).
cnf(refute_0_158,plain,
( n = j
| element(n,j) ),
inference(resolve,[$cnf( element(n,k) )],[refute_0_155,refute_0_157]) ).
cnf(refute_0_159,plain,
( ~ element(n,j)
| n = j ),
inference(subst,[],[refute_0_148:[bind(Y,$fot(n))]]) ).
cnf(refute_0_160,plain,
n = j,
inference(resolve,[$cnf( element(n,j) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
( j != j
| n != j
| j = n ),
introduced(tautology,[equality,[$cnf( ~ $equal(j,n) ),[1],$fot(j)]]) ).
cnf(refute_0_162,plain,
( j != j
| j = n ),
inference(resolve,[$cnf( $equal(n,j) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
( j != j
| m = n ),
inference(resolve,[$cnf( $equal(j,n) )],[refute_0_162,refute_0_152]) ).
cnf(refute_0_164,plain,
j != j,
inference(resolve,[$cnf( $equal(m,n) )],[refute_0_163,c_1]) ).
cnf(refute_0_165,plain,
$false,
inference(resolve,[$cnf( $equal(j,j) )],[refute_0_34,refute_0_164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SYN014-1 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.08 % Command : metis --show proof --show saturation %s
% 0.07/0.26 % Computer : n004.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 600
% 0.07/0.26 % DateTime : Mon Jul 11 15:25:07 EDT 2022
% 0.07/0.27 % CPUTime :
% 0.07/0.27 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.10/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.41
% 0.10/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.10/0.41
%------------------------------------------------------------------------------