%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN015-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of clauses : 58 ( 11 unt; 25 nHn; 57 RR)
% Number of literals : 154 ( 0 equ; 50 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(reflexivityish,axiom,
equalish(X,X) ).
cnf(symmetryish,axiom,
( ~ equalish(X,Y)
| equalish(Y,X) ) ).
cnf(transitivityish,axiom,
( ~ equalish(X,Y)
| ~ equalish(Y,Z)
| equalish(X,Z) ) ).
cnf(element_substitutionish1,axiom,
( ~ equalish(A,B)
| ~ element(C,A)
| element(C,B) ) ).
cnf(c_5,negated_conjecture,
( ~ equalish(f(A),m)
| ~ element(A,m)
| equalish(A,m) ) ).
cnf(c_6,negated_conjecture,
( ~ equalish(f(A),A)
| ~ element(A,m)
| equalish(A,m) ) ).
cnf(c_7,negated_conjecture,
( element(A,f(A))
| ~ element(A,m)
| equalish(A,m) ) ).
cnf(c_8,negated_conjecture,
( element(f(A),A)
| ~ element(A,m)
| equalish(A,m) ) ).
cnf(c_9,negated_conjecture,
( ~ element(A,B)
| ~ element(B,A)
| equalish(A,B)
| equalish(A,m)
| element(B,m)
| equalish(B,m) ) ).
cnf(c_16,negated_conjecture,
( ~ equalish(A,n)
| element(A,k)
| equalish(A,k) ) ).
cnf(c_17,negated_conjecture,
( ~ element(A,k)
| equalish(A,n)
| equalish(A,m)
| equalish(A,k) ) ).
cnf(c_19,negated_conjecture,
~ equalish(m,n) ).
cnf(c_20,negated_conjecture,
~ equalish(n,k) ).
cnf(c_23,negated_conjecture,
equalish(m,k) ).
cnf(refute_0_0,plain,
( ~ equalish(n,m)
| equalish(m,n) ),
inference(subst,[],[symmetryish:[bind(X,$fot(n)),bind(Y,$fot(m))]]) ).
cnf(refute_0_1,plain,
( ~ equalish(f(n),n)
| ~ element(n,m)
| equalish(n,m) ),
inference(subst,[],[c_6:[bind(A,$fot(n))]]) ).
cnf(refute_0_2,plain,
( ~ equalish(n,f(n))
| equalish(f(n),n) ),
inference(subst,[],[symmetryish:[bind(X,$fot(n)),bind(Y,$fot(f(n)))]]) ).
cnf(refute_0_3,plain,
( ~ equalish(f(n),m)
| ~ element(n,m)
| equalish(n,m) ),
inference(subst,[],[c_5:[bind(A,$fot(n))]]) ).
cnf(refute_0_4,plain,
( ~ equalish(m,k)
| equalish(k,m) ),
inference(subst,[],[symmetryish:[bind(X,$fot(m)),bind(Y,$fot(k))]]) ).
cnf(refute_0_5,plain,
equalish(k,m),
inference(resolve,[$cnf( equalish(m,k) )],[c_23,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ equalish(X_16,k)
| ~ equalish(k,m)
| equalish(X_16,m) ),
inference(subst,[],[transitivityish:[bind(X,$fot(X_16)),bind(Y,$fot(k)),bind(Z,$fot(m))]]) ).
cnf(refute_0_7,plain,
( ~ equalish(X_16,k)
| equalish(X_16,m) ),
inference(resolve,[$cnf( equalish(k,m) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ equalish(f(n),k)
| equalish(f(n),m) ),
inference(subst,[],[refute_0_7:[bind(X_16,$fot(f(n)))]]) ).
cnf(refute_0_9,plain,
( ~ equalish(X_16,m)
| ~ equalish(m,k)
| equalish(X_16,k) ),
inference(subst,[],[transitivityish:[bind(X,$fot(X_16)),bind(Y,$fot(m)),bind(Z,$fot(k))]]) ).
cnf(refute_0_10,plain,
( ~ equalish(X_16,m)
| equalish(X_16,k) ),
inference(resolve,[$cnf( equalish(m,k) )],[c_23,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ equalish(f(n),m)
| equalish(f(n),k) ),
inference(subst,[],[refute_0_10:[bind(X_16,$fot(f(n)))]]) ).
cnf(refute_0_12,plain,
( ~ equalish(f(n),n)
| equalish(n,f(n)) ),
inference(subst,[],[symmetryish:[bind(X,$fot(f(n))),bind(Y,$fot(n))]]) ).
cnf(refute_0_13,plain,
( ~ element(f(n),k)
| equalish(f(n),k)
| equalish(f(n),m)
| equalish(f(n),n) ),
inference(subst,[],[c_17:[bind(A,$fot(f(n)))]]) ).
cnf(refute_0_14,plain,
( ~ equalish(m,B)
| ~ element(f(n),m)
| element(f(n),B) ),
inference(subst,[],[element_substitutionish1:[bind(A,$fot(m)),bind(C,$fot(f(n)))]]) ).
cnf(refute_0_15,plain,
( ~ element(n,m)
| equalish(n,m)
| element(n,f(n)) ),
inference(subst,[],[c_7:[bind(A,$fot(n))]]) ).
cnf(refute_0_16,plain,
equalish(n,n),
inference(subst,[],[reflexivityish:[bind(X,$fot(n))]]) ).
cnf(refute_0_17,plain,
( ~ equalish(n,n)
| equalish(n,k)
| element(n,k) ),
inference(subst,[],[c_16:[bind(A,$fot(n))]]) ).
cnf(refute_0_18,plain,
( equalish(n,k)
| element(n,k) ),
inference(resolve,[$cnf( equalish(n,n) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
element(n,k),
inference(resolve,[$cnf( equalish(n,k) )],[refute_0_18,c_20]) ).
cnf(refute_0_20,plain,
( ~ equalish(k,X_23)
| ~ element(n,k)
| element(n,X_23) ),
inference(subst,[],[element_substitutionish1:[bind(A,$fot(k)),bind(B,$fot(X_23)),bind(C,$fot(n))]]) ).
cnf(refute_0_21,plain,
( ~ equalish(k,X_23)
| element(n,X_23) ),
inference(resolve,[$cnf( element(n,k) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ equalish(k,m)
| element(n,m) ),
inference(subst,[],[refute_0_21:[bind(X_23,$fot(m))]]) ).
cnf(refute_0_23,plain,
element(n,m),
inference(resolve,[$cnf( equalish(k,m) )],[refute_0_5,refute_0_22]) ).
cnf(refute_0_24,plain,
( equalish(n,m)
| element(n,f(n)) ),
inference(resolve,[$cnf( element(n,m) )],[refute_0_23,refute_0_15]) ).
cnf(refute_0_25,plain,
( ~ element(n,m)
| equalish(n,m)
| element(f(n),n) ),
inference(subst,[],[c_8:[bind(A,$fot(n))]]) ).
cnf(refute_0_26,plain,
( equalish(n,m)
| element(f(n),n) ),
inference(resolve,[$cnf( element(n,m) )],[refute_0_23,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ element(f(n),n)
| ~ element(n,f(n))
| equalish(f(n),m)
| equalish(n,f(n))
| equalish(n,m)
| element(f(n),m) ),
inference(subst,[],[c_9:[bind(A,$fot(n)),bind(B,$fot(f(n)))]]) ).
cnf(refute_0_28,plain,
( ~ element(n,f(n))
| equalish(f(n),m)
| equalish(n,f(n))
| equalish(n,m)
| element(f(n),m) ),
inference(resolve,[$cnf( element(f(n),n) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( equalish(f(n),m)
| equalish(n,f(n))
| equalish(n,m)
| element(f(n),m) ),
inference(resolve,[$cnf( element(n,f(n)) )],[refute_0_24,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ equalish(m,B)
| equalish(f(n),m)
| equalish(n,f(n))
| equalish(n,m)
| element(f(n),B) ),
inference(resolve,[$cnf( element(f(n),m) )],[refute_0_29,refute_0_14]) ).
cnf(refute_0_31,plain,
( ~ equalish(m,k)
| equalish(f(n),m)
| equalish(n,f(n))
| equalish(n,m)
| element(f(n),k) ),
inference(subst,[],[refute_0_30:[bind(B,$fot(k))]]) ).
cnf(refute_0_32,plain,
( equalish(f(n),m)
| equalish(n,f(n))
| equalish(n,m)
| element(f(n),k) ),
inference(resolve,[$cnf( equalish(m,k) )],[c_23,refute_0_31]) ).
cnf(refute_0_33,plain,
( equalish(f(n),k)
| equalish(f(n),m)
| equalish(f(n),n)
| equalish(n,f(n))
| equalish(n,m) ),
inference(resolve,[$cnf( element(f(n),k) )],[refute_0_32,refute_0_13]) ).
cnf(refute_0_34,plain,
( equalish(f(n),k)
| equalish(f(n),m)
| equalish(n,f(n))
| equalish(n,m) ),
inference(resolve,[$cnf( equalish(f(n),n) )],[refute_0_33,refute_0_12]) ).
cnf(refute_0_35,plain,
( equalish(f(n),k)
| equalish(n,f(n))
| equalish(n,m) ),
inference(resolve,[$cnf( equalish(f(n),m) )],[refute_0_34,refute_0_11]) ).
cnf(refute_0_36,plain,
( equalish(f(n),m)
| equalish(n,f(n))
| equalish(n,m) ),
inference(resolve,[$cnf( equalish(f(n),k) )],[refute_0_35,refute_0_8]) ).
cnf(refute_0_37,plain,
( ~ element(n,m)
| equalish(n,f(n))
| equalish(n,m) ),
inference(resolve,[$cnf( equalish(f(n),m) )],[refute_0_36,refute_0_3]) ).
cnf(refute_0_38,plain,
( equalish(n,f(n))
| equalish(n,m) ),
inference(resolve,[$cnf( element(n,m) )],[refute_0_23,refute_0_37]) ).
cnf(refute_0_39,plain,
( equalish(f(n),n)
| equalish(n,m) ),
inference(resolve,[$cnf( equalish(n,f(n)) )],[refute_0_38,refute_0_2]) ).
cnf(refute_0_40,plain,
( ~ element(n,m)
| equalish(n,m) ),
inference(resolve,[$cnf( equalish(f(n),n) )],[refute_0_39,refute_0_1]) ).
cnf(refute_0_41,plain,
equalish(n,m),
inference(resolve,[$cnf( element(n,m) )],[refute_0_23,refute_0_40]) ).
cnf(refute_0_42,plain,
equalish(m,n),
inference(resolve,[$cnf( equalish(n,m) )],[refute_0_41,refute_0_0]) ).
cnf(refute_0_43,plain,
$false,
inference(resolve,[$cnf( equalish(m,n) )],[refute_0_42,c_19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN015-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n025.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 : Tue Jul 12 04:55:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.40
%------------------------------------------------------------------------------