%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ALG235-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 14 17:39:43 EDT 2022
% Result : Unsatisfiable 0.46s 0.66s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 24
% Syntax : Number of clauses : 84 ( 45 unt; 0 nHn; 42 RR)
% Number of literals : 138 ( 137 equ; 56 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 232 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c01,axiom,
mult(A,mult(B,mult(A,B))) = mult(A,B) ).
cnf(c02,axiom,
mult(A,mult(B,mult(C,D))) = mult(C,mult(B,mult(A,D))) ).
cnf(c03,axiom,
mult(mult(A,mult(B,mult(C,B))),D) = mult(A,mult(D,mult(mult(C,B),D))) ).
cnf(goals,negated_conjecture,
mult(a,mult(b,mult(a,mult(c,mult(d,c))))) != mult(a,mult(b,mult(d,c))) ).
cnf(refute_0_0,plain,
mult(X_4,mult(X_5,mult(X_6,mult(B,mult(X_6,B))))) = mult(X_6,mult(X_5,mult(X_4,mult(B,mult(X_6,B))))),
inference(subst,[],[c02:[bind(A,$fot(X_4)),bind(B,$fot(X_5)),bind(C,$fot(X_6)),bind(D,$fot(mult(B,mult(X_6,B))))]]) ).
cnf(refute_0_1,plain,
mult(X_6,mult(B,mult(X_6,B))) = mult(X_6,B),
inference(subst,[],[c01:[bind(A,$fot(X_6))]]) ).
cnf(refute_0_2,plain,
( mult(X_4,mult(X_5,mult(X_6,mult(B,mult(X_6,B))))) != mult(X_6,mult(X_5,mult(X_4,mult(B,mult(X_6,B)))))
| mult(X_6,mult(B,mult(X_6,B))) != mult(X_6,B)
| mult(X_4,mult(X_5,mult(X_6,B))) = mult(X_6,mult(X_5,mult(X_4,mult(B,mult(X_6,B))))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_4,mult(X_5,mult(X_6,mult(B,mult(X_6,B))))),mult(X_6,mult(X_5,mult(X_4,mult(B,mult(X_6,B)))))) ),[0,1,1],$fot(mult(X_6,B))]]) ).
cnf(refute_0_3,plain,
( mult(X_4,mult(X_5,mult(X_6,mult(B,mult(X_6,B))))) != mult(X_6,mult(X_5,mult(X_4,mult(B,mult(X_6,B)))))
| mult(X_4,mult(X_5,mult(X_6,B))) = mult(X_6,mult(X_5,mult(X_4,mult(B,mult(X_6,B))))) ),
inference(resolve,[$cnf( $equal(mult(X_6,mult(B,mult(X_6,B))),mult(X_6,B)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
mult(X_4,mult(X_5,mult(X_6,B))) = mult(X_6,mult(X_5,mult(X_4,mult(B,mult(X_6,B))))),
inference(resolve,[$cnf( $equal(mult(X_4,mult(X_5,mult(X_6,mult(B,mult(X_6,B))))),mult(X_6,mult(X_5,mult(X_4,mult(B,mult(X_6,B)))))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
mult(X_4,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))) = mult(X_6,mult(X_5,mult(X_4,mult(mult(X_15,mult(X_4,X_15)),mult(X_6,mult(X_15,mult(X_4,X_15))))))),
inference(subst,[],[refute_0_4:[bind(B,$fot(mult(X_15,mult(X_4,X_15))))]]) ).
cnf(refute_0_6,plain,
mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))) = mult(X_4,mult(mult(X_15,mult(X_4,X_15)),mult(X_6,mult(X_15,mult(X_4,X_15))))),
inference(subst,[],[refute_0_4:[bind(B,$fot(X_15)),bind(X_4,$fot(X_6)),bind(X_5,$fot(mult(X_15,mult(X_4,X_15)))),bind(X_6,$fot(X_4))]]) ).
cnf(refute_0_7,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_8,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_9,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))) != mult(X_4,mult(mult(X_15,mult(X_4,X_15)),mult(X_6,mult(X_15,mult(X_4,X_15)))))
| mult(X_4,mult(mult(X_15,mult(X_4,X_15)),mult(X_6,mult(X_15,mult(X_4,X_15))))) = mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))),bind(Y,$fot(mult(X_4,mult(mult(X_15,mult(X_4,X_15)),mult(X_6,mult(X_15,mult(X_4,X_15)))))))]]) ).
cnf(refute_0_11,plain,
mult(X_4,mult(mult(X_15,mult(X_4,X_15)),mult(X_6,mult(X_15,mult(X_4,X_15))))) = mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))),
inference(resolve,[$cnf( $equal(mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))),mult(X_4,mult(mult(X_15,mult(X_4,X_15)),mult(X_6,mult(X_15,mult(X_4,X_15)))))) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
( mult(X_4,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))) != mult(X_6,mult(X_5,mult(X_4,mult(mult(X_15,mult(X_4,X_15)),mult(X_6,mult(X_15,mult(X_4,X_15)))))))
| mult(X_4,mult(mult(X_15,mult(X_4,X_15)),mult(X_6,mult(X_15,mult(X_4,X_15))))) != mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))
| mult(X_4,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))) = mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_4,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))),mult(X_6,mult(X_5,mult(X_4,mult(mult(X_15,mult(X_4,X_15)),mult(X_6,mult(X_15,mult(X_4,X_15)))))))) ),[1,1,1],$fot(mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))]]) ).
cnf(refute_0_13,plain,
( mult(X_4,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))) != mult(X_6,mult(X_5,mult(X_4,mult(mult(X_15,mult(X_4,X_15)),mult(X_6,mult(X_15,mult(X_4,X_15)))))))
| mult(X_4,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))) = mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))) ),
inference(resolve,[$cnf( $equal(mult(X_4,mult(mult(X_15,mult(X_4,X_15)),mult(X_6,mult(X_15,mult(X_4,X_15))))),mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
mult(X_4,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))) = mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))),
inference(resolve,[$cnf( $equal(mult(X_4,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))),mult(X_6,mult(X_5,mult(X_4,mult(mult(X_15,mult(X_4,X_15)),mult(X_6,mult(X_15,mult(X_4,X_15)))))))) )],[refute_0_5,refute_0_13]) ).
cnf(refute_0_15,plain,
( mult(X_4,mult(X_5,mult(X_6,B))) != mult(X_6,mult(X_5,mult(X_4,mult(B,mult(X_6,B)))))
| mult(X_6,mult(X_5,mult(X_4,mult(B,mult(X_6,B))))) = mult(X_4,mult(X_5,mult(X_6,B))) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(mult(X_4,mult(X_5,mult(X_6,B))))),bind(Y,$fot(mult(X_6,mult(X_5,mult(X_4,mult(B,mult(X_6,B)))))))]]) ).
cnf(refute_0_16,plain,
mult(X_6,mult(X_5,mult(X_4,mult(B,mult(X_6,B))))) = mult(X_4,mult(X_5,mult(X_6,B))),
inference(resolve,[$cnf( $equal(mult(X_4,mult(X_5,mult(X_6,B))),mult(X_6,mult(X_5,mult(X_4,mult(B,mult(X_6,B)))))) )],[refute_0_4,refute_0_15]) ).
cnf(refute_0_17,plain,
mult(X_4,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))) = mult(X_6,mult(X_5,mult(X_4,X_15))),
inference(subst,[],[refute_0_16:[bind(B,$fot(X_15)),bind(X_4,$fot(X_6)),bind(X_6,$fot(X_4))]]) ).
cnf(refute_0_18,plain,
( mult(X_4,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))) != mult(X_6,mult(X_5,mult(X_4,X_15)))
| mult(X_4,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))) != mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))))
| mult(X_6,mult(X_5,mult(X_4,X_15))) = mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_4,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))),mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))))) ),[0],$fot(mult(X_6,mult(X_5,mult(X_4,X_15))))]]) ).
cnf(refute_0_19,plain,
( mult(X_4,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))) != mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))))
| mult(X_6,mult(X_5,mult(X_4,X_15))) = mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))) ),
inference(resolve,[$cnf( $equal(mult(X_4,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))),mult(X_6,mult(X_5,mult(X_4,X_15)))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
mult(X_4,mult(X_5,mult(X_6,mult(X_5,X_6)))) = mult(X_6,mult(X_5,mult(X_4,mult(X_5,X_6)))),
inference(subst,[],[c02:[bind(A,$fot(X_4)),bind(B,$fot(X_5)),bind(C,$fot(X_6)),bind(D,$fot(mult(X_5,X_6)))]]) ).
cnf(refute_0_21,plain,
mult(X_5,mult(X_6,mult(X_5,X_6))) = mult(X_5,X_6),
inference(subst,[],[c01:[bind(A,$fot(X_5)),bind(B,$fot(X_6))]]) ).
cnf(refute_0_22,plain,
( mult(X_4,mult(X_5,mult(X_6,mult(X_5,X_6)))) != mult(X_6,mult(X_5,mult(X_4,mult(X_5,X_6))))
| mult(X_5,mult(X_6,mult(X_5,X_6))) != mult(X_5,X_6)
| mult(X_4,mult(X_5,X_6)) = mult(X_6,mult(X_5,mult(X_4,mult(X_5,X_6)))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_4,mult(X_5,mult(X_6,mult(X_5,X_6)))),mult(X_6,mult(X_5,mult(X_4,mult(X_5,X_6))))) ),[0,1],$fot(mult(X_5,X_6))]]) ).
cnf(refute_0_23,plain,
( mult(X_4,mult(X_5,mult(X_6,mult(X_5,X_6)))) != mult(X_6,mult(X_5,mult(X_4,mult(X_5,X_6))))
| mult(X_4,mult(X_5,X_6)) = mult(X_6,mult(X_5,mult(X_4,mult(X_5,X_6)))) ),
inference(resolve,[$cnf( $equal(mult(X_5,mult(X_6,mult(X_5,X_6))),mult(X_5,X_6)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
mult(X_4,mult(X_5,X_6)) = mult(X_6,mult(X_5,mult(X_4,mult(X_5,X_6)))),
inference(resolve,[$cnf( $equal(mult(X_4,mult(X_5,mult(X_6,mult(X_5,X_6)))),mult(X_6,mult(X_5,mult(X_4,mult(X_5,X_6))))) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
mult(X_4,mult(X_5,mult(X_4,X_5))) = mult(mult(X_4,X_5),mult(X_5,mult(X_4,mult(X_5,mult(X_4,X_5))))),
inference(subst,[],[refute_0_24:[bind(X_6,$fot(mult(X_4,X_5)))]]) ).
cnf(refute_0_26,plain,
mult(X_5,mult(X_4,X_5)) = mult(X_5,mult(X_4,mult(X_5,mult(X_4,X_5)))),
inference(subst,[],[refute_0_24:[bind(X_4,$fot(X_5)),bind(X_5,$fot(X_4)),bind(X_6,$fot(X_5))]]) ).
cnf(refute_0_27,plain,
( mult(X_5,mult(X_4,X_5)) != mult(X_5,mult(X_4,mult(X_5,mult(X_4,X_5))))
| mult(X_5,mult(X_4,mult(X_5,mult(X_4,X_5)))) = mult(X_5,mult(X_4,X_5)) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(mult(X_5,mult(X_4,X_5)))),bind(Y,$fot(mult(X_5,mult(X_4,mult(X_5,mult(X_4,X_5))))))]]) ).
cnf(refute_0_28,plain,
mult(X_5,mult(X_4,mult(X_5,mult(X_4,X_5)))) = mult(X_5,mult(X_4,X_5)),
inference(resolve,[$cnf( $equal(mult(X_5,mult(X_4,X_5)),mult(X_5,mult(X_4,mult(X_5,mult(X_4,X_5))))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( mult(X_4,mult(X_5,mult(X_4,X_5))) != mult(mult(X_4,X_5),mult(X_5,mult(X_4,mult(X_5,mult(X_4,X_5)))))
| mult(X_5,mult(X_4,mult(X_5,mult(X_4,X_5)))) != mult(X_5,mult(X_4,X_5))
| mult(X_4,mult(X_5,mult(X_4,X_5))) = mult(mult(X_4,X_5),mult(X_5,mult(X_4,X_5))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_4,mult(X_5,mult(X_4,X_5))),mult(mult(X_4,X_5),mult(X_5,mult(X_4,mult(X_5,mult(X_4,X_5)))))) ),[1,1],$fot(mult(X_5,mult(X_4,X_5)))]]) ).
cnf(refute_0_30,plain,
( mult(X_4,mult(X_5,mult(X_4,X_5))) != mult(mult(X_4,X_5),mult(X_5,mult(X_4,mult(X_5,mult(X_4,X_5)))))
| mult(X_4,mult(X_5,mult(X_4,X_5))) = mult(mult(X_4,X_5),mult(X_5,mult(X_4,X_5))) ),
inference(resolve,[$cnf( $equal(mult(X_5,mult(X_4,mult(X_5,mult(X_4,X_5)))),mult(X_5,mult(X_4,X_5))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
mult(X_4,mult(X_5,mult(X_4,X_5))) = mult(mult(X_4,X_5),mult(X_5,mult(X_4,X_5))),
inference(resolve,[$cnf( $equal(mult(X_4,mult(X_5,mult(X_4,X_5))),mult(mult(X_4,X_5),mult(X_5,mult(X_4,mult(X_5,mult(X_4,X_5)))))) )],[refute_0_25,refute_0_30]) ).
cnf(refute_0_32,plain,
mult(X_4,mult(X_5,mult(X_4,X_5))) = mult(X_4,X_5),
inference(subst,[],[c01:[bind(A,$fot(X_4)),bind(B,$fot(X_5))]]) ).
cnf(refute_0_33,plain,
( mult(X_4,mult(X_5,mult(X_4,X_5))) != mult(X_4,X_5)
| mult(X_4,mult(X_5,mult(X_4,X_5))) != mult(mult(X_4,X_5),mult(X_5,mult(X_4,X_5)))
| mult(X_4,X_5) = mult(mult(X_4,X_5),mult(X_5,mult(X_4,X_5))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_4,mult(X_5,mult(X_4,X_5))),mult(mult(X_4,X_5),mult(X_5,mult(X_4,X_5)))) ),[0],$fot(mult(X_4,X_5))]]) ).
cnf(refute_0_34,plain,
( mult(X_4,mult(X_5,mult(X_4,X_5))) != mult(mult(X_4,X_5),mult(X_5,mult(X_4,X_5)))
| mult(X_4,X_5) = mult(mult(X_4,X_5),mult(X_5,mult(X_4,X_5))) ),
inference(resolve,[$cnf( $equal(mult(X_4,mult(X_5,mult(X_4,X_5))),mult(X_4,X_5)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( mult(A,mult(B,mult(C,D))) != mult(C,mult(B,mult(A,D)))
| mult(C,mult(B,mult(A,D))) = mult(A,mult(B,mult(C,D))) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(mult(A,mult(B,mult(C,D))))),bind(Y,$fot(mult(C,mult(B,mult(A,D)))))]]) ).
cnf(refute_0_36,plain,
mult(C,mult(B,mult(A,D))) = mult(A,mult(B,mult(C,D))),
inference(resolve,[$cnf( $equal(mult(A,mult(B,mult(C,D))),mult(C,mult(B,mult(A,D)))) )],[c02,refute_0_35]) ).
cnf(refute_0_37,plain,
mult(mult(X_4,X_5),mult(X_5,mult(X_4,X_5))) = mult(X_4,mult(X_5,mult(mult(X_4,X_5),X_5))),
inference(subst,[],[refute_0_36:[bind(A,$fot(X_4)),bind(B,$fot(X_5)),bind(C,$fot(mult(X_4,X_5))),bind(D,$fot(X_5))]]) ).
cnf(refute_0_38,plain,
( mult(X_4,X_5) != mult(mult(X_4,X_5),mult(X_5,mult(X_4,X_5)))
| mult(mult(X_4,X_5),mult(X_5,mult(X_4,X_5))) != mult(X_4,mult(X_5,mult(mult(X_4,X_5),X_5)))
| mult(X_4,X_5) = mult(X_4,mult(X_5,mult(mult(X_4,X_5),X_5))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(X_4,X_5),mult(X_4,mult(X_5,mult(mult(X_4,X_5),X_5)))) ),[0],$fot(mult(mult(X_4,X_5),mult(X_5,mult(X_4,X_5))))]]) ).
cnf(refute_0_39,plain,
( mult(X_4,X_5) != mult(mult(X_4,X_5),mult(X_5,mult(X_4,X_5)))
| mult(X_4,X_5) = mult(X_4,mult(X_5,mult(mult(X_4,X_5),X_5))) ),
inference(resolve,[$cnf( $equal(mult(mult(X_4,X_5),mult(X_5,mult(X_4,X_5))),mult(X_4,mult(X_5,mult(mult(X_4,X_5),X_5)))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( mult(X_4,mult(X_5,mult(X_4,X_5))) != mult(mult(X_4,X_5),mult(X_5,mult(X_4,X_5)))
| mult(X_4,X_5) = mult(X_4,mult(X_5,mult(mult(X_4,X_5),X_5))) ),
inference(resolve,[$cnf( $equal(mult(X_4,X_5),mult(mult(X_4,X_5),mult(X_5,mult(X_4,X_5)))) )],[refute_0_34,refute_0_39]) ).
cnf(refute_0_41,plain,
mult(X_4,X_5) = mult(X_4,mult(X_5,mult(mult(X_4,X_5),X_5))),
inference(resolve,[$cnf( $equal(mult(X_4,mult(X_5,mult(X_4,X_5))),mult(mult(X_4,X_5),mult(X_5,mult(X_4,X_5)))) )],[refute_0_31,refute_0_40]) ).
cnf(refute_0_42,plain,
mult(mult(X_13,mult(X_12,mult(X_13,X_12))),X_14) = mult(X_13,mult(X_14,mult(mult(X_13,X_12),X_14))),
inference(subst,[],[c03:[bind(A,$fot(X_13)),bind(B,$fot(X_12)),bind(C,$fot(X_13)),bind(D,$fot(X_14))]]) ).
cnf(refute_0_43,plain,
mult(X_13,mult(X_12,mult(X_13,X_12))) = mult(X_13,X_12),
inference(subst,[],[c01:[bind(A,$fot(X_13)),bind(B,$fot(X_12))]]) ).
cnf(refute_0_44,plain,
( mult(X_13,mult(X_12,mult(X_13,X_12))) != mult(X_13,X_12)
| mult(mult(X_13,mult(X_12,mult(X_13,X_12))),X_14) != mult(X_13,mult(X_14,mult(mult(X_13,X_12),X_14)))
| mult(mult(X_13,X_12),X_14) = mult(X_13,mult(X_14,mult(mult(X_13,X_12),X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(mult(X_13,mult(X_12,mult(X_13,X_12))),X_14),mult(X_13,mult(X_14,mult(mult(X_13,X_12),X_14)))) ),[0,0],$fot(mult(X_13,X_12))]]) ).
cnf(refute_0_45,plain,
( mult(mult(X_13,mult(X_12,mult(X_13,X_12))),X_14) != mult(X_13,mult(X_14,mult(mult(X_13,X_12),X_14)))
| mult(mult(X_13,X_12),X_14) = mult(X_13,mult(X_14,mult(mult(X_13,X_12),X_14))) ),
inference(resolve,[$cnf( $equal(mult(X_13,mult(X_12,mult(X_13,X_12))),mult(X_13,X_12)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
mult(mult(X_13,X_12),X_14) = mult(X_13,mult(X_14,mult(mult(X_13,X_12),X_14))),
inference(resolve,[$cnf( $equal(mult(mult(X_13,mult(X_12,mult(X_13,X_12))),X_14),mult(X_13,mult(X_14,mult(mult(X_13,X_12),X_14)))) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
( mult(mult(X_13,X_12),X_14) != mult(X_13,mult(X_14,mult(mult(X_13,X_12),X_14)))
| mult(X_13,mult(X_14,mult(mult(X_13,X_12),X_14))) = mult(mult(X_13,X_12),X_14) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(mult(mult(X_13,X_12),X_14))),bind(Y,$fot(mult(X_13,mult(X_14,mult(mult(X_13,X_12),X_14)))))]]) ).
cnf(refute_0_48,plain,
mult(X_13,mult(X_14,mult(mult(X_13,X_12),X_14))) = mult(mult(X_13,X_12),X_14),
inference(resolve,[$cnf( $equal(mult(mult(X_13,X_12),X_14),mult(X_13,mult(X_14,mult(mult(X_13,X_12),X_14)))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
mult(X_4,mult(X_5,mult(mult(X_4,X_5),X_5))) = mult(mult(X_4,X_5),X_5),
inference(subst,[],[refute_0_48:[bind(X_12,$fot(X_5)),bind(X_13,$fot(X_4)),bind(X_14,$fot(X_5))]]) ).
cnf(refute_0_50,plain,
( mult(X_4,X_5) != mult(X_4,mult(X_5,mult(mult(X_4,X_5),X_5)))
| mult(X_4,mult(X_5,mult(mult(X_4,X_5),X_5))) != mult(mult(X_4,X_5),X_5)
| mult(X_4,X_5) = mult(mult(X_4,X_5),X_5) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(X_4,X_5),mult(mult(X_4,X_5),X_5)) ),[0],$fot(mult(X_4,mult(X_5,mult(mult(X_4,X_5),X_5))))]]) ).
cnf(refute_0_51,plain,
( mult(X_4,X_5) != mult(X_4,mult(X_5,mult(mult(X_4,X_5),X_5)))
| mult(X_4,X_5) = mult(mult(X_4,X_5),X_5) ),
inference(resolve,[$cnf( $equal(mult(X_4,mult(X_5,mult(mult(X_4,X_5),X_5))),mult(mult(X_4,X_5),X_5)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
mult(X_4,X_5) = mult(mult(X_4,X_5),X_5),
inference(resolve,[$cnf( $equal(mult(X_4,X_5),mult(X_4,mult(X_5,mult(mult(X_4,X_5),X_5)))) )],[refute_0_41,refute_0_51]) ).
cnf(refute_0_53,plain,
( mult(X_4,X_5) != mult(mult(X_4,X_5),X_5)
| mult(mult(X_4,X_5),X_5) = mult(X_4,X_5) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(mult(X_4,X_5))),bind(Y,$fot(mult(mult(X_4,X_5),X_5)))]]) ).
cnf(refute_0_54,plain,
mult(mult(X_4,X_5),X_5) = mult(X_4,X_5),
inference(resolve,[$cnf( $equal(mult(X_4,X_5),mult(mult(X_4,X_5),X_5)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)) = mult(X_15,mult(X_4,X_15)),
inference(subst,[],[refute_0_54:[bind(X_4,$fot(X_15)),bind(X_5,$fot(mult(X_4,X_15)))]]) ).
cnf(refute_0_56,plain,
mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))) = mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))),
introduced(tautology,[refl,[$fot(mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))]]) ).
cnf(refute_0_57,plain,
( mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))) != mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))
| mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)) != mult(X_15,mult(X_4,X_15))
| mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))) = mult(X_6,mult(X_15,mult(X_4,X_15))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))),mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))) ),[1,1],$fot(mult(X_15,mult(X_4,X_15)))]]) ).
cnf(refute_0_58,plain,
( mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)) != mult(X_15,mult(X_4,X_15))
| mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))) = mult(X_6,mult(X_15,mult(X_4,X_15))) ),
inference(resolve,[$cnf( $equal(mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))),mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))) = mult(X_6,mult(X_15,mult(X_4,X_15))),
inference(resolve,[$cnf( $equal(mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)),mult(X_15,mult(X_4,X_15))) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))) = mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))),
introduced(tautology,[refl,[$fot(mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))))]]) ).
cnf(refute_0_61,plain,
( mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))) != mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))
| mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))) != mult(X_6,mult(X_15,mult(X_4,X_15)))
| mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))) = mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15)))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))),mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))) ),[1,1],$fot(mult(X_6,mult(X_15,mult(X_4,X_15))))]]) ).
cnf(refute_0_62,plain,
( mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))) != mult(X_6,mult(X_15,mult(X_4,X_15)))
| mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))) = mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15)))) ),
inference(resolve,[$cnf( $equal(mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))),mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))) = mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15)))),
inference(resolve,[$cnf( $equal(mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))),mult(X_6,mult(X_15,mult(X_4,X_15)))) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))) = mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))),
introduced(tautology,[refl,[$fot(mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))))]]) ).
cnf(refute_0_65,plain,
( mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))) != mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))
| mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))) != mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))))
| mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))) = mult(X_6,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))) ),
introduced(tautology,[equality,[$cnf( $equal(mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))),mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))))) ),[1,1],$fot(mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15)))))]]) ).
cnf(refute_0_66,plain,
( mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))) != mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))
| mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))) = mult(X_6,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))) ),
inference(resolve,[$cnf( $equal(mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))),mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))) = mult(X_6,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))),
inference(resolve,[$cnf( $equal(mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))),mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
( mult(X_6,mult(X_5,mult(X_4,X_15))) != mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))))
| mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))) != mult(X_6,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15)))))
| mult(X_6,mult(X_5,mult(X_4,X_15))) = mult(X_6,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(X_6,mult(X_5,mult(X_4,X_15))),mult(X_6,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15)))))) ),[0],$fot(mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))))]]) ).
cnf(refute_0_69,plain,
( mult(X_6,mult(X_5,mult(X_4,X_15))) != mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))))
| mult(X_6,mult(X_5,mult(X_4,X_15))) = mult(X_6,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))) ),
inference(resolve,[$cnf( $equal(mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15))))),mult(X_6,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15)))))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( mult(X_4,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))) != mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))))
| mult(X_6,mult(X_5,mult(X_4,X_15))) = mult(X_6,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))) ),
inference(resolve,[$cnf( $equal(mult(X_6,mult(X_5,mult(X_4,X_15))),mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))))) )],[refute_0_19,refute_0_69]) ).
cnf(refute_0_71,plain,
mult(X_6,mult(X_5,mult(X_4,X_15))) = mult(X_6,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))),
inference(resolve,[$cnf( $equal(mult(X_4,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))),mult(X_6,mult(X_5,mult(X_6,mult(mult(X_15,mult(X_4,X_15)),mult(X_4,X_15)))))) )],[refute_0_14,refute_0_70]) ).
cnf(refute_0_72,plain,
( mult(X_6,mult(X_5,mult(X_4,X_15))) != mult(X_6,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15)))))
| mult(X_6,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))) = mult(X_6,mult(X_5,mult(X_4,X_15))) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(mult(X_6,mult(X_5,mult(X_4,X_15))))),bind(Y,$fot(mult(X_6,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15)))))))]]) ).
cnf(refute_0_73,plain,
mult(X_6,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15))))) = mult(X_6,mult(X_5,mult(X_4,X_15))),
inference(resolve,[$cnf( $equal(mult(X_6,mult(X_5,mult(X_4,X_15))),mult(X_6,mult(X_5,mult(X_6,mult(X_15,mult(X_4,X_15)))))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
mult(a,mult(b,mult(a,mult(c,mult(d,c))))) = mult(a,mult(b,mult(d,c))),
inference(subst,[],[refute_0_73:[bind(X_15,$fot(c)),bind(X_4,$fot(d)),bind(X_5,$fot(b)),bind(X_6,$fot(a))]]) ).
cnf(refute_0_75,plain,
( mult(a,mult(b,mult(a,mult(c,mult(d,c))))) != mult(a,mult(b,mult(d,c)))
| mult(a,mult(b,mult(d,c))) != mult(a,mult(b,mult(d,c)))
| mult(a,mult(b,mult(a,mult(c,mult(d,c))))) = mult(a,mult(b,mult(d,c))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(mult(a,mult(b,mult(a,mult(c,mult(d,c))))),mult(a,mult(b,mult(d,c)))) ),[0],$fot(mult(a,mult(b,mult(d,c))))]]) ).
cnf(refute_0_76,plain,
( mult(a,mult(b,mult(d,c))) != mult(a,mult(b,mult(d,c)))
| mult(a,mult(b,mult(a,mult(c,mult(d,c))))) = mult(a,mult(b,mult(d,c))) ),
inference(resolve,[$cnf( $equal(mult(a,mult(b,mult(a,mult(c,mult(d,c))))),mult(a,mult(b,mult(d,c)))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
mult(a,mult(b,mult(d,c))) != mult(a,mult(b,mult(d,c))),
inference(resolve,[$cnf( $equal(mult(a,mult(b,mult(a,mult(c,mult(d,c))))),mult(a,mult(b,mult(d,c)))) )],[refute_0_76,goals]) ).
cnf(refute_0_78,plain,
mult(a,mult(b,mult(d,c))) = mult(a,mult(b,mult(d,c))),
introduced(tautology,[refl,[$fot(mult(a,mult(b,mult(d,c))))]]) ).
cnf(refute_0_79,plain,
$false,
inference(resolve,[$cnf( $equal(mult(a,mult(b,mult(d,c))),mult(a,mult(b,mult(d,c)))) )],[refute_0_78,refute_0_77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : ALG235-1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n023.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 8 16:19:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.46/0.66 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.66
% 0.46/0.66 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.46/0.67
%------------------------------------------------------------------------------