TSTP Solution File: NUN134-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUN134-1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 : Mon Jul 18 16:35:01 EDT 2022
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 30
% Syntax : Number of clauses : 116 ( 62 unt; 0 nHn; 72 RR)
% Number of literals : 192 ( 191 equ; 78 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 135 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(plus_comm,axiom,
add(X,Y) = add(Y,X) ).
cnf(plus_assoc,axiom,
add(X,add(Y,Z)) = add(add(X,Y),Z) ).
cnf(times_comm,axiom,
times(X,Y) = times(Y,X) ).
cnf(times_one,axiom,
times(X,one) = X ).
cnf(plus_s,axiom,
add(s(X),Y) = s(add(X,Y)) ).
cnf(times_s,axiom,
times(s(X),Y) = add(Y,times(X,Y)) ).
cnf(sum_s,axiom,
sum(s(N)) = add(s(N),sum(N)) ).
cnf(induction_hypothesis,axiom,
add(sum(a),sum(a)) = times(a,s(a)) ).
cnf(goal,negated_conjecture,
add(sum(s(a)),sum(s(a))) != times(s(a),s(s(a))) ).
cnf(refute_0_0,plain,
add(s(add(X_9,sum(X_9))),Y) = s(add(add(X_9,sum(X_9)),Y)),
inference(subst,[],[plus_s:[bind(X,$fot(add(X_9,sum(X_9))))]]) ).
cnf(refute_0_1,plain,
add(s(N),sum(N)) = s(add(N,sum(N))),
inference(subst,[],[plus_s:[bind(X,$fot(N)),bind(Y,$fot(sum(N)))]]) ).
cnf(refute_0_2,plain,
( add(s(N),sum(N)) != s(add(N,sum(N)))
| sum(s(N)) != add(s(N),sum(N))
| sum(s(N)) = s(add(N,sum(N))) ),
introduced(tautology,[equality,[$cnf( $equal(sum(s(N)),add(s(N),sum(N))) ),[1],$fot(s(add(N,sum(N))))]]) ).
cnf(refute_0_3,plain,
( sum(s(N)) != add(s(N),sum(N))
| sum(s(N)) = s(add(N,sum(N))) ),
inference(resolve,[$cnf( $equal(add(s(N),sum(N)),s(add(N,sum(N)))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
sum(s(N)) = s(add(N,sum(N))),
inference(resolve,[$cnf( $equal(sum(s(N)),add(s(N),sum(N))) )],[sum_s,refute_0_3]) ).
cnf(refute_0_5,plain,
sum(s(X_9)) = s(add(X_9,sum(X_9))),
inference(subst,[],[refute_0_4:[bind(N,$fot(X_9))]]) ).
cnf(refute_0_6,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_7,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_8,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( sum(s(X_9)) != s(add(X_9,sum(X_9)))
| s(add(X_9,sum(X_9))) = sum(s(X_9)) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(sum(s(X_9)))),bind(Y0,$fot(s(add(X_9,sum(X_9)))))]]) ).
cnf(refute_0_10,plain,
s(add(X_9,sum(X_9))) = sum(s(X_9)),
inference(resolve,[$cnf( $equal(sum(s(X_9)),s(add(X_9,sum(X_9)))) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
( add(s(add(X_9,sum(X_9))),Y) != s(add(add(X_9,sum(X_9)),Y))
| s(add(X_9,sum(X_9))) != sum(s(X_9))
| add(sum(s(X_9)),Y) = s(add(add(X_9,sum(X_9)),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(add(s(add(X_9,sum(X_9))),Y),s(add(add(X_9,sum(X_9)),Y))) ),[0,0],$fot(sum(s(X_9)))]]) ).
cnf(refute_0_12,plain,
( add(s(add(X_9,sum(X_9))),Y) != s(add(add(X_9,sum(X_9)),Y))
| add(sum(s(X_9)),Y) = s(add(add(X_9,sum(X_9)),Y)) ),
inference(resolve,[$cnf( $equal(s(add(X_9,sum(X_9))),sum(s(X_9))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
add(sum(s(X_9)),Y) = s(add(add(X_9,sum(X_9)),Y)),
inference(resolve,[$cnf( $equal(add(s(add(X_9,sum(X_9))),Y),s(add(add(X_9,sum(X_9)),Y))) )],[refute_0_0,refute_0_12]) ).
cnf(refute_0_14,plain,
( add(X,add(Y,Z)) != add(add(X,Y),Z)
| add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(add(X,add(Y,Z)))),bind(Y0,$fot(add(add(X,Y),Z)))]]) ).
cnf(refute_0_15,plain,
add(add(X,Y),Z) = add(X,add(Y,Z)),
inference(resolve,[$cnf( $equal(add(X,add(Y,Z)),add(add(X,Y),Z)) )],[plus_assoc,refute_0_14]) ).
cnf(refute_0_16,plain,
add(add(X_9,sum(X_9)),Y) = add(X_9,add(sum(X_9),Y)),
inference(subst,[],[refute_0_15:[bind(X,$fot(X_9)),bind(Y,$fot(sum(X_9))),bind(Z,$fot(Y))]]) ).
cnf(refute_0_17,plain,
s(add(add(X_9,sum(X_9)),Y)) = s(add(add(X_9,sum(X_9)),Y)),
introduced(tautology,[refl,[$fot(s(add(add(X_9,sum(X_9)),Y)))]]) ).
cnf(refute_0_18,plain,
( add(add(X_9,sum(X_9)),Y) != add(X_9,add(sum(X_9),Y))
| s(add(add(X_9,sum(X_9)),Y)) != s(add(add(X_9,sum(X_9)),Y))
| s(add(add(X_9,sum(X_9)),Y)) = s(add(X_9,add(sum(X_9),Y))) ),
introduced(tautology,[equality,[$cnf( $equal(s(add(add(X_9,sum(X_9)),Y)),s(add(add(X_9,sum(X_9)),Y))) ),[1,0],$fot(add(X_9,add(sum(X_9),Y)))]]) ).
cnf(refute_0_19,plain,
( add(add(X_9,sum(X_9)),Y) != add(X_9,add(sum(X_9),Y))
| s(add(add(X_9,sum(X_9)),Y)) = s(add(X_9,add(sum(X_9),Y))) ),
inference(resolve,[$cnf( $equal(s(add(add(X_9,sum(X_9)),Y)),s(add(add(X_9,sum(X_9)),Y))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
s(add(add(X_9,sum(X_9)),Y)) = s(add(X_9,add(sum(X_9),Y))),
inference(resolve,[$cnf( $equal(add(add(X_9,sum(X_9)),Y),add(X_9,add(sum(X_9),Y))) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
( add(sum(s(X_9)),Y) != s(add(add(X_9,sum(X_9)),Y))
| s(add(add(X_9,sum(X_9)),Y)) != s(add(X_9,add(sum(X_9),Y)))
| add(sum(s(X_9)),Y) = s(add(X_9,add(sum(X_9),Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(sum(s(X_9)),Y),s(add(X_9,add(sum(X_9),Y)))) ),[0],$fot(s(add(add(X_9,sum(X_9)),Y)))]]) ).
cnf(refute_0_22,plain,
( add(sum(s(X_9)),Y) != s(add(add(X_9,sum(X_9)),Y))
| add(sum(s(X_9)),Y) = s(add(X_9,add(sum(X_9),Y))) ),
inference(resolve,[$cnf( $equal(s(add(add(X_9,sum(X_9)),Y)),s(add(X_9,add(sum(X_9),Y)))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
add(sum(s(X_9)),Y) = s(add(X_9,add(sum(X_9),Y))),
inference(resolve,[$cnf( $equal(add(sum(s(X_9)),Y),s(add(add(X_9,sum(X_9)),Y))) )],[refute_0_13,refute_0_22]) ).
cnf(refute_0_24,plain,
add(sum(s(a)),sum(s(a))) = s(add(a,add(sum(a),sum(s(a))))),
inference(subst,[],[refute_0_23:[bind(Y,$fot(sum(s(a)))),bind(X_9,$fot(a))]]) ).
cnf(refute_0_25,plain,
add(sum(s(a)),sum(a)) = s(add(a,add(sum(a),sum(a)))),
inference(subst,[],[refute_0_23:[bind(Y,$fot(sum(a))),bind(X_9,$fot(a))]]) ).
cnf(refute_0_26,plain,
( add(sum(a),sum(a)) != times(a,s(a))
| add(sum(s(a)),sum(a)) != s(add(a,add(sum(a),sum(a))))
| add(sum(s(a)),sum(a)) = s(add(a,times(a,s(a)))) ),
introduced(tautology,[equality,[$cnf( $equal(add(sum(s(a)),sum(a)),s(add(a,add(sum(a),sum(a))))) ),[1,0,1],$fot(times(a,s(a)))]]) ).
cnf(refute_0_27,plain,
( add(sum(s(a)),sum(a)) != s(add(a,add(sum(a),sum(a))))
| add(sum(s(a)),sum(a)) = s(add(a,times(a,s(a)))) ),
inference(resolve,[$cnf( $equal(add(sum(a),sum(a)),times(a,s(a))) )],[induction_hypothesis,refute_0_26]) ).
cnf(refute_0_28,plain,
add(sum(s(a)),sum(a)) = s(add(a,times(a,s(a)))),
inference(resolve,[$cnf( $equal(add(sum(s(a)),sum(a)),s(add(a,add(sum(a),sum(a))))) )],[refute_0_25,refute_0_27]) ).
cnf(refute_0_29,plain,
( add(X,Y) != add(Y,X)
| add(Y,X) = add(X,Y) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(add(X,Y))),bind(Y0,$fot(add(Y,X)))]]) ).
cnf(refute_0_30,plain,
add(Y,X) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X,Y),add(Y,X)) )],[plus_comm,refute_0_29]) ).
cnf(refute_0_31,plain,
add(sum(s(a)),sum(a)) = add(sum(a),sum(s(a))),
inference(subst,[],[refute_0_30:[bind(X,$fot(sum(a))),bind(Y,$fot(sum(s(a))))]]) ).
cnf(refute_0_32,plain,
( add(sum(s(a)),sum(a)) != add(sum(a),sum(s(a)))
| add(sum(s(a)),sum(a)) != s(add(a,times(a,s(a))))
| add(sum(a),sum(s(a))) = s(add(a,times(a,s(a)))) ),
introduced(tautology,[equality,[$cnf( $equal(add(sum(s(a)),sum(a)),s(add(a,times(a,s(a))))) ),[0],$fot(add(sum(a),sum(s(a))))]]) ).
cnf(refute_0_33,plain,
( add(sum(s(a)),sum(a)) != s(add(a,times(a,s(a))))
| add(sum(a),sum(s(a))) = s(add(a,times(a,s(a)))) ),
inference(resolve,[$cnf( $equal(add(sum(s(a)),sum(a)),add(sum(a),sum(s(a)))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
add(s(X),times(X_10,s(X))) = s(add(X,times(X_10,s(X)))),
inference(subst,[],[plus_s:[bind(Y,$fot(times(X_10,s(X))))]]) ).
cnf(refute_0_35,plain,
times(s(X_10),s(X)) = add(s(X),times(X_10,s(X))),
inference(subst,[],[times_s:[bind(X,$fot(X_10)),bind(Y,$fot(s(X)))]]) ).
cnf(refute_0_36,plain,
( times(s(X_10),s(X)) != add(s(X),times(X_10,s(X)))
| add(s(X),times(X_10,s(X))) = times(s(X_10),s(X)) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(times(s(X_10),s(X)))),bind(Y0,$fot(add(s(X),times(X_10,s(X)))))]]) ).
cnf(refute_0_37,plain,
add(s(X),times(X_10,s(X))) = times(s(X_10),s(X)),
inference(resolve,[$cnf( $equal(times(s(X_10),s(X)),add(s(X),times(X_10,s(X)))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( add(s(X),times(X_10,s(X))) != s(add(X,times(X_10,s(X))))
| add(s(X),times(X_10,s(X))) != times(s(X_10),s(X))
| times(s(X_10),s(X)) = s(add(X,times(X_10,s(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(add(s(X),times(X_10,s(X))),s(add(X,times(X_10,s(X))))) ),[0],$fot(times(s(X_10),s(X)))]]) ).
cnf(refute_0_39,plain,
( add(s(X),times(X_10,s(X))) != s(add(X,times(X_10,s(X))))
| times(s(X_10),s(X)) = s(add(X,times(X_10,s(X)))) ),
inference(resolve,[$cnf( $equal(add(s(X),times(X_10,s(X))),times(s(X_10),s(X))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
times(s(X_10),s(X)) = s(add(X,times(X_10,s(X)))),
inference(resolve,[$cnf( $equal(add(s(X),times(X_10,s(X))),s(add(X,times(X_10,s(X))))) )],[refute_0_34,refute_0_39]) ).
cnf(refute_0_41,plain,
( times(s(X_10),s(X)) != s(add(X,times(X_10,s(X))))
| s(add(X,times(X_10,s(X)))) = times(s(X_10),s(X)) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(times(s(X_10),s(X)))),bind(Y0,$fot(s(add(X,times(X_10,s(X))))))]]) ).
cnf(refute_0_42,plain,
s(add(X,times(X_10,s(X)))) = times(s(X_10),s(X)),
inference(resolve,[$cnf( $equal(times(s(X_10),s(X)),s(add(X,times(X_10,s(X))))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
s(add(a,times(a,s(a)))) = times(s(a),s(a)),
inference(subst,[],[refute_0_42:[bind(X,$fot(a)),bind(X_10,$fot(a))]]) ).
cnf(refute_0_44,plain,
( add(sum(a),sum(s(a))) != s(add(a,times(a,s(a))))
| s(add(a,times(a,s(a)))) != times(s(a),s(a))
| add(sum(a),sum(s(a))) = times(s(a),s(a)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(sum(a),sum(s(a))),times(s(a),s(a))) ),[0],$fot(s(add(a,times(a,s(a)))))]]) ).
cnf(refute_0_45,plain,
( add(sum(a),sum(s(a))) != s(add(a,times(a,s(a))))
| add(sum(a),sum(s(a))) = times(s(a),s(a)) ),
inference(resolve,[$cnf( $equal(s(add(a,times(a,s(a)))),times(s(a),s(a))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( add(sum(s(a)),sum(a)) != s(add(a,times(a,s(a))))
| add(sum(a),sum(s(a))) = times(s(a),s(a)) ),
inference(resolve,[$cnf( $equal(add(sum(a),sum(s(a))),s(add(a,times(a,s(a))))) )],[refute_0_33,refute_0_45]) ).
cnf(refute_0_47,plain,
add(sum(a),sum(s(a))) = times(s(a),s(a)),
inference(resolve,[$cnf( $equal(add(sum(s(a)),sum(a)),s(add(a,times(a,s(a))))) )],[refute_0_28,refute_0_46]) ).
cnf(refute_0_48,plain,
( add(sum(a),sum(s(a))) != times(s(a),s(a))
| add(sum(s(a)),sum(s(a))) != s(add(a,add(sum(a),sum(s(a)))))
| add(sum(s(a)),sum(s(a))) = s(add(a,times(s(a),s(a)))) ),
introduced(tautology,[equality,[$cnf( $equal(add(sum(s(a)),sum(s(a))),s(add(a,add(sum(a),sum(s(a)))))) ),[1,0,1],$fot(times(s(a),s(a)))]]) ).
cnf(refute_0_49,plain,
( add(sum(s(a)),sum(s(a))) != s(add(a,add(sum(a),sum(s(a)))))
| add(sum(s(a)),sum(s(a))) = s(add(a,times(s(a),s(a)))) ),
inference(resolve,[$cnf( $equal(add(sum(a),sum(s(a))),times(s(a),s(a))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
add(sum(s(a)),sum(s(a))) = s(add(a,times(s(a),s(a)))),
inference(resolve,[$cnf( $equal(add(sum(s(a)),sum(s(a))),s(add(a,add(sum(a),sum(s(a)))))) )],[refute_0_24,refute_0_49]) ).
cnf(refute_0_51,plain,
( times(X,Y) != times(Y,X)
| times(Y,X) = times(X,Y) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(times(X,Y))),bind(Y0,$fot(times(Y,X)))]]) ).
cnf(refute_0_52,plain,
times(Y,X) = times(X,Y),
inference(resolve,[$cnf( $equal(times(X,Y),times(Y,X)) )],[times_comm,refute_0_51]) ).
cnf(refute_0_53,plain,
times(sum(s(a)),s(one)) = times(s(one),sum(s(a))),
inference(subst,[],[refute_0_52:[bind(X,$fot(s(one))),bind(Y,$fot(sum(s(a))))]]) ).
cnf(refute_0_54,plain,
times(X,s(one)) = times(s(one),X),
inference(subst,[],[times_comm:[bind(Y,$fot(s(one)))]]) ).
cnf(refute_0_55,plain,
times(s(one),X_11) = add(X_11,times(one,X_11)),
inference(subst,[],[times_s:[bind(X,$fot(one)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_56,plain,
times(X,one) = times(one,X),
inference(subst,[],[times_comm:[bind(Y,$fot(one))]]) ).
cnf(refute_0_57,plain,
( times(X,one) != X
| times(X,one) != times(one,X)
| times(one,X) = X ),
introduced(tautology,[equality,[$cnf( $equal(times(X,one),X) ),[0],$fot(times(one,X))]]) ).
cnf(refute_0_58,plain,
( times(X,one) != X
| times(one,X) = X ),
inference(resolve,[$cnf( $equal(times(X,one),times(one,X)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
times(one,X) = X,
inference(resolve,[$cnf( $equal(times(X,one),X) )],[times_one,refute_0_58]) ).
cnf(refute_0_60,plain,
times(one,X_11) = X_11,
inference(subst,[],[refute_0_59:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_61,plain,
( times(one,X_11) != X_11
| times(s(one),X_11) != add(X_11,times(one,X_11))
| times(s(one),X_11) = add(X_11,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(times(s(one),X_11),add(X_11,times(one,X_11))) ),[1,1],$fot(X_11)]]) ).
cnf(refute_0_62,plain,
( times(s(one),X_11) != add(X_11,times(one,X_11))
| times(s(one),X_11) = add(X_11,X_11) ),
inference(resolve,[$cnf( $equal(times(one,X_11),X_11) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
times(s(one),X_11) = add(X_11,X_11),
inference(resolve,[$cnf( $equal(times(s(one),X_11),add(X_11,times(one,X_11))) )],[refute_0_55,refute_0_62]) ).
cnf(refute_0_64,plain,
times(s(one),X) = add(X,X),
inference(subst,[],[refute_0_63:[bind(X_11,$fot(X))]]) ).
cnf(refute_0_65,plain,
( times(X,s(one)) != times(s(one),X)
| times(s(one),X) != add(X,X)
| times(X,s(one)) = add(X,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(times(X,s(one)),add(X,X)) ),[0],$fot(times(s(one),X))]]) ).
cnf(refute_0_66,plain,
( times(X,s(one)) != times(s(one),X)
| times(X,s(one)) = add(X,X) ),
inference(resolve,[$cnf( $equal(times(s(one),X),add(X,X)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
times(X,s(one)) = add(X,X),
inference(resolve,[$cnf( $equal(times(X,s(one)),times(s(one),X)) )],[refute_0_54,refute_0_66]) ).
cnf(refute_0_68,plain,
( times(X,s(one)) != add(X,X)
| add(X,X) = times(X,s(one)) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(times(X,s(one)))),bind(Y0,$fot(add(X,X)))]]) ).
cnf(refute_0_69,plain,
add(X,X) = times(X,s(one)),
inference(resolve,[$cnf( $equal(times(X,s(one)),add(X,X)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
add(sum(s(a)),sum(s(a))) = times(sum(s(a)),s(one)),
inference(subst,[],[refute_0_69:[bind(X,$fot(sum(s(a))))]]) ).
cnf(refute_0_71,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_72,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_8,refute_0_71]) ).
cnf(refute_0_73,plain,
( add(sum(s(a)),sum(s(a))) != times(sum(s(a)),s(one))
| times(sum(s(a)),s(one)) != times(s(one),sum(s(a)))
| add(sum(s(a)),sum(s(a))) = times(s(one),sum(s(a))) ),
inference(subst,[],[refute_0_72:[bind(X0,$fot(add(sum(s(a)),sum(s(a))))),bind(Y0,$fot(times(sum(s(a)),s(one)))),bind(Z0,$fot(times(s(one),sum(s(a)))))]]) ).
cnf(refute_0_74,plain,
( times(sum(s(a)),s(one)) != times(s(one),sum(s(a)))
| add(sum(s(a)),sum(s(a))) = times(s(one),sum(s(a))) ),
inference(resolve,[$cnf( $equal(add(sum(s(a)),sum(s(a))),times(sum(s(a)),s(one))) )],[refute_0_70,refute_0_73]) ).
cnf(refute_0_75,plain,
add(sum(s(a)),sum(s(a))) = times(s(one),sum(s(a))),
inference(resolve,[$cnf( $equal(times(sum(s(a)),s(one)),times(s(one),sum(s(a)))) )],[refute_0_53,refute_0_74]) ).
cnf(refute_0_76,plain,
( add(sum(s(a)),sum(s(a))) != s(add(a,times(s(a),s(a))))
| add(sum(s(a)),sum(s(a))) != times(s(one),sum(s(a)))
| times(s(one),sum(s(a))) = s(add(a,times(s(a),s(a)))) ),
introduced(tautology,[equality,[$cnf( $equal(add(sum(s(a)),sum(s(a))),s(add(a,times(s(a),s(a))))) ),[0],$fot(times(s(one),sum(s(a))))]]) ).
cnf(refute_0_77,plain,
( add(sum(s(a)),sum(s(a))) != s(add(a,times(s(a),s(a))))
| times(s(one),sum(s(a))) = s(add(a,times(s(a),s(a)))) ),
inference(resolve,[$cnf( $equal(add(sum(s(a)),sum(s(a))),times(s(one),sum(s(a)))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
times(s(s(a)),s(a)) = times(s(a),s(s(a))),
inference(subst,[],[refute_0_52:[bind(X,$fot(s(a))),bind(Y,$fot(s(s(a))))]]) ).
cnf(refute_0_79,plain,
add(s(X),times(s(X),X_22)) = s(add(X,times(s(X),X_22))),
inference(subst,[],[plus_s:[bind(Y,$fot(times(s(X),X_22)))]]) ).
cnf(refute_0_80,plain,
times(s(X_10),X_11) = add(X_11,times(X_10,X_11)),
inference(subst,[],[times_s:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_81,plain,
times(X_11,X_10) = times(X_10,X_11),
inference(subst,[],[times_comm:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_82,plain,
( times(X_11,X_10) != times(X_10,X_11)
| times(X_10,X_11) = times(X_11,X_10) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(times(X_11,X_10))),bind(Y0,$fot(times(X_10,X_11)))]]) ).
cnf(refute_0_83,plain,
times(X_10,X_11) = times(X_11,X_10),
inference(resolve,[$cnf( $equal(times(X_11,X_10),times(X_10,X_11)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
( times(X_10,X_11) != times(X_11,X_10)
| times(s(X_10),X_11) != add(X_11,times(X_10,X_11))
| times(s(X_10),X_11) = add(X_11,times(X_11,X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(times(s(X_10),X_11),add(X_11,times(X_10,X_11))) ),[1,1],$fot(times(X_11,X_10))]]) ).
cnf(refute_0_85,plain,
( times(s(X_10),X_11) != add(X_11,times(X_10,X_11))
| times(s(X_10),X_11) = add(X_11,times(X_11,X_10)) ),
inference(resolve,[$cnf( $equal(times(X_10,X_11),times(X_11,X_10)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
times(s(X_10),X_11) = add(X_11,times(X_11,X_10)),
inference(resolve,[$cnf( $equal(times(s(X_10),X_11),add(X_11,times(X_10,X_11))) )],[refute_0_80,refute_0_85]) ).
cnf(refute_0_87,plain,
times(s(X_22),s(X)) = add(s(X),times(s(X),X_22)),
inference(subst,[],[refute_0_86:[bind(X_10,$fot(X_22)),bind(X_11,$fot(s(X)))]]) ).
cnf(refute_0_88,plain,
( times(s(X_22),s(X)) != add(s(X),times(s(X),X_22))
| add(s(X),times(s(X),X_22)) = times(s(X_22),s(X)) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(times(s(X_22),s(X)))),bind(Y0,$fot(add(s(X),times(s(X),X_22))))]]) ).
cnf(refute_0_89,plain,
add(s(X),times(s(X),X_22)) = times(s(X_22),s(X)),
inference(resolve,[$cnf( $equal(times(s(X_22),s(X)),add(s(X),times(s(X),X_22))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( add(s(X),times(s(X),X_22)) != s(add(X,times(s(X),X_22)))
| add(s(X),times(s(X),X_22)) != times(s(X_22),s(X))
| times(s(X_22),s(X)) = s(add(X,times(s(X),X_22))) ),
introduced(tautology,[equality,[$cnf( $equal(add(s(X),times(s(X),X_22)),s(add(X,times(s(X),X_22)))) ),[0],$fot(times(s(X_22),s(X)))]]) ).
cnf(refute_0_91,plain,
( add(s(X),times(s(X),X_22)) != s(add(X,times(s(X),X_22)))
| times(s(X_22),s(X)) = s(add(X,times(s(X),X_22))) ),
inference(resolve,[$cnf( $equal(add(s(X),times(s(X),X_22)),times(s(X_22),s(X))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
times(s(X_22),s(X)) = s(add(X,times(s(X),X_22))),
inference(resolve,[$cnf( $equal(add(s(X),times(s(X),X_22)),s(add(X,times(s(X),X_22)))) )],[refute_0_79,refute_0_91]) ).
cnf(refute_0_93,plain,
( times(s(X_22),s(X)) != s(add(X,times(s(X),X_22)))
| s(add(X,times(s(X),X_22))) = times(s(X_22),s(X)) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(times(s(X_22),s(X)))),bind(Y0,$fot(s(add(X,times(s(X),X_22)))))]]) ).
cnf(refute_0_94,plain,
s(add(X,times(s(X),X_22))) = times(s(X_22),s(X)),
inference(resolve,[$cnf( $equal(times(s(X_22),s(X)),s(add(X,times(s(X),X_22)))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
s(add(a,times(s(a),s(a)))) = times(s(s(a)),s(a)),
inference(subst,[],[refute_0_94:[bind(X,$fot(a)),bind(X_22,$fot(s(a)))]]) ).
cnf(refute_0_96,plain,
( s(add(a,times(s(a),s(a)))) != times(s(s(a)),s(a))
| times(s(s(a)),s(a)) != times(s(a),s(s(a)))
| s(add(a,times(s(a),s(a)))) = times(s(a),s(s(a))) ),
inference(subst,[],[refute_0_72:[bind(X0,$fot(s(add(a,times(s(a),s(a)))))),bind(Y0,$fot(times(s(s(a)),s(a)))),bind(Z0,$fot(times(s(a),s(s(a)))))]]) ).
cnf(refute_0_97,plain,
( times(s(s(a)),s(a)) != times(s(a),s(s(a)))
| s(add(a,times(s(a),s(a)))) = times(s(a),s(s(a))) ),
inference(resolve,[$cnf( $equal(s(add(a,times(s(a),s(a)))),times(s(s(a)),s(a))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
s(add(a,times(s(a),s(a)))) = times(s(a),s(s(a))),
inference(resolve,[$cnf( $equal(times(s(s(a)),s(a)),times(s(a),s(s(a)))) )],[refute_0_78,refute_0_97]) ).
cnf(refute_0_99,plain,
( s(add(a,times(s(a),s(a)))) != times(s(a),s(s(a)))
| times(s(one),sum(s(a))) != s(add(a,times(s(a),s(a))))
| times(s(one),sum(s(a))) = times(s(a),s(s(a))) ),
introduced(tautology,[equality,[$cnf( $equal(times(s(one),sum(s(a))),s(add(a,times(s(a),s(a))))) ),[1],$fot(times(s(a),s(s(a))))]]) ).
cnf(refute_0_100,plain,
( times(s(one),sum(s(a))) != s(add(a,times(s(a),s(a))))
| times(s(one),sum(s(a))) = times(s(a),s(s(a))) ),
inference(resolve,[$cnf( $equal(s(add(a,times(s(a),s(a)))),times(s(a),s(s(a)))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
( add(sum(s(a)),sum(s(a))) != s(add(a,times(s(a),s(a))))
| times(s(one),sum(s(a))) = times(s(a),s(s(a))) ),
inference(resolve,[$cnf( $equal(times(s(one),sum(s(a))),s(add(a,times(s(a),s(a))))) )],[refute_0_77,refute_0_100]) ).
cnf(refute_0_102,plain,
times(s(one),sum(s(a))) = times(s(a),s(s(a))),
inference(resolve,[$cnf( $equal(add(sum(s(a)),sum(s(a))),s(add(a,times(s(a),s(a))))) )],[refute_0_50,refute_0_101]) ).
cnf(refute_0_103,plain,
( add(sum(s(a)),sum(s(a))) != times(s(one),sum(s(a)))
| times(s(one),sum(s(a))) != times(s(a),s(s(a)))
| add(sum(s(a)),sum(s(a))) = times(s(a),s(s(a))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(sum(s(a)),sum(s(a))),times(s(a),s(s(a)))) ),[0],$fot(times(s(one),sum(s(a))))]]) ).
cnf(refute_0_104,plain,
( times(s(one),sum(s(a))) != times(s(a),s(s(a)))
| add(sum(s(a)),sum(s(a))) = times(s(a),s(s(a))) ),
inference(resolve,[$cnf( $equal(add(sum(s(a)),sum(s(a))),times(s(one),sum(s(a)))) )],[refute_0_75,refute_0_103]) ).
cnf(refute_0_105,plain,
times(s(one),sum(s(a))) != times(s(a),s(s(a))),
inference(resolve,[$cnf( $equal(add(sum(s(a)),sum(s(a))),times(s(a),s(s(a)))) )],[refute_0_104,goal]) ).
cnf(refute_0_106,plain,
$false,
inference(resolve,[$cnf( $equal(times(s(one),sum(s(a))),times(s(a),s(s(a)))) )],[refute_0_102,refute_0_105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUN134-1 : TPTP v8.1.0. Released v8.1.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n024.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 : Thu Jun 2 04:30:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.43
%------------------------------------------------------------------------------