TSTP Solution File: BOO009-4 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : BOO009-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 23:44:33 EDT 2022
% Result : Unsatisfiable 0.18s 0.49s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 37
% Syntax : Number of clauses : 122 ( 67 unt; 0 nHn; 59 RR)
% Number of literals : 204 ( 203 equ; 84 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 182 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_of_add,axiom,
add(X,Y) = add(Y,X) ).
cnf(commutativity_of_multiply,axiom,
multiply(X,Y) = multiply(Y,X) ).
cnf(distributivity1,axiom,
add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ).
cnf(distributivity2,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ).
cnf(additive_id1,axiom,
add(X,additive_identity) = X ).
cnf(multiplicative_id1,axiom,
multiply(X,multiplicative_identity) = X ).
cnf(additive_inverse1,axiom,
add(X,inverse(X)) = multiplicative_identity ).
cnf(multiplicative_inverse1,axiom,
multiply(X,inverse(X)) = additive_identity ).
cnf(prove_operation,negated_conjecture,
multiply(a,add(a,b)) != a ).
cnf(refute_0_0,plain,
multiply(X_31,add(inverse(X_31),X_33)) = add(multiply(X_31,inverse(X_31)),multiply(X_31,X_33)),
inference(subst,[],[distributivity2:[bind(X,$fot(X_31)),bind(Y,$fot(inverse(X_31))),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_1,plain,
multiply(X_31,inverse(X_31)) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(X_31))]]) ).
cnf(refute_0_2,plain,
( multiply(X_31,add(inverse(X_31),X_33)) != add(multiply(X_31,inverse(X_31)),multiply(X_31,X_33))
| multiply(X_31,inverse(X_31)) != additive_identity
| multiply(X_31,add(inverse(X_31),X_33)) = add(additive_identity,multiply(X_31,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_31,add(inverse(X_31),X_33)),add(multiply(X_31,inverse(X_31)),multiply(X_31,X_33))) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_3,plain,
( multiply(X_31,add(inverse(X_31),X_33)) != add(multiply(X_31,inverse(X_31)),multiply(X_31,X_33))
| multiply(X_31,add(inverse(X_31),X_33)) = add(additive_identity,multiply(X_31,X_33)) ),
inference(resolve,[$cnf( $equal(multiply(X_31,inverse(X_31)),additive_identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(X_31,add(inverse(X_31),X_33)) = add(additive_identity,multiply(X_31,X_33)),
inference(resolve,[$cnf( $equal(multiply(X_31,add(inverse(X_31),X_33)),add(multiply(X_31,inverse(X_31)),multiply(X_31,X_33))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
add(X,additive_identity) = add(additive_identity,X),
inference(subst,[],[commutativity_of_add:[bind(Y,$fot(additive_identity))]]) ).
cnf(refute_0_6,plain,
( add(X,additive_identity) != X
| add(X,additive_identity) != add(additive_identity,X)
| add(additive_identity,X) = X ),
introduced(tautology,[equality,[$cnf( $equal(add(X,additive_identity),X) ),[0],$fot(add(additive_identity,X))]]) ).
cnf(refute_0_7,plain,
( add(X,additive_identity) != X
| add(additive_identity,X) = X ),
inference(resolve,[$cnf( $equal(add(X,additive_identity),add(additive_identity,X)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
add(additive_identity,X) = X,
inference(resolve,[$cnf( $equal(add(X,additive_identity),X) )],[additive_id1,refute_0_7]) ).
cnf(refute_0_9,plain,
add(additive_identity,multiply(X_31,X_33)) = multiply(X_31,X_33),
inference(subst,[],[refute_0_8:[bind(X,$fot(multiply(X_31,X_33)))]]) ).
cnf(refute_0_10,plain,
( multiply(X_31,add(inverse(X_31),X_33)) != add(additive_identity,multiply(X_31,X_33))
| add(additive_identity,multiply(X_31,X_33)) != multiply(X_31,X_33)
| multiply(X_31,add(inverse(X_31),X_33)) = multiply(X_31,X_33) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_31,add(inverse(X_31),X_33)),multiply(X_31,X_33)) ),[0],$fot(add(additive_identity,multiply(X_31,X_33)))]]) ).
cnf(refute_0_11,plain,
( multiply(X_31,add(inverse(X_31),X_33)) != add(additive_identity,multiply(X_31,X_33))
| multiply(X_31,add(inverse(X_31),X_33)) = multiply(X_31,X_33) ),
inference(resolve,[$cnf( $equal(add(additive_identity,multiply(X_31,X_33)),multiply(X_31,X_33)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
multiply(X_31,add(inverse(X_31),X_33)) = multiply(X_31,X_33),
inference(resolve,[$cnf( $equal(multiply(X_31,add(inverse(X_31),X_33)),add(additive_identity,multiply(X_31,X_33))) )],[refute_0_4,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(X_34,add(inverse(X_34),add(X_34,X_25))) = multiply(X_34,add(X_34,X_25)),
inference(subst,[],[refute_0_12:[bind(X_31,$fot(X_34)),bind(X_33,$fot(add(X_34,X_25)))]]) ).
cnf(refute_0_14,plain,
add(multiply(additive_identity,X_25),Y) = add(Y,multiply(additive_identity,X_25)),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(multiply(additive_identity,X_25)))]]) ).
cnf(refute_0_15,plain,
add(X_10,multiply(additive_identity,X_12)) = multiply(add(X_10,additive_identity),add(X_10,X_12)),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(additive_identity)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_16,plain,
add(X_10,additive_identity) = X_10,
inference(subst,[],[additive_id1:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_17,plain,
( add(X_10,multiply(additive_identity,X_12)) != multiply(add(X_10,additive_identity),add(X_10,X_12))
| add(X_10,additive_identity) != X_10
| add(X_10,multiply(additive_identity,X_12)) = multiply(X_10,add(X_10,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(additive_identity,X_12)),multiply(add(X_10,additive_identity),add(X_10,X_12))) ),[1,0],$fot(X_10)]]) ).
cnf(refute_0_18,plain,
( add(X_10,multiply(additive_identity,X_12)) != multiply(add(X_10,additive_identity),add(X_10,X_12))
| add(X_10,multiply(additive_identity,X_12)) = multiply(X_10,add(X_10,X_12)) ),
inference(resolve,[$cnf( $equal(add(X_10,additive_identity),X_10) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
add(X_10,multiply(additive_identity,X_12)) = multiply(X_10,add(X_10,X_12)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(additive_identity,X_12)),multiply(add(X_10,additive_identity),add(X_10,X_12))) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
add(Y,multiply(additive_identity,X_25)) = multiply(Y,add(Y,X_25)),
inference(subst,[],[refute_0_19:[bind(X_10,$fot(Y)),bind(X_12,$fot(X_25))]]) ).
cnf(refute_0_21,plain,
( add(Y,multiply(additive_identity,X_25)) != multiply(Y,add(Y,X_25))
| add(multiply(additive_identity,X_25),Y) != add(Y,multiply(additive_identity,X_25))
| add(multiply(additive_identity,X_25),Y) = multiply(Y,add(Y,X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_25),Y),add(Y,multiply(additive_identity,X_25))) ),[1],$fot(multiply(Y,add(Y,X_25)))]]) ).
cnf(refute_0_22,plain,
( add(multiply(additive_identity,X_25),Y) != add(Y,multiply(additive_identity,X_25))
| add(multiply(additive_identity,X_25),Y) = multiply(Y,add(Y,X_25)) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(additive_identity,X_25)),multiply(Y,add(Y,X_25))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
add(multiply(additive_identity,X_25),Y) = multiply(Y,add(Y,X_25)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_25),Y),add(Y,multiply(additive_identity,X_25))) )],[refute_0_14,refute_0_22]) ).
cnf(refute_0_24,plain,
add(multiply(additive_identity,X_25),X_34) = multiply(X_34,add(X_34,X_25)),
inference(subst,[],[refute_0_23:[bind(Y,$fot(X_34))]]) ).
cnf(refute_0_25,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_26,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_27,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( add(multiply(additive_identity,X_25),X_34) != multiply(X_34,add(X_34,X_25))
| multiply(X_34,add(X_34,X_25)) = add(multiply(additive_identity,X_25),X_34) ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(add(multiply(additive_identity,X_25),X_34))),bind(Y0,$fot(multiply(X_34,add(X_34,X_25))))]]) ).
cnf(refute_0_29,plain,
multiply(X_34,add(X_34,X_25)) = add(multiply(additive_identity,X_25),X_34),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_25),X_34),multiply(X_34,add(X_34,X_25))) )],[refute_0_24,refute_0_28]) ).
cnf(refute_0_30,plain,
( multiply(X_34,add(X_34,X_25)) != add(multiply(additive_identity,X_25),X_34)
| multiply(X_34,add(inverse(X_34),add(X_34,X_25))) != multiply(X_34,add(X_34,X_25))
| multiply(X_34,add(inverse(X_34),add(X_34,X_25))) = add(multiply(additive_identity,X_25),X_34) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_34,add(inverse(X_34),add(X_34,X_25))),multiply(X_34,add(X_34,X_25))) ),[1],$fot(add(multiply(additive_identity,X_25),X_34))]]) ).
cnf(refute_0_31,plain,
( multiply(X_34,add(inverse(X_34),add(X_34,X_25))) != multiply(X_34,add(X_34,X_25))
| multiply(X_34,add(inverse(X_34),add(X_34,X_25))) = add(multiply(additive_identity,X_25),X_34) ),
inference(resolve,[$cnf( $equal(multiply(X_34,add(X_34,X_25)),add(multiply(additive_identity,X_25),X_34)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
multiply(X_34,add(inverse(X_34),add(X_34,X_25))) = add(multiply(additive_identity,X_25),X_34),
inference(resolve,[$cnf( $equal(multiply(X_34,add(inverse(X_34),add(X_34,X_25))),multiply(X_34,add(X_34,X_25))) )],[refute_0_13,refute_0_31]) ).
cnf(refute_0_33,plain,
( multiply(X_34,add(inverse(X_34),add(X_34,X_25))) != multiply(X_34,add(X_34,X_25))
| multiply(X_34,add(inverse(X_34),add(X_34,X_25))) != add(multiply(additive_identity,X_25),X_34)
| multiply(X_34,add(X_34,X_25)) = add(multiply(additive_identity,X_25),X_34) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_34,add(inverse(X_34),add(X_34,X_25))),add(multiply(additive_identity,X_25),X_34)) ),[0],$fot(multiply(X_34,add(X_34,X_25)))]]) ).
cnf(refute_0_34,plain,
( multiply(X_34,add(inverse(X_34),add(X_34,X_25))) != add(multiply(additive_identity,X_25),X_34)
| multiply(X_34,add(X_34,X_25)) = add(multiply(additive_identity,X_25),X_34) ),
inference(resolve,[$cnf( $equal(multiply(X_34,add(inverse(X_34),add(X_34,X_25))),multiply(X_34,add(X_34,X_25))) )],[refute_0_13,refute_0_33]) ).
cnf(refute_0_35,plain,
add(multiply(additive_identity,add(inverse(additive_identity),X_35)),Y) = multiply(Y,add(Y,add(inverse(additive_identity),X_35))),
inference(subst,[],[refute_0_23:[bind(X_25,$fot(add(inverse(additive_identity),X_35)))]]) ).
cnf(refute_0_36,plain,
multiply(additive_identity,add(inverse(additive_identity),X_35)) = multiply(additive_identity,X_35),
inference(subst,[],[refute_0_12:[bind(X_31,$fot(additive_identity)),bind(X_33,$fot(X_35))]]) ).
cnf(refute_0_37,plain,
( multiply(additive_identity,add(inverse(additive_identity),X_35)) != multiply(additive_identity,X_35)
| add(multiply(additive_identity,add(inverse(additive_identity),X_35)),Y) != multiply(Y,add(Y,add(inverse(additive_identity),X_35)))
| add(multiply(additive_identity,X_35),Y) = multiply(Y,add(Y,add(inverse(additive_identity),X_35))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,add(inverse(additive_identity),X_35)),Y),multiply(Y,add(Y,add(inverse(additive_identity),X_35)))) ),[0,0],$fot(multiply(additive_identity,X_35))]]) ).
cnf(refute_0_38,plain,
( add(multiply(additive_identity,add(inverse(additive_identity),X_35)),Y) != multiply(Y,add(Y,add(inverse(additive_identity),X_35)))
| add(multiply(additive_identity,X_35),Y) = multiply(Y,add(Y,add(inverse(additive_identity),X_35))) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(inverse(additive_identity),X_35)),multiply(additive_identity,X_35)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
add(multiply(additive_identity,X_35),Y) = multiply(Y,add(Y,add(inverse(additive_identity),X_35))),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,add(inverse(additive_identity),X_35)),Y),multiply(Y,add(Y,add(inverse(additive_identity),X_35)))) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
multiply(Y,multiplicative_identity) = Y,
inference(subst,[],[multiplicative_id1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_41,plain,
add(X_10,multiply(inverse(X_10),X_12)) = multiply(add(X_10,inverse(X_10)),add(X_10,X_12)),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(inverse(X_10))),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_42,plain,
add(X_10,inverse(X_10)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_43,plain,
( add(X_10,multiply(inverse(X_10),X_12)) != multiply(add(X_10,inverse(X_10)),add(X_10,X_12))
| add(X_10,inverse(X_10)) != multiplicative_identity
| add(X_10,multiply(inverse(X_10),X_12)) = multiply(multiplicative_identity,add(X_10,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(inverse(X_10),X_12)),multiply(add(X_10,inverse(X_10)),add(X_10,X_12))) ),[1,0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_44,plain,
( add(X_10,multiply(inverse(X_10),X_12)) != multiply(add(X_10,inverse(X_10)),add(X_10,X_12))
| add(X_10,multiply(inverse(X_10),X_12)) = multiply(multiplicative_identity,add(X_10,X_12)) ),
inference(resolve,[$cnf( $equal(add(X_10,inverse(X_10)),multiplicative_identity) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
add(X_10,multiply(inverse(X_10),X_12)) = multiply(multiplicative_identity,add(X_10,X_12)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(inverse(X_10),X_12)),multiply(add(X_10,inverse(X_10)),add(X_10,X_12))) )],[refute_0_41,refute_0_44]) ).
cnf(refute_0_46,plain,
multiply(X,multiplicative_identity) = multiply(multiplicative_identity,X),
inference(subst,[],[commutativity_of_multiply:[bind(Y,$fot(multiplicative_identity))]]) ).
cnf(refute_0_47,plain,
( multiply(X,multiplicative_identity) != X
| multiply(X,multiplicative_identity) != multiply(multiplicative_identity,X)
| multiply(multiplicative_identity,X) = X ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,multiplicative_identity),X) ),[0],$fot(multiply(multiplicative_identity,X))]]) ).
cnf(refute_0_48,plain,
( multiply(X,multiplicative_identity) != X
| multiply(multiplicative_identity,X) = X ),
inference(resolve,[$cnf( $equal(multiply(X,multiplicative_identity),multiply(multiplicative_identity,X)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
multiply(multiplicative_identity,X) = X,
inference(resolve,[$cnf( $equal(multiply(X,multiplicative_identity),X) )],[multiplicative_id1,refute_0_48]) ).
cnf(refute_0_50,plain,
multiply(multiplicative_identity,add(X_10,X_12)) = add(X_10,X_12),
inference(subst,[],[refute_0_49:[bind(X,$fot(add(X_10,X_12)))]]) ).
cnf(refute_0_51,plain,
( multiply(multiplicative_identity,add(X_10,X_12)) != add(X_10,X_12)
| add(X_10,multiply(inverse(X_10),X_12)) != multiply(multiplicative_identity,add(X_10,X_12))
| add(X_10,multiply(inverse(X_10),X_12)) = add(X_10,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(inverse(X_10),X_12)),multiply(multiplicative_identity,add(X_10,X_12))) ),[1],$fot(add(X_10,X_12))]]) ).
cnf(refute_0_52,plain,
( add(X_10,multiply(inverse(X_10),X_12)) != multiply(multiplicative_identity,add(X_10,X_12))
| add(X_10,multiply(inverse(X_10),X_12)) = add(X_10,X_12) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,add(X_10,X_12)),add(X_10,X_12)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
add(X_10,multiply(inverse(X_10),X_12)) = add(X_10,X_12),
inference(resolve,[$cnf( $equal(add(X_10,multiply(inverse(X_10),X_12)),multiply(multiplicative_identity,add(X_10,X_12))) )],[refute_0_45,refute_0_52]) ).
cnf(refute_0_54,plain,
add(X_19,multiply(inverse(X_19),multiplicative_identity)) = add(X_19,multiplicative_identity),
inference(subst,[],[refute_0_53:[bind(X_10,$fot(X_19)),bind(X_12,$fot(multiplicative_identity))]]) ).
cnf(refute_0_55,plain,
multiply(inverse(X_19),multiplicative_identity) = inverse(X_19),
inference(subst,[],[multiplicative_id1:[bind(X,$fot(inverse(X_19)))]]) ).
cnf(refute_0_56,plain,
( multiply(inverse(X_19),multiplicative_identity) != inverse(X_19)
| add(X_19,multiply(inverse(X_19),multiplicative_identity)) != add(X_19,multiplicative_identity)
| add(X_19,inverse(X_19)) = add(X_19,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_19,multiply(inverse(X_19),multiplicative_identity)),add(X_19,multiplicative_identity)) ),[0,1],$fot(inverse(X_19))]]) ).
cnf(refute_0_57,plain,
( add(X_19,multiply(inverse(X_19),multiplicative_identity)) != add(X_19,multiplicative_identity)
| add(X_19,inverse(X_19)) = add(X_19,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_19),multiplicative_identity),inverse(X_19)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
add(X_19,inverse(X_19)) = add(X_19,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_19,multiply(inverse(X_19),multiplicative_identity)),add(X_19,multiplicative_identity)) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
add(X_19,inverse(X_19)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_60,plain,
( add(X_19,inverse(X_19)) != add(X_19,multiplicative_identity)
| add(X_19,inverse(X_19)) != multiplicative_identity
| multiplicative_identity = add(X_19,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_19,inverse(X_19)),add(X_19,multiplicative_identity)) ),[0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_61,plain,
( add(X_19,inverse(X_19)) != add(X_19,multiplicative_identity)
| multiplicative_identity = add(X_19,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(X_19,inverse(X_19)),multiplicative_identity) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
multiplicative_identity = add(X_19,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_19,inverse(X_19)),add(X_19,multiplicative_identity)) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
( multiplicative_identity != add(X_19,multiplicative_identity)
| add(X_19,multiplicative_identity) = multiplicative_identity ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(multiplicative_identity)),bind(Y0,$fot(add(X_19,multiplicative_identity)))]]) ).
cnf(refute_0_64,plain,
add(X_19,multiplicative_identity) = multiplicative_identity,
inference(resolve,[$cnf( $equal(multiplicative_identity,add(X_19,multiplicative_identity)) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
add(Y,multiplicative_identity) = multiplicative_identity,
inference(subst,[],[refute_0_64:[bind(X_19,$fot(Y))]]) ).
cnf(refute_0_66,plain,
add(multiplicative_identity,Y) = add(Y,multiplicative_identity),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(multiplicative_identity))]]) ).
cnf(refute_0_67,plain,
( add(Y,multiplicative_identity) != multiplicative_identity
| add(multiplicative_identity,Y) != add(Y,multiplicative_identity)
| add(multiplicative_identity,Y) = multiplicative_identity ),
introduced(tautology,[equality,[$cnf( $equal(add(multiplicative_identity,Y),add(Y,multiplicative_identity)) ),[1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_68,plain,
( add(multiplicative_identity,Y) != add(Y,multiplicative_identity)
| add(multiplicative_identity,Y) = multiplicative_identity ),
inference(resolve,[$cnf( $equal(add(Y,multiplicative_identity),multiplicative_identity) )],[refute_0_65,refute_0_67]) ).
cnf(refute_0_69,plain,
add(multiplicative_identity,Y) = multiplicative_identity,
inference(resolve,[$cnf( $equal(add(multiplicative_identity,Y),add(Y,multiplicative_identity)) )],[refute_0_66,refute_0_68]) ).
cnf(refute_0_70,plain,
add(multiplicative_identity,X_35) = multiplicative_identity,
inference(subst,[],[refute_0_69:[bind(Y,$fot(X_35))]]) ).
cnf(refute_0_71,plain,
add(additive_identity,inverse(additive_identity)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(additive_identity))]]) ).
cnf(refute_0_72,plain,
add(additive_identity,inverse(additive_identity)) = inverse(additive_identity),
inference(subst,[],[refute_0_8:[bind(X,$fot(inverse(additive_identity)))]]) ).
cnf(refute_0_73,plain,
( add(additive_identity,inverse(additive_identity)) != inverse(additive_identity)
| add(additive_identity,inverse(additive_identity)) != multiplicative_identity
| inverse(additive_identity) = multiplicative_identity ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_identity,inverse(additive_identity)),multiplicative_identity) ),[0],$fot(inverse(additive_identity))]]) ).
cnf(refute_0_74,plain,
( add(additive_identity,inverse(additive_identity)) != multiplicative_identity
| inverse(additive_identity) = multiplicative_identity ),
inference(resolve,[$cnf( $equal(add(additive_identity,inverse(additive_identity)),inverse(additive_identity)) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
inverse(additive_identity) = multiplicative_identity,
inference(resolve,[$cnf( $equal(add(additive_identity,inverse(additive_identity)),multiplicative_identity) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
add(inverse(additive_identity),X_35) = add(inverse(additive_identity),X_35),
introduced(tautology,[refl,[$fot(add(inverse(additive_identity),X_35))]]) ).
cnf(refute_0_77,plain,
( add(inverse(additive_identity),X_35) != add(inverse(additive_identity),X_35)
| inverse(additive_identity) != multiplicative_identity
| add(inverse(additive_identity),X_35) = add(multiplicative_identity,X_35) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(additive_identity),X_35),add(inverse(additive_identity),X_35)) ),[1,0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_78,plain,
( inverse(additive_identity) != multiplicative_identity
| add(inverse(additive_identity),X_35) = add(multiplicative_identity,X_35) ),
inference(resolve,[$cnf( $equal(add(inverse(additive_identity),X_35),add(inverse(additive_identity),X_35)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
add(inverse(additive_identity),X_35) = add(multiplicative_identity,X_35),
inference(resolve,[$cnf( $equal(inverse(additive_identity),multiplicative_identity) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_81,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_27,refute_0_80]) ).
cnf(refute_0_82,plain,
( add(inverse(additive_identity),X_35) != add(multiplicative_identity,X_35)
| add(multiplicative_identity,X_35) != multiplicative_identity
| add(inverse(additive_identity),X_35) = multiplicative_identity ),
inference(subst,[],[refute_0_81:[bind(X0,$fot(add(inverse(additive_identity),X_35))),bind(Y0,$fot(add(multiplicative_identity,X_35))),bind(Z0,$fot(multiplicative_identity))]]) ).
cnf(refute_0_83,plain,
( add(multiplicative_identity,X_35) != multiplicative_identity
| add(inverse(additive_identity),X_35) = multiplicative_identity ),
inference(resolve,[$cnf( $equal(add(inverse(additive_identity),X_35),add(multiplicative_identity,X_35)) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
add(inverse(additive_identity),X_35) = multiplicative_identity,
inference(resolve,[$cnf( $equal(add(multiplicative_identity,X_35),multiplicative_identity) )],[refute_0_70,refute_0_83]) ).
cnf(refute_0_85,plain,
add(Y,add(inverse(additive_identity),X_35)) = add(Y,add(inverse(additive_identity),X_35)),
introduced(tautology,[refl,[$fot(add(Y,add(inverse(additive_identity),X_35)))]]) ).
cnf(refute_0_86,plain,
( add(Y,add(inverse(additive_identity),X_35)) != add(Y,add(inverse(additive_identity),X_35))
| add(inverse(additive_identity),X_35) != multiplicative_identity
| add(Y,add(inverse(additive_identity),X_35)) = add(Y,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(Y,add(inverse(additive_identity),X_35)),add(Y,add(inverse(additive_identity),X_35))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_87,plain,
( add(inverse(additive_identity),X_35) != multiplicative_identity
| add(Y,add(inverse(additive_identity),X_35)) = add(Y,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(Y,add(inverse(additive_identity),X_35)),add(Y,add(inverse(additive_identity),X_35))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
add(Y,add(inverse(additive_identity),X_35)) = add(Y,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(inverse(additive_identity),X_35),multiplicative_identity) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
( add(Y,add(inverse(additive_identity),X_35)) != add(Y,multiplicative_identity)
| add(Y,multiplicative_identity) != multiplicative_identity
| add(Y,add(inverse(additive_identity),X_35)) = multiplicative_identity ),
inference(subst,[],[refute_0_81:[bind(X0,$fot(add(Y,add(inverse(additive_identity),X_35)))),bind(Y0,$fot(add(Y,multiplicative_identity))),bind(Z0,$fot(multiplicative_identity))]]) ).
cnf(refute_0_90,plain,
( add(Y,multiplicative_identity) != multiplicative_identity
| add(Y,add(inverse(additive_identity),X_35)) = multiplicative_identity ),
inference(resolve,[$cnf( $equal(add(Y,add(inverse(additive_identity),X_35)),add(Y,multiplicative_identity)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
add(Y,add(inverse(additive_identity),X_35)) = multiplicative_identity,
inference(resolve,[$cnf( $equal(add(Y,multiplicative_identity),multiplicative_identity) )],[refute_0_65,refute_0_90]) ).
cnf(refute_0_92,plain,
multiply(Y,add(Y,add(inverse(additive_identity),X_35))) = multiply(Y,add(Y,add(inverse(additive_identity),X_35))),
introduced(tautology,[refl,[$fot(multiply(Y,add(Y,add(inverse(additive_identity),X_35))))]]) ).
cnf(refute_0_93,plain,
( multiply(Y,add(Y,add(inverse(additive_identity),X_35))) != multiply(Y,add(Y,add(inverse(additive_identity),X_35)))
| add(Y,add(inverse(additive_identity),X_35)) != multiplicative_identity
| multiply(Y,add(Y,add(inverse(additive_identity),X_35))) = multiply(Y,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(Y,add(Y,add(inverse(additive_identity),X_35))),multiply(Y,add(Y,add(inverse(additive_identity),X_35)))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_94,plain,
( add(Y,add(inverse(additive_identity),X_35)) != multiplicative_identity
| multiply(Y,add(Y,add(inverse(additive_identity),X_35))) = multiply(Y,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(multiply(Y,add(Y,add(inverse(additive_identity),X_35))),multiply(Y,add(Y,add(inverse(additive_identity),X_35)))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
multiply(Y,add(Y,add(inverse(additive_identity),X_35))) = multiply(Y,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(Y,add(inverse(additive_identity),X_35)),multiplicative_identity) )],[refute_0_91,refute_0_94]) ).
cnf(refute_0_96,plain,
( multiply(Y,add(Y,add(inverse(additive_identity),X_35))) != multiply(Y,multiplicative_identity)
| multiply(Y,multiplicative_identity) != Y
| multiply(Y,add(Y,add(inverse(additive_identity),X_35))) = Y ),
inference(subst,[],[refute_0_81:[bind(X0,$fot(multiply(Y,add(Y,add(inverse(additive_identity),X_35))))),bind(Y0,$fot(multiply(Y,multiplicative_identity))),bind(Z0,$fot(Y))]]) ).
cnf(refute_0_97,plain,
( multiply(Y,multiplicative_identity) != Y
| multiply(Y,add(Y,add(inverse(additive_identity),X_35))) = Y ),
inference(resolve,[$cnf( $equal(multiply(Y,add(Y,add(inverse(additive_identity),X_35))),multiply(Y,multiplicative_identity)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
multiply(Y,add(Y,add(inverse(additive_identity),X_35))) = Y,
inference(resolve,[$cnf( $equal(multiply(Y,multiplicative_identity),Y) )],[refute_0_40,refute_0_97]) ).
cnf(refute_0_99,plain,
( multiply(Y,add(Y,add(inverse(additive_identity),X_35))) != Y
| add(multiply(additive_identity,X_35),Y) != multiply(Y,add(Y,add(inverse(additive_identity),X_35)))
| add(multiply(additive_identity,X_35),Y) = Y ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_35),Y),multiply(Y,add(Y,add(inverse(additive_identity),X_35)))) ),[1],$fot(Y)]]) ).
cnf(refute_0_100,plain,
( add(multiply(additive_identity,X_35),Y) != multiply(Y,add(Y,add(inverse(additive_identity),X_35)))
| add(multiply(additive_identity,X_35),Y) = Y ),
inference(resolve,[$cnf( $equal(multiply(Y,add(Y,add(inverse(additive_identity),X_35))),Y) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
add(multiply(additive_identity,X_35),Y) = Y,
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_35),Y),multiply(Y,add(Y,add(inverse(additive_identity),X_35)))) )],[refute_0_39,refute_0_100]) ).
cnf(refute_0_102,plain,
add(multiply(additive_identity,X_25),X_34) = X_34,
inference(subst,[],[refute_0_101:[bind(Y,$fot(X_34)),bind(X_35,$fot(X_25))]]) ).
cnf(refute_0_103,plain,
( multiply(X_34,add(X_34,X_25)) != add(multiply(additive_identity,X_25),X_34)
| add(multiply(additive_identity,X_25),X_34) != X_34
| multiply(X_34,add(X_34,X_25)) = X_34 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_34,add(X_34,X_25)),X_34) ),[0],$fot(add(multiply(additive_identity,X_25),X_34))]]) ).
cnf(refute_0_104,plain,
( multiply(X_34,add(X_34,X_25)) != add(multiply(additive_identity,X_25),X_34)
| multiply(X_34,add(X_34,X_25)) = X_34 ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_25),X_34),X_34) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
( multiply(X_34,add(inverse(X_34),add(X_34,X_25))) != add(multiply(additive_identity,X_25),X_34)
| multiply(X_34,add(X_34,X_25)) = X_34 ),
inference(resolve,[$cnf( $equal(multiply(X_34,add(X_34,X_25)),add(multiply(additive_identity,X_25),X_34)) )],[refute_0_34,refute_0_104]) ).
cnf(refute_0_106,plain,
multiply(X_34,add(X_34,X_25)) = X_34,
inference(resolve,[$cnf( $equal(multiply(X_34,add(inverse(X_34),add(X_34,X_25))),add(multiply(additive_identity,X_25),X_34)) )],[refute_0_32,refute_0_105]) ).
cnf(refute_0_107,plain,
multiply(a,add(a,b)) = a,
inference(subst,[],[refute_0_106:[bind(X_25,$fot(b)),bind(X_34,$fot(a))]]) ).
cnf(refute_0_108,plain,
( multiply(a,add(a,b)) != a
| a != a
| multiply(a,add(a,b)) = a ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,add(a,b)),a) ),[0],$fot(a)]]) ).
cnf(refute_0_109,plain,
( a != a
| multiply(a,add(a,b)) = a ),
inference(resolve,[$cnf( $equal(multiply(a,add(a,b)),a) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
a != a,
inference(resolve,[$cnf( $equal(multiply(a,add(a,b)),a) )],[refute_0_109,prove_operation]) ).
cnf(refute_0_111,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_112,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_111,refute_0_110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO009-4 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n018.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 1 23:48:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.49
% 0.18/0.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.51
%------------------------------------------------------------------------------