TSTP Solution File: BOO012-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : BOO012-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 23:44:34 EDT 2022
% Result : Unsatisfiable 0.45s 0.61s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 23
% Syntax : Number of clauses : 66 ( 38 unt; 0 nHn; 33 RR)
% Number of literals : 106 ( 105 equ; 42 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_of_add,axiom,
add(X,Y) = add(Y,X) ).
cnf(distributivity1,axiom,
add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ).
cnf(distributivity2,axiom,
add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ).
cnf(additive_inverse1,axiom,
add(X,inverse(X)) = multiplicative_identity ).
cnf(multiplicative_inverse1,axiom,
multiply(X,inverse(X)) = additive_identity ).
cnf(multiplicative_id1,axiom,
multiply(X,multiplicative_identity) = X ).
cnf(multiplicative_id2,axiom,
multiply(multiplicative_identity,X) = X ).
cnf(additive_id1,axiom,
add(X,additive_identity) = X ).
cnf(prove_inverse_is_an_involution,negated_conjecture,
inverse(inverse(x)) != x ).
cnf(refute_0_0,plain,
add(multiply(X_10,X_11),inverse(X_11)) = multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11))),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(inverse(X_11)))]]) ).
cnf(refute_0_1,plain,
add(X_11,inverse(X_11)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_2,plain,
( add(X_11,inverse(X_11)) != multiplicative_identity
| add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11)))
| add(multiply(X_10,X_11),inverse(X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11)))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_3,plain,
( add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11)))
| add(multiply(X_10,X_11),inverse(X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(X_11,inverse(X_11)),multiplicative_identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
add(multiply(X_10,X_11),inverse(X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity),
inference(resolve,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11)))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( add(X,Y) != add(Y,X)
| add(Y,X) = add(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(add(X,Y))),bind(Y0,$fot(add(Y,X)))]]) ).
cnf(refute_0_9,plain,
add(Y,X) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X,Y),add(Y,X)) )],[commutativity_of_add,refute_0_8]) ).
cnf(refute_0_10,plain,
add(multiply(X_10,X_11),inverse(X_11)) = add(inverse(X_11),multiply(X_10,X_11)),
inference(subst,[],[refute_0_9:[bind(X,$fot(inverse(X_11))),bind(Y,$fot(multiply(X_10,X_11)))]]) ).
cnf(refute_0_11,plain,
( add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(multiply(X_10,X_11),inverse(X_11)) != add(inverse(X_11),multiply(X_10,X_11))
| add(inverse(X_11),multiply(X_10,X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),multiply(add(X_10,inverse(X_11)),multiplicative_identity)) ),[0],$fot(add(inverse(X_11),multiply(X_10,X_11)))]]) ).
cnf(refute_0_12,plain,
( add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(inverse(X_11),multiply(X_10,X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),add(inverse(X_11),multiply(X_10,X_11))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(add(X_10,inverse(X_11)),multiplicative_identity) = add(X_10,inverse(X_11)),
inference(subst,[],[multiplicative_id1:[bind(X,$fot(add(X_10,inverse(X_11))))]]) ).
cnf(refute_0_14,plain,
( multiply(add(X_10,inverse(X_11)),multiplicative_identity) != add(X_10,inverse(X_11))
| add(inverse(X_11),multiply(X_10,X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(inverse(X_11),multiply(X_10,X_11)) = add(X_10,inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(X_11),multiply(X_10,X_11)),multiply(add(X_10,inverse(X_11)),multiplicative_identity)) ),[1],$fot(add(X_10,inverse(X_11)))]]) ).
cnf(refute_0_15,plain,
( add(inverse(X_11),multiply(X_10,X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(inverse(X_11),multiply(X_10,X_11)) = add(X_10,inverse(X_11)) ),
inference(resolve,[$cnf( $equal(multiply(add(X_10,inverse(X_11)),multiplicative_identity),add(X_10,inverse(X_11))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(inverse(X_11),multiply(X_10,X_11)) = add(X_10,inverse(X_11)) ),
inference(resolve,[$cnf( $equal(add(inverse(X_11),multiply(X_10,X_11)),multiply(add(X_10,inverse(X_11)),multiplicative_identity)) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
add(inverse(X_11),multiply(X_10,X_11)) = add(X_10,inverse(X_11)),
inference(resolve,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),multiply(add(X_10,inverse(X_11)),multiplicative_identity)) )],[refute_0_4,refute_0_16]) ).
cnf(refute_0_18,plain,
add(inverse(inverse(X_41)),multiply(X_41,inverse(X_41))) = add(X_41,inverse(inverse(X_41))),
inference(subst,[],[refute_0_17:[bind(X_10,$fot(X_41)),bind(X_11,$fot(inverse(X_41)))]]) ).
cnf(refute_0_19,plain,
multiply(X_41,inverse(X_41)) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(X_41))]]) ).
cnf(refute_0_20,plain,
( multiply(X_41,inverse(X_41)) != additive_identity
| add(inverse(inverse(X_41)),multiply(X_41,inverse(X_41))) != add(X_41,inverse(inverse(X_41)))
| add(inverse(inverse(X_41)),additive_identity) = add(X_41,inverse(inverse(X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(inverse(X_41)),multiply(X_41,inverse(X_41))),add(X_41,inverse(inverse(X_41)))) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_21,plain,
( add(inverse(inverse(X_41)),multiply(X_41,inverse(X_41))) != add(X_41,inverse(inverse(X_41)))
| add(inverse(inverse(X_41)),additive_identity) = add(X_41,inverse(inverse(X_41))) ),
inference(resolve,[$cnf( $equal(multiply(X_41,inverse(X_41)),additive_identity) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
add(inverse(inverse(X_41)),additive_identity) = add(X_41,inverse(inverse(X_41))),
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_41)),multiply(X_41,inverse(X_41))),add(X_41,inverse(inverse(X_41)))) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
add(inverse(inverse(X_41)),additive_identity) = inverse(inverse(X_41)),
inference(subst,[],[additive_id1:[bind(X,$fot(inverse(inverse(X_41))))]]) ).
cnf(refute_0_24,plain,
( add(inverse(inverse(X_41)),additive_identity) != add(X_41,inverse(inverse(X_41)))
| add(inverse(inverse(X_41)),additive_identity) != inverse(inverse(X_41))
| inverse(inverse(X_41)) = add(X_41,inverse(inverse(X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(inverse(X_41)),additive_identity),add(X_41,inverse(inverse(X_41)))) ),[0],$fot(inverse(inverse(X_41)))]]) ).
cnf(refute_0_25,plain,
( add(inverse(inverse(X_41)),additive_identity) != add(X_41,inverse(inverse(X_41)))
| inverse(inverse(X_41)) = add(X_41,inverse(inverse(X_41))) ),
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_41)),additive_identity),inverse(inverse(X_41))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
add(X_21,multiply(inverse(X_21),X_23)) = multiply(add(X_21,inverse(X_21)),add(X_21,X_23)),
inference(subst,[],[distributivity2:[bind(X,$fot(X_21)),bind(Y,$fot(inverse(X_21))),bind(Z,$fot(X_23))]]) ).
cnf(refute_0_27,plain,
add(X_21,inverse(X_21)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_21))]]) ).
cnf(refute_0_28,plain,
( add(X_21,multiply(inverse(X_21),X_23)) != multiply(add(X_21,inverse(X_21)),add(X_21,X_23))
| add(X_21,inverse(X_21)) != multiplicative_identity
| add(X_21,multiply(inverse(X_21),X_23)) = multiply(multiplicative_identity,add(X_21,X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_21,multiply(inverse(X_21),X_23)),multiply(add(X_21,inverse(X_21)),add(X_21,X_23))) ),[1,0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_29,plain,
( add(X_21,multiply(inverse(X_21),X_23)) != multiply(add(X_21,inverse(X_21)),add(X_21,X_23))
| add(X_21,multiply(inverse(X_21),X_23)) = multiply(multiplicative_identity,add(X_21,X_23)) ),
inference(resolve,[$cnf( $equal(add(X_21,inverse(X_21)),multiplicative_identity) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
add(X_21,multiply(inverse(X_21),X_23)) = multiply(multiplicative_identity,add(X_21,X_23)),
inference(resolve,[$cnf( $equal(add(X_21,multiply(inverse(X_21),X_23)),multiply(add(X_21,inverse(X_21)),add(X_21,X_23))) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
multiply(multiplicative_identity,add(X_21,X_23)) = add(X_21,X_23),
inference(subst,[],[multiplicative_id2:[bind(X,$fot(add(X_21,X_23)))]]) ).
cnf(refute_0_32,plain,
( multiply(multiplicative_identity,add(X_21,X_23)) != add(X_21,X_23)
| add(X_21,multiply(inverse(X_21),X_23)) != multiply(multiplicative_identity,add(X_21,X_23))
| add(X_21,multiply(inverse(X_21),X_23)) = add(X_21,X_23) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_21,multiply(inverse(X_21),X_23)),multiply(multiplicative_identity,add(X_21,X_23))) ),[1],$fot(add(X_21,X_23))]]) ).
cnf(refute_0_33,plain,
( add(X_21,multiply(inverse(X_21),X_23)) != multiply(multiplicative_identity,add(X_21,X_23))
| add(X_21,multiply(inverse(X_21),X_23)) = add(X_21,X_23) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,add(X_21,X_23)),add(X_21,X_23)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
add(X_21,multiply(inverse(X_21),X_23)) = add(X_21,X_23),
inference(resolve,[$cnf( $equal(add(X_21,multiply(inverse(X_21),X_23)),multiply(multiplicative_identity,add(X_21,X_23))) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
add(X_29,multiply(inverse(X_29),inverse(inverse(X_29)))) = add(X_29,inverse(inverse(X_29))),
inference(subst,[],[refute_0_34:[bind(X_21,$fot(X_29)),bind(X_23,$fot(inverse(inverse(X_29))))]]) ).
cnf(refute_0_36,plain,
multiply(inverse(X_29),inverse(inverse(X_29))) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(inverse(X_29)))]]) ).
cnf(refute_0_37,plain,
( multiply(inverse(X_29),inverse(inverse(X_29))) != additive_identity
| add(X_29,multiply(inverse(X_29),inverse(inverse(X_29)))) != add(X_29,inverse(inverse(X_29)))
| add(X_29,additive_identity) = add(X_29,inverse(inverse(X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_29,multiply(inverse(X_29),inverse(inverse(X_29)))),add(X_29,inverse(inverse(X_29)))) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_38,plain,
( add(X_29,multiply(inverse(X_29),inverse(inverse(X_29)))) != add(X_29,inverse(inverse(X_29)))
| add(X_29,additive_identity) = add(X_29,inverse(inverse(X_29))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_29),inverse(inverse(X_29))),additive_identity) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
add(X_29,additive_identity) = add(X_29,inverse(inverse(X_29))),
inference(resolve,[$cnf( $equal(add(X_29,multiply(inverse(X_29),inverse(inverse(X_29)))),add(X_29,inverse(inverse(X_29)))) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
add(X_29,additive_identity) = X_29,
inference(subst,[],[additive_id1:[bind(X,$fot(X_29))]]) ).
cnf(refute_0_41,plain,
( add(X_29,additive_identity) != X_29
| add(X_29,additive_identity) != add(X_29,inverse(inverse(X_29)))
| X_29 = add(X_29,inverse(inverse(X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_29,additive_identity),add(X_29,inverse(inverse(X_29)))) ),[0],$fot(X_29)]]) ).
cnf(refute_0_42,plain,
( add(X_29,additive_identity) != add(X_29,inverse(inverse(X_29)))
| X_29 = add(X_29,inverse(inverse(X_29))) ),
inference(resolve,[$cnf( $equal(add(X_29,additive_identity),X_29) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
X_29 = add(X_29,inverse(inverse(X_29))),
inference(resolve,[$cnf( $equal(add(X_29,additive_identity),add(X_29,inverse(inverse(X_29)))) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
( X_29 != add(X_29,inverse(inverse(X_29)))
| add(X_29,inverse(inverse(X_29))) = X_29 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(X_29)),bind(Y0,$fot(add(X_29,inverse(inverse(X_29)))))]]) ).
cnf(refute_0_45,plain,
add(X_29,inverse(inverse(X_29))) = X_29,
inference(resolve,[$cnf( $equal(X_29,add(X_29,inverse(inverse(X_29)))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
add(X_41,inverse(inverse(X_41))) = X_41,
inference(subst,[],[refute_0_45:[bind(X_29,$fot(X_41))]]) ).
cnf(refute_0_47,plain,
( add(X_41,inverse(inverse(X_41))) != X_41
| inverse(inverse(X_41)) != add(X_41,inverse(inverse(X_41)))
| inverse(inverse(X_41)) = X_41 ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_41)),add(X_41,inverse(inverse(X_41)))) ),[1],$fot(X_41)]]) ).
cnf(refute_0_48,plain,
( inverse(inverse(X_41)) != add(X_41,inverse(inverse(X_41)))
| inverse(inverse(X_41)) = X_41 ),
inference(resolve,[$cnf( $equal(add(X_41,inverse(inverse(X_41))),X_41) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( add(inverse(inverse(X_41)),additive_identity) != add(X_41,inverse(inverse(X_41)))
| inverse(inverse(X_41)) = X_41 ),
inference(resolve,[$cnf( $equal(inverse(inverse(X_41)),add(X_41,inverse(inverse(X_41)))) )],[refute_0_25,refute_0_48]) ).
cnf(refute_0_50,plain,
inverse(inverse(X_41)) = X_41,
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_41)),additive_identity),add(X_41,inverse(inverse(X_41)))) )],[refute_0_22,refute_0_49]) ).
cnf(refute_0_51,plain,
inverse(inverse(x)) = x,
inference(subst,[],[refute_0_50:[bind(X_41,$fot(x))]]) ).
cnf(refute_0_52,plain,
( inverse(inverse(x)) != x
| x != x
| inverse(inverse(x)) = x ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse(inverse(x)),x) ),[0],$fot(x)]]) ).
cnf(refute_0_53,plain,
( x != x
| inverse(inverse(x)) = x ),
inference(resolve,[$cnf( $equal(inverse(inverse(x)),x) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
x != x,
inference(resolve,[$cnf( $equal(inverse(inverse(x)),x) )],[refute_0_53,prove_inverse_is_an_involution]) ).
cnf(refute_0_55,plain,
x = x,
introduced(tautology,[refl,[$fot(x)]]) ).
cnf(refute_0_56,plain,
$false,
inference(resolve,[$cnf( $equal(x,x) )],[refute_0_55,refute_0_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO012-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n019.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
% 0.12/0.34 % DateTime : Wed Jun 1 15:42:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.45/0.61 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/0.61
% 0.45/0.61 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.45/0.62
%------------------------------------------------------------------------------