TSTP Solution File: BOO005-4 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : BOO005-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 23:44:25 EDT 2022
% Result : Unsatisfiable 0.19s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of clauses : 38 ( 23 unt; 0 nHn; 20 RR)
% Number of literals : 60 ( 59 equ; 24 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
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(multiplicative_id1,axiom,
multiply(X,multiplicative_identity) = X ).
cnf(additive_inverse1,axiom,
add(X,inverse(X)) = multiplicative_identity ).
cnf(prove_a_plus_1_is_a,negated_conjecture,
add(a,multiplicative_identity) != multiplicative_identity ).
cnf(refute_0_0,plain,
add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),add(X_10,inverse(X_10))),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(inverse(X_10)))]]) ).
cnf(refute_0_1,plain,
add(X_10,inverse(X_10)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_2,plain,
( add(X_10,multiply(X_11,inverse(X_10))) != multiply(add(X_10,X_11),add(X_10,inverse(X_10)))
| add(X_10,inverse(X_10)) != multiplicative_identity
| add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),add(X_10,inverse(X_10)))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_3,plain,
( add(X_10,multiply(X_11,inverse(X_10))) != multiply(add(X_10,X_11),add(X_10,inverse(X_10)))
| add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(X_10,inverse(X_10)),multiplicative_identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),add(X_10,inverse(X_10)))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(add(X_10,X_11),multiplicative_identity) = add(X_10,X_11),
inference(subst,[],[multiplicative_id1:[bind(X,$fot(add(X_10,X_11)))]]) ).
cnf(refute_0_6,plain,
( multiply(add(X_10,X_11),multiplicative_identity) != add(X_10,X_11)
| add(X_10,multiply(X_11,inverse(X_10))) != multiply(add(X_10,X_11),multiplicative_identity)
| add(X_10,multiply(X_11,inverse(X_10))) = add(X_10,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),multiplicative_identity)) ),[1],$fot(add(X_10,X_11))]]) ).
cnf(refute_0_7,plain,
( add(X_10,multiply(X_11,inverse(X_10))) != multiply(add(X_10,X_11),multiplicative_identity)
| add(X_10,multiply(X_11,inverse(X_10))) = add(X_10,X_11) ),
inference(resolve,[$cnf( $equal(multiply(add(X_10,X_11),multiplicative_identity),add(X_10,X_11)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
add(X_10,multiply(X_11,inverse(X_10))) = add(X_10,X_11),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),multiplicative_identity)) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
add(X_13,multiply(multiplicative_identity,inverse(X_13))) = add(X_13,multiplicative_identity),
inference(subst,[],[refute_0_8:[bind(X_10,$fot(X_13)),bind(X_11,$fot(multiplicative_identity))]]) ).
cnf(refute_0_10,plain,
multiply(X,multiplicative_identity) = multiply(multiplicative_identity,X),
inference(subst,[],[commutativity_of_multiply:[bind(Y,$fot(multiplicative_identity))]]) ).
cnf(refute_0_11,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_12,plain,
( multiply(X,multiplicative_identity) != X
| multiply(multiplicative_identity,X) = X ),
inference(resolve,[$cnf( $equal(multiply(X,multiplicative_identity),multiply(multiplicative_identity,X)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(multiplicative_identity,X) = X,
inference(resolve,[$cnf( $equal(multiply(X,multiplicative_identity),X) )],[multiplicative_id1,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(multiplicative_identity,inverse(X_13)) = inverse(X_13),
inference(subst,[],[refute_0_13:[bind(X,$fot(inverse(X_13)))]]) ).
cnf(refute_0_15,plain,
( multiply(multiplicative_identity,inverse(X_13)) != inverse(X_13)
| add(X_13,multiply(multiplicative_identity,inverse(X_13))) != add(X_13,multiplicative_identity)
| add(X_13,inverse(X_13)) = add(X_13,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_13,multiply(multiplicative_identity,inverse(X_13))),add(X_13,multiplicative_identity)) ),[0,1],$fot(inverse(X_13))]]) ).
cnf(refute_0_16,plain,
( add(X_13,multiply(multiplicative_identity,inverse(X_13))) != add(X_13,multiplicative_identity)
| add(X_13,inverse(X_13)) = add(X_13,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,inverse(X_13)),inverse(X_13)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
add(X_13,inverse(X_13)) = add(X_13,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_13,multiply(multiplicative_identity,inverse(X_13))),add(X_13,multiplicative_identity)) )],[refute_0_9,refute_0_16]) ).
cnf(refute_0_18,plain,
add(X_13,inverse(X_13)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_19,plain,
( add(X_13,inverse(X_13)) != add(X_13,multiplicative_identity)
| add(X_13,inverse(X_13)) != multiplicative_identity
| multiplicative_identity = add(X_13,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_13,inverse(X_13)),add(X_13,multiplicative_identity)) ),[0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_20,plain,
( add(X_13,inverse(X_13)) != add(X_13,multiplicative_identity)
| multiplicative_identity = add(X_13,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(X_13,inverse(X_13)),multiplicative_identity) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
multiplicative_identity = add(X_13,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_13,inverse(X_13)),add(X_13,multiplicative_identity)) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_23,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_24,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( multiplicative_identity != add(X_13,multiplicative_identity)
| add(X_13,multiplicative_identity) = multiplicative_identity ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(multiplicative_identity)),bind(Y0,$fot(add(X_13,multiplicative_identity)))]]) ).
cnf(refute_0_26,plain,
add(X_13,multiplicative_identity) = multiplicative_identity,
inference(resolve,[$cnf( $equal(multiplicative_identity,add(X_13,multiplicative_identity)) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
add(a,multiplicative_identity) = multiplicative_identity,
inference(subst,[],[refute_0_26:[bind(X_13,$fot(a))]]) ).
cnf(refute_0_28,plain,
( add(a,multiplicative_identity) != multiplicative_identity
| multiplicative_identity != multiplicative_identity
| add(a,multiplicative_identity) = multiplicative_identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(a,multiplicative_identity),multiplicative_identity) ),[0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_29,plain,
( multiplicative_identity != multiplicative_identity
| add(a,multiplicative_identity) = multiplicative_identity ),
inference(resolve,[$cnf( $equal(add(a,multiplicative_identity),multiplicative_identity) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
multiplicative_identity != multiplicative_identity,
inference(resolve,[$cnf( $equal(add(a,multiplicative_identity),multiplicative_identity) )],[refute_0_29,prove_a_plus_1_is_a]) ).
cnf(refute_0_31,plain,
multiplicative_identity = multiplicative_identity,
introduced(tautology,[refl,[$fot(multiplicative_identity)]]) ).
cnf(refute_0_32,plain,
$false,
inference(resolve,[$cnf( $equal(multiplicative_identity,multiplicative_identity) )],[refute_0_31,refute_0_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : BOO005-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 1 22:07:19 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.36
% 0.19/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.36
%------------------------------------------------------------------------------