TSTP Solution File: RNG023-7 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : RNG023-7 : TPTP v8.1.0. Released v1.0.0.
% 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 : Mon Jul 18 20:35:47 EDT 2022
% Result : Unsatisfiable 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of clauses : 40 ( 23 unt; 0 nHn; 21 RR)
% Number of literals : 66 ( 65 equ; 28 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; 3 con; 0-3 aty)
% Number of variables : 68 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_multiplicative_zero,axiom,
multiply(additive_identity,X) = additive_identity ).
cnf(right_additive_inverse,axiom,
add(X,additive_inverse(X)) = additive_identity ).
cnf(left_alternative,axiom,
multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)) ).
cnf(associator,axiom,
associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ).
cnf(distributivity_of_difference2,axiom,
multiply(add(X,additive_inverse(Y)),Z) = add(multiply(X,Z),additive_inverse(multiply(Y,Z))) ).
cnf(prove_left_alternative,negated_conjecture,
associator(x,x,y) != additive_identity ).
cnf(refute_0_0,plain,
associator(X_32,X_32,X_33) = add(multiply(multiply(X_32,X_32),X_33),additive_inverse(multiply(X_32,multiply(X_32,X_33)))),
inference(subst,[],[associator:[bind(X,$fot(X_32)),bind(Y,$fot(X_32)),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_1,plain,
multiply(multiply(X_32,X_32),X_33) = multiply(X_32,multiply(X_32,X_33)),
inference(subst,[],[left_alternative:[bind(X,$fot(X_32)),bind(Y,$fot(X_33))]]) ).
cnf(refute_0_2,plain,
( multiply(multiply(X_32,X_32),X_33) != multiply(X_32,multiply(X_32,X_33))
| associator(X_32,X_32,X_33) != add(multiply(multiply(X_32,X_32),X_33),additive_inverse(multiply(X_32,multiply(X_32,X_33))))
| associator(X_32,X_32,X_33) = add(multiply(X_32,multiply(X_32,X_33)),additive_inverse(multiply(X_32,multiply(X_32,X_33)))) ),
introduced(tautology,[equality,[$cnf( $equal(associator(X_32,X_32,X_33),add(multiply(multiply(X_32,X_32),X_33),additive_inverse(multiply(X_32,multiply(X_32,X_33))))) ),[1,0],$fot(multiply(X_32,multiply(X_32,X_33)))]]) ).
cnf(refute_0_3,plain,
( associator(X_32,X_32,X_33) != add(multiply(multiply(X_32,X_32),X_33),additive_inverse(multiply(X_32,multiply(X_32,X_33))))
| associator(X_32,X_32,X_33) = add(multiply(X_32,multiply(X_32,X_33)),additive_inverse(multiply(X_32,multiply(X_32,X_33)))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_32,X_32),X_33),multiply(X_32,multiply(X_32,X_33))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
associator(X_32,X_32,X_33) = add(multiply(X_32,multiply(X_32,X_33)),additive_inverse(multiply(X_32,multiply(X_32,X_33)))),
inference(resolve,[$cnf( $equal(associator(X_32,X_32,X_33),add(multiply(multiply(X_32,X_32),X_33),additive_inverse(multiply(X_32,multiply(X_32,X_33))))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
multiply(additive_identity,multiply(X_32,X_33)) = additive_identity,
inference(subst,[],[left_multiplicative_zero:[bind(X,$fot(multiply(X_32,X_33)))]]) ).
cnf(refute_0_6,plain,
add(X_32,additive_inverse(X_32)) = additive_identity,
inference(subst,[],[right_additive_inverse:[bind(X,$fot(X_32))]]) ).
cnf(refute_0_7,plain,
multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33)) = multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33)),
introduced(tautology,[refl,[$fot(multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33)))]]) ).
cnf(refute_0_8,plain,
( multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33)) != multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33))
| add(X_32,additive_inverse(X_32)) != additive_identity
| multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33)) = multiply(additive_identity,multiply(X_32,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33)),multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33))) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_9,plain,
( add(X_32,additive_inverse(X_32)) != additive_identity
| multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33)) = multiply(additive_identity,multiply(X_32,X_33)) ),
inference(resolve,[$cnf( $equal(multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33)),multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33)) = multiply(additive_identity,multiply(X_32,X_33)),
inference(resolve,[$cnf( $equal(add(X_32,additive_inverse(X_32)),additive_identity) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_12,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_13,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_15,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33)) != multiply(additive_identity,multiply(X_32,X_33))
| multiply(additive_identity,multiply(X_32,X_33)) != additive_identity
| multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33)) = additive_identity ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33)))),bind(Y0,$fot(multiply(additive_identity,multiply(X_32,X_33)))),bind(Z0,$fot(additive_identity))]]) ).
cnf(refute_0_17,plain,
( multiply(additive_identity,multiply(X_32,X_33)) != additive_identity
| multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33)) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33)),multiply(additive_identity,multiply(X_32,X_33))) )],[refute_0_10,refute_0_16]) ).
cnf(refute_0_18,plain,
multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33)) = additive_identity,
inference(resolve,[$cnf( $equal(multiply(additive_identity,multiply(X_32,X_33)),additive_identity) )],[refute_0_5,refute_0_17]) ).
cnf(refute_0_19,plain,
( multiply(add(X,additive_inverse(Y)),Z) != add(multiply(X,Z),additive_inverse(multiply(Y,Z)))
| add(multiply(X,Z),additive_inverse(multiply(Y,Z))) = multiply(add(X,additive_inverse(Y)),Z) ),
inference(subst,[],[refute_0_13:[bind(X0,$fot(multiply(add(X,additive_inverse(Y)),Z))),bind(Y0,$fot(add(multiply(X,Z),additive_inverse(multiply(Y,Z)))))]]) ).
cnf(refute_0_20,plain,
add(multiply(X,Z),additive_inverse(multiply(Y,Z))) = multiply(add(X,additive_inverse(Y)),Z),
inference(resolve,[$cnf( $equal(multiply(add(X,additive_inverse(Y)),Z),add(multiply(X,Z),additive_inverse(multiply(Y,Z)))) )],[distributivity_of_difference2,refute_0_19]) ).
cnf(refute_0_21,plain,
add(multiply(X_32,multiply(X_32,X_33)),additive_inverse(multiply(X_32,multiply(X_32,X_33)))) = multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33)),
inference(subst,[],[refute_0_20:[bind(X,$fot(X_32)),bind(Y,$fot(X_32)),bind(Z,$fot(multiply(X_32,X_33)))]]) ).
cnf(refute_0_22,plain,
( multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33)) != additive_identity
| add(multiply(X_32,multiply(X_32,X_33)),additive_inverse(multiply(X_32,multiply(X_32,X_33)))) != multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33))
| add(multiply(X_32,multiply(X_32,X_33)),additive_inverse(multiply(X_32,multiply(X_32,X_33)))) = additive_identity ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(add(multiply(X_32,multiply(X_32,X_33)),additive_inverse(multiply(X_32,multiply(X_32,X_33)))))),bind(Y0,$fot(multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33)))),bind(Z0,$fot(additive_identity))]]) ).
cnf(refute_0_23,plain,
( multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33)) != additive_identity
| add(multiply(X_32,multiply(X_32,X_33)),additive_inverse(multiply(X_32,multiply(X_32,X_33)))) = additive_identity ),
inference(resolve,[$cnf( $equal(add(multiply(X_32,multiply(X_32,X_33)),additive_inverse(multiply(X_32,multiply(X_32,X_33)))),multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
add(multiply(X_32,multiply(X_32,X_33)),additive_inverse(multiply(X_32,multiply(X_32,X_33)))) = additive_identity,
inference(resolve,[$cnf( $equal(multiply(add(X_32,additive_inverse(X_32)),multiply(X_32,X_33)),additive_identity) )],[refute_0_18,refute_0_23]) ).
cnf(refute_0_25,plain,
( add(multiply(X_32,multiply(X_32,X_33)),additive_inverse(multiply(X_32,multiply(X_32,X_33)))) != additive_identity
| associator(X_32,X_32,X_33) != add(multiply(X_32,multiply(X_32,X_33)),additive_inverse(multiply(X_32,multiply(X_32,X_33))))
| associator(X_32,X_32,X_33) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(associator(X_32,X_32,X_33),add(multiply(X_32,multiply(X_32,X_33)),additive_inverse(multiply(X_32,multiply(X_32,X_33))))) ),[1],$fot(additive_identity)]]) ).
cnf(refute_0_26,plain,
( associator(X_32,X_32,X_33) != add(multiply(X_32,multiply(X_32,X_33)),additive_inverse(multiply(X_32,multiply(X_32,X_33))))
| associator(X_32,X_32,X_33) = additive_identity ),
inference(resolve,[$cnf( $equal(add(multiply(X_32,multiply(X_32,X_33)),additive_inverse(multiply(X_32,multiply(X_32,X_33)))),additive_identity) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
associator(X_32,X_32,X_33) = additive_identity,
inference(resolve,[$cnf( $equal(associator(X_32,X_32,X_33),add(multiply(X_32,multiply(X_32,X_33)),additive_inverse(multiply(X_32,multiply(X_32,X_33))))) )],[refute_0_4,refute_0_26]) ).
cnf(refute_0_28,plain,
associator(x,x,y) = additive_identity,
inference(subst,[],[refute_0_27:[bind(X_32,$fot(x)),bind(X_33,$fot(y))]]) ).
cnf(refute_0_29,plain,
( additive_identity != additive_identity
| associator(x,x,y) != additive_identity
| associator(x,x,y) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(associator(x,x,y),additive_identity) ),[1],$fot(additive_identity)]]) ).
cnf(refute_0_30,plain,
( additive_identity != additive_identity
| associator(x,x,y) = additive_identity ),
inference(resolve,[$cnf( $equal(associator(x,x,y),additive_identity) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
additive_identity != additive_identity,
inference(resolve,[$cnf( $equal(associator(x,x,y),additive_identity) )],[refute_0_30,prove_left_alternative]) ).
cnf(refute_0_32,plain,
additive_identity = additive_identity,
introduced(tautology,[refl,[$fot(additive_identity)]]) ).
cnf(refute_0_33,plain,
$false,
inference(resolve,[$cnf( $equal(additive_identity,additive_identity) )],[refute_0_32,refute_0_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : RNG023-7 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.12 % Command : metis --show proof --show saturation %s
% 0.09/0.32 % Computer : n023.cluster.edu
% 0.09/0.32 % Model : x86_64 x86_64
% 0.09/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.32 % Memory : 8042.1875MB
% 0.09/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.32 % CPULimit : 300
% 0.09/0.32 % WCLimit : 600
% 0.09/0.32 % DateTime : Mon May 30 22:45:27 EDT 2022
% 0.09/0.32 % CPUTime :
% 0.09/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.09/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37
% 0.09/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.09/0.38
%------------------------------------------------------------------------------