TSTP Solution File: RNG007-4 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : RNG007-4 : TPTP v8.1.0. Released v1.0.0.
% 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 : Mon Jul 18 20:35:42 EDT 2022
% Result : Unsatisfiable 0.21s 0.36s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 22
% Syntax : Number of clauses : 59 ( 33 unt; 0 nHn; 31 RR)
% Number of literals : 98 ( 97 equ; 41 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 : 63 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_additive_inverse,axiom,
add(additive_inverse(X),X) = additive_identity ).
cnf(additive_inverse_additive_inverse,axiom,
additive_inverse(additive_inverse(X)) = X ).
cnf(multiply_additive_inverse1,axiom,
multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ).
cnf(multiply_additive_inverse2,axiom,
multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ).
cnf(commutative_addition,axiom,
add(X,Y) = add(Y,X) ).
cnf(boolean_ring,hypothesis,
multiply(X,X) = X ).
cnf(prove_inverse,negated_conjecture,
add(a,a) != additive_identity ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( add(X,Y) != add(Y,X)
| add(Y,X) = add(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X,Y))),bind(Y0,$fot(add(Y,X)))]]) ).
cnf(refute_0_4,plain,
add(Y,X) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X,Y),add(Y,X)) )],[commutative_addition,refute_0_3]) ).
cnf(refute_0_5,plain,
add(additive_inverse(X),X) = add(X,additive_inverse(X)),
inference(subst,[],[refute_0_4:[bind(Y,$fot(additive_inverse(X)))]]) ).
cnf(refute_0_6,plain,
( add(additive_inverse(X),X) != add(X,additive_inverse(X))
| add(additive_inverse(X),X) != additive_identity
| add(X,additive_inverse(X)) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(X),X),additive_identity) ),[0],$fot(add(X,additive_inverse(X)))]]) ).
cnf(refute_0_7,plain,
( add(additive_inverse(X),X) != additive_identity
| add(X,additive_inverse(X)) = additive_identity ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X),X),add(X,additive_inverse(X))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
add(X,additive_inverse(X)) = additive_identity,
inference(resolve,[$cnf( $equal(add(additive_inverse(X),X),additive_identity) )],[left_additive_inverse,refute_0_7]) ).
cnf(refute_0_9,plain,
multiply(additive_inverse(X_10),additive_inverse(X_10)) = additive_inverse(X_10),
inference(subst,[],[boolean_ring:[bind(X,$fot(additive_inverse(X_10)))]]) ).
cnf(refute_0_10,plain,
multiply(additive_inverse(X_10),additive_inverse(X_10)) = additive_inverse(multiply(additive_inverse(X_10),X_10)),
inference(subst,[],[multiply_additive_inverse1:[bind(X,$fot(additive_inverse(X_10))),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_11,plain,
( multiply(additive_inverse(X_10),additive_inverse(X_10)) != additive_inverse(X_10)
| multiply(additive_inverse(X_10),additive_inverse(X_10)) != additive_inverse(multiply(additive_inverse(X_10),X_10))
| additive_inverse(multiply(additive_inverse(X_10),X_10)) = additive_inverse(X_10) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_inverse(X_10),additive_inverse(X_10)),additive_inverse(X_10)) ),[0],$fot(additive_inverse(multiply(additive_inverse(X_10),X_10)))]]) ).
cnf(refute_0_12,plain,
( multiply(additive_inverse(X_10),additive_inverse(X_10)) != additive_inverse(X_10)
| additive_inverse(multiply(additive_inverse(X_10),X_10)) = additive_inverse(X_10) ),
inference(resolve,[$cnf( $equal(multiply(additive_inverse(X_10),additive_inverse(X_10)),additive_inverse(multiply(additive_inverse(X_10),X_10))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
additive_inverse(multiply(additive_inverse(X_10),X_10)) = additive_inverse(X_10),
inference(resolve,[$cnf( $equal(multiply(additive_inverse(X_10),additive_inverse(X_10)),additive_inverse(X_10)) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
additive_inverse(additive_inverse(X_10)) = X_10,
inference(subst,[],[additive_inverse_additive_inverse:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_15,plain,
multiply(X_10,X_10) = X_10,
inference(subst,[],[boolean_ring:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_16,plain,
additive_inverse(multiply(X_10,X_10)) = additive_inverse(multiply(X_10,X_10)),
introduced(tautology,[refl,[$fot(additive_inverse(multiply(X_10,X_10)))]]) ).
cnf(refute_0_17,plain,
( multiply(X_10,X_10) != X_10
| additive_inverse(multiply(X_10,X_10)) != additive_inverse(multiply(X_10,X_10))
| additive_inverse(multiply(X_10,X_10)) = additive_inverse(X_10) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(X_10,X_10)),additive_inverse(multiply(X_10,X_10))) ),[1,0],$fot(X_10)]]) ).
cnf(refute_0_18,plain,
( multiply(X_10,X_10) != X_10
| additive_inverse(multiply(X_10,X_10)) = additive_inverse(X_10) ),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X_10,X_10)),additive_inverse(multiply(X_10,X_10))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
additive_inverse(multiply(X_10,X_10)) = additive_inverse(X_10),
inference(resolve,[$cnf( $equal(multiply(X_10,X_10),X_10) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
multiply(additive_inverse(X_10),X_10) = additive_inverse(multiply(X_10,X_10)),
inference(subst,[],[multiply_additive_inverse2:[bind(X,$fot(X_10)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_21,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_22,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_21]) ).
cnf(refute_0_23,plain,
( multiply(additive_inverse(X_10),X_10) != additive_inverse(multiply(X_10,X_10))
| additive_inverse(multiply(X_10,X_10)) != additive_inverse(X_10)
| multiply(additive_inverse(X_10),X_10) = additive_inverse(X_10) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(multiply(additive_inverse(X_10),X_10))),bind(Y0,$fot(additive_inverse(multiply(X_10,X_10)))),bind(Z,$fot(additive_inverse(X_10)))]]) ).
cnf(refute_0_24,plain,
( additive_inverse(multiply(X_10,X_10)) != additive_inverse(X_10)
| multiply(additive_inverse(X_10),X_10) = additive_inverse(X_10) ),
inference(resolve,[$cnf( $equal(multiply(additive_inverse(X_10),X_10),additive_inverse(multiply(X_10,X_10))) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
multiply(additive_inverse(X_10),X_10) = additive_inverse(X_10),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X_10,X_10)),additive_inverse(X_10)) )],[refute_0_19,refute_0_24]) ).
cnf(refute_0_26,plain,
additive_inverse(multiply(additive_inverse(X_10),X_10)) = additive_inverse(multiply(additive_inverse(X_10),X_10)),
introduced(tautology,[refl,[$fot(additive_inverse(multiply(additive_inverse(X_10),X_10)))]]) ).
cnf(refute_0_27,plain,
( multiply(additive_inverse(X_10),X_10) != additive_inverse(X_10)
| additive_inverse(multiply(additive_inverse(X_10),X_10)) != additive_inverse(multiply(additive_inverse(X_10),X_10))
| additive_inverse(multiply(additive_inverse(X_10),X_10)) = additive_inverse(additive_inverse(X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_10),X_10)),additive_inverse(multiply(additive_inverse(X_10),X_10))) ),[1,0],$fot(additive_inverse(X_10))]]) ).
cnf(refute_0_28,plain,
( multiply(additive_inverse(X_10),X_10) != additive_inverse(X_10)
| additive_inverse(multiply(additive_inverse(X_10),X_10)) = additive_inverse(additive_inverse(X_10)) ),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_10),X_10)),additive_inverse(multiply(additive_inverse(X_10),X_10))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
additive_inverse(multiply(additive_inverse(X_10),X_10)) = additive_inverse(additive_inverse(X_10)),
inference(resolve,[$cnf( $equal(multiply(additive_inverse(X_10),X_10),additive_inverse(X_10)) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
( additive_inverse(multiply(additive_inverse(X_10),X_10)) != additive_inverse(additive_inverse(X_10))
| additive_inverse(additive_inverse(X_10)) != X_10
| additive_inverse(multiply(additive_inverse(X_10),X_10)) = X_10 ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(additive_inverse(multiply(additive_inverse(X_10),X_10)))),bind(Y0,$fot(additive_inverse(additive_inverse(X_10)))),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_31,plain,
( additive_inverse(additive_inverse(X_10)) != X_10
| additive_inverse(multiply(additive_inverse(X_10),X_10)) = X_10 ),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_10),X_10)),additive_inverse(additive_inverse(X_10))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
additive_inverse(multiply(additive_inverse(X_10),X_10)) = X_10,
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(X_10)),X_10) )],[refute_0_14,refute_0_31]) ).
cnf(refute_0_33,plain,
( additive_inverse(multiply(additive_inverse(X_10),X_10)) != X_10
| additive_inverse(multiply(additive_inverse(X_10),X_10)) != additive_inverse(X_10)
| X_10 = additive_inverse(X_10) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_10),X_10)),additive_inverse(X_10)) ),[0],$fot(X_10)]]) ).
cnf(refute_0_34,plain,
( additive_inverse(multiply(additive_inverse(X_10),X_10)) != additive_inverse(X_10)
| X_10 = additive_inverse(X_10) ),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_10),X_10)),X_10) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
X_10 = additive_inverse(X_10),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_10),X_10)),additive_inverse(X_10)) )],[refute_0_13,refute_0_34]) ).
cnf(refute_0_36,plain,
( X_10 != additive_inverse(X_10)
| additive_inverse(X_10) = X_10 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_10)),bind(Y0,$fot(additive_inverse(X_10)))]]) ).
cnf(refute_0_37,plain,
additive_inverse(X_10) = X_10,
inference(resolve,[$cnf( $equal(X_10,additive_inverse(X_10)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
additive_inverse(X) = X,
inference(subst,[],[refute_0_37:[bind(X_10,$fot(X))]]) ).
cnf(refute_0_39,plain,
add(X,additive_inverse(X)) = add(X,additive_inverse(X)),
introduced(tautology,[refl,[$fot(add(X,additive_inverse(X)))]]) ).
cnf(refute_0_40,plain,
( add(X,additive_inverse(X)) != add(X,additive_inverse(X))
| additive_inverse(X) != X
| add(X,additive_inverse(X)) = add(X,X) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,additive_inverse(X)),add(X,additive_inverse(X))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_41,plain,
( additive_inverse(X) != X
| add(X,additive_inverse(X)) = add(X,X) ),
inference(resolve,[$cnf( $equal(add(X,additive_inverse(X)),add(X,additive_inverse(X))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
add(X,additive_inverse(X)) = add(X,X),
inference(resolve,[$cnf( $equal(additive_inverse(X),X) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
( add(X,additive_inverse(X)) != add(X,X)
| add(X,additive_inverse(X)) != additive_identity
| add(X,X) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(add(X,additive_inverse(X)),additive_identity) ),[0],$fot(add(X,X))]]) ).
cnf(refute_0_44,plain,
( add(X,additive_inverse(X)) != additive_identity
| add(X,X) = additive_identity ),
inference(resolve,[$cnf( $equal(add(X,additive_inverse(X)),add(X,X)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
add(X,X) = additive_identity,
inference(resolve,[$cnf( $equal(add(X,additive_inverse(X)),additive_identity) )],[refute_0_8,refute_0_44]) ).
cnf(refute_0_46,plain,
add(a,a) = additive_identity,
inference(subst,[],[refute_0_45:[bind(X,$fot(a))]]) ).
cnf(refute_0_47,plain,
( add(a,a) != additive_identity
| additive_identity != additive_identity
| add(a,a) = additive_identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(a,a),additive_identity) ),[0],$fot(additive_identity)]]) ).
cnf(refute_0_48,plain,
( additive_identity != additive_identity
| add(a,a) = additive_identity ),
inference(resolve,[$cnf( $equal(add(a,a),additive_identity) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
additive_identity != additive_identity,
inference(resolve,[$cnf( $equal(add(a,a),additive_identity) )],[refute_0_48,prove_inverse]) ).
cnf(refute_0_50,plain,
additive_identity = additive_identity,
introduced(tautology,[refl,[$fot(additive_identity)]]) ).
cnf(refute_0_51,plain,
$false,
inference(resolve,[$cnf( $equal(additive_identity,additive_identity) )],[refute_0_50,refute_0_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG007-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon May 30 05:10:16 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.36
% 0.21/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.37
%------------------------------------------------------------------------------