TSTP Solution File: BOO004-4 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : BOO004-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of clauses : 35 ( 22 unt; 0 nHn; 18 RR)
% Number of literals : 54 ( 53 equ; 21 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity1,axiom,
add(X,multiply(Y,Z)) = multiply(add(X,Y),add(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_a_plus_a_is_a,negated_conjecture,
add(a,a) != a ).
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( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),multiplicative_identity)) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
add(X_13,multiply(X_13,inverse(X_13))) = add(X_13,X_13),
inference(subst,[],[refute_0_8:[bind(X_10,$fot(X_13)),bind(X_11,$fot(X_13))]]) ).
cnf(refute_0_10,plain,
multiply(X_13,inverse(X_13)) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_11,plain,
( multiply(X_13,inverse(X_13)) != additive_identity
| add(X_13,multiply(X_13,inverse(X_13))) != add(X_13,X_13)
| add(X_13,additive_identity) = add(X_13,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_13,multiply(X_13,inverse(X_13))),add(X_13,X_13)) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_12,plain,
( add(X_13,multiply(X_13,inverse(X_13))) != add(X_13,X_13)
| add(X_13,additive_identity) = add(X_13,X_13) ),
inference(resolve,[$cnf( $equal(multiply(X_13,inverse(X_13)),additive_identity) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
add(X_13,additive_identity) = add(X_13,X_13),
inference(resolve,[$cnf( $equal(add(X_13,multiply(X_13,inverse(X_13))),add(X_13,X_13)) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
add(X_13,additive_identity) = X_13,
inference(subst,[],[additive_id1:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_15,plain,
( add(X_13,additive_identity) != X_13
| add(X_13,additive_identity) != add(X_13,X_13)
| X_13 = add(X_13,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_13,additive_identity),add(X_13,X_13)) ),[0],$fot(X_13)]]) ).
cnf(refute_0_16,plain,
( add(X_13,additive_identity) != add(X_13,X_13)
| X_13 = add(X_13,X_13) ),
inference(resolve,[$cnf( $equal(add(X_13,additive_identity),X_13) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
X_13 = add(X_13,X_13),
inference(resolve,[$cnf( $equal(add(X_13,additive_identity),add(X_13,X_13)) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_19,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_20,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( X_13 != add(X_13,X_13)
| add(X_13,X_13) = X_13 ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(X_13)),bind(Y0,$fot(add(X_13,X_13)))]]) ).
cnf(refute_0_22,plain,
add(X_13,X_13) = X_13,
inference(resolve,[$cnf( $equal(X_13,add(X_13,X_13)) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
add(a,a) = a,
inference(subst,[],[refute_0_22:[bind(X_13,$fot(a))]]) ).
cnf(refute_0_24,plain,
( add(a,a) != a
| a != a
| add(a,a) = a ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(a,a),a) ),[0],$fot(a)]]) ).
cnf(refute_0_25,plain,
( a != a
| add(a,a) = a ),
inference(resolve,[$cnf( $equal(add(a,a),a) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
a != a,
inference(resolve,[$cnf( $equal(add(a,a),a) )],[refute_0_25,prove_a_plus_a_is_a]) ).
cnf(refute_0_27,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_28,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_27,refute_0_26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : BOO004-4 : TPTP v8.1.0. Released v1.1.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jun 1 16:56:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36
%------------------------------------------------------------------------------