TSTP Solution File: BOO010-4 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : BOO010-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 0.36s 0.57s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 28
% Syntax : Number of clauses : 92 ( 51 unt; 0 nHn; 46 RR)
% Number of literals : 152 ( 151 equ; 63 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 131 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_of_add,axiom,
add(X,Y) = add(Y,X) ).
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(distributivity2,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(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_ab_is_a,negated_conjecture,
add(a,multiply(a,b)) != a ).
cnf(refute_0_0,plain,
add(Y,multiply(Y,Z)) = multiply(add(Y,Y),add(Y,Z)),
inference(subst,[],[distributivity1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_1,plain,
add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),add(X_10,inverse(X_10))),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(inverse(X_10)))]]) ).
cnf(refute_0_2,plain,
add(X_10,inverse(X_10)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_3,plain,
( add(X_10,multiply(X_11,inverse(X_10))) != multiply(add(X_10,X_11),add(X_10,inverse(X_10)))
| add(X_10,inverse(X_10)) != multiplicative_identity
| add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),multiplicative_identity) ),
introduced(tautology,[equality,[$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_4,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( $equal(add(X_10,inverse(X_10)),multiplicative_identity) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),add(X_10,inverse(X_10)))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
multiply(add(X_10,X_11),multiplicative_identity) = add(X_10,X_11),
inference(subst,[],[multiplicative_id1:[bind(X,$fot(add(X_10,X_11)))]]) ).
cnf(refute_0_7,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_8,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( $equal(multiply(add(X_10,X_11),multiplicative_identity),add(X_10,X_11)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
add(X_10,multiply(X_11,inverse(X_10))) = add(X_10,X_11),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),multiplicative_identity)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
add(X_19,multiply(X_19,inverse(X_19))) = add(X_19,X_19),
inference(subst,[],[refute_0_9:[bind(X_10,$fot(X_19)),bind(X_11,$fot(X_19))]]) ).
cnf(refute_0_11,plain,
multiply(X_19,inverse(X_19)) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_12,plain,
( multiply(X_19,inverse(X_19)) != additive_identity
| add(X_19,multiply(X_19,inverse(X_19))) != add(X_19,X_19)
| add(X_19,additive_identity) = add(X_19,X_19) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_19,multiply(X_19,inverse(X_19))),add(X_19,X_19)) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_13,plain,
( add(X_19,multiply(X_19,inverse(X_19))) != add(X_19,X_19)
| add(X_19,additive_identity) = add(X_19,X_19) ),
inference(resolve,[$cnf( $equal(multiply(X_19,inverse(X_19)),additive_identity) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
add(X_19,additive_identity) = add(X_19,X_19),
inference(resolve,[$cnf( $equal(add(X_19,multiply(X_19,inverse(X_19))),add(X_19,X_19)) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
add(X_19,additive_identity) = X_19,
inference(subst,[],[additive_id1:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_16,plain,
( add(X_19,additive_identity) != X_19
| add(X_19,additive_identity) != add(X_19,X_19)
| X_19 = add(X_19,X_19) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_19,additive_identity),add(X_19,X_19)) ),[0],$fot(X_19)]]) ).
cnf(refute_0_17,plain,
( add(X_19,additive_identity) != add(X_19,X_19)
| X_19 = add(X_19,X_19) ),
inference(resolve,[$cnf( $equal(add(X_19,additive_identity),X_19) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
X_19 = add(X_19,X_19),
inference(resolve,[$cnf( $equal(add(X_19,additive_identity),add(X_19,X_19)) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
Y = add(Y,Y),
inference(subst,[],[refute_0_18:[bind(X_19,$fot(Y))]]) ).
cnf(refute_0_20,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_21,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_22,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( Y != add(Y,Y)
| add(Y,Y) = Y ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(Y)),bind(Y0,$fot(add(Y,Y)))]]) ).
cnf(refute_0_24,plain,
add(Y,Y) = Y,
inference(resolve,[$cnf( $equal(Y,add(Y,Y)) )],[refute_0_19,refute_0_23]) ).
cnf(refute_0_25,plain,
( add(Y,Y) != Y
| add(Y,multiply(Y,Z)) != multiply(add(Y,Y),add(Y,Z))
| add(Y,multiply(Y,Z)) = multiply(Y,add(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(Y,multiply(Y,Z)),multiply(add(Y,Y),add(Y,Z))) ),[1,0],$fot(Y)]]) ).
cnf(refute_0_26,plain,
( add(Y,multiply(Y,Z)) != multiply(add(Y,Y),add(Y,Z))
| add(Y,multiply(Y,Z)) = multiply(Y,add(Y,Z)) ),
inference(resolve,[$cnf( $equal(add(Y,Y),Y) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
add(Y,multiply(Y,Z)) = multiply(Y,add(Y,Z)),
inference(resolve,[$cnf( $equal(add(Y,multiply(Y,Z)),multiply(add(Y,Y),add(Y,Z))) )],[refute_0_0,refute_0_26]) ).
cnf(refute_0_28,plain,
add(a,multiply(a,b)) = multiply(a,add(a,b)),
inference(subst,[],[refute_0_27:[bind(Y,$fot(a)),bind(Z,$fot(b))]]) ).
cnf(refute_0_29,plain,
( multiply(a,add(a,b)) != a
| add(a,multiply(a,b)) != multiply(a,add(a,b))
| add(a,multiply(a,b)) = a ),
introduced(tautology,[equality,[$cnf( $equal(add(a,multiply(a,b)),multiply(a,add(a,b))) ),[1],$fot(a)]]) ).
cnf(refute_0_30,plain,
( multiply(a,add(a,b)) != a
| add(a,multiply(a,b)) = a ),
inference(resolve,[$cnf( $equal(add(a,multiply(a,b)),multiply(a,add(a,b))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
multiply(a,add(a,b)) != a,
inference(resolve,[$cnf( $equal(add(a,multiply(a,b)),a) )],[refute_0_30,prove_a_plus_ab_is_a]) ).
cnf(refute_0_32,plain,
multiply(X_41,add(X_42,multiplicative_identity)) = add(multiply(X_41,X_42),multiply(X_41,multiplicative_identity)),
inference(subst,[],[distributivity2:[bind(X,$fot(X_41)),bind(Y,$fot(X_42)),bind(Z,$fot(multiplicative_identity))]]) ).
cnf(refute_0_33,plain,
multiply(X_41,multiplicative_identity) = X_41,
inference(subst,[],[multiplicative_id1:[bind(X,$fot(X_41))]]) ).
cnf(refute_0_34,plain,
( multiply(X_41,add(X_42,multiplicative_identity)) != add(multiply(X_41,X_42),multiply(X_41,multiplicative_identity))
| multiply(X_41,multiplicative_identity) != X_41
| multiply(X_41,add(X_42,multiplicative_identity)) = add(multiply(X_41,X_42),X_41) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_41,add(X_42,multiplicative_identity)),add(multiply(X_41,X_42),multiply(X_41,multiplicative_identity))) ),[1,1],$fot(X_41)]]) ).
cnf(refute_0_35,plain,
( multiply(X_41,add(X_42,multiplicative_identity)) != add(multiply(X_41,X_42),multiply(X_41,multiplicative_identity))
| multiply(X_41,add(X_42,multiplicative_identity)) = add(multiply(X_41,X_42),X_41) ),
inference(resolve,[$cnf( $equal(multiply(X_41,multiplicative_identity),X_41) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
multiply(X_41,add(X_42,multiplicative_identity)) = add(multiply(X_41,X_42),X_41),
inference(resolve,[$cnf( $equal(multiply(X_41,add(X_42,multiplicative_identity)),add(multiply(X_41,X_42),multiply(X_41,multiplicative_identity))) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
add(X_19,multiply(multiplicative_identity,inverse(X_19))) = add(X_19,multiplicative_identity),
inference(subst,[],[refute_0_9:[bind(X_10,$fot(X_19)),bind(X_11,$fot(multiplicative_identity))]]) ).
cnf(refute_0_38,plain,
multiply(X,multiplicative_identity) = multiply(multiplicative_identity,X),
inference(subst,[],[commutativity_of_multiply:[bind(Y,$fot(multiplicative_identity))]]) ).
cnf(refute_0_39,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_40,plain,
( multiply(X,multiplicative_identity) != X
| multiply(multiplicative_identity,X) = X ),
inference(resolve,[$cnf( $equal(multiply(X,multiplicative_identity),multiply(multiplicative_identity,X)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
multiply(multiplicative_identity,X) = X,
inference(resolve,[$cnf( $equal(multiply(X,multiplicative_identity),X) )],[multiplicative_id1,refute_0_40]) ).
cnf(refute_0_42,plain,
multiply(multiplicative_identity,inverse(X_19)) = inverse(X_19),
inference(subst,[],[refute_0_41:[bind(X,$fot(inverse(X_19)))]]) ).
cnf(refute_0_43,plain,
( multiply(multiplicative_identity,inverse(X_19)) != inverse(X_19)
| add(X_19,multiply(multiplicative_identity,inverse(X_19))) != add(X_19,multiplicative_identity)
| add(X_19,inverse(X_19)) = add(X_19,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_19,multiply(multiplicative_identity,inverse(X_19))),add(X_19,multiplicative_identity)) ),[0,1],$fot(inverse(X_19))]]) ).
cnf(refute_0_44,plain,
( add(X_19,multiply(multiplicative_identity,inverse(X_19))) != add(X_19,multiplicative_identity)
| add(X_19,inverse(X_19)) = add(X_19,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,inverse(X_19)),inverse(X_19)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
add(X_19,inverse(X_19)) = add(X_19,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_19,multiply(multiplicative_identity,inverse(X_19))),add(X_19,multiplicative_identity)) )],[refute_0_37,refute_0_44]) ).
cnf(refute_0_46,plain,
add(X_19,inverse(X_19)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_47,plain,
( add(X_19,inverse(X_19)) != add(X_19,multiplicative_identity)
| add(X_19,inverse(X_19)) != multiplicative_identity
| multiplicative_identity = add(X_19,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_19,inverse(X_19)),add(X_19,multiplicative_identity)) ),[0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_48,plain,
( add(X_19,inverse(X_19)) != add(X_19,multiplicative_identity)
| multiplicative_identity = add(X_19,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(X_19,inverse(X_19)),multiplicative_identity) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
multiplicative_identity = add(X_19,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_19,inverse(X_19)),add(X_19,multiplicative_identity)) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
( multiplicative_identity != add(X_19,multiplicative_identity)
| add(X_19,multiplicative_identity) = multiplicative_identity ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(multiplicative_identity)),bind(Y0,$fot(add(X_19,multiplicative_identity)))]]) ).
cnf(refute_0_51,plain,
add(X_19,multiplicative_identity) = multiplicative_identity,
inference(resolve,[$cnf( $equal(multiplicative_identity,add(X_19,multiplicative_identity)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
add(X_42,multiplicative_identity) = multiplicative_identity,
inference(subst,[],[refute_0_51:[bind(X_19,$fot(X_42))]]) ).
cnf(refute_0_53,plain,
multiply(X_41,add(X_42,multiplicative_identity)) = multiply(X_41,add(X_42,multiplicative_identity)),
introduced(tautology,[refl,[$fot(multiply(X_41,add(X_42,multiplicative_identity)))]]) ).
cnf(refute_0_54,plain,
( multiply(X_41,add(X_42,multiplicative_identity)) != multiply(X_41,add(X_42,multiplicative_identity))
| add(X_42,multiplicative_identity) != multiplicative_identity
| multiply(X_41,add(X_42,multiplicative_identity)) = multiply(X_41,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_41,add(X_42,multiplicative_identity)),multiply(X_41,add(X_42,multiplicative_identity))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_55,plain,
( add(X_42,multiplicative_identity) != multiplicative_identity
| multiply(X_41,add(X_42,multiplicative_identity)) = multiply(X_41,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(multiply(X_41,add(X_42,multiplicative_identity)),multiply(X_41,add(X_42,multiplicative_identity))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
multiply(X_41,add(X_42,multiplicative_identity)) = multiply(X_41,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_42,multiplicative_identity),multiplicative_identity) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_58,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_22,refute_0_57]) ).
cnf(refute_0_59,plain,
( multiply(X_41,add(X_42,multiplicative_identity)) != multiply(X_41,multiplicative_identity)
| multiply(X_41,multiplicative_identity) != X_41
| multiply(X_41,add(X_42,multiplicative_identity)) = X_41 ),
inference(subst,[],[refute_0_58:[bind(X0,$fot(multiply(X_41,add(X_42,multiplicative_identity)))),bind(Y0,$fot(multiply(X_41,multiplicative_identity))),bind(Z0,$fot(X_41))]]) ).
cnf(refute_0_60,plain,
( multiply(X_41,multiplicative_identity) != X_41
| multiply(X_41,add(X_42,multiplicative_identity)) = X_41 ),
inference(resolve,[$cnf( $equal(multiply(X_41,add(X_42,multiplicative_identity)),multiply(X_41,multiplicative_identity)) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
multiply(X_41,add(X_42,multiplicative_identity)) = X_41,
inference(resolve,[$cnf( $equal(multiply(X_41,multiplicative_identity),X_41) )],[refute_0_33,refute_0_60]) ).
cnf(refute_0_62,plain,
( multiply(X_41,add(X_42,multiplicative_identity)) != X_41
| multiply(X_41,add(X_42,multiplicative_identity)) != add(multiply(X_41,X_42),X_41)
| X_41 = add(multiply(X_41,X_42),X_41) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_41,add(X_42,multiplicative_identity)),add(multiply(X_41,X_42),X_41)) ),[0],$fot(X_41)]]) ).
cnf(refute_0_63,plain,
( multiply(X_41,add(X_42,multiplicative_identity)) != add(multiply(X_41,X_42),X_41)
| X_41 = add(multiply(X_41,X_42),X_41) ),
inference(resolve,[$cnf( $equal(multiply(X_41,add(X_42,multiplicative_identity)),X_41) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
add(X_41,multiply(X_41,X_42)) = multiply(X_41,add(X_41,X_42)),
inference(subst,[],[refute_0_27:[bind(Y,$fot(X_41)),bind(Z,$fot(X_42))]]) ).
cnf(refute_0_65,plain,
( add(X,Y) != add(Y,X)
| add(Y,X) = add(X,Y) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(add(X,Y))),bind(Y0,$fot(add(Y,X)))]]) ).
cnf(refute_0_66,plain,
add(Y,X) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X,Y),add(Y,X)) )],[commutativity_of_add,refute_0_65]) ).
cnf(refute_0_67,plain,
add(multiply(X_41,X_42),X_41) = add(X_41,multiply(X_41,X_42)),
inference(subst,[],[refute_0_66:[bind(X,$fot(X_41)),bind(Y,$fot(multiply(X_41,X_42)))]]) ).
cnf(refute_0_68,plain,
( add(X_41,multiply(X_41,X_42)) != multiply(X_41,add(X_41,X_42))
| add(multiply(X_41,X_42),X_41) != add(X_41,multiply(X_41,X_42))
| add(multiply(X_41,X_42),X_41) = multiply(X_41,add(X_41,X_42)) ),
inference(subst,[],[refute_0_58:[bind(X0,$fot(add(multiply(X_41,X_42),X_41))),bind(Y0,$fot(add(X_41,multiply(X_41,X_42)))),bind(Z0,$fot(multiply(X_41,add(X_41,X_42))))]]) ).
cnf(refute_0_69,plain,
( add(X_41,multiply(X_41,X_42)) != multiply(X_41,add(X_41,X_42))
| add(multiply(X_41,X_42),X_41) = multiply(X_41,add(X_41,X_42)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_41,X_42),X_41),add(X_41,multiply(X_41,X_42))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
add(multiply(X_41,X_42),X_41) = multiply(X_41,add(X_41,X_42)),
inference(resolve,[$cnf( $equal(add(X_41,multiply(X_41,X_42)),multiply(X_41,add(X_41,X_42))) )],[refute_0_64,refute_0_69]) ).
cnf(refute_0_71,plain,
( X_41 != add(multiply(X_41,X_42),X_41)
| add(multiply(X_41,X_42),X_41) != multiply(X_41,add(X_41,X_42))
| X_41 = multiply(X_41,add(X_41,X_42)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_41,multiply(X_41,add(X_41,X_42))) ),[0],$fot(add(multiply(X_41,X_42),X_41))]]) ).
cnf(refute_0_72,plain,
( X_41 != add(multiply(X_41,X_42),X_41)
| X_41 = multiply(X_41,add(X_41,X_42)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_41,X_42),X_41),multiply(X_41,add(X_41,X_42))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
( multiply(X_41,add(X_42,multiplicative_identity)) != add(multiply(X_41,X_42),X_41)
| X_41 = multiply(X_41,add(X_41,X_42)) ),
inference(resolve,[$cnf( $equal(X_41,add(multiply(X_41,X_42),X_41)) )],[refute_0_63,refute_0_72]) ).
cnf(refute_0_74,plain,
X_41 = multiply(X_41,add(X_41,X_42)),
inference(resolve,[$cnf( $equal(multiply(X_41,add(X_42,multiplicative_identity)),add(multiply(X_41,X_42),X_41)) )],[refute_0_36,refute_0_73]) ).
cnf(refute_0_75,plain,
( X_41 != multiply(X_41,add(X_41,X_42))
| multiply(X_41,add(X_41,X_42)) = X_41 ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(X_41)),bind(Y0,$fot(multiply(X_41,add(X_41,X_42))))]]) ).
cnf(refute_0_76,plain,
multiply(X_41,add(X_41,X_42)) = X_41,
inference(resolve,[$cnf( $equal(X_41,multiply(X_41,add(X_41,X_42))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
multiply(a,add(a,b)) = a,
inference(subst,[],[refute_0_76:[bind(X_41,$fot(a)),bind(X_42,$fot(b))]]) ).
cnf(refute_0_78,plain,
( multiply(a,add(a,b)) != a
| a != a
| multiply(a,add(a,b)) = a ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,add(a,b)),a) ),[0],$fot(a)]]) ).
cnf(refute_0_79,plain,
( a != a
| multiply(a,add(a,b)) = a ),
inference(resolve,[$cnf( $equal(multiply(a,add(a,b)),a) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
a != a,
inference(resolve,[$cnf( $equal(multiply(a,add(a,b)),a) )],[refute_0_79,refute_0_31]) ).
cnf(refute_0_81,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_82,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_81,refute_0_80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO010-4 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n028.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 : Thu Jun 2 00:25:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.36/0.57 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.36/0.57
% 0.36/0.57 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.36/0.58
%------------------------------------------------------------------------------