%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : BOO006-4 : TPTP v8.1.0. Released v1.1.0.
% 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 : Thu Jul 14 23:44:26 EDT 2022
% Result : Unsatisfiable 0.39s 0.59s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 54
% Syntax : Number of clauses : 228 ( 122 unt; 0 nHn; 109 RR)
% Number of literals : 380 ( 379 equ; 154 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 : 314 ( 15 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_right_identity,negated_conjecture,
multiply(a,additive_identity) != additive_identity ).
cnf(refute_0_0,plain,
add(X_10,multiply(X_11,additive_identity)) = multiply(add(X_10,X_11),add(X_10,additive_identity)),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_1,plain,
add(X_10,additive_identity) = X_10,
inference(subst,[],[additive_id1:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_2,plain,
( add(X_10,multiply(X_11,additive_identity)) != multiply(add(X_10,X_11),add(X_10,additive_identity))
| add(X_10,additive_identity) != X_10
| add(X_10,multiply(X_11,additive_identity)) = multiply(add(X_10,X_11),X_10) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(add(X_10,X_11),add(X_10,additive_identity))) ),[1,1],$fot(X_10)]]) ).
cnf(refute_0_3,plain,
( add(X_10,multiply(X_11,additive_identity)) != multiply(add(X_10,X_11),add(X_10,additive_identity))
| add(X_10,multiply(X_11,additive_identity)) = multiply(add(X_10,X_11),X_10) ),
inference(resolve,[$cnf( $equal(add(X_10,additive_identity),X_10) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
add(X_10,multiply(X_11,additive_identity)) = multiply(add(X_10,X_11),X_10),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(add(X_10,X_11),add(X_10,additive_identity))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( multiply(X,Y) != multiply(Y,X)
| multiply(Y,X) = multiply(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(X,Y))),bind(Y0,$fot(multiply(Y,X)))]]) ).
cnf(refute_0_9,plain,
multiply(Y,X) = multiply(X,Y),
inference(resolve,[$cnf( $equal(multiply(X,Y),multiply(Y,X)) )],[commutativity_of_multiply,refute_0_8]) ).
cnf(refute_0_10,plain,
multiply(add(X_10,X_11),X_10) = multiply(X_10,add(X_10,X_11)),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_10)),bind(Y,$fot(add(X_10,X_11)))]]) ).
cnf(refute_0_11,plain,
( multiply(add(X_10,X_11),X_10) != multiply(X_10,add(X_10,X_11))
| add(X_10,multiply(X_11,additive_identity)) != multiply(add(X_10,X_11),X_10)
| add(X_10,multiply(X_11,additive_identity)) = multiply(X_10,add(X_10,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(add(X_10,X_11),X_10)) ),[1],$fot(multiply(X_10,add(X_10,X_11)))]]) ).
cnf(refute_0_12,plain,
( add(X_10,multiply(X_11,additive_identity)) != multiply(add(X_10,X_11),X_10)
| add(X_10,multiply(X_11,additive_identity)) = multiply(X_10,add(X_10,X_11)) ),
inference(resolve,[$cnf( $equal(multiply(add(X_10,X_11),X_10),multiply(X_10,add(X_10,X_11))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
add(X_10,multiply(X_11,additive_identity)) = multiply(X_10,add(X_10,X_11)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,additive_identity)),multiply(add(X_10,X_11),X_10)) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11)),
inference(subst,[],[refute_0_13:[bind(X_10,$fot(multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_15,plain,
add(multiply(additive_identity,additive_identity),Y) = add(Y,multiply(additive_identity,additive_identity)),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_16,plain,
add(X_21,multiply(additive_identity,additive_identity)) = multiply(X_21,add(X_21,additive_identity)),
inference(subst,[],[refute_0_13:[bind(X_10,$fot(X_21)),bind(X_11,$fot(additive_identity))]]) ).
cnf(refute_0_17,plain,
add(X_21,additive_identity) = X_21,
inference(subst,[],[additive_id1:[bind(X,$fot(X_21))]]) ).
cnf(refute_0_18,plain,
( add(X_21,multiply(additive_identity,additive_identity)) != multiply(X_21,add(X_21,additive_identity))
| add(X_21,additive_identity) != X_21
| add(X_21,multiply(additive_identity,additive_identity)) = multiply(X_21,X_21) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_21,multiply(additive_identity,additive_identity)),multiply(X_21,add(X_21,additive_identity))) ),[1,1],$fot(X_21)]]) ).
cnf(refute_0_19,plain,
( add(X_21,multiply(additive_identity,additive_identity)) != multiply(X_21,add(X_21,additive_identity))
| add(X_21,multiply(additive_identity,additive_identity)) = multiply(X_21,X_21) ),
inference(resolve,[$cnf( $equal(add(X_21,additive_identity),X_21) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
add(X_21,multiply(additive_identity,additive_identity)) = multiply(X_21,X_21),
inference(resolve,[$cnf( $equal(add(X_21,multiply(additive_identity,additive_identity)),multiply(X_21,add(X_21,additive_identity))) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,Y),
inference(subst,[],[refute_0_20:[bind(X_21,$fot(Y))]]) ).
cnf(refute_0_22,plain,
( add(Y,multiply(additive_identity,additive_identity)) != multiply(Y,Y)
| add(multiply(additive_identity,additive_identity),Y) != add(Y,multiply(additive_identity,additive_identity))
| add(multiply(additive_identity,additive_identity),Y) = multiply(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),add(Y,multiply(additive_identity,additive_identity))) ),[1],$fot(multiply(Y,Y))]]) ).
cnf(refute_0_23,plain,
( add(multiply(additive_identity,additive_identity),Y) != add(Y,multiply(additive_identity,additive_identity))
| add(multiply(additive_identity,additive_identity),Y) = multiply(Y,Y) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(additive_identity,additive_identity)),multiply(Y,Y)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
add(multiply(additive_identity,additive_identity),Y) = multiply(Y,Y),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),add(Y,multiply(additive_identity,additive_identity))) )],[refute_0_15,refute_0_23]) ).
cnf(refute_0_25,plain,
add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity)) = multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity)),
inference(subst,[],[refute_0_24:[bind(Y,$fot(multiply(X_11,additive_identity)))]]) ).
cnf(refute_0_26,plain,
( add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity)) != multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity))
| add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11))
| multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11))) ),[0],$fot(multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity)))]]) ).
cnf(refute_0_27,plain,
( add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11))
| multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity)),multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_11,additive_identity)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11))) )],[refute_0_14,refute_0_27]) ).
cnf(refute_0_29,plain,
add(X_11,additive_identity) = X_11,
inference(subst,[],[additive_id1:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_30,plain,
multiply(additive_identity,add(X_11,additive_identity)) = multiply(additive_identity,add(X_11,additive_identity)),
introduced(tautology,[refl,[$fot(multiply(additive_identity,add(X_11,additive_identity)))]]) ).
cnf(refute_0_31,plain,
( multiply(additive_identity,add(X_11,additive_identity)) != multiply(additive_identity,add(X_11,additive_identity))
| add(X_11,additive_identity) != X_11
| multiply(additive_identity,add(X_11,additive_identity)) = multiply(additive_identity,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(X_11,additive_identity)),multiply(additive_identity,add(X_11,additive_identity))) ),[1,1],$fot(X_11)]]) ).
cnf(refute_0_32,plain,
( add(X_11,additive_identity) != X_11
| multiply(additive_identity,add(X_11,additive_identity)) = multiply(additive_identity,X_11) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_11,additive_identity)),multiply(additive_identity,add(X_11,additive_identity))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(additive_identity,add(X_11,additive_identity)) = multiply(additive_identity,X_11),
inference(resolve,[$cnf( $equal(add(X_11,additive_identity),X_11) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
( multiply(X,add(Y,Z)) != add(multiply(X,Y),multiply(X,Z))
| add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(X,add(Y,Z)))),bind(Y0,$fot(add(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_35,plain,
add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,add(Y,Z)),add(multiply(X,Y),multiply(X,Z))) )],[distributivity2,refute_0_34]) ).
cnf(refute_0_36,plain,
add(multiply(additive_identity,X_11),multiply(additive_identity,additive_identity)) = multiply(additive_identity,add(X_11,additive_identity)),
inference(subst,[],[refute_0_35:[bind(X,$fot(additive_identity)),bind(Y,$fot(X_11)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_37,plain,
add(multiply(additive_identity,X_24),Y) = add(Y,multiply(additive_identity,X_24)),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(multiply(additive_identity,X_24)))]]) ).
cnf(refute_0_38,plain,
add(X_10,multiply(additive_identity,X_12)) = multiply(add(X_10,additive_identity),add(X_10,X_12)),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(additive_identity)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_39,plain,
( add(X_10,multiply(additive_identity,X_12)) != multiply(add(X_10,additive_identity),add(X_10,X_12))
| add(X_10,additive_identity) != X_10
| add(X_10,multiply(additive_identity,X_12)) = multiply(X_10,add(X_10,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_10,multiply(additive_identity,X_12)),multiply(add(X_10,additive_identity),add(X_10,X_12))) ),[1,0],$fot(X_10)]]) ).
cnf(refute_0_40,plain,
( add(X_10,multiply(additive_identity,X_12)) != multiply(add(X_10,additive_identity),add(X_10,X_12))
| add(X_10,multiply(additive_identity,X_12)) = multiply(X_10,add(X_10,X_12)) ),
inference(resolve,[$cnf( $equal(add(X_10,additive_identity),X_10) )],[refute_0_1,refute_0_39]) ).
cnf(refute_0_41,plain,
add(X_10,multiply(additive_identity,X_12)) = multiply(X_10,add(X_10,X_12)),
inference(resolve,[$cnf( $equal(add(X_10,multiply(additive_identity,X_12)),multiply(add(X_10,additive_identity),add(X_10,X_12))) )],[refute_0_38,refute_0_40]) ).
cnf(refute_0_42,plain,
add(Y,multiply(additive_identity,X_24)) = multiply(Y,add(Y,X_24)),
inference(subst,[],[refute_0_41:[bind(X_10,$fot(Y)),bind(X_12,$fot(X_24))]]) ).
cnf(refute_0_43,plain,
( add(Y,multiply(additive_identity,X_24)) != multiply(Y,add(Y,X_24))
| add(multiply(additive_identity,X_24),Y) != add(Y,multiply(additive_identity,X_24))
| add(multiply(additive_identity,X_24),Y) = multiply(Y,add(Y,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_24),Y),add(Y,multiply(additive_identity,X_24))) ),[1],$fot(multiply(Y,add(Y,X_24)))]]) ).
cnf(refute_0_44,plain,
( add(multiply(additive_identity,X_24),Y) != add(Y,multiply(additive_identity,X_24))
| add(multiply(additive_identity,X_24),Y) = multiply(Y,add(Y,X_24)) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(additive_identity,X_24)),multiply(Y,add(Y,X_24))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
add(multiply(additive_identity,X_24),Y) = multiply(Y,add(Y,X_24)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_24),Y),add(Y,multiply(additive_identity,X_24))) )],[refute_0_37,refute_0_44]) ).
cnf(refute_0_46,plain,
( add(multiply(additive_identity,X_24),Y) != multiply(Y,add(Y,X_24))
| multiply(Y,add(Y,X_24)) = add(multiply(additive_identity,X_24),Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(add(multiply(additive_identity,X_24),Y))),bind(Y0,$fot(multiply(Y,add(Y,X_24))))]]) ).
cnf(refute_0_47,plain,
multiply(Y,add(Y,X_24)) = add(multiply(additive_identity,X_24),Y),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_24),Y),multiply(Y,add(Y,X_24))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11)) = add(multiply(additive_identity,X_11),multiply(additive_identity,additive_identity)),
inference(subst,[],[refute_0_47:[bind(Y,$fot(multiply(additive_identity,additive_identity))),bind(X_24,$fot(X_11))]]) ).
cnf(refute_0_49,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_50,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_7,refute_0_49]) ).
cnf(refute_0_51,plain,
( multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11)) != add(multiply(additive_identity,X_11),multiply(additive_identity,additive_identity))
| add(multiply(additive_identity,X_11),multiply(additive_identity,additive_identity)) != multiply(additive_identity,add(X_11,additive_identity))
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11)) = multiply(additive_identity,add(X_11,additive_identity)) ),
inference(subst,[],[refute_0_50:[bind(X0,$fot(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11)))),bind(Y0,$fot(add(multiply(additive_identity,X_11),multiply(additive_identity,additive_identity)))),bind(Z0,$fot(multiply(additive_identity,add(X_11,additive_identity))))]]) ).
cnf(refute_0_52,plain,
( add(multiply(additive_identity,X_11),multiply(additive_identity,additive_identity)) != multiply(additive_identity,add(X_11,additive_identity))
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11)) = multiply(additive_identity,add(X_11,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11)),add(multiply(additive_identity,X_11),multiply(additive_identity,additive_identity))) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11)) = multiply(additive_identity,add(X_11,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_11),multiply(additive_identity,additive_identity)),multiply(additive_identity,add(X_11,additive_identity))) )],[refute_0_36,refute_0_52]) ).
cnf(refute_0_54,plain,
( multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11)) != multiply(additive_identity,add(X_11,additive_identity))
| multiply(additive_identity,add(X_11,additive_identity)) != multiply(additive_identity,X_11)
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11)) = multiply(additive_identity,X_11) ),
inference(subst,[],[refute_0_50:[bind(X0,$fot(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11)))),bind(Y0,$fot(multiply(additive_identity,add(X_11,additive_identity)))),bind(Z0,$fot(multiply(additive_identity,X_11)))]]) ).
cnf(refute_0_55,plain,
( multiply(additive_identity,add(X_11,additive_identity)) != multiply(additive_identity,X_11)
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11)) = multiply(additive_identity,X_11) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11)),multiply(additive_identity,add(X_11,additive_identity))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11)) = multiply(additive_identity,X_11),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_11,additive_identity)),multiply(additive_identity,X_11)) )],[refute_0_33,refute_0_55]) ).
cnf(refute_0_57,plain,
( multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11))
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11)) != multiply(additive_identity,X_11)
| multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity)) = multiply(additive_identity,X_11) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity)),multiply(additive_identity,X_11)) ),[0],$fot(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11)))]]) ).
cnf(refute_0_58,plain,
( multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11))
| multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity)) = multiply(additive_identity,X_11) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11)),multiply(additive_identity,X_11)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity)) = multiply(additive_identity,X_11),
inference(resolve,[$cnf( $equal(multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_11))) )],[refute_0_28,refute_0_58]) ).
cnf(refute_0_60,plain,
add(Y,multiply(Y,Z)) = multiply(add(Y,Y),add(Y,Z)),
inference(subst,[],[distributivity1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_61,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,$fot(inverse(X_10)))]]) ).
cnf(refute_0_62,plain,
add(X_10,inverse(X_10)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_63,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_64,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( $equal(add(X_10,inverse(X_10)),multiplicative_identity) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
add(X_10,multiply(X_11,inverse(X_10))) = multiply(add(X_10,X_11),multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),add(X_10,inverse(X_10)))) )],[refute_0_61,refute_0_64]) ).
cnf(refute_0_66,plain,
multiply(add(X_10,X_11),multiplicative_identity) = add(X_10,X_11),
inference(subst,[],[multiplicative_id1:[bind(X,$fot(add(X_10,X_11)))]]) ).
cnf(refute_0_67,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_68,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( $equal(multiply(add(X_10,X_11),multiplicative_identity),add(X_10,X_11)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
add(X_10,multiply(X_11,inverse(X_10))) = add(X_10,X_11),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_11,inverse(X_10))),multiply(add(X_10,X_11),multiplicative_identity)) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
add(X_13,multiply(X_13,inverse(X_13))) = add(X_13,X_13),
inference(subst,[],[refute_0_69:[bind(X_10,$fot(X_13)),bind(X_11,$fot(X_13))]]) ).
cnf(refute_0_71,plain,
multiply(X_13,inverse(X_13)) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_72,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_73,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( $equal(multiply(X_13,inverse(X_13)),additive_identity) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
add(X_13,additive_identity) = add(X_13,X_13),
inference(resolve,[$cnf( $equal(add(X_13,multiply(X_13,inverse(X_13))),add(X_13,X_13)) )],[refute_0_70,refute_0_73]) ).
cnf(refute_0_75,plain,
add(X_13,additive_identity) = X_13,
inference(subst,[],[additive_id1:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_76,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_77,plain,
( add(X_13,additive_identity) != add(X_13,X_13)
| X_13 = add(X_13,X_13) ),
inference(resolve,[$cnf( $equal(add(X_13,additive_identity),X_13) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
X_13 = add(X_13,X_13),
inference(resolve,[$cnf( $equal(add(X_13,additive_identity),add(X_13,X_13)) )],[refute_0_74,refute_0_77]) ).
cnf(refute_0_79,plain,
Y = add(Y,Y),
inference(subst,[],[refute_0_78:[bind(X_13,$fot(Y))]]) ).
cnf(refute_0_80,plain,
( Y != add(Y,Y)
| add(Y,Y) = Y ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(Y)),bind(Y0,$fot(add(Y,Y)))]]) ).
cnf(refute_0_81,plain,
add(Y,Y) = Y,
inference(resolve,[$cnf( $equal(Y,add(Y,Y)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( add(Y,Y) != Y
| add(Y,multiply(Y,Z)) != multiply(add(Y,Y),add(Y,Z))
| add(Y,multiply(Y,Z)) = multiply(Y,add(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(Y,multiply(Y,Z)),multiply(add(Y,Y),add(Y,Z))) ),[1,0],$fot(Y)]]) ).
cnf(refute_0_83,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( $equal(add(Y,Y),Y) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
add(Y,multiply(Y,Z)) = multiply(Y,add(Y,Z)),
inference(resolve,[$cnf( $equal(add(Y,multiply(Y,Z)),multiply(add(Y,Y),add(Y,Z))) )],[refute_0_60,refute_0_83]) ).
cnf(refute_0_85,plain,
add(X_28,multiply(X_28,X_28)) = multiply(X_28,add(X_28,X_28)),
inference(subst,[],[refute_0_84:[bind(Y,$fot(X_28)),bind(Z,$fot(X_28))]]) ).
cnf(refute_0_86,plain,
add(X_28,multiply(additive_identity,additive_identity)) = multiply(X_28,X_28),
inference(subst,[],[refute_0_20:[bind(X_21,$fot(X_28))]]) ).
cnf(refute_0_87,plain,
( add(X_28,multiply(additive_identity,additive_identity)) != multiply(X_28,X_28)
| multiply(X_28,X_28) = add(X_28,multiply(additive_identity,additive_identity)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(add(X_28,multiply(additive_identity,additive_identity)))),bind(Y0,$fot(multiply(X_28,X_28)))]]) ).
cnf(refute_0_88,plain,
multiply(X_28,X_28) = add(X_28,multiply(additive_identity,additive_identity)),
inference(resolve,[$cnf( $equal(add(X_28,multiply(additive_identity,additive_identity)),multiply(X_28,X_28)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
( multiply(X_28,X_28) != add(X_28,multiply(additive_identity,additive_identity))
| add(X_28,multiply(X_28,X_28)) != multiply(X_28,add(X_28,X_28))
| add(X_28,add(X_28,multiply(additive_identity,additive_identity))) = multiply(X_28,add(X_28,X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_28,multiply(X_28,X_28)),multiply(X_28,add(X_28,X_28))) ),[0,1],$fot(add(X_28,multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_90,plain,
( add(X_28,multiply(X_28,X_28)) != multiply(X_28,add(X_28,X_28))
| add(X_28,add(X_28,multiply(additive_identity,additive_identity))) = multiply(X_28,add(X_28,X_28)) ),
inference(resolve,[$cnf( $equal(multiply(X_28,X_28),add(X_28,multiply(additive_identity,additive_identity))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
add(X_28,add(X_28,multiply(additive_identity,additive_identity))) = multiply(X_28,add(X_28,X_28)),
inference(resolve,[$cnf( $equal(add(X_28,multiply(X_28,X_28)),multiply(X_28,add(X_28,X_28))) )],[refute_0_85,refute_0_90]) ).
cnf(refute_0_92,plain,
( X_13 != add(X_13,X_13)
| add(X_13,X_13) = X_13 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(X_13)),bind(Y0,$fot(add(X_13,X_13)))]]) ).
cnf(refute_0_93,plain,
add(X_13,X_13) = X_13,
inference(resolve,[$cnf( $equal(X_13,add(X_13,X_13)) )],[refute_0_78,refute_0_92]) ).
cnf(refute_0_94,plain,
add(X_28,X_28) = X_28,
inference(subst,[],[refute_0_93:[bind(X_13,$fot(X_28))]]) ).
cnf(refute_0_95,plain,
multiply(X_28,add(X_28,X_28)) = multiply(X_28,add(X_28,X_28)),
introduced(tautology,[refl,[$fot(multiply(X_28,add(X_28,X_28)))]]) ).
cnf(refute_0_96,plain,
( multiply(X_28,add(X_28,X_28)) != multiply(X_28,add(X_28,X_28))
| add(X_28,X_28) != X_28
| multiply(X_28,add(X_28,X_28)) = multiply(X_28,X_28) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_28,add(X_28,X_28)),multiply(X_28,add(X_28,X_28))) ),[1,1],$fot(X_28)]]) ).
cnf(refute_0_97,plain,
( add(X_28,X_28) != X_28
| multiply(X_28,add(X_28,X_28)) = multiply(X_28,X_28) ),
inference(resolve,[$cnf( $equal(multiply(X_28,add(X_28,X_28)),multiply(X_28,add(X_28,X_28))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
multiply(X_28,add(X_28,X_28)) = multiply(X_28,X_28),
inference(resolve,[$cnf( $equal(add(X_28,X_28),X_28) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
( multiply(X_28,add(X_28,X_28)) != multiply(X_28,X_28)
| add(X_28,add(X_28,multiply(additive_identity,additive_identity))) != multiply(X_28,add(X_28,X_28))
| add(X_28,add(X_28,multiply(additive_identity,additive_identity))) = multiply(X_28,X_28) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_28,add(X_28,multiply(additive_identity,additive_identity))),multiply(X_28,add(X_28,X_28))) ),[1],$fot(multiply(X_28,X_28))]]) ).
cnf(refute_0_100,plain,
( add(X_28,add(X_28,multiply(additive_identity,additive_identity))) != multiply(X_28,add(X_28,X_28))
| add(X_28,add(X_28,multiply(additive_identity,additive_identity))) = multiply(X_28,X_28) ),
inference(resolve,[$cnf( $equal(multiply(X_28,add(X_28,X_28)),multiply(X_28,X_28)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
add(X_28,add(X_28,multiply(additive_identity,additive_identity))) = multiply(X_28,X_28),
inference(resolve,[$cnf( $equal(add(X_28,add(X_28,multiply(additive_identity,additive_identity))),multiply(X_28,add(X_28,X_28))) )],[refute_0_91,refute_0_100]) ).
cnf(refute_0_102,plain,
add(Y,multiply(Y,add(X_32,Y))) = multiply(Y,add(Y,add(X_32,Y))),
inference(subst,[],[refute_0_84:[bind(Z,$fot(add(X_32,Y)))]]) ).
cnf(refute_0_103,plain,
add(X_21,multiply(X_22,additive_identity)) = multiply(X_21,add(X_21,X_22)),
inference(subst,[],[refute_0_13:[bind(X_10,$fot(X_21)),bind(X_11,$fot(X_22))]]) ).
cnf(refute_0_104,plain,
add(X_22,X_21) = add(X_21,X_22),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(X_22)),bind(Y,$fot(X_21))]]) ).
cnf(refute_0_105,plain,
( add(X_22,X_21) != add(X_21,X_22)
| add(X_21,X_22) = add(X_22,X_21) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(add(X_22,X_21))),bind(Y0,$fot(add(X_21,X_22)))]]) ).
cnf(refute_0_106,plain,
add(X_21,X_22) = add(X_22,X_21),
inference(resolve,[$cnf( $equal(add(X_22,X_21),add(X_21,X_22)) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
( add(X_21,X_22) != add(X_22,X_21)
| add(X_21,multiply(X_22,additive_identity)) != multiply(X_21,add(X_21,X_22))
| add(X_21,multiply(X_22,additive_identity)) = multiply(X_21,add(X_22,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_21,multiply(X_22,additive_identity)),multiply(X_21,add(X_21,X_22))) ),[1,1],$fot(add(X_22,X_21))]]) ).
cnf(refute_0_108,plain,
( add(X_21,multiply(X_22,additive_identity)) != multiply(X_21,add(X_21,X_22))
| add(X_21,multiply(X_22,additive_identity)) = multiply(X_21,add(X_22,X_21)) ),
inference(resolve,[$cnf( $equal(add(X_21,X_22),add(X_22,X_21)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
add(X_21,multiply(X_22,additive_identity)) = multiply(X_21,add(X_22,X_21)),
inference(resolve,[$cnf( $equal(add(X_21,multiply(X_22,additive_identity)),multiply(X_21,add(X_21,X_22))) )],[refute_0_103,refute_0_108]) ).
cnf(refute_0_110,plain,
add(Y,multiply(X_32,additive_identity)) = multiply(Y,add(X_32,Y)),
inference(subst,[],[refute_0_109:[bind(X_21,$fot(Y)),bind(X_22,$fot(X_32))]]) ).
cnf(refute_0_111,plain,
( add(Y,multiply(X_32,additive_identity)) != multiply(Y,add(X_32,Y))
| multiply(Y,add(X_32,Y)) = add(Y,multiply(X_32,additive_identity)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(add(Y,multiply(X_32,additive_identity)))),bind(Y0,$fot(multiply(Y,add(X_32,Y))))]]) ).
cnf(refute_0_112,plain,
multiply(Y,add(X_32,Y)) = add(Y,multiply(X_32,additive_identity)),
inference(resolve,[$cnf( $equal(add(Y,multiply(X_32,additive_identity)),multiply(Y,add(X_32,Y))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
( multiply(Y,add(X_32,Y)) != add(Y,multiply(X_32,additive_identity))
| add(Y,multiply(Y,add(X_32,Y))) != multiply(Y,add(Y,add(X_32,Y)))
| add(Y,add(Y,multiply(X_32,additive_identity))) = multiply(Y,add(Y,add(X_32,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(add(Y,multiply(Y,add(X_32,Y))),multiply(Y,add(Y,add(X_32,Y)))) ),[0,1],$fot(add(Y,multiply(X_32,additive_identity)))]]) ).
cnf(refute_0_114,plain,
( add(Y,multiply(Y,add(X_32,Y))) != multiply(Y,add(Y,add(X_32,Y)))
| add(Y,add(Y,multiply(X_32,additive_identity))) = multiply(Y,add(Y,add(X_32,Y))) ),
inference(resolve,[$cnf( $equal(multiply(Y,add(X_32,Y)),add(Y,multiply(X_32,additive_identity))) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
add(Y,add(Y,multiply(X_32,additive_identity))) = multiply(Y,add(Y,add(X_32,Y))),
inference(resolve,[$cnf( $equal(add(Y,multiply(Y,add(X_32,Y))),multiply(Y,add(Y,add(X_32,Y)))) )],[refute_0_102,refute_0_114]) ).
cnf(refute_0_116,plain,
multiply(X_37,add(X_38,multiplicative_identity)) = add(multiply(X_37,X_38),multiply(X_37,multiplicative_identity)),
inference(subst,[],[distributivity2:[bind(X,$fot(X_37)),bind(Y,$fot(X_38)),bind(Z,$fot(multiplicative_identity))]]) ).
cnf(refute_0_117,plain,
multiply(X_37,multiplicative_identity) = X_37,
inference(subst,[],[multiplicative_id1:[bind(X,$fot(X_37))]]) ).
cnf(refute_0_118,plain,
( multiply(X_37,add(X_38,multiplicative_identity)) != add(multiply(X_37,X_38),multiply(X_37,multiplicative_identity))
| multiply(X_37,multiplicative_identity) != X_37
| multiply(X_37,add(X_38,multiplicative_identity)) = add(multiply(X_37,X_38),X_37) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_37,add(X_38,multiplicative_identity)),add(multiply(X_37,X_38),multiply(X_37,multiplicative_identity))) ),[1,1],$fot(X_37)]]) ).
cnf(refute_0_119,plain,
( multiply(X_37,add(X_38,multiplicative_identity)) != add(multiply(X_37,X_38),multiply(X_37,multiplicative_identity))
| multiply(X_37,add(X_38,multiplicative_identity)) = add(multiply(X_37,X_38),X_37) ),
inference(resolve,[$cnf( $equal(multiply(X_37,multiplicative_identity),X_37) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
multiply(X_37,add(X_38,multiplicative_identity)) = add(multiply(X_37,X_38),X_37),
inference(resolve,[$cnf( $equal(multiply(X_37,add(X_38,multiplicative_identity)),add(multiply(X_37,X_38),multiply(X_37,multiplicative_identity))) )],[refute_0_116,refute_0_119]) ).
cnf(refute_0_121,plain,
add(X_13,multiply(multiplicative_identity,inverse(X_13))) = add(X_13,multiplicative_identity),
inference(subst,[],[refute_0_69:[bind(X_10,$fot(X_13)),bind(X_11,$fot(multiplicative_identity))]]) ).
cnf(refute_0_122,plain,
multiply(X,multiplicative_identity) = multiply(multiplicative_identity,X),
inference(subst,[],[commutativity_of_multiply:[bind(Y,$fot(multiplicative_identity))]]) ).
cnf(refute_0_123,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_124,plain,
( multiply(X,multiplicative_identity) != X
| multiply(multiplicative_identity,X) = X ),
inference(resolve,[$cnf( $equal(multiply(X,multiplicative_identity),multiply(multiplicative_identity,X)) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
multiply(multiplicative_identity,X) = X,
inference(resolve,[$cnf( $equal(multiply(X,multiplicative_identity),X) )],[multiplicative_id1,refute_0_124]) ).
cnf(refute_0_126,plain,
multiply(multiplicative_identity,inverse(X_13)) = inverse(X_13),
inference(subst,[],[refute_0_125:[bind(X,$fot(inverse(X_13)))]]) ).
cnf(refute_0_127,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_128,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( $equal(multiply(multiplicative_identity,inverse(X_13)),inverse(X_13)) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
add(X_13,inverse(X_13)) = add(X_13,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_13,multiply(multiplicative_identity,inverse(X_13))),add(X_13,multiplicative_identity)) )],[refute_0_121,refute_0_128]) ).
cnf(refute_0_130,plain,
add(X_13,inverse(X_13)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_131,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_132,plain,
( add(X_13,inverse(X_13)) != add(X_13,multiplicative_identity)
| multiplicative_identity = add(X_13,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(X_13,inverse(X_13)),multiplicative_identity) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
multiplicative_identity = add(X_13,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_13,inverse(X_13)),add(X_13,multiplicative_identity)) )],[refute_0_129,refute_0_132]) ).
cnf(refute_0_134,plain,
( multiplicative_identity != add(X_13,multiplicative_identity)
| add(X_13,multiplicative_identity) = multiplicative_identity ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiplicative_identity)),bind(Y0,$fot(add(X_13,multiplicative_identity)))]]) ).
cnf(refute_0_135,plain,
add(X_13,multiplicative_identity) = multiplicative_identity,
inference(resolve,[$cnf( $equal(multiplicative_identity,add(X_13,multiplicative_identity)) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
add(X_38,multiplicative_identity) = multiplicative_identity,
inference(subst,[],[refute_0_135:[bind(X_13,$fot(X_38))]]) ).
cnf(refute_0_137,plain,
multiply(X_37,add(X_38,multiplicative_identity)) = multiply(X_37,add(X_38,multiplicative_identity)),
introduced(tautology,[refl,[$fot(multiply(X_37,add(X_38,multiplicative_identity)))]]) ).
cnf(refute_0_138,plain,
( multiply(X_37,add(X_38,multiplicative_identity)) != multiply(X_37,add(X_38,multiplicative_identity))
| add(X_38,multiplicative_identity) != multiplicative_identity
| multiply(X_37,add(X_38,multiplicative_identity)) = multiply(X_37,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_37,add(X_38,multiplicative_identity)),multiply(X_37,add(X_38,multiplicative_identity))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_139,plain,
( add(X_38,multiplicative_identity) != multiplicative_identity
| multiply(X_37,add(X_38,multiplicative_identity)) = multiply(X_37,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(multiply(X_37,add(X_38,multiplicative_identity)),multiply(X_37,add(X_38,multiplicative_identity))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
multiply(X_37,add(X_38,multiplicative_identity)) = multiply(X_37,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_38,multiplicative_identity),multiplicative_identity) )],[refute_0_136,refute_0_139]) ).
cnf(refute_0_141,plain,
( multiply(X_37,add(X_38,multiplicative_identity)) != multiply(X_37,multiplicative_identity)
| multiply(X_37,multiplicative_identity) != X_37
| multiply(X_37,add(X_38,multiplicative_identity)) = X_37 ),
inference(subst,[],[refute_0_50:[bind(X0,$fot(multiply(X_37,add(X_38,multiplicative_identity)))),bind(Y0,$fot(multiply(X_37,multiplicative_identity))),bind(Z0,$fot(X_37))]]) ).
cnf(refute_0_142,plain,
( multiply(X_37,multiplicative_identity) != X_37
| multiply(X_37,add(X_38,multiplicative_identity)) = X_37 ),
inference(resolve,[$cnf( $equal(multiply(X_37,add(X_38,multiplicative_identity)),multiply(X_37,multiplicative_identity)) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
multiply(X_37,add(X_38,multiplicative_identity)) = X_37,
inference(resolve,[$cnf( $equal(multiply(X_37,multiplicative_identity),X_37) )],[refute_0_117,refute_0_142]) ).
cnf(refute_0_144,plain,
( multiply(X_37,add(X_38,multiplicative_identity)) != X_37
| multiply(X_37,add(X_38,multiplicative_identity)) != add(multiply(X_37,X_38),X_37)
| X_37 = add(multiply(X_37,X_38),X_37) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_37,add(X_38,multiplicative_identity)),add(multiply(X_37,X_38),X_37)) ),[0],$fot(X_37)]]) ).
cnf(refute_0_145,plain,
( multiply(X_37,add(X_38,multiplicative_identity)) != add(multiply(X_37,X_38),X_37)
| X_37 = add(multiply(X_37,X_38),X_37) ),
inference(resolve,[$cnf( $equal(multiply(X_37,add(X_38,multiplicative_identity)),X_37) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
add(X_37,multiply(X_37,X_38)) = multiply(X_37,add(X_37,X_38)),
inference(subst,[],[refute_0_84:[bind(Y,$fot(X_37)),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_147,plain,
( add(X,Y) != add(Y,X)
| add(Y,X) = add(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(add(X,Y))),bind(Y0,$fot(add(Y,X)))]]) ).
cnf(refute_0_148,plain,
add(Y,X) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X,Y),add(Y,X)) )],[commutativity_of_add,refute_0_147]) ).
cnf(refute_0_149,plain,
add(multiply(X_37,X_38),X_37) = add(X_37,multiply(X_37,X_38)),
inference(subst,[],[refute_0_148:[bind(X,$fot(X_37)),bind(Y,$fot(multiply(X_37,X_38)))]]) ).
cnf(refute_0_150,plain,
( add(X_37,multiply(X_37,X_38)) != multiply(X_37,add(X_37,X_38))
| add(multiply(X_37,X_38),X_37) != add(X_37,multiply(X_37,X_38))
| add(multiply(X_37,X_38),X_37) = multiply(X_37,add(X_37,X_38)) ),
inference(subst,[],[refute_0_50:[bind(X0,$fot(add(multiply(X_37,X_38),X_37))),bind(Y0,$fot(add(X_37,multiply(X_37,X_38)))),bind(Z0,$fot(multiply(X_37,add(X_37,X_38))))]]) ).
cnf(refute_0_151,plain,
( add(X_37,multiply(X_37,X_38)) != multiply(X_37,add(X_37,X_38))
| add(multiply(X_37,X_38),X_37) = multiply(X_37,add(X_37,X_38)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_37,X_38),X_37),add(X_37,multiply(X_37,X_38))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
add(multiply(X_37,X_38),X_37) = multiply(X_37,add(X_37,X_38)),
inference(resolve,[$cnf( $equal(add(X_37,multiply(X_37,X_38)),multiply(X_37,add(X_37,X_38))) )],[refute_0_146,refute_0_151]) ).
cnf(refute_0_153,plain,
( X_37 != add(multiply(X_37,X_38),X_37)
| add(multiply(X_37,X_38),X_37) != multiply(X_37,add(X_37,X_38))
| X_37 = multiply(X_37,add(X_37,X_38)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_37,multiply(X_37,add(X_37,X_38))) ),[0],$fot(add(multiply(X_37,X_38),X_37))]]) ).
cnf(refute_0_154,plain,
( X_37 != add(multiply(X_37,X_38),X_37)
| X_37 = multiply(X_37,add(X_37,X_38)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_37,X_38),X_37),multiply(X_37,add(X_37,X_38))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
( multiply(X_37,add(X_38,multiplicative_identity)) != add(multiply(X_37,X_38),X_37)
| X_37 = multiply(X_37,add(X_37,X_38)) ),
inference(resolve,[$cnf( $equal(X_37,add(multiply(X_37,X_38),X_37)) )],[refute_0_145,refute_0_154]) ).
cnf(refute_0_156,plain,
X_37 = multiply(X_37,add(X_37,X_38)),
inference(resolve,[$cnf( $equal(multiply(X_37,add(X_38,multiplicative_identity)),add(multiply(X_37,X_38),X_37)) )],[refute_0_120,refute_0_155]) ).
cnf(refute_0_157,plain,
( X_37 != multiply(X_37,add(X_37,X_38))
| multiply(X_37,add(X_37,X_38)) = X_37 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(X_37)),bind(Y0,$fot(multiply(X_37,add(X_37,X_38))))]]) ).
cnf(refute_0_158,plain,
multiply(X_37,add(X_37,X_38)) = X_37,
inference(resolve,[$cnf( $equal(X_37,multiply(X_37,add(X_37,X_38))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
multiply(Y,add(Y,add(X_32,Y))) = Y,
inference(subst,[],[refute_0_158:[bind(X_37,$fot(Y)),bind(X_38,$fot(add(X_32,Y)))]]) ).
cnf(refute_0_160,plain,
( multiply(Y,add(Y,add(X_32,Y))) != Y
| add(Y,add(Y,multiply(X_32,additive_identity))) != multiply(Y,add(Y,add(X_32,Y)))
| add(Y,add(Y,multiply(X_32,additive_identity))) = Y ),
introduced(tautology,[equality,[$cnf( $equal(add(Y,add(Y,multiply(X_32,additive_identity))),multiply(Y,add(Y,add(X_32,Y)))) ),[1],$fot(Y)]]) ).
cnf(refute_0_161,plain,
( add(Y,add(Y,multiply(X_32,additive_identity))) != multiply(Y,add(Y,add(X_32,Y)))
| add(Y,add(Y,multiply(X_32,additive_identity))) = Y ),
inference(resolve,[$cnf( $equal(multiply(Y,add(Y,add(X_32,Y))),Y) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
add(Y,add(Y,multiply(X_32,additive_identity))) = Y,
inference(resolve,[$cnf( $equal(add(Y,add(Y,multiply(X_32,additive_identity))),multiply(Y,add(Y,add(X_32,Y)))) )],[refute_0_115,refute_0_161]) ).
cnf(refute_0_163,plain,
add(X_28,add(X_28,multiply(additive_identity,additive_identity))) = X_28,
inference(subst,[],[refute_0_162:[bind(Y,$fot(X_28)),bind(X_32,$fot(additive_identity))]]) ).
cnf(refute_0_164,plain,
( add(X_28,add(X_28,multiply(additive_identity,additive_identity))) != X_28
| add(X_28,add(X_28,multiply(additive_identity,additive_identity))) != multiply(X_28,X_28)
| X_28 = multiply(X_28,X_28) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_28,add(X_28,multiply(additive_identity,additive_identity))),multiply(X_28,X_28)) ),[0],$fot(X_28)]]) ).
cnf(refute_0_165,plain,
( add(X_28,add(X_28,multiply(additive_identity,additive_identity))) != multiply(X_28,X_28)
| X_28 = multiply(X_28,X_28) ),
inference(resolve,[$cnf( $equal(add(X_28,add(X_28,multiply(additive_identity,additive_identity))),X_28) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
X_28 = multiply(X_28,X_28),
inference(resolve,[$cnf( $equal(add(X_28,add(X_28,multiply(additive_identity,additive_identity))),multiply(X_28,X_28)) )],[refute_0_101,refute_0_165]) ).
cnf(refute_0_167,plain,
( X_28 != multiply(X_28,X_28)
| multiply(X_28,X_28) = X_28 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(X_28)),bind(Y0,$fot(multiply(X_28,X_28)))]]) ).
cnf(refute_0_168,plain,
multiply(X_28,X_28) = X_28,
inference(resolve,[$cnf( $equal(X_28,multiply(X_28,X_28)) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity)) = multiply(X_11,additive_identity),
inference(subst,[],[refute_0_168:[bind(X_28,$fot(multiply(X_11,additive_identity)))]]) ).
cnf(refute_0_170,plain,
( multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity)) != multiply(X_11,additive_identity)
| multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity)) != multiply(additive_identity,X_11)
| multiply(X_11,additive_identity) = multiply(additive_identity,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity)),multiply(additive_identity,X_11)) ),[0],$fot(multiply(X_11,additive_identity))]]) ).
cnf(refute_0_171,plain,
( multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity)) != multiply(additive_identity,X_11)
| multiply(X_11,additive_identity) = multiply(additive_identity,X_11) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity)),multiply(X_11,additive_identity)) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
multiply(additive_identity,add(additive_identity,X_39)) = add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_39)),
inference(subst,[],[distributivity2:[bind(X,$fot(additive_identity)),bind(Y,$fot(additive_identity)),bind(Z,$fot(X_39))]]) ).
cnf(refute_0_173,plain,
add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_39)) = multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39)),
inference(subst,[],[refute_0_24:[bind(Y,$fot(multiply(additive_identity,X_39)))]]) ).
cnf(refute_0_174,plain,
( multiply(additive_identity,add(additive_identity,X_39)) != add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_39))
| add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_39)) != multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))
| multiply(additive_identity,add(additive_identity,X_39)) = multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(additive_identity,add(additive_identity,X_39)),multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))) ),[0],$fot(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_39)))]]) ).
cnf(refute_0_175,plain,
( multiply(additive_identity,add(additive_identity,X_39)) != add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_39))
| multiply(additive_identity,add(additive_identity,X_39)) = multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_39)),multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
multiply(additive_identity,add(additive_identity,X_39)) = multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39)),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_39)),add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_39))) )],[refute_0_172,refute_0_175]) ).
cnf(refute_0_177,plain,
multiply(additive_identity,add(additive_identity,X_39)) = additive_identity,
inference(subst,[],[refute_0_158:[bind(X_37,$fot(additive_identity)),bind(X_38,$fot(X_39))]]) ).
cnf(refute_0_178,plain,
( multiply(additive_identity,add(additive_identity,X_39)) != multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))
| multiply(additive_identity,add(additive_identity,X_39)) != additive_identity
| additive_identity = multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_39)),multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))) ),[0],$fot(additive_identity)]]) ).
cnf(refute_0_179,plain,
( multiply(additive_identity,add(additive_identity,X_39)) != multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))
| additive_identity = multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39)) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_39)),additive_identity) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),
inference(subst,[],[refute_0_41:[bind(X_10,$fot(multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_181,plain,
add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)),
inference(subst,[],[refute_0_24:[bind(Y,$fot(multiply(additive_identity,X_12)))]]) ).
cnf(refute_0_182,plain,
( add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12))
| add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))
| multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))) ),[0],$fot(multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)))]]) ).
cnf(refute_0_183,plain,
( add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))
| multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12))) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))) )],[refute_0_180,refute_0_183]) ).
cnf(refute_0_185,plain,
add(X_12,additive_identity) = X_12,
inference(subst,[],[additive_id1:[bind(X,$fot(X_12))]]) ).
cnf(refute_0_186,plain,
multiply(additive_identity,add(X_12,additive_identity)) = multiply(additive_identity,add(X_12,additive_identity)),
introduced(tautology,[refl,[$fot(multiply(additive_identity,add(X_12,additive_identity)))]]) ).
cnf(refute_0_187,plain,
( multiply(additive_identity,add(X_12,additive_identity)) != multiply(additive_identity,add(X_12,additive_identity))
| add(X_12,additive_identity) != X_12
| multiply(additive_identity,add(X_12,additive_identity)) = multiply(additive_identity,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(X_12,additive_identity)),multiply(additive_identity,add(X_12,additive_identity))) ),[1,1],$fot(X_12)]]) ).
cnf(refute_0_188,plain,
( add(X_12,additive_identity) != X_12
| multiply(additive_identity,add(X_12,additive_identity)) = multiply(additive_identity,X_12) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_12,additive_identity)),multiply(additive_identity,add(X_12,additive_identity))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
multiply(additive_identity,add(X_12,additive_identity)) = multiply(additive_identity,X_12),
inference(resolve,[$cnf( $equal(add(X_12,additive_identity),X_12) )],[refute_0_185,refute_0_188]) ).
cnf(refute_0_190,plain,
add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)) = multiply(additive_identity,add(X_12,additive_identity)),
inference(subst,[],[refute_0_35:[bind(X,$fot(additive_identity)),bind(Y,$fot(X_12)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_191,plain,
multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)),
inference(subst,[],[refute_0_47:[bind(Y,$fot(multiply(additive_identity,additive_identity))),bind(X_24,$fot(X_12))]]) ).
cnf(refute_0_192,plain,
( multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) != add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity))
| add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)) != multiply(additive_identity,add(X_12,additive_identity))
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,add(X_12,additive_identity)) ),
inference(subst,[],[refute_0_50:[bind(X0,$fot(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)))),bind(Y0,$fot(add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)))),bind(Z0,$fot(multiply(additive_identity,add(X_12,additive_identity))))]]) ).
cnf(refute_0_193,plain,
( add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)) != multiply(additive_identity,add(X_12,additive_identity))
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,add(X_12,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity))) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,add(X_12,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_12),multiply(additive_identity,additive_identity)),multiply(additive_identity,add(X_12,additive_identity))) )],[refute_0_190,refute_0_193]) ).
cnf(refute_0_195,plain,
( multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) != multiply(additive_identity,add(X_12,additive_identity))
| multiply(additive_identity,add(X_12,additive_identity)) != multiply(additive_identity,X_12)
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,X_12) ),
inference(subst,[],[refute_0_50:[bind(X0,$fot(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)))),bind(Y0,$fot(multiply(additive_identity,add(X_12,additive_identity)))),bind(Z0,$fot(multiply(additive_identity,X_12)))]]) ).
cnf(refute_0_196,plain,
( multiply(additive_identity,add(X_12,additive_identity)) != multiply(additive_identity,X_12)
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,X_12) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),multiply(additive_identity,add(X_12,additive_identity))) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) = multiply(additive_identity,X_12),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_12,additive_identity)),multiply(additive_identity,X_12)) )],[refute_0_189,refute_0_196]) ).
cnf(refute_0_198,plain,
( multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))
| multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)) != multiply(additive_identity,X_12)
| multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(additive_identity,X_12) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)),multiply(additive_identity,X_12)) ),[0],$fot(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)))]]) ).
cnf(refute_0_199,plain,
( multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))
| multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(additive_identity,X_12) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12)),multiply(additive_identity,X_12)) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)) = multiply(additive_identity,X_12),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,X_12),multiply(additive_identity,X_12)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_12))) )],[refute_0_184,refute_0_199]) ).
cnf(refute_0_201,plain,
multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39)) = multiply(additive_identity,X_39),
inference(subst,[],[refute_0_200:[bind(X_12,$fot(X_39))]]) ).
cnf(refute_0_202,plain,
( multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39)) != multiply(additive_identity,X_39)
| additive_identity != multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))
| additive_identity = multiply(additive_identity,X_39) ),
introduced(tautology,[equality,[$cnf( $equal(additive_identity,multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))) ),[1],$fot(multiply(additive_identity,X_39))]]) ).
cnf(refute_0_203,plain,
( additive_identity != multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))
| additive_identity = multiply(additive_identity,X_39) ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39)),multiply(additive_identity,X_39)) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
( multiply(additive_identity,add(additive_identity,X_39)) != multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))
| additive_identity = multiply(additive_identity,X_39) ),
inference(resolve,[$cnf( $equal(additive_identity,multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))) )],[refute_0_179,refute_0_203]) ).
cnf(refute_0_205,plain,
additive_identity = multiply(additive_identity,X_39),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_39)),multiply(multiply(additive_identity,X_39),multiply(additive_identity,X_39))) )],[refute_0_176,refute_0_204]) ).
cnf(refute_0_206,plain,
( additive_identity != multiply(additive_identity,X_39)
| multiply(additive_identity,X_39) = additive_identity ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(additive_identity)),bind(Y0,$fot(multiply(additive_identity,X_39)))]]) ).
cnf(refute_0_207,plain,
multiply(additive_identity,X_39) = additive_identity,
inference(resolve,[$cnf( $equal(additive_identity,multiply(additive_identity,X_39)) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
multiply(additive_identity,X_11) = additive_identity,
inference(subst,[],[refute_0_207:[bind(X_39,$fot(X_11))]]) ).
cnf(refute_0_209,plain,
( multiply(X_11,additive_identity) != multiply(additive_identity,X_11)
| multiply(additive_identity,X_11) != additive_identity
| multiply(X_11,additive_identity) = additive_identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_11,additive_identity),additive_identity) ),[0],$fot(multiply(additive_identity,X_11))]]) ).
cnf(refute_0_210,plain,
( multiply(X_11,additive_identity) != multiply(additive_identity,X_11)
| multiply(X_11,additive_identity) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_11),additive_identity) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
( multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity)) != multiply(additive_identity,X_11)
| multiply(X_11,additive_identity) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(X_11,additive_identity),multiply(additive_identity,X_11)) )],[refute_0_171,refute_0_210]) ).
cnf(refute_0_212,plain,
multiply(X_11,additive_identity) = additive_identity,
inference(resolve,[$cnf( $equal(multiply(multiply(X_11,additive_identity),multiply(X_11,additive_identity)),multiply(additive_identity,X_11)) )],[refute_0_59,refute_0_211]) ).
cnf(refute_0_213,plain,
multiply(a,additive_identity) = additive_identity,
inference(subst,[],[refute_0_212:[bind(X_11,$fot(a))]]) ).
cnf(refute_0_214,plain,
( multiply(a,additive_identity) != additive_identity
| additive_identity != additive_identity
| multiply(a,additive_identity) = additive_identity ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,additive_identity),additive_identity) ),[0],$fot(additive_identity)]]) ).
cnf(refute_0_215,plain,
( additive_identity != additive_identity
| multiply(a,additive_identity) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(a,additive_identity),additive_identity) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
additive_identity != additive_identity,
inference(resolve,[$cnf( $equal(multiply(a,additive_identity),additive_identity) )],[refute_0_215,prove_right_identity]) ).
cnf(refute_0_217,plain,
additive_identity = additive_identity,
introduced(tautology,[refl,[$fot(additive_identity)]]) ).
cnf(refute_0_218,plain,
$false,
inference(resolve,[$cnf( $equal(additive_identity,additive_identity) )],[refute_0_217,refute_0_216]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : BOO006-4 : TPTP v8.1.0. Released v1.1.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 1 19:12:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.39/0.59 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.59
% 0.39/0.59 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.39/0.62
%------------------------------------------------------------------------------