TSTP Solution File: BOO003-2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : BOO003-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 23:44:23 EDT 2022
% Result : Unsatisfiable 0.18s 0.52s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 44
% Syntax : Number of clauses : 162 ( 87 unt; 0 nHn; 87 RR)
% Number of literals : 271 ( 270 equ; 111 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 218 ( 0 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(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ).
cnf(distributivity2,axiom,
add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ).
cnf(distributivity3,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ).
cnf(multiplicative_id1,axiom,
multiply(X,multiplicative_identity) = X ).
cnf(multiplicative_id2,axiom,
multiply(multiplicative_identity,X) = X ).
cnf(additive_id1,axiom,
add(X,additive_identity) = X ).
cnf(additive_id2,axiom,
add(additive_identity,X) = X ).
cnf(prove_a_times_a_is_a,negated_conjecture,
multiply(a,a) != a ).
cnf(refute_0_0,plain,
add(multiply(additive_identity,additive_identity),Y) = add(Y,multiply(additive_identity,additive_identity)),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_1,plain,
add(multiply(Y,Y),Z) = multiply(add(Y,Z),add(Y,Z)),
inference(subst,[],[distributivity1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_2,plain,
add(Y,multiply(Z,Z)) = multiply(add(Y,Z),add(Y,Z)),
inference(subst,[],[distributivity2:[bind(X,$fot(Y)),bind(Y,$fot(Z))]]) ).
cnf(refute_0_3,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_4,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_5,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( add(Y,multiply(Z,Z)) != multiply(add(Y,Z),add(Y,Z))
| multiply(add(Y,Z),add(Y,Z)) = add(Y,multiply(Z,Z)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(add(Y,multiply(Z,Z)))),bind(Y0,$fot(multiply(add(Y,Z),add(Y,Z))))]]) ).
cnf(refute_0_7,plain,
multiply(add(Y,Z),add(Y,Z)) = add(Y,multiply(Z,Z)),
inference(resolve,[$cnf( $equal(add(Y,multiply(Z,Z)),multiply(add(Y,Z),add(Y,Z))) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( multiply(add(Y,Z),add(Y,Z)) != add(Y,multiply(Z,Z))
| add(multiply(Y,Y),Z) != multiply(add(Y,Z),add(Y,Z))
| add(multiply(Y,Y),Z) = add(Y,multiply(Z,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(Y,Y),Z),multiply(add(Y,Z),add(Y,Z))) ),[1],$fot(add(Y,multiply(Z,Z)))]]) ).
cnf(refute_0_9,plain,
( add(multiply(Y,Y),Z) != multiply(add(Y,Z),add(Y,Z))
| add(multiply(Y,Y),Z) = add(Y,multiply(Z,Z)) ),
inference(resolve,[$cnf( $equal(multiply(add(Y,Z),add(Y,Z)),add(Y,multiply(Z,Z))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
add(multiply(Y,Y),Z) = add(Y,multiply(Z,Z)),
inference(resolve,[$cnf( $equal(add(multiply(Y,Y),Z),multiply(add(Y,Z),add(Y,Z))) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
add(multiply(Y,Y),additive_identity) = add(Y,multiply(additive_identity,additive_identity)),
inference(subst,[],[refute_0_10:[bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_12,plain,
add(X_20,multiply(additive_identity,X_22)) = multiply(add(X_20,additive_identity),add(X_20,X_22)),
inference(subst,[],[distributivity2:[bind(X,$fot(X_20)),bind(Y,$fot(additive_identity)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_13,plain,
add(X_20,additive_identity) = X_20,
inference(subst,[],[additive_id1:[bind(X,$fot(X_20))]]) ).
cnf(refute_0_14,plain,
( add(X_20,multiply(additive_identity,X_22)) != multiply(add(X_20,additive_identity),add(X_20,X_22))
| add(X_20,additive_identity) != X_20
| add(X_20,multiply(additive_identity,X_22)) = multiply(X_20,add(X_20,X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_20,multiply(additive_identity,X_22)),multiply(add(X_20,additive_identity),add(X_20,X_22))) ),[1,0],$fot(X_20)]]) ).
cnf(refute_0_15,plain,
( add(X_20,multiply(additive_identity,X_22)) != multiply(add(X_20,additive_identity),add(X_20,X_22))
| add(X_20,multiply(additive_identity,X_22)) = multiply(X_20,add(X_20,X_22)) ),
inference(resolve,[$cnf( $equal(add(X_20,additive_identity),X_20) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
add(X_20,multiply(additive_identity,X_22)) = multiply(X_20,add(X_20,X_22)),
inference(resolve,[$cnf( $equal(add(X_20,multiply(additive_identity,X_22)),multiply(add(X_20,additive_identity),add(X_20,X_22))) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,add(Y,additive_identity)),
inference(subst,[],[refute_0_16:[bind(X_20,$fot(Y)),bind(X_22,$fot(additive_identity))]]) ).
cnf(refute_0_18,plain,
( add(Y,multiply(additive_identity,additive_identity)) != multiply(Y,add(Y,additive_identity))
| add(multiply(Y,Y),additive_identity) != add(Y,multiply(additive_identity,additive_identity))
| add(multiply(Y,Y),additive_identity) = multiply(Y,add(Y,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(Y,Y),additive_identity),add(Y,multiply(additive_identity,additive_identity))) ),[1],$fot(multiply(Y,add(Y,additive_identity)))]]) ).
cnf(refute_0_19,plain,
( add(multiply(Y,Y),additive_identity) != add(Y,multiply(additive_identity,additive_identity))
| add(multiply(Y,Y),additive_identity) = multiply(Y,add(Y,additive_identity)) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(additive_identity,additive_identity)),multiply(Y,add(Y,additive_identity))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
add(multiply(Y,Y),additive_identity) = multiply(Y,add(Y,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(Y,Y),additive_identity),add(Y,multiply(additive_identity,additive_identity))) )],[refute_0_11,refute_0_19]) ).
cnf(refute_0_21,plain,
( add(multiply(Y,Y),additive_identity) != multiply(Y,add(Y,additive_identity))
| add(multiply(Y,Y),additive_identity) != add(Y,multiply(additive_identity,additive_identity))
| add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,add(Y,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(Y,Y),additive_identity),multiply(Y,add(Y,additive_identity))) ),[0],$fot(add(Y,multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_22,plain,
( add(multiply(Y,Y),additive_identity) != multiply(Y,add(Y,additive_identity))
| add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,add(Y,additive_identity)) ),
inference(resolve,[$cnf( $equal(add(multiply(Y,Y),additive_identity),add(Y,multiply(additive_identity,additive_identity))) )],[refute_0_11,refute_0_21]) ).
cnf(refute_0_23,plain,
add(Y,additive_identity) = Y,
inference(subst,[],[additive_id1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_24,plain,
multiply(Y,add(Y,additive_identity)) = multiply(Y,add(Y,additive_identity)),
introduced(tautology,[refl,[$fot(multiply(Y,add(Y,additive_identity)))]]) ).
cnf(refute_0_25,plain,
( multiply(Y,add(Y,additive_identity)) != multiply(Y,add(Y,additive_identity))
| add(Y,additive_identity) != Y
| multiply(Y,add(Y,additive_identity)) = multiply(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(Y,add(Y,additive_identity)),multiply(Y,add(Y,additive_identity))) ),[1,1],$fot(Y)]]) ).
cnf(refute_0_26,plain,
( add(Y,additive_identity) != Y
| multiply(Y,add(Y,additive_identity)) = multiply(Y,Y) ),
inference(resolve,[$cnf( $equal(multiply(Y,add(Y,additive_identity)),multiply(Y,add(Y,additive_identity))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(Y,add(Y,additive_identity)) = multiply(Y,Y),
inference(resolve,[$cnf( $equal(add(Y,additive_identity),Y) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
( multiply(Y,add(Y,additive_identity)) != multiply(Y,Y)
| add(Y,multiply(additive_identity,additive_identity)) != multiply(Y,add(Y,additive_identity))
| add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(Y,multiply(additive_identity,additive_identity)),multiply(Y,add(Y,additive_identity))) ),[1],$fot(multiply(Y,Y))]]) ).
cnf(refute_0_29,plain,
( add(Y,multiply(additive_identity,additive_identity)) != multiply(Y,add(Y,additive_identity))
| add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,Y) ),
inference(resolve,[$cnf( $equal(multiply(Y,add(Y,additive_identity)),multiply(Y,Y)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( add(multiply(Y,Y),additive_identity) != multiply(Y,add(Y,additive_identity))
| add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,Y) ),
inference(resolve,[$cnf( $equal(add(Y,multiply(additive_identity,additive_identity)),multiply(Y,add(Y,additive_identity))) )],[refute_0_22,refute_0_29]) ).
cnf(refute_0_31,plain,
add(Y,multiply(additive_identity,additive_identity)) = multiply(Y,Y),
inference(resolve,[$cnf( $equal(add(multiply(Y,Y),additive_identity),multiply(Y,add(Y,additive_identity))) )],[refute_0_20,refute_0_30]) ).
cnf(refute_0_32,plain,
( add(Y,multiply(additive_identity,additive_identity)) != multiply(Y,Y)
| add(multiply(additive_identity,additive_identity),Y) != add(Y,multiply(additive_identity,additive_identity))
| add(multiply(additive_identity,additive_identity),Y) = multiply(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),add(Y,multiply(additive_identity,additive_identity))) ),[1],$fot(multiply(Y,Y))]]) ).
cnf(refute_0_33,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( $equal(add(Y,multiply(additive_identity,additive_identity)),multiply(Y,Y)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
add(multiply(additive_identity,additive_identity),Y) = multiply(Y,Y),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),add(Y,multiply(additive_identity,additive_identity))) )],[refute_0_0,refute_0_33]) ).
cnf(refute_0_35,plain,
add(additive_identity,Y) = Y,
inference(subst,[],[additive_id2:[bind(X,$fot(Y))]]) ).
cnf(refute_0_36,plain,
add(multiply(X_10,additive_identity),X_12) = multiply(add(X_10,X_12),add(additive_identity,X_12)),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(additive_identity)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_37,plain,
add(additive_identity,X_12) = X_12,
inference(subst,[],[additive_id2:[bind(X,$fot(X_12))]]) ).
cnf(refute_0_38,plain,
( add(multiply(X_10,additive_identity),X_12) != multiply(add(X_10,X_12),add(additive_identity,X_12))
| add(additive_identity,X_12) != X_12
| add(multiply(X_10,additive_identity),X_12) = multiply(add(X_10,X_12),X_12) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,additive_identity),X_12),multiply(add(X_10,X_12),add(additive_identity,X_12))) ),[1,1],$fot(X_12)]]) ).
cnf(refute_0_39,plain,
( add(multiply(X_10,additive_identity),X_12) != multiply(add(X_10,X_12),add(additive_identity,X_12))
| add(multiply(X_10,additive_identity),X_12) = multiply(add(X_10,X_12),X_12) ),
inference(resolve,[$cnf( $equal(add(additive_identity,X_12),X_12) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
add(multiply(X_10,additive_identity),X_12) = multiply(add(X_10,X_12),X_12),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),X_12),multiply(add(X_10,X_12),add(additive_identity,X_12))) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
( multiply(X,Y) != multiply(Y,X)
| multiply(Y,X) = multiply(X,Y) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(multiply(X,Y))),bind(Y0,$fot(multiply(Y,X)))]]) ).
cnf(refute_0_42,plain,
multiply(Y,X) = multiply(X,Y),
inference(resolve,[$cnf( $equal(multiply(X,Y),multiply(Y,X)) )],[commutativity_of_multiply,refute_0_41]) ).
cnf(refute_0_43,plain,
multiply(add(X_10,X_12),X_12) = multiply(X_12,add(X_10,X_12)),
inference(subst,[],[refute_0_42:[bind(X,$fot(X_12)),bind(Y,$fot(add(X_10,X_12)))]]) ).
cnf(refute_0_44,plain,
( multiply(add(X_10,X_12),X_12) != multiply(X_12,add(X_10,X_12))
| add(multiply(X_10,additive_identity),X_12) != multiply(add(X_10,X_12),X_12)
| add(multiply(X_10,additive_identity),X_12) = multiply(X_12,add(X_10,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,additive_identity),X_12),multiply(add(X_10,X_12),X_12)) ),[1],$fot(multiply(X_12,add(X_10,X_12)))]]) ).
cnf(refute_0_45,plain,
( add(multiply(X_10,additive_identity),X_12) != multiply(add(X_10,X_12),X_12)
| add(multiply(X_10,additive_identity),X_12) = multiply(X_12,add(X_10,X_12)) ),
inference(resolve,[$cnf( $equal(multiply(add(X_10,X_12),X_12),multiply(X_12,add(X_10,X_12))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
add(multiply(X_10,additive_identity),X_12) = multiply(X_12,add(X_10,X_12)),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),X_12),multiply(add(X_10,X_12),X_12)) )],[refute_0_40,refute_0_45]) ).
cnf(refute_0_47,plain,
add(multiply(multiplicative_identity,additive_identity),X_14) = multiply(X_14,add(multiplicative_identity,X_14)),
inference(subst,[],[refute_0_46:[bind(X_10,$fot(multiplicative_identity)),bind(X_12,$fot(X_14))]]) ).
cnf(refute_0_48,plain,
multiply(multiplicative_identity,additive_identity) = additive_identity,
inference(subst,[],[multiplicative_id2:[bind(X,$fot(additive_identity))]]) ).
cnf(refute_0_49,plain,
( multiply(multiplicative_identity,additive_identity) != additive_identity
| add(multiply(multiplicative_identity,additive_identity),X_14) != multiply(X_14,add(multiplicative_identity,X_14))
| add(additive_identity,X_14) = multiply(X_14,add(multiplicative_identity,X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(multiplicative_identity,additive_identity),X_14),multiply(X_14,add(multiplicative_identity,X_14))) ),[0,0],$fot(additive_identity)]]) ).
cnf(refute_0_50,plain,
( add(multiply(multiplicative_identity,additive_identity),X_14) != multiply(X_14,add(multiplicative_identity,X_14))
| add(additive_identity,X_14) = multiply(X_14,add(multiplicative_identity,X_14)) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,additive_identity),additive_identity) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
add(additive_identity,X_14) = multiply(X_14,add(multiplicative_identity,X_14)),
inference(resolve,[$cnf( $equal(add(multiply(multiplicative_identity,additive_identity),X_14),multiply(X_14,add(multiplicative_identity,X_14))) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
add(additive_identity,X_14) = X_14,
inference(subst,[],[additive_id2:[bind(X,$fot(X_14))]]) ).
cnf(refute_0_53,plain,
( add(additive_identity,X_14) != X_14
| add(additive_identity,X_14) != multiply(X_14,add(multiplicative_identity,X_14))
| X_14 = multiply(X_14,add(multiplicative_identity,X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_identity,X_14),multiply(X_14,add(multiplicative_identity,X_14))) ),[0],$fot(X_14)]]) ).
cnf(refute_0_54,plain,
( add(additive_identity,X_14) != multiply(X_14,add(multiplicative_identity,X_14))
| X_14 = multiply(X_14,add(multiplicative_identity,X_14)) ),
inference(resolve,[$cnf( $equal(add(additive_identity,X_14),X_14) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
X_14 = multiply(X_14,add(multiplicative_identity,X_14)),
inference(resolve,[$cnf( $equal(add(additive_identity,X_14),multiply(X_14,add(multiplicative_identity,X_14))) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
multiply(additive_identity,additive_identity) = multiply(multiply(additive_identity,additive_identity),add(multiplicative_identity,multiply(additive_identity,additive_identity))),
inference(subst,[],[refute_0_55:[bind(X_14,$fot(multiply(additive_identity,additive_identity)))]]) ).
cnf(refute_0_57,plain,
add(multiplicative_identity,multiply(additive_identity,additive_identity)) = multiply(multiplicative_identity,multiplicative_identity),
inference(subst,[],[refute_0_31:[bind(Y,$fot(multiplicative_identity))]]) ).
cnf(refute_0_58,plain,
( multiply(additive_identity,additive_identity) != multiply(multiply(additive_identity,additive_identity),add(multiplicative_identity,multiply(additive_identity,additive_identity)))
| add(multiplicative_identity,multiply(additive_identity,additive_identity)) != multiply(multiplicative_identity,multiplicative_identity)
| multiply(additive_identity,additive_identity) = multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,additive_identity),multiply(multiply(additive_identity,additive_identity),add(multiplicative_identity,multiply(additive_identity,additive_identity)))) ),[1,1],$fot(multiply(multiplicative_identity,multiplicative_identity))]]) ).
cnf(refute_0_59,plain,
( multiply(additive_identity,additive_identity) != multiply(multiply(additive_identity,additive_identity),add(multiplicative_identity,multiply(additive_identity,additive_identity)))
| multiply(additive_identity,additive_identity) = multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)) ),
inference(resolve,[$cnf( $equal(add(multiplicative_identity,multiply(additive_identity,additive_identity)),multiply(multiplicative_identity,multiplicative_identity)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
multiply(additive_identity,additive_identity) = multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)),
inference(resolve,[$cnf( $equal(multiply(additive_identity,additive_identity),multiply(multiply(additive_identity,additive_identity),add(multiplicative_identity,multiply(additive_identity,additive_identity)))) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
multiply(additive_identity,multiplicative_identity) = additive_identity,
inference(subst,[],[multiplicative_id1:[bind(X,$fot(additive_identity))]]) ).
cnf(refute_0_62,plain,
add(X_20,multiply(X_21,additive_identity)) = multiply(add(X_20,X_21),add(X_20,additive_identity)),
inference(subst,[],[distributivity2:[bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_63,plain,
( add(X_20,multiply(X_21,additive_identity)) != multiply(add(X_20,X_21),add(X_20,additive_identity))
| add(X_20,additive_identity) != X_20
| add(X_20,multiply(X_21,additive_identity)) = multiply(add(X_20,X_21),X_20) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_20,multiply(X_21,additive_identity)),multiply(add(X_20,X_21),add(X_20,additive_identity))) ),[1,1],$fot(X_20)]]) ).
cnf(refute_0_64,plain,
( add(X_20,multiply(X_21,additive_identity)) != multiply(add(X_20,X_21),add(X_20,additive_identity))
| add(X_20,multiply(X_21,additive_identity)) = multiply(add(X_20,X_21),X_20) ),
inference(resolve,[$cnf( $equal(add(X_20,additive_identity),X_20) )],[refute_0_13,refute_0_63]) ).
cnf(refute_0_65,plain,
add(X_20,multiply(X_21,additive_identity)) = multiply(add(X_20,X_21),X_20),
inference(resolve,[$cnf( $equal(add(X_20,multiply(X_21,additive_identity)),multiply(add(X_20,X_21),add(X_20,additive_identity))) )],[refute_0_62,refute_0_64]) ).
cnf(refute_0_66,plain,
multiply(add(X_20,X_21),X_20) = multiply(X_20,add(X_20,X_21)),
inference(subst,[],[refute_0_42:[bind(X,$fot(X_20)),bind(Y,$fot(add(X_20,X_21)))]]) ).
cnf(refute_0_67,plain,
( multiply(add(X_20,X_21),X_20) != multiply(X_20,add(X_20,X_21))
| add(X_20,multiply(X_21,additive_identity)) != multiply(add(X_20,X_21),X_20)
| add(X_20,multiply(X_21,additive_identity)) = multiply(X_20,add(X_20,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_20,multiply(X_21,additive_identity)),multiply(add(X_20,X_21),X_20)) ),[1],$fot(multiply(X_20,add(X_20,X_21)))]]) ).
cnf(refute_0_68,plain,
( add(X_20,multiply(X_21,additive_identity)) != multiply(add(X_20,X_21),X_20)
| add(X_20,multiply(X_21,additive_identity)) = multiply(X_20,add(X_20,X_21)) ),
inference(resolve,[$cnf( $equal(multiply(add(X_20,X_21),X_20),multiply(X_20,add(X_20,X_21))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
add(X_20,multiply(X_21,additive_identity)) = multiply(X_20,add(X_20,X_21)),
inference(resolve,[$cnf( $equal(add(X_20,multiply(X_21,additive_identity)),multiply(add(X_20,X_21),X_20)) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)) = multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_26)),
inference(subst,[],[refute_0_69:[bind(X_20,$fot(multiply(additive_identity,additive_identity))),bind(X_21,$fot(X_26))]]) ).
cnf(refute_0_71,plain,
add(multiply(additive_identity,additive_identity),X_14) = multiply(X_14,add(additive_identity,X_14)),
inference(subst,[],[refute_0_46:[bind(X_10,$fot(additive_identity)),bind(X_12,$fot(X_14))]]) ).
cnf(refute_0_72,plain,
( add(multiply(additive_identity,additive_identity),X_14) != multiply(X_14,add(additive_identity,X_14))
| add(additive_identity,X_14) != X_14
| add(multiply(additive_identity,additive_identity),X_14) = multiply(X_14,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),X_14),multiply(X_14,add(additive_identity,X_14))) ),[1,1],$fot(X_14)]]) ).
cnf(refute_0_73,plain,
( add(multiply(additive_identity,additive_identity),X_14) != multiply(X_14,add(additive_identity,X_14))
| add(multiply(additive_identity,additive_identity),X_14) = multiply(X_14,X_14) ),
inference(resolve,[$cnf( $equal(add(additive_identity,X_14),X_14) )],[refute_0_52,refute_0_72]) ).
cnf(refute_0_74,plain,
add(multiply(additive_identity,additive_identity),X_14) = multiply(X_14,X_14),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),X_14),multiply(X_14,add(additive_identity,X_14))) )],[refute_0_71,refute_0_73]) ).
cnf(refute_0_75,plain,
add(multiply(additive_identity,additive_identity),X_26) = multiply(X_26,X_26),
inference(subst,[],[refute_0_74:[bind(X_14,$fot(X_26))]]) ).
cnf(refute_0_76,plain,
( add(multiply(additive_identity,additive_identity),X_26) != multiply(X_26,X_26)
| add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_26))
| add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)) = multiply(multiply(additive_identity,additive_identity),multiply(X_26,X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_26))) ),[1,1],$fot(multiply(X_26,X_26))]]) ).
cnf(refute_0_77,plain,
( add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)) != multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_26))
| add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)) = multiply(multiply(additive_identity,additive_identity),multiply(X_26,X_26)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),X_26),multiply(X_26,X_26)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)) = multiply(multiply(additive_identity,additive_identity),multiply(X_26,X_26)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)),multiply(multiply(additive_identity,additive_identity),add(multiply(additive_identity,additive_identity),X_26))) )],[refute_0_70,refute_0_77]) ).
cnf(refute_0_79,plain,
add(additive_identity,X_26) = X_26,
inference(subst,[],[additive_id2:[bind(X,$fot(X_26))]]) ).
cnf(refute_0_80,plain,
multiply(additive_identity,add(additive_identity,X_26)) = multiply(additive_identity,add(additive_identity,X_26)),
introduced(tautology,[refl,[$fot(multiply(additive_identity,add(additive_identity,X_26)))]]) ).
cnf(refute_0_81,plain,
( multiply(additive_identity,add(additive_identity,X_26)) != multiply(additive_identity,add(additive_identity,X_26))
| add(additive_identity,X_26) != X_26
| multiply(additive_identity,add(additive_identity,X_26)) = multiply(additive_identity,X_26) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_26)),multiply(additive_identity,add(additive_identity,X_26))) ),[1,1],$fot(X_26)]]) ).
cnf(refute_0_82,plain,
( add(additive_identity,X_26) != X_26
| multiply(additive_identity,add(additive_identity,X_26)) = multiply(additive_identity,X_26) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_26)),multiply(additive_identity,add(additive_identity,X_26))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
multiply(additive_identity,add(additive_identity,X_26)) = multiply(additive_identity,X_26),
inference(resolve,[$cnf( $equal(add(additive_identity,X_26),X_26) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)) = multiply(multiply(X_26,additive_identity),add(X_10,multiply(X_26,additive_identity))),
inference(subst,[],[refute_0_46:[bind(X_12,$fot(multiply(X_26,additive_identity)))]]) ).
cnf(refute_0_85,plain,
add(X_10,multiply(X_26,additive_identity)) = multiply(X_10,add(X_10,X_26)),
inference(subst,[],[refute_0_69:[bind(X_20,$fot(X_10)),bind(X_21,$fot(X_26))]]) ).
cnf(refute_0_86,plain,
( add(X_10,multiply(X_26,additive_identity)) != multiply(X_10,add(X_10,X_26))
| add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)) != multiply(multiply(X_26,additive_identity),add(X_10,multiply(X_26,additive_identity)))
| add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)) = multiply(multiply(X_26,additive_identity),multiply(X_10,add(X_10,X_26))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)),multiply(multiply(X_26,additive_identity),add(X_10,multiply(X_26,additive_identity)))) ),[1,1],$fot(multiply(X_10,add(X_10,X_26)))]]) ).
cnf(refute_0_87,plain,
( add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)) != multiply(multiply(X_26,additive_identity),add(X_10,multiply(X_26,additive_identity)))
| add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)) = multiply(multiply(X_26,additive_identity),multiply(X_10,add(X_10,X_26))) ),
inference(resolve,[$cnf( $equal(add(X_10,multiply(X_26,additive_identity)),multiply(X_10,add(X_10,X_26))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)) = multiply(multiply(X_26,additive_identity),multiply(X_10,add(X_10,X_26))),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)),multiply(multiply(X_26,additive_identity),add(X_10,multiply(X_26,additive_identity)))) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
multiply(add(X_10,X_26),additive_identity) = multiply(additive_identity,add(X_10,X_26)),
inference(subst,[],[refute_0_42:[bind(X,$fot(additive_identity)),bind(Y,$fot(add(X_10,X_26)))]]) ).
cnf(refute_0_90,plain,
( multiply(add(X,Y),Z) != add(multiply(X,Z),multiply(Y,Z))
| add(multiply(X,Z),multiply(Y,Z)) = multiply(add(X,Y),Z) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(multiply(add(X,Y),Z))),bind(Y0,$fot(add(multiply(X,Z),multiply(Y,Z))))]]) ).
cnf(refute_0_91,plain,
add(multiply(X,Z),multiply(Y,Z)) = multiply(add(X,Y),Z),
inference(resolve,[$cnf( $equal(multiply(add(X,Y),Z),add(multiply(X,Z),multiply(Y,Z))) )],[distributivity3,refute_0_90]) ).
cnf(refute_0_92,plain,
add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)) = multiply(add(X_10,X_26),additive_identity),
inference(subst,[],[refute_0_91:[bind(X,$fot(X_10)),bind(Y,$fot(X_26)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_93,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_94,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_5,refute_0_93]) ).
cnf(refute_0_95,plain,
( multiply(add(X_10,X_26),additive_identity) != multiply(additive_identity,add(X_10,X_26))
| add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)) != multiply(add(X_10,X_26),additive_identity)
| add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)) = multiply(additive_identity,add(X_10,X_26)) ),
inference(subst,[],[refute_0_94:[bind(X0,$fot(add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)))),bind(Y0,$fot(multiply(add(X_10,X_26),additive_identity))),bind(Z0,$fot(multiply(additive_identity,add(X_10,X_26))))]]) ).
cnf(refute_0_96,plain,
( multiply(add(X_10,X_26),additive_identity) != multiply(additive_identity,add(X_10,X_26))
| add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)) = multiply(additive_identity,add(X_10,X_26)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)),multiply(add(X_10,X_26),additive_identity)) )],[refute_0_92,refute_0_95]) ).
cnf(refute_0_97,plain,
add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)) = multiply(additive_identity,add(X_10,X_26)),
inference(resolve,[$cnf( $equal(multiply(add(X_10,X_26),additive_identity),multiply(additive_identity,add(X_10,X_26))) )],[refute_0_89,refute_0_96]) ).
cnf(refute_0_98,plain,
( add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)) != multiply(multiply(X_26,additive_identity),multiply(X_10,add(X_10,X_26)))
| add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)) != multiply(additive_identity,add(X_10,X_26))
| multiply(additive_identity,add(X_10,X_26)) = multiply(multiply(X_26,additive_identity),multiply(X_10,add(X_10,X_26))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)),multiply(multiply(X_26,additive_identity),multiply(X_10,add(X_10,X_26)))) ),[0],$fot(multiply(additive_identity,add(X_10,X_26)))]]) ).
cnf(refute_0_99,plain,
( add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)) != multiply(multiply(X_26,additive_identity),multiply(X_10,add(X_10,X_26)))
| multiply(additive_identity,add(X_10,X_26)) = multiply(multiply(X_26,additive_identity),multiply(X_10,add(X_10,X_26))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)),multiply(additive_identity,add(X_10,X_26))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
add(multiply(additive_identity,X_11),X_12) = multiply(add(additive_identity,X_12),add(X_11,X_12)),
inference(subst,[],[distributivity1:[bind(X,$fot(additive_identity)),bind(Y,$fot(X_11)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_101,plain,
( add(multiply(additive_identity,X_11),X_12) != multiply(add(additive_identity,X_12),add(X_11,X_12))
| add(additive_identity,X_12) != X_12
| add(multiply(additive_identity,X_11),X_12) = multiply(X_12,add(X_11,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_11),X_12),multiply(add(additive_identity,X_12),add(X_11,X_12))) ),[1,0],$fot(X_12)]]) ).
cnf(refute_0_102,plain,
( add(multiply(additive_identity,X_11),X_12) != multiply(add(additive_identity,X_12),add(X_11,X_12))
| add(multiply(additive_identity,X_11),X_12) = multiply(X_12,add(X_11,X_12)) ),
inference(resolve,[$cnf( $equal(add(additive_identity,X_12),X_12) )],[refute_0_37,refute_0_101]) ).
cnf(refute_0_103,plain,
add(multiply(additive_identity,X_11),X_12) = multiply(X_12,add(X_11,X_12)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_11),X_12),multiply(add(additive_identity,X_12),add(X_11,X_12))) )],[refute_0_100,refute_0_102]) ).
cnf(refute_0_104,plain,
add(multiply(additive_identity,X_11),multiply(X_26,additive_identity)) = multiply(multiply(X_26,additive_identity),add(X_11,multiply(X_26,additive_identity))),
inference(subst,[],[refute_0_103:[bind(X_12,$fot(multiply(X_26,additive_identity)))]]) ).
cnf(refute_0_105,plain,
add(X_11,multiply(X_26,additive_identity)) = multiply(X_11,add(X_11,X_26)),
inference(subst,[],[refute_0_69:[bind(X_20,$fot(X_11)),bind(X_21,$fot(X_26))]]) ).
cnf(refute_0_106,plain,
( add(X_11,multiply(X_26,additive_identity)) != multiply(X_11,add(X_11,X_26))
| add(multiply(additive_identity,X_11),multiply(X_26,additive_identity)) != multiply(multiply(X_26,additive_identity),add(X_11,multiply(X_26,additive_identity)))
| add(multiply(additive_identity,X_11),multiply(X_26,additive_identity)) = multiply(multiply(X_26,additive_identity),multiply(X_11,add(X_11,X_26))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,X_11),multiply(X_26,additive_identity)),multiply(multiply(X_26,additive_identity),add(X_11,multiply(X_26,additive_identity)))) ),[1,1],$fot(multiply(X_11,add(X_11,X_26)))]]) ).
cnf(refute_0_107,plain,
( add(multiply(additive_identity,X_11),multiply(X_26,additive_identity)) != multiply(multiply(X_26,additive_identity),add(X_11,multiply(X_26,additive_identity)))
| add(multiply(additive_identity,X_11),multiply(X_26,additive_identity)) = multiply(multiply(X_26,additive_identity),multiply(X_11,add(X_11,X_26))) ),
inference(resolve,[$cnf( $equal(add(X_11,multiply(X_26,additive_identity)),multiply(X_11,add(X_11,X_26))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
add(multiply(additive_identity,X_11),multiply(X_26,additive_identity)) = multiply(multiply(X_26,additive_identity),multiply(X_11,add(X_11,X_26))),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_11),multiply(X_26,additive_identity)),multiply(multiply(X_26,additive_identity),add(X_11,multiply(X_26,additive_identity)))) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
( add(multiply(additive_identity,X_11),multiply(X_26,additive_identity)) != multiply(multiply(X_26,additive_identity),multiply(X_11,add(X_11,X_26)))
| multiply(multiply(X_26,additive_identity),multiply(X_11,add(X_11,X_26))) = add(multiply(additive_identity,X_11),multiply(X_26,additive_identity)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(add(multiply(additive_identity,X_11),multiply(X_26,additive_identity)))),bind(Y0,$fot(multiply(multiply(X_26,additive_identity),multiply(X_11,add(X_11,X_26)))))]]) ).
cnf(refute_0_110,plain,
multiply(multiply(X_26,additive_identity),multiply(X_11,add(X_11,X_26))) = add(multiply(additive_identity,X_11),multiply(X_26,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,X_11),multiply(X_26,additive_identity)),multiply(multiply(X_26,additive_identity),multiply(X_11,add(X_11,X_26)))) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
multiply(multiply(X_26,additive_identity),multiply(X_10,add(X_10,X_26))) = add(multiply(additive_identity,X_10),multiply(X_26,additive_identity)),
inference(subst,[],[refute_0_110:[bind(X_11,$fot(X_10))]]) ).
cnf(refute_0_112,plain,
( multiply(multiply(X_26,additive_identity),multiply(X_10,add(X_10,X_26))) != add(multiply(additive_identity,X_10),multiply(X_26,additive_identity))
| multiply(additive_identity,add(X_10,X_26)) != multiply(multiply(X_26,additive_identity),multiply(X_10,add(X_10,X_26)))
| multiply(additive_identity,add(X_10,X_26)) = add(multiply(additive_identity,X_10),multiply(X_26,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,add(X_10,X_26)),multiply(multiply(X_26,additive_identity),multiply(X_10,add(X_10,X_26)))) ),[1],$fot(add(multiply(additive_identity,X_10),multiply(X_26,additive_identity)))]]) ).
cnf(refute_0_113,plain,
( multiply(additive_identity,add(X_10,X_26)) != multiply(multiply(X_26,additive_identity),multiply(X_10,add(X_10,X_26)))
| multiply(additive_identity,add(X_10,X_26)) = add(multiply(additive_identity,X_10),multiply(X_26,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_26,additive_identity),multiply(X_10,add(X_10,X_26))),add(multiply(additive_identity,X_10),multiply(X_26,additive_identity))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
( add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)) != multiply(multiply(X_26,additive_identity),multiply(X_10,add(X_10,X_26)))
| multiply(additive_identity,add(X_10,X_26)) = add(multiply(additive_identity,X_10),multiply(X_26,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_10,X_26)),multiply(multiply(X_26,additive_identity),multiply(X_10,add(X_10,X_26)))) )],[refute_0_99,refute_0_113]) ).
cnf(refute_0_115,plain,
multiply(additive_identity,add(X_10,X_26)) = add(multiply(additive_identity,X_10),multiply(X_26,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),multiply(X_26,additive_identity)),multiply(multiply(X_26,additive_identity),multiply(X_10,add(X_10,X_26)))) )],[refute_0_88,refute_0_114]) ).
cnf(refute_0_116,plain,
( multiply(additive_identity,add(X_10,X_26)) != add(multiply(additive_identity,X_10),multiply(X_26,additive_identity))
| add(multiply(additive_identity,X_10),multiply(X_26,additive_identity)) = multiply(additive_identity,add(X_10,X_26)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(multiply(additive_identity,add(X_10,X_26)))),bind(Y0,$fot(add(multiply(additive_identity,X_10),multiply(X_26,additive_identity))))]]) ).
cnf(refute_0_117,plain,
add(multiply(additive_identity,X_10),multiply(X_26,additive_identity)) = multiply(additive_identity,add(X_10,X_26)),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(X_10,X_26)),add(multiply(additive_identity,X_10),multiply(X_26,additive_identity))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)) = multiply(additive_identity,add(additive_identity,X_26)),
inference(subst,[],[refute_0_117:[bind(X_10,$fot(additive_identity))]]) ).
cnf(refute_0_119,plain,
( multiply(additive_identity,add(additive_identity,X_26)) != multiply(additive_identity,X_26)
| add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)) != multiply(additive_identity,add(additive_identity,X_26))
| add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)) = multiply(additive_identity,X_26) ),
inference(subst,[],[refute_0_94:[bind(X0,$fot(add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)))),bind(Y0,$fot(multiply(additive_identity,add(additive_identity,X_26)))),bind(Z0,$fot(multiply(additive_identity,X_26)))]]) ).
cnf(refute_0_120,plain,
( multiply(additive_identity,add(additive_identity,X_26)) != multiply(additive_identity,X_26)
| add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)) = multiply(additive_identity,X_26) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)),multiply(additive_identity,add(additive_identity,X_26))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)) = multiply(additive_identity,X_26),
inference(resolve,[$cnf( $equal(multiply(additive_identity,add(additive_identity,X_26)),multiply(additive_identity,X_26)) )],[refute_0_83,refute_0_120]) ).
cnf(refute_0_122,plain,
( add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)) != multiply(multiply(additive_identity,additive_identity),multiply(X_26,X_26))
| add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)) != multiply(additive_identity,X_26)
| multiply(additive_identity,X_26) = multiply(multiply(additive_identity,additive_identity),multiply(X_26,X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)),multiply(multiply(additive_identity,additive_identity),multiply(X_26,X_26))) ),[0],$fot(multiply(additive_identity,X_26))]]) ).
cnf(refute_0_123,plain,
( add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)) != multiply(multiply(additive_identity,additive_identity),multiply(X_26,X_26))
| multiply(additive_identity,X_26) = multiply(multiply(additive_identity,additive_identity),multiply(X_26,X_26)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)),multiply(additive_identity,X_26)) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
multiply(additive_identity,X_26) = multiply(multiply(additive_identity,additive_identity),multiply(X_26,X_26)),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),multiply(X_26,additive_identity)),multiply(multiply(additive_identity,additive_identity),multiply(X_26,X_26))) )],[refute_0_78,refute_0_123]) ).
cnf(refute_0_125,plain,
( multiply(additive_identity,X_26) != multiply(multiply(additive_identity,additive_identity),multiply(X_26,X_26))
| multiply(multiply(additive_identity,additive_identity),multiply(X_26,X_26)) = multiply(additive_identity,X_26) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(multiply(additive_identity,X_26))),bind(Y0,$fot(multiply(multiply(additive_identity,additive_identity),multiply(X_26,X_26))))]]) ).
cnf(refute_0_126,plain,
multiply(multiply(additive_identity,additive_identity),multiply(X_26,X_26)) = multiply(additive_identity,X_26),
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_26),multiply(multiply(additive_identity,additive_identity),multiply(X_26,X_26))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)) = multiply(additive_identity,multiplicative_identity),
inference(subst,[],[refute_0_126:[bind(X_26,$fot(multiplicative_identity))]]) ).
cnf(refute_0_128,plain,
( multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)) != multiply(additive_identity,multiplicative_identity)
| multiply(additive_identity,multiplicative_identity) != additive_identity
| multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)) = additive_identity ),
inference(subst,[],[refute_0_94:[bind(X0,$fot(multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)))),bind(Y0,$fot(multiply(additive_identity,multiplicative_identity))),bind(Z0,$fot(additive_identity))]]) ).
cnf(refute_0_129,plain,
( multiply(additive_identity,multiplicative_identity) != additive_identity
| multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)),multiply(additive_identity,multiplicative_identity)) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)) = additive_identity,
inference(resolve,[$cnf( $equal(multiply(additive_identity,multiplicative_identity),additive_identity) )],[refute_0_61,refute_0_129]) ).
cnf(refute_0_131,plain,
( multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)) != additive_identity
| multiply(additive_identity,additive_identity) != multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity))
| multiply(additive_identity,additive_identity) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,additive_identity),multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity))) ),[1],$fot(additive_identity)]]) ).
cnf(refute_0_132,plain,
( multiply(additive_identity,additive_identity) != multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity))
| multiply(additive_identity,additive_identity) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity)),additive_identity) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
multiply(additive_identity,additive_identity) = additive_identity,
inference(resolve,[$cnf( $equal(multiply(additive_identity,additive_identity),multiply(multiply(additive_identity,additive_identity),multiply(multiplicative_identity,multiplicative_identity))) )],[refute_0_60,refute_0_132]) ).
cnf(refute_0_134,plain,
add(multiply(additive_identity,additive_identity),Y) = add(multiply(additive_identity,additive_identity),Y),
introduced(tautology,[refl,[$fot(add(multiply(additive_identity,additive_identity),Y))]]) ).
cnf(refute_0_135,plain,
( multiply(additive_identity,additive_identity) != additive_identity
| add(multiply(additive_identity,additive_identity),Y) != add(multiply(additive_identity,additive_identity),Y)
| add(multiply(additive_identity,additive_identity),Y) = add(additive_identity,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),add(multiply(additive_identity,additive_identity),Y)) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_136,plain,
( multiply(additive_identity,additive_identity) != additive_identity
| add(multiply(additive_identity,additive_identity),Y) = add(additive_identity,Y) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),add(multiply(additive_identity,additive_identity),Y)) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
add(multiply(additive_identity,additive_identity),Y) = add(additive_identity,Y),
inference(resolve,[$cnf( $equal(multiply(additive_identity,additive_identity),additive_identity) )],[refute_0_133,refute_0_136]) ).
cnf(refute_0_138,plain,
( add(multiply(additive_identity,additive_identity),Y) != add(additive_identity,Y)
| add(additive_identity,Y) != Y
| add(multiply(additive_identity,additive_identity),Y) = Y ),
inference(subst,[],[refute_0_94:[bind(X0,$fot(add(multiply(additive_identity,additive_identity),Y))),bind(Y0,$fot(add(additive_identity,Y))),bind(Z0,$fot(Y))]]) ).
cnf(refute_0_139,plain,
( add(additive_identity,Y) != Y
| add(multiply(additive_identity,additive_identity),Y) = Y ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),add(additive_identity,Y)) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
add(multiply(additive_identity,additive_identity),Y) = Y,
inference(resolve,[$cnf( $equal(add(additive_identity,Y),Y) )],[refute_0_35,refute_0_139]) ).
cnf(refute_0_141,plain,
( add(multiply(additive_identity,additive_identity),Y) != Y
| add(multiply(additive_identity,additive_identity),Y) != multiply(Y,Y)
| Y = multiply(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),multiply(Y,Y)) ),[0],$fot(Y)]]) ).
cnf(refute_0_142,plain,
( add(multiply(additive_identity,additive_identity),Y) != multiply(Y,Y)
| Y = multiply(Y,Y) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),Y) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
Y = multiply(Y,Y),
inference(resolve,[$cnf( $equal(add(multiply(additive_identity,additive_identity),Y),multiply(Y,Y)) )],[refute_0_34,refute_0_142]) ).
cnf(refute_0_144,plain,
( Y != multiply(Y,Y)
| multiply(Y,Y) = Y ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(Y)),bind(Y0,$fot(multiply(Y,Y)))]]) ).
cnf(refute_0_145,plain,
multiply(Y,Y) = Y,
inference(resolve,[$cnf( $equal(Y,multiply(Y,Y)) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
multiply(a,a) = a,
inference(subst,[],[refute_0_145:[bind(Y,$fot(a))]]) ).
cnf(refute_0_147,plain,
( multiply(a,a) != a
| a != a
| multiply(a,a) = a ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,a),a) ),[0],$fot(a)]]) ).
cnf(refute_0_148,plain,
( a != a
| multiply(a,a) = a ),
inference(resolve,[$cnf( $equal(multiply(a,a),a) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
a != a,
inference(resolve,[$cnf( $equal(multiply(a,a),a) )],[refute_0_148,prove_a_times_a_is_a]) ).
cnf(refute_0_150,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_151,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_150,refute_0_149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO003-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 1 21:36:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.52 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.52
% 0.18/0.52 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.53
%------------------------------------------------------------------------------