TSTP Solution File: BOO009-2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : BOO009-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 23:44:33 EDT 2022
% Result : Unsatisfiable 0.69s 0.91s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 53
% Syntax : Number of clauses : 185 ( 97 unt; 0 nHn; 90 RR)
% Number of literals : 311 ( 310 equ; 128 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 273 ( 11 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(additive_inverse1,axiom,
add(X,inverse(X)) = multiplicative_identity ).
cnf(multiplicative_inverse1,axiom,
multiply(X,inverse(X)) = additive_identity ).
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_operation,negated_conjecture,
multiply(a,add(a,b)) != a ).
cnf(refute_0_0,plain,
multiply(add(X_57,multiplicative_identity),X_59) = add(multiply(X_57,X_59),multiply(multiplicative_identity,X_59)),
inference(subst,[],[distributivity3:[bind(X,$fot(X_57)),bind(Y,$fot(multiplicative_identity)),bind(Z,$fot(X_59))]]) ).
cnf(refute_0_1,plain,
multiply(multiplicative_identity,X_59) = X_59,
inference(subst,[],[multiplicative_id2:[bind(X,$fot(X_59))]]) ).
cnf(refute_0_2,plain,
( multiply(add(X_57,multiplicative_identity),X_59) != add(multiply(X_57,X_59),multiply(multiplicative_identity,X_59))
| multiply(multiplicative_identity,X_59) != X_59
| multiply(add(X_57,multiplicative_identity),X_59) = add(multiply(X_57,X_59),X_59) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_57,multiplicative_identity),X_59),add(multiply(X_57,X_59),multiply(multiplicative_identity,X_59))) ),[1,1],$fot(X_59)]]) ).
cnf(refute_0_3,plain,
( multiply(add(X_57,multiplicative_identity),X_59) != add(multiply(X_57,X_59),multiply(multiplicative_identity,X_59))
| multiply(add(X_57,multiplicative_identity),X_59) = add(multiply(X_57,X_59),X_59) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,X_59),X_59) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(add(X_57,multiplicative_identity),X_59) = add(multiply(X_57,X_59),X_59),
inference(resolve,[$cnf( $equal(multiply(add(X_57,multiplicative_identity),X_59),add(multiply(X_57,X_59),multiply(multiplicative_identity,X_59))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
add(X_30,multiply(inverse(X_30),X_32)) = multiply(add(X_30,inverse(X_30)),add(X_30,X_32)),
inference(subst,[],[distributivity2:[bind(X,$fot(X_30)),bind(Y,$fot(inverse(X_30))),bind(Z,$fot(X_32))]]) ).
cnf(refute_0_6,plain,
add(X_30,inverse(X_30)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_30))]]) ).
cnf(refute_0_7,plain,
( add(X_30,multiply(inverse(X_30),X_32)) != multiply(add(X_30,inverse(X_30)),add(X_30,X_32))
| add(X_30,inverse(X_30)) != multiplicative_identity
| add(X_30,multiply(inverse(X_30),X_32)) = multiply(multiplicative_identity,add(X_30,X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_30,multiply(inverse(X_30),X_32)),multiply(add(X_30,inverse(X_30)),add(X_30,X_32))) ),[1,0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_8,plain,
( add(X_30,multiply(inverse(X_30),X_32)) != multiply(add(X_30,inverse(X_30)),add(X_30,X_32))
| add(X_30,multiply(inverse(X_30),X_32)) = multiply(multiplicative_identity,add(X_30,X_32)) ),
inference(resolve,[$cnf( $equal(add(X_30,inverse(X_30)),multiplicative_identity) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
add(X_30,multiply(inverse(X_30),X_32)) = multiply(multiplicative_identity,add(X_30,X_32)),
inference(resolve,[$cnf( $equal(add(X_30,multiply(inverse(X_30),X_32)),multiply(add(X_30,inverse(X_30)),add(X_30,X_32))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
multiply(multiplicative_identity,add(X_30,X_32)) = add(X_30,X_32),
inference(subst,[],[multiplicative_id2:[bind(X,$fot(add(X_30,X_32)))]]) ).
cnf(refute_0_11,plain,
( multiply(multiplicative_identity,add(X_30,X_32)) != add(X_30,X_32)
| add(X_30,multiply(inverse(X_30),X_32)) != multiply(multiplicative_identity,add(X_30,X_32))
| add(X_30,multiply(inverse(X_30),X_32)) = add(X_30,X_32) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_30,multiply(inverse(X_30),X_32)),multiply(multiplicative_identity,add(X_30,X_32))) ),[1],$fot(add(X_30,X_32))]]) ).
cnf(refute_0_12,plain,
( add(X_30,multiply(inverse(X_30),X_32)) != multiply(multiplicative_identity,add(X_30,X_32))
| add(X_30,multiply(inverse(X_30),X_32)) = add(X_30,X_32) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,add(X_30,X_32)),add(X_30,X_32)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
add(X_30,multiply(inverse(X_30),X_32)) = add(X_30,X_32),
inference(resolve,[$cnf( $equal(add(X_30,multiply(inverse(X_30),X_32)),multiply(multiplicative_identity,add(X_30,X_32))) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
add(X_35,multiply(inverse(X_35),add(multiplicative_identity,inverse(X_35)))) = add(X_35,add(multiplicative_identity,inverse(X_35))),
inference(subst,[],[refute_0_13:[bind(X_30,$fot(X_35)),bind(X_32,$fot(add(multiplicative_identity,inverse(X_35))))]]) ).
cnf(refute_0_15,plain,
add(multiply(X_10,additive_identity),X_12) = multiply(add(X_10,X_12),add(additive_identity,X_12)),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(additive_identity)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_16,plain,
add(additive_identity,X_12) = X_12,
inference(subst,[],[additive_id2:[bind(X,$fot(X_12))]]) ).
cnf(refute_0_17,plain,
( add(multiply(X_10,additive_identity),X_12) != multiply(add(X_10,X_12),add(additive_identity,X_12))
| add(additive_identity,X_12) != X_12
| add(multiply(X_10,additive_identity),X_12) = multiply(add(X_10,X_12),X_12) ),
introduced(tautology,[equality,[$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_18,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( $equal(add(additive_identity,X_12),X_12) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
add(multiply(X_10,additive_identity),X_12) = multiply(add(X_10,X_12),X_12),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),X_12),multiply(add(X_10,X_12),add(additive_identity,X_12))) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_21,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_22,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( multiply(X,Y) != multiply(Y,X)
| multiply(Y,X) = multiply(X,Y) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(multiply(X,Y))),bind(Y0,$fot(multiply(Y,X)))]]) ).
cnf(refute_0_24,plain,
multiply(Y,X) = multiply(X,Y),
inference(resolve,[$cnf( $equal(multiply(X,Y),multiply(Y,X)) )],[commutativity_of_multiply,refute_0_23]) ).
cnf(refute_0_25,plain,
multiply(add(X_10,X_12),X_12) = multiply(X_12,add(X_10,X_12)),
inference(subst,[],[refute_0_24:[bind(X,$fot(X_12)),bind(Y,$fot(add(X_10,X_12)))]]) ).
cnf(refute_0_26,plain,
( multiply(add(X_10,X_12),X_12) != multiply(X_12,add(X_10,X_12))
| add(multiply(X_10,additive_identity),X_12) != multiply(add(X_10,X_12),X_12)
| add(multiply(X_10,additive_identity),X_12) = multiply(X_12,add(X_10,X_12)) ),
introduced(tautology,[equality,[$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_27,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( $equal(multiply(add(X_10,X_12),X_12),multiply(X_12,add(X_10,X_12))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
add(multiply(X_10,additive_identity),X_12) = multiply(X_12,add(X_10,X_12)),
inference(resolve,[$cnf( $equal(add(multiply(X_10,additive_identity),X_12),multiply(add(X_10,X_12),X_12)) )],[refute_0_19,refute_0_27]) ).
cnf(refute_0_29,plain,
add(multiply(multiplicative_identity,additive_identity),X_14) = multiply(X_14,add(multiplicative_identity,X_14)),
inference(subst,[],[refute_0_28:[bind(X_10,$fot(multiplicative_identity)),bind(X_12,$fot(X_14))]]) ).
cnf(refute_0_30,plain,
multiply(multiplicative_identity,additive_identity) = additive_identity,
inference(subst,[],[multiplicative_id2:[bind(X,$fot(additive_identity))]]) ).
cnf(refute_0_31,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_32,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( $equal(multiply(multiplicative_identity,additive_identity),additive_identity) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
add(additive_identity,X_14) = multiply(X_14,add(multiplicative_identity,X_14)),
inference(resolve,[$cnf( $equal(add(multiply(multiplicative_identity,additive_identity),X_14),multiply(X_14,add(multiplicative_identity,X_14))) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
add(additive_identity,X_14) = X_14,
inference(subst,[],[additive_id2:[bind(X,$fot(X_14))]]) ).
cnf(refute_0_35,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_36,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( $equal(add(additive_identity,X_14),X_14) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
X_14 = multiply(X_14,add(multiplicative_identity,X_14)),
inference(resolve,[$cnf( $equal(add(additive_identity,X_14),multiply(X_14,add(multiplicative_identity,X_14))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
inverse(X_35) = multiply(inverse(X_35),add(multiplicative_identity,inverse(X_35))),
inference(subst,[],[refute_0_37:[bind(X_14,$fot(inverse(X_35)))]]) ).
cnf(refute_0_39,plain,
( inverse(X_35) != multiply(inverse(X_35),add(multiplicative_identity,inverse(X_35)))
| multiply(inverse(X_35),add(multiplicative_identity,inverse(X_35))) = inverse(X_35) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(inverse(X_35))),bind(Y0,$fot(multiply(inverse(X_35),add(multiplicative_identity,inverse(X_35)))))]]) ).
cnf(refute_0_40,plain,
multiply(inverse(X_35),add(multiplicative_identity,inverse(X_35))) = inverse(X_35),
inference(resolve,[$cnf( $equal(inverse(X_35),multiply(inverse(X_35),add(multiplicative_identity,inverse(X_35)))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( multiply(inverse(X_35),add(multiplicative_identity,inverse(X_35))) != inverse(X_35)
| add(X_35,multiply(inverse(X_35),add(multiplicative_identity,inverse(X_35)))) != add(X_35,add(multiplicative_identity,inverse(X_35)))
| add(X_35,inverse(X_35)) = add(X_35,add(multiplicative_identity,inverse(X_35))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_35,multiply(inverse(X_35),add(multiplicative_identity,inverse(X_35)))),add(X_35,add(multiplicative_identity,inverse(X_35)))) ),[0,1],$fot(inverse(X_35))]]) ).
cnf(refute_0_42,plain,
( add(X_35,multiply(inverse(X_35),add(multiplicative_identity,inverse(X_35)))) != add(X_35,add(multiplicative_identity,inverse(X_35)))
| add(X_35,inverse(X_35)) = add(X_35,add(multiplicative_identity,inverse(X_35))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_35),add(multiplicative_identity,inverse(X_35))),inverse(X_35)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
add(X_35,inverse(X_35)) = add(X_35,add(multiplicative_identity,inverse(X_35))),
inference(resolve,[$cnf( $equal(add(X_35,multiply(inverse(X_35),add(multiplicative_identity,inverse(X_35)))),add(X_35,add(multiplicative_identity,inverse(X_35)))) )],[refute_0_14,refute_0_42]) ).
cnf(refute_0_44,plain,
add(X_35,inverse(X_35)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_35))]]) ).
cnf(refute_0_45,plain,
( add(X_35,inverse(X_35)) != add(X_35,add(multiplicative_identity,inverse(X_35)))
| add(X_35,inverse(X_35)) != multiplicative_identity
| multiplicative_identity = add(X_35,add(multiplicative_identity,inverse(X_35))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_35,inverse(X_35)),add(X_35,add(multiplicative_identity,inverse(X_35)))) ),[0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_46,plain,
( add(X_35,inverse(X_35)) != add(X_35,add(multiplicative_identity,inverse(X_35)))
| multiplicative_identity = add(X_35,add(multiplicative_identity,inverse(X_35))) ),
inference(resolve,[$cnf( $equal(add(X_35,inverse(X_35)),multiplicative_identity) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
add(multiply(X_10,X_11),inverse(X_11)) = multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11))),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(inverse(X_11)))]]) ).
cnf(refute_0_48,plain,
add(X_11,inverse(X_11)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_49,plain,
( add(X_11,inverse(X_11)) != multiplicative_identity
| add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11)))
| add(multiply(X_10,X_11),inverse(X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11)))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_50,plain,
( add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11)))
| add(multiply(X_10,X_11),inverse(X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(X_11,inverse(X_11)),multiplicative_identity) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
add(multiply(X_10,X_11),inverse(X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity),
inference(resolve,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11)))) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
( add(X,Y) != add(Y,X)
| add(Y,X) = add(X,Y) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(add(X,Y))),bind(Y0,$fot(add(Y,X)))]]) ).
cnf(refute_0_53,plain,
add(Y,X) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X,Y),add(Y,X)) )],[commutativity_of_add,refute_0_52]) ).
cnf(refute_0_54,plain,
add(multiply(X_10,X_11),inverse(X_11)) = add(inverse(X_11),multiply(X_10,X_11)),
inference(subst,[],[refute_0_53:[bind(X,$fot(inverse(X_11))),bind(Y,$fot(multiply(X_10,X_11)))]]) ).
cnf(refute_0_55,plain,
( add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(multiply(X_10,X_11),inverse(X_11)) != add(inverse(X_11),multiply(X_10,X_11))
| add(inverse(X_11),multiply(X_10,X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),multiply(add(X_10,inverse(X_11)),multiplicative_identity)) ),[0],$fot(add(inverse(X_11),multiply(X_10,X_11)))]]) ).
cnf(refute_0_56,plain,
( add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(inverse(X_11),multiply(X_10,X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),add(inverse(X_11),multiply(X_10,X_11))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
multiply(add(X_10,inverse(X_11)),multiplicative_identity) = add(X_10,inverse(X_11)),
inference(subst,[],[multiplicative_id1:[bind(X,$fot(add(X_10,inverse(X_11))))]]) ).
cnf(refute_0_58,plain,
( multiply(add(X_10,inverse(X_11)),multiplicative_identity) != add(X_10,inverse(X_11))
| add(inverse(X_11),multiply(X_10,X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(inverse(X_11),multiply(X_10,X_11)) = add(X_10,inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(X_11),multiply(X_10,X_11)),multiply(add(X_10,inverse(X_11)),multiplicative_identity)) ),[1],$fot(add(X_10,inverse(X_11)))]]) ).
cnf(refute_0_59,plain,
( add(inverse(X_11),multiply(X_10,X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(inverse(X_11),multiply(X_10,X_11)) = add(X_10,inverse(X_11)) ),
inference(resolve,[$cnf( $equal(multiply(add(X_10,inverse(X_11)),multiplicative_identity),add(X_10,inverse(X_11))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(inverse(X_11),multiply(X_10,X_11)) = add(X_10,inverse(X_11)) ),
inference(resolve,[$cnf( $equal(add(inverse(X_11),multiply(X_10,X_11)),multiply(add(X_10,inverse(X_11)),multiplicative_identity)) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
add(inverse(X_11),multiply(X_10,X_11)) = add(X_10,inverse(X_11)),
inference(resolve,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),multiply(add(X_10,inverse(X_11)),multiplicative_identity)) )],[refute_0_51,refute_0_60]) ).
cnf(refute_0_62,plain,
add(inverse(X_19),multiply(multiplicative_identity,X_19)) = add(multiplicative_identity,inverse(X_19)),
inference(subst,[],[refute_0_61:[bind(X_10,$fot(multiplicative_identity)),bind(X_11,$fot(X_19))]]) ).
cnf(refute_0_63,plain,
multiply(multiplicative_identity,X_19) = X_19,
inference(subst,[],[multiplicative_id2:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_64,plain,
( multiply(multiplicative_identity,X_19) != X_19
| add(inverse(X_19),multiply(multiplicative_identity,X_19)) != add(multiplicative_identity,inverse(X_19))
| add(inverse(X_19),X_19) = add(multiplicative_identity,inverse(X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(X_19),multiply(multiplicative_identity,X_19)),add(multiplicative_identity,inverse(X_19))) ),[0,1],$fot(X_19)]]) ).
cnf(refute_0_65,plain,
( add(inverse(X_19),multiply(multiplicative_identity,X_19)) != add(multiplicative_identity,inverse(X_19))
| add(inverse(X_19),X_19) = add(multiplicative_identity,inverse(X_19)) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,X_19),X_19) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
add(inverse(X_19),X_19) = add(multiplicative_identity,inverse(X_19)),
inference(resolve,[$cnf( $equal(add(inverse(X_19),multiply(multiplicative_identity,X_19)),add(multiplicative_identity,inverse(X_19))) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
add(X_19,inverse(X_19)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_68,plain,
add(inverse(X_19),X_19) = add(X_19,inverse(X_19)),
inference(subst,[],[refute_0_53:[bind(X,$fot(X_19)),bind(Y,$fot(inverse(X_19)))]]) ).
cnf(refute_0_69,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_70,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_22,refute_0_69]) ).
cnf(refute_0_71,plain,
( add(X_19,inverse(X_19)) != multiplicative_identity
| add(inverse(X_19),X_19) != add(X_19,inverse(X_19))
| add(inverse(X_19),X_19) = multiplicative_identity ),
inference(subst,[],[refute_0_70:[bind(X0,$fot(add(inverse(X_19),X_19))),bind(Y0,$fot(add(X_19,inverse(X_19)))),bind(Z0,$fot(multiplicative_identity))]]) ).
cnf(refute_0_72,plain,
( add(X_19,inverse(X_19)) != multiplicative_identity
| add(inverse(X_19),X_19) = multiplicative_identity ),
inference(resolve,[$cnf( $equal(add(inverse(X_19),X_19),add(X_19,inverse(X_19))) )],[refute_0_68,refute_0_71]) ).
cnf(refute_0_73,plain,
add(inverse(X_19),X_19) = multiplicative_identity,
inference(resolve,[$cnf( $equal(add(X_19,inverse(X_19)),multiplicative_identity) )],[refute_0_67,refute_0_72]) ).
cnf(refute_0_74,plain,
( add(inverse(X_19),X_19) != add(multiplicative_identity,inverse(X_19))
| add(inverse(X_19),X_19) != multiplicative_identity
| multiplicative_identity = add(multiplicative_identity,inverse(X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(X_19),X_19),add(multiplicative_identity,inverse(X_19))) ),[0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_75,plain,
( add(inverse(X_19),X_19) != add(multiplicative_identity,inverse(X_19))
| multiplicative_identity = add(multiplicative_identity,inverse(X_19)) ),
inference(resolve,[$cnf( $equal(add(inverse(X_19),X_19),multiplicative_identity) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
multiplicative_identity = add(multiplicative_identity,inverse(X_19)),
inference(resolve,[$cnf( $equal(add(inverse(X_19),X_19),add(multiplicative_identity,inverse(X_19))) )],[refute_0_66,refute_0_75]) ).
cnf(refute_0_77,plain,
( multiplicative_identity != add(multiplicative_identity,inverse(X_19))
| add(multiplicative_identity,inverse(X_19)) = multiplicative_identity ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(multiplicative_identity)),bind(Y0,$fot(add(multiplicative_identity,inverse(X_19))))]]) ).
cnf(refute_0_78,plain,
add(multiplicative_identity,inverse(X_19)) = multiplicative_identity,
inference(resolve,[$cnf( $equal(multiplicative_identity,add(multiplicative_identity,inverse(X_19))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
add(multiplicative_identity,inverse(X_35)) = multiplicative_identity,
inference(subst,[],[refute_0_78:[bind(X_19,$fot(X_35))]]) ).
cnf(refute_0_80,plain,
add(X_35,add(multiplicative_identity,inverse(X_35))) = add(X_35,add(multiplicative_identity,inverse(X_35))),
introduced(tautology,[refl,[$fot(add(X_35,add(multiplicative_identity,inverse(X_35))))]]) ).
cnf(refute_0_81,plain,
( add(X_35,add(multiplicative_identity,inverse(X_35))) != add(X_35,add(multiplicative_identity,inverse(X_35)))
| add(multiplicative_identity,inverse(X_35)) != multiplicative_identity
| add(X_35,add(multiplicative_identity,inverse(X_35))) = add(X_35,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_35,add(multiplicative_identity,inverse(X_35))),add(X_35,add(multiplicative_identity,inverse(X_35)))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_82,plain,
( add(multiplicative_identity,inverse(X_35)) != multiplicative_identity
| add(X_35,add(multiplicative_identity,inverse(X_35))) = add(X_35,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(X_35,add(multiplicative_identity,inverse(X_35))),add(X_35,add(multiplicative_identity,inverse(X_35)))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
add(X_35,add(multiplicative_identity,inverse(X_35))) = add(X_35,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(multiplicative_identity,inverse(X_35)),multiplicative_identity) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
( add(X_35,add(multiplicative_identity,inverse(X_35))) != add(X_35,multiplicative_identity)
| multiplicative_identity != add(X_35,add(multiplicative_identity,inverse(X_35)))
| multiplicative_identity = add(X_35,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(multiplicative_identity,add(X_35,add(multiplicative_identity,inverse(X_35)))) ),[1],$fot(add(X_35,multiplicative_identity))]]) ).
cnf(refute_0_85,plain,
( multiplicative_identity != add(X_35,add(multiplicative_identity,inverse(X_35)))
| multiplicative_identity = add(X_35,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(X_35,add(multiplicative_identity,inverse(X_35))),add(X_35,multiplicative_identity)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
( add(X_35,inverse(X_35)) != add(X_35,add(multiplicative_identity,inverse(X_35)))
| multiplicative_identity = add(X_35,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(multiplicative_identity,add(X_35,add(multiplicative_identity,inverse(X_35)))) )],[refute_0_46,refute_0_85]) ).
cnf(refute_0_87,plain,
multiplicative_identity = add(X_35,multiplicative_identity),
inference(resolve,[$cnf( $equal(add(X_35,inverse(X_35)),add(X_35,add(multiplicative_identity,inverse(X_35)))) )],[refute_0_43,refute_0_86]) ).
cnf(refute_0_88,plain,
( multiplicative_identity != add(X_35,multiplicative_identity)
| add(X_35,multiplicative_identity) = multiplicative_identity ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(multiplicative_identity)),bind(Y0,$fot(add(X_35,multiplicative_identity)))]]) ).
cnf(refute_0_89,plain,
add(X_35,multiplicative_identity) = multiplicative_identity,
inference(resolve,[$cnf( $equal(multiplicative_identity,add(X_35,multiplicative_identity)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
add(X_57,multiplicative_identity) = multiplicative_identity,
inference(subst,[],[refute_0_89:[bind(X_35,$fot(X_57))]]) ).
cnf(refute_0_91,plain,
multiply(add(X_57,multiplicative_identity),X_59) = multiply(add(X_57,multiplicative_identity),X_59),
introduced(tautology,[refl,[$fot(multiply(add(X_57,multiplicative_identity),X_59))]]) ).
cnf(refute_0_92,plain,
( multiply(add(X_57,multiplicative_identity),X_59) != multiply(add(X_57,multiplicative_identity),X_59)
| add(X_57,multiplicative_identity) != multiplicative_identity
| multiply(add(X_57,multiplicative_identity),X_59) = multiply(multiplicative_identity,X_59) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_57,multiplicative_identity),X_59),multiply(add(X_57,multiplicative_identity),X_59)) ),[1,0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_93,plain,
( add(X_57,multiplicative_identity) != multiplicative_identity
| multiply(add(X_57,multiplicative_identity),X_59) = multiply(multiplicative_identity,X_59) ),
inference(resolve,[$cnf( $equal(multiply(add(X_57,multiplicative_identity),X_59),multiply(add(X_57,multiplicative_identity),X_59)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
multiply(add(X_57,multiplicative_identity),X_59) = multiply(multiplicative_identity,X_59),
inference(resolve,[$cnf( $equal(add(X_57,multiplicative_identity),multiplicative_identity) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
( multiply(add(X_57,multiplicative_identity),X_59) != multiply(multiplicative_identity,X_59)
| multiply(multiplicative_identity,X_59) != X_59
| multiply(add(X_57,multiplicative_identity),X_59) = X_59 ),
inference(subst,[],[refute_0_70:[bind(X0,$fot(multiply(add(X_57,multiplicative_identity),X_59))),bind(Y0,$fot(multiply(multiplicative_identity,X_59))),bind(Z0,$fot(X_59))]]) ).
cnf(refute_0_96,plain,
( multiply(multiplicative_identity,X_59) != X_59
| multiply(add(X_57,multiplicative_identity),X_59) = X_59 ),
inference(resolve,[$cnf( $equal(multiply(add(X_57,multiplicative_identity),X_59),multiply(multiplicative_identity,X_59)) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
multiply(add(X_57,multiplicative_identity),X_59) = X_59,
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,X_59),X_59) )],[refute_0_1,refute_0_96]) ).
cnf(refute_0_98,plain,
( multiply(add(X_57,multiplicative_identity),X_59) != X_59
| multiply(add(X_57,multiplicative_identity),X_59) != add(multiply(X_57,X_59),X_59)
| X_59 = add(multiply(X_57,X_59),X_59) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_57,multiplicative_identity),X_59),add(multiply(X_57,X_59),X_59)) ),[0],$fot(X_59)]]) ).
cnf(refute_0_99,plain,
( multiply(add(X_57,multiplicative_identity),X_59) != add(multiply(X_57,X_59),X_59)
| X_59 = add(multiply(X_57,X_59),X_59) ),
inference(resolve,[$cnf( $equal(multiply(add(X_57,multiplicative_identity),X_59),X_59) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
add(X_30,multiply(X_31,inverse(inverse(X_30)))) = multiply(add(X_30,X_31),add(X_30,inverse(inverse(X_30)))),
inference(subst,[],[distributivity2:[bind(X,$fot(X_30)),bind(Y,$fot(X_31)),bind(Z,$fot(inverse(inverse(X_30))))]]) ).
cnf(refute_0_101,plain,
add(inverse(inverse(X_18)),multiply(X_18,inverse(X_18))) = add(X_18,inverse(inverse(X_18))),
inference(subst,[],[refute_0_61:[bind(X_10,$fot(X_18)),bind(X_11,$fot(inverse(X_18)))]]) ).
cnf(refute_0_102,plain,
multiply(X_18,inverse(X_18)) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(X_18))]]) ).
cnf(refute_0_103,plain,
( multiply(X_18,inverse(X_18)) != additive_identity
| add(inverse(inverse(X_18)),multiply(X_18,inverse(X_18))) != add(X_18,inverse(inverse(X_18)))
| add(inverse(inverse(X_18)),additive_identity) = add(X_18,inverse(inverse(X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(inverse(X_18)),multiply(X_18,inverse(X_18))),add(X_18,inverse(inverse(X_18)))) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_104,plain,
( add(inverse(inverse(X_18)),multiply(X_18,inverse(X_18))) != add(X_18,inverse(inverse(X_18)))
| add(inverse(inverse(X_18)),additive_identity) = add(X_18,inverse(inverse(X_18))) ),
inference(resolve,[$cnf( $equal(multiply(X_18,inverse(X_18)),additive_identity) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
add(inverse(inverse(X_18)),additive_identity) = add(X_18,inverse(inverse(X_18))),
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_18)),multiply(X_18,inverse(X_18))),add(X_18,inverse(inverse(X_18)))) )],[refute_0_101,refute_0_104]) ).
cnf(refute_0_106,plain,
add(inverse(inverse(X_18)),additive_identity) = inverse(inverse(X_18)),
inference(subst,[],[additive_id1:[bind(X,$fot(inverse(inverse(X_18))))]]) ).
cnf(refute_0_107,plain,
( add(inverse(inverse(X_18)),additive_identity) != add(X_18,inverse(inverse(X_18)))
| add(inverse(inverse(X_18)),additive_identity) != inverse(inverse(X_18))
| inverse(inverse(X_18)) = add(X_18,inverse(inverse(X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(inverse(X_18)),additive_identity),add(X_18,inverse(inverse(X_18)))) ),[0],$fot(inverse(inverse(X_18)))]]) ).
cnf(refute_0_108,plain,
( add(inverse(inverse(X_18)),additive_identity) != add(X_18,inverse(inverse(X_18)))
| inverse(inverse(X_18)) = add(X_18,inverse(inverse(X_18))) ),
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_18)),additive_identity),inverse(inverse(X_18))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
inverse(inverse(X_18)) = add(X_18,inverse(inverse(X_18))),
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_18)),additive_identity),add(X_18,inverse(inverse(X_18)))) )],[refute_0_105,refute_0_108]) ).
cnf(refute_0_110,plain,
inverse(inverse(X_30)) = add(X_30,inverse(inverse(X_30))),
inference(subst,[],[refute_0_109:[bind(X_18,$fot(X_30))]]) ).
cnf(refute_0_111,plain,
( inverse(inverse(X_30)) != add(X_30,inverse(inverse(X_30)))
| add(X_30,inverse(inverse(X_30))) = inverse(inverse(X_30)) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(inverse(inverse(X_30)))),bind(Y0,$fot(add(X_30,inverse(inverse(X_30)))))]]) ).
cnf(refute_0_112,plain,
add(X_30,inverse(inverse(X_30))) = inverse(inverse(X_30)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_30)),add(X_30,inverse(inverse(X_30)))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
( add(X_30,multiply(X_31,inverse(inverse(X_30)))) != multiply(add(X_30,X_31),add(X_30,inverse(inverse(X_30))))
| add(X_30,inverse(inverse(X_30))) != inverse(inverse(X_30))
| add(X_30,multiply(X_31,inverse(inverse(X_30)))) = multiply(add(X_30,X_31),inverse(inverse(X_30))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_30,multiply(X_31,inverse(inverse(X_30)))),multiply(add(X_30,X_31),add(X_30,inverse(inverse(X_30))))) ),[1,1],$fot(inverse(inverse(X_30)))]]) ).
cnf(refute_0_114,plain,
( add(X_30,multiply(X_31,inverse(inverse(X_30)))) != multiply(add(X_30,X_31),add(X_30,inverse(inverse(X_30))))
| add(X_30,multiply(X_31,inverse(inverse(X_30)))) = multiply(add(X_30,X_31),inverse(inverse(X_30))) ),
inference(resolve,[$cnf( $equal(add(X_30,inverse(inverse(X_30))),inverse(inverse(X_30))) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
add(X_30,multiply(X_31,inverse(inverse(X_30)))) = multiply(add(X_30,X_31),inverse(inverse(X_30))),
inference(resolve,[$cnf( $equal(add(X_30,multiply(X_31,inverse(inverse(X_30)))),multiply(add(X_30,X_31),add(X_30,inverse(inverse(X_30))))) )],[refute_0_100,refute_0_114]) ).
cnf(refute_0_116,plain,
multiply(add(X_30,X_31),inverse(inverse(X_30))) = multiply(inverse(inverse(X_30)),add(X_30,X_31)),
inference(subst,[],[refute_0_24:[bind(X,$fot(inverse(inverse(X_30)))),bind(Y,$fot(add(X_30,X_31)))]]) ).
cnf(refute_0_117,plain,
( multiply(add(X_30,X_31),inverse(inverse(X_30))) != multiply(inverse(inverse(X_30)),add(X_30,X_31))
| add(X_30,multiply(X_31,inverse(inverse(X_30)))) != multiply(add(X_30,X_31),inverse(inverse(X_30)))
| add(X_30,multiply(X_31,inverse(inverse(X_30)))) = multiply(inverse(inverse(X_30)),add(X_30,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_30,multiply(X_31,inverse(inverse(X_30)))),multiply(add(X_30,X_31),inverse(inverse(X_30)))) ),[1],$fot(multiply(inverse(inverse(X_30)),add(X_30,X_31)))]]) ).
cnf(refute_0_118,plain,
( add(X_30,multiply(X_31,inverse(inverse(X_30)))) != multiply(add(X_30,X_31),inverse(inverse(X_30)))
| add(X_30,multiply(X_31,inverse(inverse(X_30)))) = multiply(inverse(inverse(X_30)),add(X_30,X_31)) ),
inference(resolve,[$cnf( $equal(multiply(add(X_30,X_31),inverse(inverse(X_30))),multiply(inverse(inverse(X_30)),add(X_30,X_31))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
add(X_30,multiply(X_31,inverse(inverse(X_30)))) = multiply(inverse(inverse(X_30)),add(X_30,X_31)),
inference(resolve,[$cnf( $equal(add(X_30,multiply(X_31,inverse(inverse(X_30)))),multiply(add(X_30,X_31),inverse(inverse(X_30)))) )],[refute_0_115,refute_0_118]) ).
cnf(refute_0_120,plain,
add(X_35,multiply(inverse(X_35),inverse(inverse(X_35)))) = add(X_35,inverse(inverse(X_35))),
inference(subst,[],[refute_0_13:[bind(X_30,$fot(X_35)),bind(X_32,$fot(inverse(inverse(X_35))))]]) ).
cnf(refute_0_121,plain,
multiply(inverse(X_35),inverse(inverse(X_35))) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(inverse(X_35)))]]) ).
cnf(refute_0_122,plain,
( multiply(inverse(X_35),inverse(inverse(X_35))) != additive_identity
| add(X_35,multiply(inverse(X_35),inverse(inverse(X_35)))) != add(X_35,inverse(inverse(X_35)))
| add(X_35,additive_identity) = add(X_35,inverse(inverse(X_35))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_35,multiply(inverse(X_35),inverse(inverse(X_35)))),add(X_35,inverse(inverse(X_35)))) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_123,plain,
( add(X_35,multiply(inverse(X_35),inverse(inverse(X_35)))) != add(X_35,inverse(inverse(X_35)))
| add(X_35,additive_identity) = add(X_35,inverse(inverse(X_35))) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_35),inverse(inverse(X_35))),additive_identity) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
add(X_35,additive_identity) = add(X_35,inverse(inverse(X_35))),
inference(resolve,[$cnf( $equal(add(X_35,multiply(inverse(X_35),inverse(inverse(X_35)))),add(X_35,inverse(inverse(X_35)))) )],[refute_0_120,refute_0_123]) ).
cnf(refute_0_125,plain,
add(X_35,additive_identity) = X_35,
inference(subst,[],[additive_id1:[bind(X,$fot(X_35))]]) ).
cnf(refute_0_126,plain,
( add(X_35,additive_identity) != X_35
| add(X_35,additive_identity) != add(X_35,inverse(inverse(X_35)))
| X_35 = add(X_35,inverse(inverse(X_35))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_35,additive_identity),add(X_35,inverse(inverse(X_35)))) ),[0],$fot(X_35)]]) ).
cnf(refute_0_127,plain,
( add(X_35,additive_identity) != add(X_35,inverse(inverse(X_35)))
| X_35 = add(X_35,inverse(inverse(X_35))) ),
inference(resolve,[$cnf( $equal(add(X_35,additive_identity),X_35) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
( inverse(inverse(X_18)) != add(X_18,inverse(inverse(X_18)))
| add(X_18,inverse(inverse(X_18))) = inverse(inverse(X_18)) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(inverse(inverse(X_18)))),bind(Y0,$fot(add(X_18,inverse(inverse(X_18)))))]]) ).
cnf(refute_0_129,plain,
add(X_18,inverse(inverse(X_18))) = inverse(inverse(X_18)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_18)),add(X_18,inverse(inverse(X_18)))) )],[refute_0_109,refute_0_128]) ).
cnf(refute_0_130,plain,
add(X_35,inverse(inverse(X_35))) = inverse(inverse(X_35)),
inference(subst,[],[refute_0_129:[bind(X_18,$fot(X_35))]]) ).
cnf(refute_0_131,plain,
( X_35 != add(X_35,inverse(inverse(X_35)))
| add(X_35,inverse(inverse(X_35))) != inverse(inverse(X_35))
| X_35 = inverse(inverse(X_35)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_35,inverse(inverse(X_35))) ),[0],$fot(add(X_35,inverse(inverse(X_35))))]]) ).
cnf(refute_0_132,plain,
( X_35 != add(X_35,inverse(inverse(X_35)))
| X_35 = inverse(inverse(X_35)) ),
inference(resolve,[$cnf( $equal(add(X_35,inverse(inverse(X_35))),inverse(inverse(X_35))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
( add(X_35,additive_identity) != add(X_35,inverse(inverse(X_35)))
| X_35 = inverse(inverse(X_35)) ),
inference(resolve,[$cnf( $equal(X_35,add(X_35,inverse(inverse(X_35)))) )],[refute_0_127,refute_0_132]) ).
cnf(refute_0_134,plain,
X_35 = inverse(inverse(X_35)),
inference(resolve,[$cnf( $equal(add(X_35,additive_identity),add(X_35,inverse(inverse(X_35)))) )],[refute_0_124,refute_0_133]) ).
cnf(refute_0_135,plain,
( X_35 != inverse(inverse(X_35))
| inverse(inverse(X_35)) = X_35 ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(X_35)),bind(Y0,$fot(inverse(inverse(X_35))))]]) ).
cnf(refute_0_136,plain,
inverse(inverse(X_35)) = X_35,
inference(resolve,[$cnf( $equal(X_35,inverse(inverse(X_35))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
inverse(inverse(X_30)) = X_30,
inference(subst,[],[refute_0_136:[bind(X_35,$fot(X_30))]]) ).
cnf(refute_0_138,plain,
multiply(X_31,inverse(inverse(X_30))) = multiply(X_31,inverse(inverse(X_30))),
introduced(tautology,[refl,[$fot(multiply(X_31,inverse(inverse(X_30))))]]) ).
cnf(refute_0_139,plain,
( multiply(X_31,inverse(inverse(X_30))) != multiply(X_31,inverse(inverse(X_30)))
| inverse(inverse(X_30)) != X_30
| multiply(X_31,inverse(inverse(X_30))) = multiply(X_31,X_30) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_31,inverse(inverse(X_30))),multiply(X_31,inverse(inverse(X_30)))) ),[1,1],$fot(X_30)]]) ).
cnf(refute_0_140,plain,
( inverse(inverse(X_30)) != X_30
| multiply(X_31,inverse(inverse(X_30))) = multiply(X_31,X_30) ),
inference(resolve,[$cnf( $equal(multiply(X_31,inverse(inverse(X_30))),multiply(X_31,inverse(inverse(X_30)))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
multiply(X_31,inverse(inverse(X_30))) = multiply(X_31,X_30),
inference(resolve,[$cnf( $equal(inverse(inverse(X_30)),X_30) )],[refute_0_137,refute_0_140]) ).
cnf(refute_0_142,plain,
add(X_30,multiply(X_31,inverse(inverse(X_30)))) = add(X_30,multiply(X_31,inverse(inverse(X_30)))),
introduced(tautology,[refl,[$fot(add(X_30,multiply(X_31,inverse(inverse(X_30)))))]]) ).
cnf(refute_0_143,plain,
( multiply(X_31,inverse(inverse(X_30))) != multiply(X_31,X_30)
| add(X_30,multiply(X_31,inverse(inverse(X_30)))) != add(X_30,multiply(X_31,inverse(inverse(X_30))))
| add(X_30,multiply(X_31,inverse(inverse(X_30)))) = add(X_30,multiply(X_31,X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_30,multiply(X_31,inverse(inverse(X_30)))),add(X_30,multiply(X_31,inverse(inverse(X_30))))) ),[1,1],$fot(multiply(X_31,X_30))]]) ).
cnf(refute_0_144,plain,
( multiply(X_31,inverse(inverse(X_30))) != multiply(X_31,X_30)
| add(X_30,multiply(X_31,inverse(inverse(X_30)))) = add(X_30,multiply(X_31,X_30)) ),
inference(resolve,[$cnf( $equal(add(X_30,multiply(X_31,inverse(inverse(X_30)))),add(X_30,multiply(X_31,inverse(inverse(X_30))))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
add(X_30,multiply(X_31,inverse(inverse(X_30)))) = add(X_30,multiply(X_31,X_30)),
inference(resolve,[$cnf( $equal(multiply(X_31,inverse(inverse(X_30))),multiply(X_31,X_30)) )],[refute_0_141,refute_0_144]) ).
cnf(refute_0_146,plain,
( add(X_30,multiply(X_31,inverse(inverse(X_30)))) != multiply(inverse(inverse(X_30)),add(X_30,X_31))
| add(X_30,multiply(X_31,inverse(inverse(X_30)))) != add(X_30,multiply(X_31,X_30))
| add(X_30,multiply(X_31,X_30)) = multiply(inverse(inverse(X_30)),add(X_30,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_30,multiply(X_31,inverse(inverse(X_30)))),multiply(inverse(inverse(X_30)),add(X_30,X_31))) ),[0],$fot(add(X_30,multiply(X_31,X_30)))]]) ).
cnf(refute_0_147,plain,
( add(X_30,multiply(X_31,inverse(inverse(X_30)))) != multiply(inverse(inverse(X_30)),add(X_30,X_31))
| add(X_30,multiply(X_31,X_30)) = multiply(inverse(inverse(X_30)),add(X_30,X_31)) ),
inference(resolve,[$cnf( $equal(add(X_30,multiply(X_31,inverse(inverse(X_30)))),add(X_30,multiply(X_31,X_30))) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
multiply(inverse(inverse(X_30)),add(X_30,X_31)) = multiply(inverse(inverse(X_30)),add(X_30,X_31)),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(X_30)),add(X_30,X_31)))]]) ).
cnf(refute_0_149,plain,
( multiply(inverse(inverse(X_30)),add(X_30,X_31)) != multiply(inverse(inverse(X_30)),add(X_30,X_31))
| inverse(inverse(X_30)) != X_30
| multiply(inverse(inverse(X_30)),add(X_30,X_31)) = multiply(X_30,add(X_30,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_30)),add(X_30,X_31)),multiply(inverse(inverse(X_30)),add(X_30,X_31))) ),[1,0],$fot(X_30)]]) ).
cnf(refute_0_150,plain,
( inverse(inverse(X_30)) != X_30
| multiply(inverse(inverse(X_30)),add(X_30,X_31)) = multiply(X_30,add(X_30,X_31)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_30)),add(X_30,X_31)),multiply(inverse(inverse(X_30)),add(X_30,X_31))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
multiply(inverse(inverse(X_30)),add(X_30,X_31)) = multiply(X_30,add(X_30,X_31)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_30)),X_30) )],[refute_0_137,refute_0_150]) ).
cnf(refute_0_152,plain,
( multiply(inverse(inverse(X_30)),add(X_30,X_31)) != multiply(X_30,add(X_30,X_31))
| add(X_30,multiply(X_31,X_30)) != multiply(inverse(inverse(X_30)),add(X_30,X_31))
| add(X_30,multiply(X_31,X_30)) = multiply(X_30,add(X_30,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_30,multiply(X_31,X_30)),multiply(inverse(inverse(X_30)),add(X_30,X_31))) ),[1],$fot(multiply(X_30,add(X_30,X_31)))]]) ).
cnf(refute_0_153,plain,
( add(X_30,multiply(X_31,X_30)) != multiply(inverse(inverse(X_30)),add(X_30,X_31))
| add(X_30,multiply(X_31,X_30)) = multiply(X_30,add(X_30,X_31)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_30)),add(X_30,X_31)),multiply(X_30,add(X_30,X_31))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
( add(X_30,multiply(X_31,inverse(inverse(X_30)))) != multiply(inverse(inverse(X_30)),add(X_30,X_31))
| add(X_30,multiply(X_31,X_30)) = multiply(X_30,add(X_30,X_31)) ),
inference(resolve,[$cnf( $equal(add(X_30,multiply(X_31,X_30)),multiply(inverse(inverse(X_30)),add(X_30,X_31))) )],[refute_0_147,refute_0_153]) ).
cnf(refute_0_155,plain,
add(X_30,multiply(X_31,X_30)) = multiply(X_30,add(X_30,X_31)),
inference(resolve,[$cnf( $equal(add(X_30,multiply(X_31,inverse(inverse(X_30)))),multiply(inverse(inverse(X_30)),add(X_30,X_31))) )],[refute_0_119,refute_0_154]) ).
cnf(refute_0_156,plain,
add(X_59,multiply(X_57,X_59)) = multiply(X_59,add(X_59,X_57)),
inference(subst,[],[refute_0_155:[bind(X_30,$fot(X_59)),bind(X_31,$fot(X_57))]]) ).
cnf(refute_0_157,plain,
add(multiply(X_57,X_59),X_59) = add(X_59,multiply(X_57,X_59)),
inference(subst,[],[refute_0_53:[bind(X,$fot(X_59)),bind(Y,$fot(multiply(X_57,X_59)))]]) ).
cnf(refute_0_158,plain,
( add(X_59,multiply(X_57,X_59)) != multiply(X_59,add(X_59,X_57))
| add(multiply(X_57,X_59),X_59) != add(X_59,multiply(X_57,X_59))
| add(multiply(X_57,X_59),X_59) = multiply(X_59,add(X_59,X_57)) ),
inference(subst,[],[refute_0_70:[bind(X0,$fot(add(multiply(X_57,X_59),X_59))),bind(Y0,$fot(add(X_59,multiply(X_57,X_59)))),bind(Z0,$fot(multiply(X_59,add(X_59,X_57))))]]) ).
cnf(refute_0_159,plain,
( add(X_59,multiply(X_57,X_59)) != multiply(X_59,add(X_59,X_57))
| add(multiply(X_57,X_59),X_59) = multiply(X_59,add(X_59,X_57)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_57,X_59),X_59),add(X_59,multiply(X_57,X_59))) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
add(multiply(X_57,X_59),X_59) = multiply(X_59,add(X_59,X_57)),
inference(resolve,[$cnf( $equal(add(X_59,multiply(X_57,X_59)),multiply(X_59,add(X_59,X_57))) )],[refute_0_156,refute_0_159]) ).
cnf(refute_0_161,plain,
( X_59 != add(multiply(X_57,X_59),X_59)
| add(multiply(X_57,X_59),X_59) != multiply(X_59,add(X_59,X_57))
| X_59 = multiply(X_59,add(X_59,X_57)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_59,multiply(X_59,add(X_59,X_57))) ),[0],$fot(add(multiply(X_57,X_59),X_59))]]) ).
cnf(refute_0_162,plain,
( X_59 != add(multiply(X_57,X_59),X_59)
| X_59 = multiply(X_59,add(X_59,X_57)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_57,X_59),X_59),multiply(X_59,add(X_59,X_57))) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
( multiply(add(X_57,multiplicative_identity),X_59) != add(multiply(X_57,X_59),X_59)
| X_59 = multiply(X_59,add(X_59,X_57)) ),
inference(resolve,[$cnf( $equal(X_59,add(multiply(X_57,X_59),X_59)) )],[refute_0_99,refute_0_162]) ).
cnf(refute_0_164,plain,
X_59 = multiply(X_59,add(X_59,X_57)),
inference(resolve,[$cnf( $equal(multiply(add(X_57,multiplicative_identity),X_59),add(multiply(X_57,X_59),X_59)) )],[refute_0_4,refute_0_163]) ).
cnf(refute_0_165,plain,
( X_59 != multiply(X_59,add(X_59,X_57))
| multiply(X_59,add(X_59,X_57)) = X_59 ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(X_59)),bind(Y0,$fot(multiply(X_59,add(X_59,X_57))))]]) ).
cnf(refute_0_166,plain,
multiply(X_59,add(X_59,X_57)) = X_59,
inference(resolve,[$cnf( $equal(X_59,multiply(X_59,add(X_59,X_57))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
multiply(a,add(a,b)) = a,
inference(subst,[],[refute_0_166:[bind(X_57,$fot(b)),bind(X_59,$fot(a))]]) ).
cnf(refute_0_168,plain,
( multiply(a,add(a,b)) != a
| a != a
| multiply(a,add(a,b)) = a ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,add(a,b)),a) ),[0],$fot(a)]]) ).
cnf(refute_0_169,plain,
( a != a
| multiply(a,add(a,b)) = a ),
inference(resolve,[$cnf( $equal(multiply(a,add(a,b)),a) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
a != a,
inference(resolve,[$cnf( $equal(multiply(a,add(a,b)),a) )],[refute_0_169,prove_operation]) ).
cnf(refute_0_171,plain,
a = a,
introduced(tautology,[refl,[$fot(a)]]) ).
cnf(refute_0_172,plain,
$false,
inference(resolve,[$cnf( $equal(a,a) )],[refute_0_171,refute_0_170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : BOO009-2 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n019.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 15:54:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.69/0.91 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.69/0.91
% 0.69/0.91 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.69/0.93
%------------------------------------------------------------------------------