TSTP Solution File: BOO004-10 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : BOO004-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 23:44:24 EDT 2022
% Result : Unsatisfiable 131.63s 131.85s
% Output : CNFRefutation 131.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 67
% Number of leaves : 160
% Syntax : Number of clauses : 545 ( 294 unt; 0 nHn; 248 RR)
% Number of literals : 918 ( 917 equ; 375 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 1129 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq2(A,A,B,C) = B ).
cnf(ifeq_axiom_001,axiom,
ifeq(A,A,B,C) = B ).
cnf(closure_of_addition,axiom,
sum(X,Y,add(X,Y)) = true ).
cnf(closure_of_multiplication,axiom,
product(X,Y,multiply(X,Y)) = true ).
cnf(commutativity_of_addition,axiom,
ifeq(sum(X,Y,Z),true,sum(Y,X,Z),true) = true ).
cnf(commutativity_of_multiplication,axiom,
ifeq(product(X,Y,Z),true,product(Y,X,Z),true) = true ).
cnf(additive_identity1,axiom,
sum(additive_identity,X,X) = true ).
cnf(additive_identity2,axiom,
sum(X,additive_identity,X) = true ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X,X) = true ).
cnf(distributivity2,axiom,
ifeq(product(X,Z,V2),true,ifeq(product(X,Y,V1),true,ifeq(sum(V1,V2,V4),true,ifeq(sum(Y,Z,V3),true,product(X,V3,V4),true),true),true),true) = true ).
cnf(distributivity5,axiom,
ifeq(product(Y,Z,V3),true,ifeq(sum(X,V3,V4),true,ifeq(sum(X,Z,V2),true,ifeq(sum(X,Y,V1),true,product(V1,V2,V4),true),true),true),true) = true ).
cnf(additive_inverse1,axiom,
sum(inverse(X),X,multiplicative_identity) = true ).
cnf(additive_inverse2,axiom,
sum(X,inverse(X),multiplicative_identity) = true ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X),X,additive_identity) = true ).
cnf(multiplicative_inverse2,axiom,
product(X,inverse(X),additive_identity) = true ).
cnf(multiplication_is_well_defined,axiom,
ifeq2(product(X,Y,V),true,ifeq2(product(X,Y,U),true,U,V),V) = V ).
cnf(prove_both_equalities,negated_conjecture,
sum(x,x,x) != true ).
cnf(refute_0_0,plain,
ifeq(sum(X_18,X_19,add(X_18,X_19)),true,sum(X_19,X_18,add(X_18,X_19)),true) = true,
inference(subst,[],[commutativity_of_addition:[bind(X,$fot(X_18)),bind(Y,$fot(X_19)),bind(Z,$fot(add(X_18,X_19)))]]) ).
cnf(refute_0_1,plain,
sum(X_18,X_19,add(X_18,X_19)) = true,
inference(subst,[],[closure_of_addition:[bind(X,$fot(X_18)),bind(Y,$fot(X_19))]]) ).
cnf(refute_0_2,plain,
( ifeq(sum(X_18,X_19,add(X_18,X_19)),true,sum(X_19,X_18,add(X_18,X_19)),true) != true
| sum(X_18,X_19,add(X_18,X_19)) != true
| ifeq(true,true,sum(X_19,X_18,add(X_18,X_19)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(sum(X_18,X_19,add(X_18,X_19)),true,sum(X_19,X_18,add(X_18,X_19)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_3,plain,
( ifeq(sum(X_18,X_19,add(X_18,X_19)),true,sum(X_19,X_18,add(X_18,X_19)),true) != true
| ifeq(true,true,sum(X_19,X_18,add(X_18,X_19)),true) = true ),
inference(resolve,[$cnf( $equal(sum(X_18,X_19,add(X_18,X_19)),true) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
ifeq(true,true,sum(X_19,X_18,add(X_18,X_19)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(sum(X_18,X_19,add(X_18,X_19)),true,sum(X_19,X_18,add(X_18,X_19)),true),true) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
ifeq(true,true,sum(X_19,X_18,add(X_18,X_19)),true) = sum(X_19,X_18,add(X_18,X_19)),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(sum(X_19,X_18,add(X_18,X_19)))),bind(C,$fot(true))]]) ).
cnf(refute_0_6,plain,
( ifeq(true,true,sum(X_19,X_18,add(X_18,X_19)),true) != sum(X_19,X_18,add(X_18,X_19))
| ifeq(true,true,sum(X_19,X_18,add(X_18,X_19)),true) != true
| sum(X_19,X_18,add(X_18,X_19)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,sum(X_19,X_18,add(X_18,X_19)),true),true) ),[0],$fot(sum(X_19,X_18,add(X_18,X_19)))]]) ).
cnf(refute_0_7,plain,
( ifeq(true,true,sum(X_19,X_18,add(X_18,X_19)),true) != true
| sum(X_19,X_18,add(X_18,X_19)) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,sum(X_19,X_18,add(X_18,X_19)),true),sum(X_19,X_18,add(X_18,X_19))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
sum(X_19,X_18,add(X_18,X_19)) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,sum(X_19,X_18,add(X_18,X_19)),true),true) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
sum(X_19,X_19,add(X_19,X_19)) = true,
inference(subst,[],[refute_0_8:[bind(X_18,$fot(X_19))]]) ).
cnf(refute_0_10,plain,
ifeq2(product(X_54,X_55,X_53),true,ifeq2(product(X_54,X_55,multiply(X_54,X_55)),true,multiply(X_54,X_55),X_53),X_53) = X_53,
inference(subst,[],[multiplication_is_well_defined:[bind(U,$fot(multiply(X_54,X_55))),bind(V,$fot(X_53)),bind(X,$fot(X_54)),bind(Y,$fot(X_55))]]) ).
cnf(refute_0_11,plain,
product(X_54,X_55,multiply(X_54,X_55)) = true,
inference(subst,[],[closure_of_multiplication:[bind(X,$fot(X_54)),bind(Y,$fot(X_55))]]) ).
cnf(refute_0_12,plain,
( ifeq2(product(X_54,X_55,X_53),true,ifeq2(product(X_54,X_55,multiply(X_54,X_55)),true,multiply(X_54,X_55),X_53),X_53) != X_53
| product(X_54,X_55,multiply(X_54,X_55)) != true
| ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53) = X_53 ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(X_54,X_55,X_53),true,ifeq2(product(X_54,X_55,multiply(X_54,X_55)),true,multiply(X_54,X_55),X_53),X_53),X_53) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_13,plain,
( ifeq2(product(X_54,X_55,X_53),true,ifeq2(product(X_54,X_55,multiply(X_54,X_55)),true,multiply(X_54,X_55),X_53),X_53) != X_53
| ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53) = X_53 ),
inference(resolve,[$cnf( $equal(product(X_54,X_55,multiply(X_54,X_55)),true) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53) = X_53,
inference(resolve,[$cnf( $equal(ifeq2(product(X_54,X_55,X_53),true,ifeq2(product(X_54,X_55,multiply(X_54,X_55)),true,multiply(X_54,X_55),X_53),X_53),X_53) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
ifeq2(true,true,multiply(X_54,X_55),X_53) = multiply(X_54,X_55),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(multiply(X_54,X_55))),bind(C,$fot(X_53))]]) ).
cnf(refute_0_16,plain,
ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53) = ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53),
introduced(tautology,[refl,[$fot(ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53))]]) ).
cnf(refute_0_17,plain,
( ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53) != ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53)
| ifeq2(true,true,multiply(X_54,X_55),X_53) != multiply(X_54,X_55)
| ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53) = ifeq2(product(X_54,X_55,X_53),true,multiply(X_54,X_55),X_53) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53),ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53)) ),[1,2],$fot(multiply(X_54,X_55))]]) ).
cnf(refute_0_18,plain,
( ifeq2(true,true,multiply(X_54,X_55),X_53) != multiply(X_54,X_55)
| ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53) = ifeq2(product(X_54,X_55,X_53),true,multiply(X_54,X_55),X_53) ),
inference(resolve,[$cnf( $equal(ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53),ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53) = ifeq2(product(X_54,X_55,X_53),true,multiply(X_54,X_55),X_53),
inference(resolve,[$cnf( $equal(ifeq2(true,true,multiply(X_54,X_55),X_53),multiply(X_54,X_55)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
( ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53) != X_53
| ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53) != ifeq2(product(X_54,X_55,X_53),true,multiply(X_54,X_55),X_53)
| ifeq2(product(X_54,X_55,X_53),true,multiply(X_54,X_55),X_53) = X_53 ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53),X_53) ),[0],$fot(ifeq2(product(X_54,X_55,X_53),true,multiply(X_54,X_55),X_53))]]) ).
cnf(refute_0_21,plain,
( ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53) != X_53
| ifeq2(product(X_54,X_55,X_53),true,multiply(X_54,X_55),X_53) = X_53 ),
inference(resolve,[$cnf( $equal(ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53),ifeq2(product(X_54,X_55,X_53),true,multiply(X_54,X_55),X_53)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
ifeq2(product(X_54,X_55,X_53),true,multiply(X_54,X_55),X_53) = X_53,
inference(resolve,[$cnf( $equal(ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_54,X_55),X_53),X_53),X_53) )],[refute_0_14,refute_0_21]) ).
cnf(refute_0_23,plain,
ifeq2(product(X_54,add(X_54,X_54),X_53),true,multiply(X_54,add(X_54,X_54)),X_53) = X_53,
inference(subst,[],[refute_0_22:[bind(X_55,$fot(add(X_54,X_54)))]]) ).
cnf(refute_0_24,plain,
ifeq2(product(X_54,X_55,multiply(X_54,X_55)),true,ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)),multiply(X_54,X_55)) = multiply(X_54,X_55),
inference(subst,[],[multiplication_is_well_defined:[bind(U,$fot(X_52)),bind(V,$fot(multiply(X_54,X_55))),bind(X,$fot(X_54)),bind(Y,$fot(X_55))]]) ).
cnf(refute_0_25,plain,
( ifeq2(product(X_54,X_55,multiply(X_54,X_55)),true,ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)),multiply(X_54,X_55)) != multiply(X_54,X_55)
| product(X_54,X_55,multiply(X_54,X_55)) != true
| ifeq2(true,true,ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)),multiply(X_54,X_55)) = multiply(X_54,X_55) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(X_54,X_55,multiply(X_54,X_55)),true,ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)),multiply(X_54,X_55)),multiply(X_54,X_55)) ),[0,0],$fot(true)]]) ).
cnf(refute_0_26,plain,
( ifeq2(product(X_54,X_55,multiply(X_54,X_55)),true,ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)),multiply(X_54,X_55)) != multiply(X_54,X_55)
| ifeq2(true,true,ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)),multiply(X_54,X_55)) = multiply(X_54,X_55) ),
inference(resolve,[$cnf( $equal(product(X_54,X_55,multiply(X_54,X_55)),true) )],[refute_0_11,refute_0_25]) ).
cnf(refute_0_27,plain,
ifeq2(true,true,ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)),multiply(X_54,X_55)) = multiply(X_54,X_55),
inference(resolve,[$cnf( $equal(ifeq2(product(X_54,X_55,multiply(X_54,X_55)),true,ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)),multiply(X_54,X_55)),multiply(X_54,X_55)) )],[refute_0_24,refute_0_26]) ).
cnf(refute_0_28,plain,
ifeq2(true,true,ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)),multiply(X_54,X_55)) = ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)))),bind(C,$fot(multiply(X_54,X_55)))]]) ).
cnf(refute_0_29,plain,
( ifeq2(true,true,ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)),multiply(X_54,X_55)) != multiply(X_54,X_55)
| ifeq2(true,true,ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)),multiply(X_54,X_55)) != ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55))
| ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)) = multiply(X_54,X_55) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(true,true,ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)),multiply(X_54,X_55)),multiply(X_54,X_55)) ),[0],$fot(ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)))]]) ).
cnf(refute_0_30,plain,
( ifeq2(true,true,ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)),multiply(X_54,X_55)) != multiply(X_54,X_55)
| ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)) = multiply(X_54,X_55) ),
inference(resolve,[$cnf( $equal(ifeq2(true,true,ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)),multiply(X_54,X_55)),ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)) = multiply(X_54,X_55),
inference(resolve,[$cnf( $equal(ifeq2(true,true,ifeq2(product(X_54,X_55,X_52),true,X_52,multiply(X_54,X_55)),multiply(X_54,X_55)),multiply(X_54,X_55)) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
ifeq2(product(add(X_659,X_659),multiplicative_identity,multiply(X_659,add(X_659,X_659))),true,multiply(X_659,add(X_659,X_659)),multiply(add(X_659,X_659),multiplicative_identity)) = multiply(add(X_659,X_659),multiplicative_identity),
inference(subst,[],[refute_0_31:[bind(X_52,$fot(multiply(X_659,add(X_659,X_659)))),bind(X_54,$fot(add(X_659,X_659))),bind(X_55,$fot(multiplicative_identity))]]) ).
cnf(refute_0_33,plain,
ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_107,additive_identity,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true) = true,
inference(subst,[],[distributivity2:[bind(V1,$fot(X_107)),bind(V2,$fot(additive_identity)),bind(V3,$fot(X_106)),bind(V4,$fot(X_107)),bind(X,$fot(X_108)),bind(Y,$fot(X_109)),bind(Z,$fot(X_110))]]) ).
cnf(refute_0_34,plain,
sum(X_107,additive_identity,X_107) = true,
inference(subst,[],[additive_identity2:[bind(X,$fot(X_107))]]) ).
cnf(refute_0_35,plain,
( ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_107,additive_identity,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true) != true
| sum(X_107,additive_identity,X_107) != true
| ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_107,additive_identity,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true),true) ),[0,2,2,0],$fot(true)]]) ).
cnf(refute_0_36,plain,
( ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_107,additive_identity,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true) != true
| ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true) = true ),
inference(resolve,[$cnf( $equal(sum(X_107,additive_identity,X_107),true) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_107,additive_identity,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true),true) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true) = ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_39,plain,
ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true) = ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),
introduced(tautology,[refl,[$fot(ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true))]]) ).
cnf(refute_0_40,plain,
( ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true) != ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true)
| ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true) != ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true)
| ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true) = ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true)) ),[1,2],$fot(ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true))]]) ).
cnf(refute_0_41,plain,
( ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true) != ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true)
| ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true) = ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true) = ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true)) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true) = ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true),
introduced(tautology,[refl,[$fot(ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true))]]) ).
cnf(refute_0_44,plain,
( ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true) != ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true)
| ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true) != ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true)
| ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true) = ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true),ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true)) ),[1,2],$fot(ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true))]]) ).
cnf(refute_0_45,plain,
( ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true) != ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true)
| ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true) = ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true),ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true) = ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),
inference(resolve,[$cnf( $equal(ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true)) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
( ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true) != ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true)
| ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true) != true
| ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true),true) ),[0],$fot(ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true))]]) ).
cnf(refute_0_48,plain,
( ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true) != true
| ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true),ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(X_108,X_110,additive_identity),true,ifeq(product(X_108,X_109,X_107),true,ifeq(true,true,ifeq(sum(X_109,X_110,X_106),true,product(X_108,X_106,X_107),true),true),true),true),true) )],[refute_0_37,refute_0_48]) ).
cnf(refute_0_50,plain,
ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(sum(inverse(X_499),X_499,multiplicative_identity),true,product(X_497,multiplicative_identity,X_496),true),true),true) = true,
inference(subst,[],[refute_0_49:[bind(X_106,$fot(multiplicative_identity)),bind(X_107,$fot(X_496)),bind(X_108,$fot(X_497)),bind(X_109,$fot(inverse(X_499))),bind(X_110,$fot(X_499))]]) ).
cnf(refute_0_51,plain,
sum(inverse(X_499),X_499,multiplicative_identity) = true,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_499))]]) ).
cnf(refute_0_52,plain,
( ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(sum(inverse(X_499),X_499,multiplicative_identity),true,product(X_497,multiplicative_identity,X_496),true),true),true) != true
| sum(inverse(X_499),X_499,multiplicative_identity) != true
| ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(sum(inverse(X_499),X_499,multiplicative_identity),true,product(X_497,multiplicative_identity,X_496),true),true),true),true) ),[0,2,2,0],$fot(true)]]) ).
cnf(refute_0_53,plain,
( ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(sum(inverse(X_499),X_499,multiplicative_identity),true,product(X_497,multiplicative_identity,X_496),true),true),true) != true
| ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) = true ),
inference(resolve,[$cnf( $equal(sum(inverse(X_499),X_499,multiplicative_identity),true) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(sum(inverse(X_499),X_499,multiplicative_identity),true,product(X_497,multiplicative_identity,X_496),true),true),true),true) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
ifeq(true,true,product(X_497,multiplicative_identity,X_496),true) = product(X_497,multiplicative_identity,X_496),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(product(X_497,multiplicative_identity,X_496))),bind(C,$fot(true))]]) ).
cnf(refute_0_56,plain,
ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true) = ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),
introduced(tautology,[refl,[$fot(ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true))]]) ).
cnf(refute_0_57,plain,
( ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true) != ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true)
| ifeq(true,true,product(X_497,multiplicative_identity,X_496),true) != product(X_497,multiplicative_identity,X_496)
| ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true) = ifeq(product(X_497,inverse(X_499),X_496),true,product(X_497,multiplicative_identity,X_496),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true)) ),[1,2],$fot(product(X_497,multiplicative_identity,X_496))]]) ).
cnf(refute_0_58,plain,
( ifeq(true,true,product(X_497,multiplicative_identity,X_496),true) != product(X_497,multiplicative_identity,X_496)
| ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true) = ifeq(product(X_497,inverse(X_499),X_496),true,product(X_497,multiplicative_identity,X_496),true) ),
inference(resolve,[$cnf( $equal(ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true) = ifeq(product(X_497,inverse(X_499),X_496),true,product(X_497,multiplicative_identity,X_496),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),product(X_497,multiplicative_identity,X_496)) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) = ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true),
introduced(tautology,[refl,[$fot(ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true))]]) ).
cnf(refute_0_61,plain,
( ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) != ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true)
| ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true) != ifeq(product(X_497,inverse(X_499),X_496),true,product(X_497,multiplicative_identity,X_496),true)
| ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) = ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,product(X_497,multiplicative_identity,X_496),true),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true),ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true)) ),[1,2],$fot(ifeq(product(X_497,inverse(X_499),X_496),true,product(X_497,multiplicative_identity,X_496),true))]]) ).
cnf(refute_0_62,plain,
( ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true) != ifeq(product(X_497,inverse(X_499),X_496),true,product(X_497,multiplicative_identity,X_496),true)
| ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) = ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,product(X_497,multiplicative_identity,X_496),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true),ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) = ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,product(X_497,multiplicative_identity,X_496),true),true),
inference(resolve,[$cnf( $equal(ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),ifeq(product(X_497,inverse(X_499),X_496),true,product(X_497,multiplicative_identity,X_496),true)) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
( ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) != ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,product(X_497,multiplicative_identity,X_496),true),true)
| ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) != true
| ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,product(X_497,multiplicative_identity,X_496),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true),true) ),[0],$fot(ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,product(X_497,multiplicative_identity,X_496),true),true))]]) ).
cnf(refute_0_65,plain,
( ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) != true
| ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,product(X_497,multiplicative_identity,X_496),true),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true),ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,product(X_497,multiplicative_identity,X_496),true),true)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,product(X_497,multiplicative_identity,X_496),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_499),X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true),true) )],[refute_0_54,refute_0_65]) ).
cnf(refute_0_67,plain,
ifeq(product(X_583,X_584,additive_identity),true,ifeq(product(X_583,inverse(X_584),multiply(X_583,inverse(X_584))),true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true) = true,
inference(subst,[],[refute_0_66:[bind(X_496,$fot(multiply(X_583,inverse(X_584)))),bind(X_497,$fot(X_583)),bind(X_499,$fot(X_584))]]) ).
cnf(refute_0_68,plain,
product(X_583,inverse(X_584),multiply(X_583,inverse(X_584))) = true,
inference(subst,[],[closure_of_multiplication:[bind(X,$fot(X_583)),bind(Y,$fot(inverse(X_584)))]]) ).
cnf(refute_0_69,plain,
( ifeq(product(X_583,X_584,additive_identity),true,ifeq(product(X_583,inverse(X_584),multiply(X_583,inverse(X_584))),true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true) != true
| product(X_583,inverse(X_584),multiply(X_583,inverse(X_584))) != true
| ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_583,X_584,additive_identity),true,ifeq(product(X_583,inverse(X_584),multiply(X_583,inverse(X_584))),true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_70,plain,
( ifeq(product(X_583,X_584,additive_identity),true,ifeq(product(X_583,inverse(X_584),multiply(X_583,inverse(X_584))),true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true) != true
| ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true) = true ),
inference(resolve,[$cnf( $equal(product(X_583,inverse(X_584),multiply(X_583,inverse(X_584))),true) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(X_583,X_584,additive_identity),true,ifeq(product(X_583,inverse(X_584),multiply(X_583,inverse(X_584))),true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true),true) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true) = product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))))),bind(C,$fot(true))]]) ).
cnf(refute_0_73,plain,
ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true) = ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true),
introduced(tautology,[refl,[$fot(ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true))]]) ).
cnf(refute_0_74,plain,
( ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true) != ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true)
| ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true) != product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584)))
| ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true) = ifeq(product(X_583,X_584,additive_identity),true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true),ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true)) ),[1,2],$fot(product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))))]]) ).
cnf(refute_0_75,plain,
( ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true) != product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584)))
| ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true) = ifeq(product(X_583,X_584,additive_identity),true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true) ),
inference(resolve,[$cnf( $equal(ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true),ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true) = ifeq(product(X_583,X_584,additive_identity),true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584)))) )],[refute_0_72,refute_0_75]) ).
cnf(refute_0_77,plain,
( ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true) != ifeq(product(X_583,X_584,additive_identity),true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true)
| ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true) != true
| ifeq(product(X_583,X_584,additive_identity),true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true),true) ),[0],$fot(ifeq(product(X_583,X_584,additive_identity),true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true))]]) ).
cnf(refute_0_78,plain,
( ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true) != true
| ifeq(product(X_583,X_584,additive_identity),true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true),ifeq(product(X_583,X_584,additive_identity),true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
ifeq(product(X_583,X_584,additive_identity),true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(X_583,X_584,additive_identity),true,ifeq(true,true,product(X_583,multiplicative_identity,multiply(X_583,inverse(X_584))),true),true),true) )],[refute_0_71,refute_0_78]) ).
cnf(refute_0_80,plain,
ifeq(product(add(X_654,X_654),inverse(X_654),additive_identity),true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true) = true,
inference(subst,[],[refute_0_79:[bind(X_583,$fot(add(X_654,X_654))),bind(X_584,$fot(inverse(X_654)))]]) ).
cnf(refute_0_81,plain,
ifeq(product(inverse(X_653),add(X_653,X_653),additive_identity),true,product(add(X_653,X_653),inverse(X_653),additive_identity),true) = true,
inference(subst,[],[commutativity_of_multiplication:[bind(X,$fot(inverse(X_653))),bind(Y,$fot(add(X_653,X_653))),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_82,plain,
ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_497),additive_identity),true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true) = true,
inference(subst,[],[refute_0_49:[bind(X_106,$fot(X_495)),bind(X_107,$fot(additive_identity)),bind(X_108,$fot(X_497)),bind(X_109,$fot(inverse(X_497))),bind(X_110,$fot(X_499))]]) ).
cnf(refute_0_83,plain,
product(X_497,inverse(X_497),additive_identity) = true,
inference(subst,[],[multiplicative_inverse2:[bind(X,$fot(X_497))]]) ).
cnf(refute_0_84,plain,
( ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_497),additive_identity),true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true) != true
| product(X_497,inverse(X_497),additive_identity) != true
| ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_497),additive_identity),true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_85,plain,
( ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_497),additive_identity),true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true) != true
| ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true) = true ),
inference(resolve,[$cnf( $equal(product(X_497,inverse(X_497),additive_identity),true) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(X_497,X_499,additive_identity),true,ifeq(product(X_497,inverse(X_497),additive_identity),true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true),true) )],[refute_0_82,refute_0_85]) ).
cnf(refute_0_87,plain,
ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true) = ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_88,plain,
ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true) = ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true),
introduced(tautology,[refl,[$fot(ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true))]]) ).
cnf(refute_0_89,plain,
( ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true) != ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true)
| ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true) != ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true)
| ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true) = ifeq(product(X_497,X_499,additive_identity),true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true),ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true)) ),[1,2],$fot(ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true))]]) ).
cnf(refute_0_90,plain,
( ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true) != ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true)
| ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true) = ifeq(product(X_497,X_499,additive_identity),true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true),ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true) = ifeq(product(X_497,X_499,additive_identity),true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true)) )],[refute_0_87,refute_0_90]) ).
cnf(refute_0_92,plain,
( ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true) != ifeq(product(X_497,X_499,additive_identity),true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true)
| ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true) != true
| ifeq(product(X_497,X_499,additive_identity),true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true),true) ),[0],$fot(ifeq(product(X_497,X_499,additive_identity),true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true))]]) ).
cnf(refute_0_93,plain,
( ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true) != true
| ifeq(product(X_497,X_499,additive_identity),true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true),ifeq(product(X_497,X_499,additive_identity),true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
ifeq(product(X_497,X_499,additive_identity),true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(X_497,X_499,additive_identity),true,ifeq(true,true,ifeq(sum(inverse(X_497),X_499,X_495),true,product(X_497,X_495,additive_identity),true),true),true),true) )],[refute_0_86,refute_0_93]) ).
cnf(refute_0_95,plain,
ifeq(product(inverse(X_646),X_646,additive_identity),true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true) = true,
inference(subst,[],[refute_0_94:[bind(X_495,$fot(X_644)),bind(X_497,$fot(inverse(X_646))),bind(X_499,$fot(X_646))]]) ).
cnf(refute_0_96,plain,
product(inverse(X_646),X_646,additive_identity) = true,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(X_646))]]) ).
cnf(refute_0_97,plain,
( ifeq(product(inverse(X_646),X_646,additive_identity),true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true) != true
| product(inverse(X_646),X_646,additive_identity) != true
| ifeq(true,true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(inverse(X_646),X_646,additive_identity),true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_98,plain,
( ifeq(product(inverse(X_646),X_646,additive_identity),true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true) != true
| ifeq(true,true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true) = true ),
inference(resolve,[$cnf( $equal(product(inverse(X_646),X_646,additive_identity),true) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
ifeq(true,true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(inverse(X_646),X_646,additive_identity),true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true),true) )],[refute_0_95,refute_0_98]) ).
cnf(refute_0_100,plain,
ifeq2(product(inverse(inverse(X_52)),multiplicative_identity,X_52),true,X_52,multiply(inverse(inverse(X_52)),multiplicative_identity)) = multiply(inverse(inverse(X_52)),multiplicative_identity),
inference(subst,[],[refute_0_31:[bind(X_54,$fot(inverse(inverse(X_52)))),bind(X_55,$fot(multiplicative_identity))]]) ).
cnf(refute_0_101,plain,
ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(sum(X_498,inverse(X_498),multiplicative_identity),true,product(X_497,multiplicative_identity,X_496),true),true),true) = true,
inference(subst,[],[refute_0_49:[bind(X_106,$fot(multiplicative_identity)),bind(X_107,$fot(X_496)),bind(X_108,$fot(X_497)),bind(X_109,$fot(X_498)),bind(X_110,$fot(inverse(X_498)))]]) ).
cnf(refute_0_102,plain,
sum(X_498,inverse(X_498),multiplicative_identity) = true,
inference(subst,[],[additive_inverse2:[bind(X,$fot(X_498))]]) ).
cnf(refute_0_103,plain,
( ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(sum(X_498,inverse(X_498),multiplicative_identity),true,product(X_497,multiplicative_identity,X_496),true),true),true) != true
| sum(X_498,inverse(X_498),multiplicative_identity) != true
| ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(sum(X_498,inverse(X_498),multiplicative_identity),true,product(X_497,multiplicative_identity,X_496),true),true),true),true) ),[0,2,2,0],$fot(true)]]) ).
cnf(refute_0_104,plain,
( ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(sum(X_498,inverse(X_498),multiplicative_identity),true,product(X_497,multiplicative_identity,X_496),true),true),true) != true
| ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) = true ),
inference(resolve,[$cnf( $equal(sum(X_498,inverse(X_498),multiplicative_identity),true) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(sum(X_498,inverse(X_498),multiplicative_identity),true,product(X_497,multiplicative_identity,X_496),true),true),true),true) )],[refute_0_101,refute_0_104]) ).
cnf(refute_0_106,plain,
ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true) = ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),
introduced(tautology,[refl,[$fot(ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true))]]) ).
cnf(refute_0_107,plain,
( ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true) != ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true)
| ifeq(true,true,product(X_497,multiplicative_identity,X_496),true) != product(X_497,multiplicative_identity,X_496)
| ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true) = ifeq(product(X_497,X_498,X_496),true,product(X_497,multiplicative_identity,X_496),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true)) ),[1,2],$fot(product(X_497,multiplicative_identity,X_496))]]) ).
cnf(refute_0_108,plain,
( ifeq(true,true,product(X_497,multiplicative_identity,X_496),true) != product(X_497,multiplicative_identity,X_496)
| ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true) = ifeq(product(X_497,X_498,X_496),true,product(X_497,multiplicative_identity,X_496),true) ),
inference(resolve,[$cnf( $equal(ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true) = ifeq(product(X_497,X_498,X_496),true,product(X_497,multiplicative_identity,X_496),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),product(X_497,multiplicative_identity,X_496)) )],[refute_0_55,refute_0_108]) ).
cnf(refute_0_110,plain,
ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) = ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true),
introduced(tautology,[refl,[$fot(ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true))]]) ).
cnf(refute_0_111,plain,
( ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true) != ifeq(product(X_497,X_498,X_496),true,product(X_497,multiplicative_identity,X_496),true)
| ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) != ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true)
| ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) = ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,product(X_497,multiplicative_identity,X_496),true),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true),ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true)) ),[1,2],$fot(ifeq(product(X_497,X_498,X_496),true,product(X_497,multiplicative_identity,X_496),true))]]) ).
cnf(refute_0_112,plain,
( ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true) != ifeq(product(X_497,X_498,X_496),true,product(X_497,multiplicative_identity,X_496),true)
| ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) = ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,product(X_497,multiplicative_identity,X_496),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true),ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true)) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) = ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,product(X_497,multiplicative_identity,X_496),true),true),
inference(resolve,[$cnf( $equal(ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),ifeq(product(X_497,X_498,X_496),true,product(X_497,multiplicative_identity,X_496),true)) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
( ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) != ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,product(X_497,multiplicative_identity,X_496),true),true)
| ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) != true
| ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,product(X_497,multiplicative_identity,X_496),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true),true) ),[0],$fot(ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,product(X_497,multiplicative_identity,X_496),true),true))]]) ).
cnf(refute_0_115,plain,
( ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true) != true
| ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,product(X_497,multiplicative_identity,X_496),true),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true),ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,product(X_497,multiplicative_identity,X_496),true),true)) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,product(X_497,multiplicative_identity,X_496),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(X_497,inverse(X_498),additive_identity),true,ifeq(product(X_497,X_498,X_496),true,ifeq(true,true,product(X_497,multiplicative_identity,X_496),true),true),true),true) )],[refute_0_105,refute_0_115]) ).
cnf(refute_0_117,plain,
ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(product(inverse(inverse(X_623)),X_623,X_623),true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) = true,
inference(subst,[],[refute_0_116:[bind(X_496,$fot(X_623)),bind(X_497,$fot(inverse(inverse(X_623)))),bind(X_498,$fot(X_623))]]) ).
cnf(refute_0_118,plain,
ifeq(product(X_23,X_24,multiply(X_23,X_24)),true,product(X_24,X_23,multiply(X_23,X_24)),true) = true,
inference(subst,[],[commutativity_of_multiplication:[bind(X,$fot(X_23)),bind(Y,$fot(X_24)),bind(Z,$fot(multiply(X_23,X_24)))]]) ).
cnf(refute_0_119,plain,
product(X_23,X_24,multiply(X_23,X_24)) = true,
inference(subst,[],[closure_of_multiplication:[bind(X,$fot(X_23)),bind(Y,$fot(X_24))]]) ).
cnf(refute_0_120,plain,
( ifeq(product(X_23,X_24,multiply(X_23,X_24)),true,product(X_24,X_23,multiply(X_23,X_24)),true) != true
| product(X_23,X_24,multiply(X_23,X_24)) != true
| ifeq(true,true,product(X_24,X_23,multiply(X_23,X_24)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_23,X_24,multiply(X_23,X_24)),true,product(X_24,X_23,multiply(X_23,X_24)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_121,plain,
( ifeq(product(X_23,X_24,multiply(X_23,X_24)),true,product(X_24,X_23,multiply(X_23,X_24)),true) != true
| ifeq(true,true,product(X_24,X_23,multiply(X_23,X_24)),true) = true ),
inference(resolve,[$cnf( $equal(product(X_23,X_24,multiply(X_23,X_24)),true) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
ifeq(true,true,product(X_24,X_23,multiply(X_23,X_24)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(X_23,X_24,multiply(X_23,X_24)),true,product(X_24,X_23,multiply(X_23,X_24)),true),true) )],[refute_0_118,refute_0_121]) ).
cnf(refute_0_123,plain,
ifeq(true,true,product(X_24,X_23,multiply(X_23,X_24)),true) = product(X_24,X_23,multiply(X_23,X_24)),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(product(X_24,X_23,multiply(X_23,X_24)))),bind(C,$fot(true))]]) ).
cnf(refute_0_124,plain,
( ifeq(true,true,product(X_24,X_23,multiply(X_23,X_24)),true) != product(X_24,X_23,multiply(X_23,X_24))
| ifeq(true,true,product(X_24,X_23,multiply(X_23,X_24)),true) != true
| product(X_24,X_23,multiply(X_23,X_24)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,product(X_24,X_23,multiply(X_23,X_24)),true),true) ),[0],$fot(product(X_24,X_23,multiply(X_23,X_24)))]]) ).
cnf(refute_0_125,plain,
( ifeq(true,true,product(X_24,X_23,multiply(X_23,X_24)),true) != true
| product(X_24,X_23,multiply(X_23,X_24)) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,product(X_24,X_23,multiply(X_23,X_24)),true),product(X_24,X_23,multiply(X_23,X_24))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
product(X_24,X_23,multiply(X_23,X_24)) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,product(X_24,X_23,multiply(X_23,X_24)),true),true) )],[refute_0_122,refute_0_125]) ).
cnf(refute_0_127,plain,
product(inverse(inverse(X_23)),X_23,multiply(X_23,inverse(inverse(X_23)))) = true,
inference(subst,[],[refute_0_126:[bind(X_24,$fot(inverse(inverse(X_23))))]]) ).
cnf(refute_0_128,plain,
ifeq2(product(X_54,multiplicative_identity,multiply(X_54,inverse(inverse(X_54)))),true,multiply(X_54,inverse(inverse(X_54))),multiply(X_54,multiplicative_identity)) = multiply(X_54,multiplicative_identity),
inference(subst,[],[refute_0_31:[bind(X_52,$fot(multiply(X_54,inverse(inverse(X_54))))),bind(X_55,$fot(multiplicative_identity))]]) ).
cnf(refute_0_129,plain,
ifeq(product(X_583,inverse(X_583),additive_identity),true,ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true),true) = true,
inference(subst,[],[refute_0_66:[bind(X_496,$fot(X_582)),bind(X_497,$fot(X_583)),bind(X_499,$fot(inverse(X_583)))]]) ).
cnf(refute_0_130,plain,
product(X_583,inverse(X_583),additive_identity) = true,
inference(subst,[],[multiplicative_inverse2:[bind(X,$fot(X_583))]]) ).
cnf(refute_0_131,plain,
( ifeq(product(X_583,inverse(X_583),additive_identity),true,ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true),true) != true
| product(X_583,inverse(X_583),additive_identity) != true
| ifeq(true,true,ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_583,inverse(X_583),additive_identity),true,ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_132,plain,
( ifeq(product(X_583,inverse(X_583),additive_identity),true,ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true),true) != true
| ifeq(true,true,ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true),true) = true ),
inference(resolve,[$cnf( $equal(product(X_583,inverse(X_583),additive_identity),true) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
ifeq(true,true,ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(X_583,inverse(X_583),additive_identity),true,ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true),true),true) )],[refute_0_129,refute_0_132]) ).
cnf(refute_0_134,plain,
ifeq(true,true,ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true),true) = ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_135,plain,
( ifeq(true,true,ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true),true) != ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true)
| ifeq(true,true,ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true),true) != true
| ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true),true),true) ),[0],$fot(ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true))]]) ).
cnf(refute_0_136,plain,
( ifeq(true,true,ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true),true) != true
| ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true),true),ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true)) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(product(X_583,inverse(inverse(X_583)),X_582),true,product(X_583,multiplicative_identity,X_582),true),true),true) )],[refute_0_133,refute_0_136]) ).
cnf(refute_0_138,plain,
ifeq(product(X_595,inverse(inverse(X_595)),multiply(inverse(inverse(X_595)),X_595)),true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true) = true,
inference(subst,[],[refute_0_137:[bind(X_582,$fot(multiply(inverse(inverse(X_595)),X_595))),bind(X_583,$fot(X_595))]]) ).
cnf(refute_0_139,plain,
product(X_595,inverse(inverse(X_595)),multiply(inverse(inverse(X_595)),X_595)) = true,
inference(subst,[],[refute_0_126:[bind(X_23,$fot(inverse(inverse(X_595)))),bind(X_24,$fot(X_595))]]) ).
cnf(refute_0_140,plain,
( ifeq(product(X_595,inverse(inverse(X_595)),multiply(inverse(inverse(X_595)),X_595)),true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true) != true
| product(X_595,inverse(inverse(X_595)),multiply(inverse(inverse(X_595)),X_595)) != true
| ifeq(true,true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_595,inverse(inverse(X_595)),multiply(inverse(inverse(X_595)),X_595)),true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_141,plain,
( ifeq(product(X_595,inverse(inverse(X_595)),multiply(inverse(inverse(X_595)),X_595)),true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true) != true
| ifeq(true,true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true) = true ),
inference(resolve,[$cnf( $equal(product(X_595,inverse(inverse(X_595)),multiply(inverse(inverse(X_595)),X_595)),true) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
ifeq(true,true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(X_595,inverse(inverse(X_595)),multiply(inverse(inverse(X_595)),X_595)),true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true),true) )],[refute_0_138,refute_0_141]) ).
cnf(refute_0_143,plain,
ifeq2(product(X_54,X_55,X_53),true,ifeq2(product(X_54,X_55,multiply(X_55,X_54)),true,multiply(X_55,X_54),X_53),X_53) = X_53,
inference(subst,[],[multiplication_is_well_defined:[bind(U,$fot(multiply(X_55,X_54))),bind(V,$fot(X_53)),bind(X,$fot(X_54)),bind(Y,$fot(X_55))]]) ).
cnf(refute_0_144,plain,
product(X_54,X_55,multiply(X_55,X_54)) = true,
inference(subst,[],[refute_0_126:[bind(X_23,$fot(X_55)),bind(X_24,$fot(X_54))]]) ).
cnf(refute_0_145,plain,
( ifeq2(product(X_54,X_55,X_53),true,ifeq2(product(X_54,X_55,multiply(X_55,X_54)),true,multiply(X_55,X_54),X_53),X_53) != X_53
| product(X_54,X_55,multiply(X_55,X_54)) != true
| ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53) = X_53 ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(X_54,X_55,X_53),true,ifeq2(product(X_54,X_55,multiply(X_55,X_54)),true,multiply(X_55,X_54),X_53),X_53),X_53) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_146,plain,
( ifeq2(product(X_54,X_55,X_53),true,ifeq2(product(X_54,X_55,multiply(X_55,X_54)),true,multiply(X_55,X_54),X_53),X_53) != X_53
| ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53) = X_53 ),
inference(resolve,[$cnf( $equal(product(X_54,X_55,multiply(X_55,X_54)),true) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53) = X_53,
inference(resolve,[$cnf( $equal(ifeq2(product(X_54,X_55,X_53),true,ifeq2(product(X_54,X_55,multiply(X_55,X_54)),true,multiply(X_55,X_54),X_53),X_53),X_53) )],[refute_0_143,refute_0_146]) ).
cnf(refute_0_148,plain,
ifeq2(true,true,multiply(X_55,X_54),X_53) = multiply(X_55,X_54),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(multiply(X_55,X_54))),bind(C,$fot(X_53))]]) ).
cnf(refute_0_149,plain,
ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53) = ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53),
introduced(tautology,[refl,[$fot(ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53))]]) ).
cnf(refute_0_150,plain,
( ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53) != ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53)
| ifeq2(true,true,multiply(X_55,X_54),X_53) != multiply(X_55,X_54)
| ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53) = ifeq2(product(X_54,X_55,X_53),true,multiply(X_55,X_54),X_53) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53),ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53)) ),[1,2],$fot(multiply(X_55,X_54))]]) ).
cnf(refute_0_151,plain,
( ifeq2(true,true,multiply(X_55,X_54),X_53) != multiply(X_55,X_54)
| ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53) = ifeq2(product(X_54,X_55,X_53),true,multiply(X_55,X_54),X_53) ),
inference(resolve,[$cnf( $equal(ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53),ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53)) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53) = ifeq2(product(X_54,X_55,X_53),true,multiply(X_55,X_54),X_53),
inference(resolve,[$cnf( $equal(ifeq2(true,true,multiply(X_55,X_54),X_53),multiply(X_55,X_54)) )],[refute_0_148,refute_0_151]) ).
cnf(refute_0_153,plain,
( ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53) != X_53
| ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53) != ifeq2(product(X_54,X_55,X_53),true,multiply(X_55,X_54),X_53)
| ifeq2(product(X_54,X_55,X_53),true,multiply(X_55,X_54),X_53) = X_53 ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53),X_53) ),[0],$fot(ifeq2(product(X_54,X_55,X_53),true,multiply(X_55,X_54),X_53))]]) ).
cnf(refute_0_154,plain,
( ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53) != X_53
| ifeq2(product(X_54,X_55,X_53),true,multiply(X_55,X_54),X_53) = X_53 ),
inference(resolve,[$cnf( $equal(ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53),ifeq2(product(X_54,X_55,X_53),true,multiply(X_55,X_54),X_53)) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
ifeq2(product(X_54,X_55,X_53),true,multiply(X_55,X_54),X_53) = X_53,
inference(resolve,[$cnf( $equal(ifeq2(product(X_54,X_55,X_53),true,ifeq2(true,true,multiply(X_55,X_54),X_53),X_53),X_53) )],[refute_0_147,refute_0_154]) ).
cnf(refute_0_156,plain,
ifeq2(product(X_85,X_86,multiply(X_85,X_86)),true,multiply(X_86,X_85),multiply(X_85,X_86)) = multiply(X_85,X_86),
inference(subst,[],[refute_0_155:[bind(X_53,$fot(multiply(X_85,X_86))),bind(X_54,$fot(X_85)),bind(X_55,$fot(X_86))]]) ).
cnf(refute_0_157,plain,
product(X_85,X_86,multiply(X_85,X_86)) = true,
inference(subst,[],[closure_of_multiplication:[bind(X,$fot(X_85)),bind(Y,$fot(X_86))]]) ).
cnf(refute_0_158,plain,
( ifeq2(product(X_85,X_86,multiply(X_85,X_86)),true,multiply(X_86,X_85),multiply(X_85,X_86)) != multiply(X_85,X_86)
| product(X_85,X_86,multiply(X_85,X_86)) != true
| ifeq2(true,true,multiply(X_86,X_85),multiply(X_85,X_86)) = multiply(X_85,X_86) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(X_85,X_86,multiply(X_85,X_86)),true,multiply(X_86,X_85),multiply(X_85,X_86)),multiply(X_85,X_86)) ),[0,0],$fot(true)]]) ).
cnf(refute_0_159,plain,
( ifeq2(product(X_85,X_86,multiply(X_85,X_86)),true,multiply(X_86,X_85),multiply(X_85,X_86)) != multiply(X_85,X_86)
| ifeq2(true,true,multiply(X_86,X_85),multiply(X_85,X_86)) = multiply(X_85,X_86) ),
inference(resolve,[$cnf( $equal(product(X_85,X_86,multiply(X_85,X_86)),true) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
ifeq2(true,true,multiply(X_86,X_85),multiply(X_85,X_86)) = multiply(X_85,X_86),
inference(resolve,[$cnf( $equal(ifeq2(product(X_85,X_86,multiply(X_85,X_86)),true,multiply(X_86,X_85),multiply(X_85,X_86)),multiply(X_85,X_86)) )],[refute_0_156,refute_0_159]) ).
cnf(refute_0_161,plain,
ifeq2(true,true,multiply(X_86,X_85),multiply(X_85,X_86)) = multiply(X_86,X_85),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(multiply(X_86,X_85))),bind(C,$fot(multiply(X_85,X_86)))]]) ).
cnf(refute_0_162,plain,
( ifeq2(true,true,multiply(X_86,X_85),multiply(X_85,X_86)) != multiply(X_85,X_86)
| ifeq2(true,true,multiply(X_86,X_85),multiply(X_85,X_86)) != multiply(X_86,X_85)
| multiply(X_86,X_85) = multiply(X_85,X_86) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(true,true,multiply(X_86,X_85),multiply(X_85,X_86)),multiply(X_85,X_86)) ),[0],$fot(multiply(X_86,X_85))]]) ).
cnf(refute_0_163,plain,
( ifeq2(true,true,multiply(X_86,X_85),multiply(X_85,X_86)) != multiply(X_85,X_86)
| multiply(X_86,X_85) = multiply(X_85,X_86) ),
inference(resolve,[$cnf( $equal(ifeq2(true,true,multiply(X_86,X_85),multiply(X_85,X_86)),multiply(X_86,X_85)) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
multiply(X_86,X_85) = multiply(X_85,X_86),
inference(resolve,[$cnf( $equal(ifeq2(true,true,multiply(X_86,X_85),multiply(X_85,X_86)),multiply(X_85,X_86)) )],[refute_0_160,refute_0_163]) ).
cnf(refute_0_165,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_166,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_167,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
( multiply(X_86,X_85) != multiply(X_85,X_86)
| multiply(X_85,X_86) = multiply(X_86,X_85) ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(multiply(X_86,X_85))),bind(Y0,$fot(multiply(X_85,X_86)))]]) ).
cnf(refute_0_169,plain,
multiply(X_85,X_86) = multiply(X_86,X_85),
inference(resolve,[$cnf( $equal(multiply(X_86,X_85),multiply(X_85,X_86)) )],[refute_0_164,refute_0_168]) ).
cnf(refute_0_170,plain,
multiply(inverse(inverse(X_595)),X_595) = multiply(X_595,inverse(inverse(X_595))),
inference(subst,[],[refute_0_169:[bind(X_85,$fot(inverse(inverse(X_595)))),bind(X_86,$fot(X_595))]]) ).
cnf(refute_0_171,plain,
product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)) = product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),
introduced(tautology,[refl,[$fot(product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)))]]) ).
cnf(refute_0_172,plain,
( multiply(inverse(inverse(X_595)),X_595) != multiply(X_595,inverse(inverse(X_595)))
| product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)) != product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595))
| product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)) = product(X_595,multiplicative_identity,multiply(X_595,inverse(inverse(X_595)))) ),
introduced(tautology,[equality,[$cnf( $equal(product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595))) ),[1,2],$fot(multiply(X_595,inverse(inverse(X_595))))]]) ).
cnf(refute_0_173,plain,
( multiply(inverse(inverse(X_595)),X_595) != multiply(X_595,inverse(inverse(X_595)))
| product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)) = product(X_595,multiplicative_identity,multiply(X_595,inverse(inverse(X_595)))) ),
inference(resolve,[$cnf( $equal(product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595))) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)) = product(X_595,multiplicative_identity,multiply(X_595,inverse(inverse(X_595)))),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_595)),X_595),multiply(X_595,inverse(inverse(X_595)))) )],[refute_0_170,refute_0_173]) ).
cnf(refute_0_175,plain,
ifeq(true,true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true) = product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)))),bind(C,$fot(true))]]) ).
cnf(refute_0_176,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_177,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_167,refute_0_176]) ).
cnf(refute_0_178,plain,
( ifeq(true,true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true) != product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595))
| product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)) != product(X_595,multiplicative_identity,multiply(X_595,inverse(inverse(X_595))))
| ifeq(true,true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true) = product(X_595,multiplicative_identity,multiply(X_595,inverse(inverse(X_595)))) ),
inference(subst,[],[refute_0_177:[bind(X0,$fot(ifeq(true,true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true))),bind(Y0,$fot(product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)))),bind(Z0,$fot(product(X_595,multiplicative_identity,multiply(X_595,inverse(inverse(X_595))))))]]) ).
cnf(refute_0_179,plain,
( product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)) != product(X_595,multiplicative_identity,multiply(X_595,inverse(inverse(X_595))))
| ifeq(true,true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true) = product(X_595,multiplicative_identity,multiply(X_595,inverse(inverse(X_595)))) ),
inference(resolve,[$cnf( $equal(ifeq(true,true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true),product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595))) )],[refute_0_175,refute_0_178]) ).
cnf(refute_0_180,plain,
ifeq(true,true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true) = product(X_595,multiplicative_identity,multiply(X_595,inverse(inverse(X_595)))),
inference(resolve,[$cnf( $equal(product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),product(X_595,multiplicative_identity,multiply(X_595,inverse(inverse(X_595))))) )],[refute_0_174,refute_0_179]) ).
cnf(refute_0_181,plain,
( ifeq(true,true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true) != product(X_595,multiplicative_identity,multiply(X_595,inverse(inverse(X_595))))
| ifeq(true,true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true) != true
| product(X_595,multiplicative_identity,multiply(X_595,inverse(inverse(X_595)))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true),true) ),[0],$fot(product(X_595,multiplicative_identity,multiply(X_595,inverse(inverse(X_595)))))]]) ).
cnf(refute_0_182,plain,
( ifeq(true,true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true) != true
| product(X_595,multiplicative_identity,multiply(X_595,inverse(inverse(X_595)))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true),product(X_595,multiplicative_identity,multiply(X_595,inverse(inverse(X_595))))) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
product(X_595,multiplicative_identity,multiply(X_595,inverse(inverse(X_595)))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,product(X_595,multiplicative_identity,multiply(inverse(inverse(X_595)),X_595)),true),true) )],[refute_0_142,refute_0_182]) ).
cnf(refute_0_184,plain,
product(X_54,multiplicative_identity,multiply(X_54,inverse(inverse(X_54)))) = true,
inference(subst,[],[refute_0_183:[bind(X_595,$fot(X_54))]]) ).
cnf(refute_0_185,plain,
( ifeq2(product(X_54,multiplicative_identity,multiply(X_54,inverse(inverse(X_54)))),true,multiply(X_54,inverse(inverse(X_54))),multiply(X_54,multiplicative_identity)) != multiply(X_54,multiplicative_identity)
| product(X_54,multiplicative_identity,multiply(X_54,inverse(inverse(X_54)))) != true
| ifeq2(true,true,multiply(X_54,inverse(inverse(X_54))),multiply(X_54,multiplicative_identity)) = multiply(X_54,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(X_54,multiplicative_identity,multiply(X_54,inverse(inverse(X_54)))),true,multiply(X_54,inverse(inverse(X_54))),multiply(X_54,multiplicative_identity)),multiply(X_54,multiplicative_identity)) ),[0,0],$fot(true)]]) ).
cnf(refute_0_186,plain,
( ifeq2(product(X_54,multiplicative_identity,multiply(X_54,inverse(inverse(X_54)))),true,multiply(X_54,inverse(inverse(X_54))),multiply(X_54,multiplicative_identity)) != multiply(X_54,multiplicative_identity)
| ifeq2(true,true,multiply(X_54,inverse(inverse(X_54))),multiply(X_54,multiplicative_identity)) = multiply(X_54,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(product(X_54,multiplicative_identity,multiply(X_54,inverse(inverse(X_54)))),true) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
ifeq2(true,true,multiply(X_54,inverse(inverse(X_54))),multiply(X_54,multiplicative_identity)) = multiply(X_54,multiplicative_identity),
inference(resolve,[$cnf( $equal(ifeq2(product(X_54,multiplicative_identity,multiply(X_54,inverse(inverse(X_54)))),true,multiply(X_54,inverse(inverse(X_54))),multiply(X_54,multiplicative_identity)),multiply(X_54,multiplicative_identity)) )],[refute_0_128,refute_0_186]) ).
cnf(refute_0_188,plain,
ifeq2(true,true,multiply(X_54,inverse(inverse(X_54))),multiply(X_54,multiplicative_identity)) = multiply(X_54,inverse(inverse(X_54))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(multiply(X_54,inverse(inverse(X_54))))),bind(C,$fot(multiply(X_54,multiplicative_identity)))]]) ).
cnf(refute_0_189,plain,
( ifeq2(true,true,multiply(X_54,inverse(inverse(X_54))),multiply(X_54,multiplicative_identity)) != multiply(X_54,inverse(inverse(X_54)))
| ifeq2(true,true,multiply(X_54,inverse(inverse(X_54))),multiply(X_54,multiplicative_identity)) != multiply(X_54,multiplicative_identity)
| multiply(X_54,inverse(inverse(X_54))) = multiply(X_54,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(true,true,multiply(X_54,inverse(inverse(X_54))),multiply(X_54,multiplicative_identity)),multiply(X_54,multiplicative_identity)) ),[0],$fot(multiply(X_54,inverse(inverse(X_54))))]]) ).
cnf(refute_0_190,plain,
( ifeq2(true,true,multiply(X_54,inverse(inverse(X_54))),multiply(X_54,multiplicative_identity)) != multiply(X_54,multiplicative_identity)
| multiply(X_54,inverse(inverse(X_54))) = multiply(X_54,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(ifeq2(true,true,multiply(X_54,inverse(inverse(X_54))),multiply(X_54,multiplicative_identity)),multiply(X_54,inverse(inverse(X_54)))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(product(multiplicative_identity,X_52,X_52),true,X_52,X_53),X_53) = X_53,
inference(subst,[],[multiplication_is_well_defined:[bind(U,$fot(X_52)),bind(V,$fot(X_53)),bind(X,$fot(multiplicative_identity)),bind(Y,$fot(X_52))]]) ).
cnf(refute_0_192,plain,
product(multiplicative_identity,X_52,X_52) = true,
inference(subst,[],[multiplicative_identity1:[bind(X,$fot(X_52))]]) ).
cnf(refute_0_193,plain,
( ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(product(multiplicative_identity,X_52,X_52),true,X_52,X_53),X_53) != X_53
| product(multiplicative_identity,X_52,X_52) != true
| ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53) = X_53 ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(product(multiplicative_identity,X_52,X_52),true,X_52,X_53),X_53),X_53) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_194,plain,
( ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(product(multiplicative_identity,X_52,X_52),true,X_52,X_53),X_53) != X_53
| ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53) = X_53 ),
inference(resolve,[$cnf( $equal(product(multiplicative_identity,X_52,X_52),true) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53) = X_53,
inference(resolve,[$cnf( $equal(ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(product(multiplicative_identity,X_52,X_52),true,X_52,X_53),X_53),X_53) )],[refute_0_191,refute_0_194]) ).
cnf(refute_0_196,plain,
ifeq2(true,true,X_52,X_53) = X_52,
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(X_52)),bind(C,$fot(X_53))]]) ).
cnf(refute_0_197,plain,
ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53) = ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53),
introduced(tautology,[refl,[$fot(ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53))]]) ).
cnf(refute_0_198,plain,
( ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53) != ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53)
| ifeq2(true,true,X_52,X_53) != X_52
| ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53) = ifeq2(product(multiplicative_identity,X_52,X_53),true,X_52,X_53) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53),ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53)) ),[1,2],$fot(X_52)]]) ).
cnf(refute_0_199,plain,
( ifeq2(true,true,X_52,X_53) != X_52
| ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53) = ifeq2(product(multiplicative_identity,X_52,X_53),true,X_52,X_53) ),
inference(resolve,[$cnf( $equal(ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53),ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53)) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53) = ifeq2(product(multiplicative_identity,X_52,X_53),true,X_52,X_53),
inference(resolve,[$cnf( $equal(ifeq2(true,true,X_52,X_53),X_52) )],[refute_0_196,refute_0_199]) ).
cnf(refute_0_201,plain,
( ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53) != X_53
| ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53) != ifeq2(product(multiplicative_identity,X_52,X_53),true,X_52,X_53)
| ifeq2(product(multiplicative_identity,X_52,X_53),true,X_52,X_53) = X_53 ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53),X_53) ),[0],$fot(ifeq2(product(multiplicative_identity,X_52,X_53),true,X_52,X_53))]]) ).
cnf(refute_0_202,plain,
( ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53) != X_53
| ifeq2(product(multiplicative_identity,X_52,X_53),true,X_52,X_53) = X_53 ),
inference(resolve,[$cnf( $equal(ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53),ifeq2(product(multiplicative_identity,X_52,X_53),true,X_52,X_53)) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
ifeq2(product(multiplicative_identity,X_52,X_53),true,X_52,X_53) = X_53,
inference(resolve,[$cnf( $equal(ifeq2(product(multiplicative_identity,X_52,X_53),true,ifeq2(true,true,X_52,X_53),X_53),X_53) )],[refute_0_195,refute_0_202]) ).
cnf(refute_0_204,plain,
ifeq2(product(multiplicative_identity,X_56,multiply(X_56,multiplicative_identity)),true,X_56,multiply(X_56,multiplicative_identity)) = multiply(X_56,multiplicative_identity),
inference(subst,[],[refute_0_203:[bind(X_52,$fot(X_56)),bind(X_53,$fot(multiply(X_56,multiplicative_identity)))]]) ).
cnf(refute_0_205,plain,
product(multiplicative_identity,X_56,multiply(X_56,multiplicative_identity)) = true,
inference(subst,[],[refute_0_126:[bind(X_23,$fot(X_56)),bind(X_24,$fot(multiplicative_identity))]]) ).
cnf(refute_0_206,plain,
( ifeq2(product(multiplicative_identity,X_56,multiply(X_56,multiplicative_identity)),true,X_56,multiply(X_56,multiplicative_identity)) != multiply(X_56,multiplicative_identity)
| product(multiplicative_identity,X_56,multiply(X_56,multiplicative_identity)) != true
| ifeq2(true,true,X_56,multiply(X_56,multiplicative_identity)) = multiply(X_56,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(multiplicative_identity,X_56,multiply(X_56,multiplicative_identity)),true,X_56,multiply(X_56,multiplicative_identity)),multiply(X_56,multiplicative_identity)) ),[0,0],$fot(true)]]) ).
cnf(refute_0_207,plain,
( ifeq2(product(multiplicative_identity,X_56,multiply(X_56,multiplicative_identity)),true,X_56,multiply(X_56,multiplicative_identity)) != multiply(X_56,multiplicative_identity)
| ifeq2(true,true,X_56,multiply(X_56,multiplicative_identity)) = multiply(X_56,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(product(multiplicative_identity,X_56,multiply(X_56,multiplicative_identity)),true) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
ifeq2(true,true,X_56,multiply(X_56,multiplicative_identity)) = multiply(X_56,multiplicative_identity),
inference(resolve,[$cnf( $equal(ifeq2(product(multiplicative_identity,X_56,multiply(X_56,multiplicative_identity)),true,X_56,multiply(X_56,multiplicative_identity)),multiply(X_56,multiplicative_identity)) )],[refute_0_204,refute_0_207]) ).
cnf(refute_0_209,plain,
ifeq2(true,true,X_56,multiply(X_56,multiplicative_identity)) = X_56,
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(X_56)),bind(C,$fot(multiply(X_56,multiplicative_identity)))]]) ).
cnf(refute_0_210,plain,
( ifeq2(true,true,X_56,multiply(X_56,multiplicative_identity)) != X_56
| ifeq2(true,true,X_56,multiply(X_56,multiplicative_identity)) != multiply(X_56,multiplicative_identity)
| X_56 = multiply(X_56,multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(true,true,X_56,multiply(X_56,multiplicative_identity)),multiply(X_56,multiplicative_identity)) ),[0],$fot(X_56)]]) ).
cnf(refute_0_211,plain,
( ifeq2(true,true,X_56,multiply(X_56,multiplicative_identity)) != multiply(X_56,multiplicative_identity)
| X_56 = multiply(X_56,multiplicative_identity) ),
inference(resolve,[$cnf( $equal(ifeq2(true,true,X_56,multiply(X_56,multiplicative_identity)),X_56) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
X_56 = multiply(X_56,multiplicative_identity),
inference(resolve,[$cnf( $equal(ifeq2(true,true,X_56,multiply(X_56,multiplicative_identity)),multiply(X_56,multiplicative_identity)) )],[refute_0_208,refute_0_211]) ).
cnf(refute_0_213,plain,
( X_56 != multiply(X_56,multiplicative_identity)
| multiply(X_56,multiplicative_identity) = X_56 ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(X_56)),bind(Y0,$fot(multiply(X_56,multiplicative_identity)))]]) ).
cnf(refute_0_214,plain,
multiply(X_56,multiplicative_identity) = X_56,
inference(resolve,[$cnf( $equal(X_56,multiply(X_56,multiplicative_identity)) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
multiply(X_54,multiplicative_identity) = X_54,
inference(subst,[],[refute_0_214:[bind(X_56,$fot(X_54))]]) ).
cnf(refute_0_216,plain,
( multiply(X_54,inverse(inverse(X_54))) != multiply(X_54,multiplicative_identity)
| multiply(X_54,multiplicative_identity) != X_54
| multiply(X_54,inverse(inverse(X_54))) = X_54 ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_54,inverse(inverse(X_54))),X_54) ),[0],$fot(multiply(X_54,multiplicative_identity))]]) ).
cnf(refute_0_217,plain,
( multiply(X_54,inverse(inverse(X_54))) != multiply(X_54,multiplicative_identity)
| multiply(X_54,inverse(inverse(X_54))) = X_54 ),
inference(resolve,[$cnf( $equal(multiply(X_54,multiplicative_identity),X_54) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
( ifeq2(true,true,multiply(X_54,inverse(inverse(X_54))),multiply(X_54,multiplicative_identity)) != multiply(X_54,multiplicative_identity)
| multiply(X_54,inverse(inverse(X_54))) = X_54 ),
inference(resolve,[$cnf( $equal(multiply(X_54,inverse(inverse(X_54))),multiply(X_54,multiplicative_identity)) )],[refute_0_190,refute_0_217]) ).
cnf(refute_0_219,plain,
multiply(X_54,inverse(inverse(X_54))) = X_54,
inference(resolve,[$cnf( $equal(ifeq2(true,true,multiply(X_54,inverse(inverse(X_54))),multiply(X_54,multiplicative_identity)),multiply(X_54,multiplicative_identity)) )],[refute_0_187,refute_0_218]) ).
cnf(refute_0_220,plain,
multiply(X_23,inverse(inverse(X_23))) = X_23,
inference(subst,[],[refute_0_219:[bind(X_54,$fot(X_23))]]) ).
cnf(refute_0_221,plain,
( multiply(X_23,inverse(inverse(X_23))) != X_23
| product(inverse(inverse(X_23)),X_23,multiply(X_23,inverse(inverse(X_23)))) != true
| product(inverse(inverse(X_23)),X_23,X_23) = true ),
introduced(tautology,[equality,[$cnf( $equal(product(inverse(inverse(X_23)),X_23,multiply(X_23,inverse(inverse(X_23)))),true) ),[0,2],$fot(X_23)]]) ).
cnf(refute_0_222,plain,
( product(inverse(inverse(X_23)),X_23,multiply(X_23,inverse(inverse(X_23)))) != true
| product(inverse(inverse(X_23)),X_23,X_23) = true ),
inference(resolve,[$cnf( $equal(multiply(X_23,inverse(inverse(X_23))),X_23) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
product(inverse(inverse(X_23)),X_23,X_23) = true,
inference(resolve,[$cnf( $equal(product(inverse(inverse(X_23)),X_23,multiply(X_23,inverse(inverse(X_23)))),true) )],[refute_0_127,refute_0_222]) ).
cnf(refute_0_224,plain,
product(inverse(inverse(X_623)),X_623,X_623) = true,
inference(subst,[],[refute_0_223:[bind(X_23,$fot(X_623))]]) ).
cnf(refute_0_225,plain,
( ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(product(inverse(inverse(X_623)),X_623,X_623),true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) != true
| product(inverse(inverse(X_623)),X_623,X_623) != true
| ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(product(inverse(inverse(X_623)),X_623,X_623),true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_226,plain,
( ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(product(inverse(inverse(X_623)),X_623,X_623),true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) != true
| ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) = true ),
inference(resolve,[$cnf( $equal(product(inverse(inverse(X_623)),X_623,X_623),true) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(product(inverse(inverse(X_623)),X_623,X_623),true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true),true) )],[refute_0_117,refute_0_226]) ).
cnf(refute_0_228,plain,
ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true) = product(inverse(inverse(X_623)),multiplicative_identity,X_623),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(product(inverse(inverse(X_623)),multiplicative_identity,X_623))),bind(C,$fot(true))]]) ).
cnf(refute_0_229,plain,
ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) = ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true),
introduced(tautology,[refl,[$fot(ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true))]]) ).
cnf(refute_0_230,plain,
( ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) != ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true)
| ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true) != product(inverse(inverse(X_623)),multiplicative_identity,X_623)
| ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) = ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true),ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true)) ),[1,2],$fot(product(inverse(inverse(X_623)),multiplicative_identity,X_623))]]) ).
cnf(refute_0_231,plain,
( ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true) != product(inverse(inverse(X_623)),multiplicative_identity,X_623)
| ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) = ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true) ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true),ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true)) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) = ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),product(inverse(inverse(X_623)),multiplicative_identity,X_623)) )],[refute_0_228,refute_0_231]) ).
cnf(refute_0_233,plain,
product(inverse(inverse(X_623)),inverse(X_623),additive_identity) = true,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(inverse(X_623)))]]) ).
cnf(refute_0_234,plain,
ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) = ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true),
introduced(tautology,[refl,[$fot(ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true))]]) ).
cnf(refute_0_235,plain,
( ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) != ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true)
| product(inverse(inverse(X_623)),inverse(X_623),additive_identity) != true
| ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) = ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true),ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true)) ),[1,0],$fot(true)]]) ).
cnf(refute_0_236,plain,
( product(inverse(inverse(X_623)),inverse(X_623),additive_identity) != true
| ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) = ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true),ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true)) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) = ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true),
inference(resolve,[$cnf( $equal(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true) )],[refute_0_233,refute_0_236]) ).
cnf(refute_0_238,plain,
( ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) != ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true)
| ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) != ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true)
| ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) = ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true) ),
inference(subst,[],[refute_0_177:[bind(X0,$fot(ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true))),bind(Y0,$fot(ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true))),bind(Z0,$fot(ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true)))]]) ).
cnf(refute_0_239,plain,
( ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) != ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true)
| ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) = ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true) ),
inference(resolve,[$cnf( $equal(ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true),ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true)) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) = ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true),ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true)) )],[refute_0_232,refute_0_239]) ).
cnf(refute_0_241,plain,
( ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) != ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true)
| ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true) != product(inverse(inverse(X_623)),multiplicative_identity,X_623)
| ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) = product(inverse(inverse(X_623)),multiplicative_identity,X_623) ),
inference(subst,[],[refute_0_177:[bind(X0,$fot(ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true))),bind(Y0,$fot(ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true))),bind(Z0,$fot(product(inverse(inverse(X_623)),multiplicative_identity,X_623)))]]) ).
cnf(refute_0_242,plain,
( ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true) != product(inverse(inverse(X_623)),multiplicative_identity,X_623)
| ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) = product(inverse(inverse(X_623)),multiplicative_identity,X_623) ),
inference(resolve,[$cnf( $equal(ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true),ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true)) )],[refute_0_240,refute_0_241]) ).
cnf(refute_0_243,plain,
ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) = product(inverse(inverse(X_623)),multiplicative_identity,X_623),
inference(resolve,[$cnf( $equal(ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),product(inverse(inverse(X_623)),multiplicative_identity,X_623)) )],[refute_0_228,refute_0_242]) ).
cnf(refute_0_244,plain,
( ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) != product(inverse(inverse(X_623)),multiplicative_identity,X_623)
| ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) != true
| product(inverse(inverse(X_623)),multiplicative_identity,X_623) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true),true) ),[0],$fot(product(inverse(inverse(X_623)),multiplicative_identity,X_623))]]) ).
cnf(refute_0_245,plain,
( ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true) != true
| product(inverse(inverse(X_623)),multiplicative_identity,X_623) = true ),
inference(resolve,[$cnf( $equal(ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true),product(inverse(inverse(X_623)),multiplicative_identity,X_623)) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
product(inverse(inverse(X_623)),multiplicative_identity,X_623) = true,
inference(resolve,[$cnf( $equal(ifeq(product(inverse(inverse(X_623)),inverse(X_623),additive_identity),true,ifeq(true,true,product(inverse(inverse(X_623)),multiplicative_identity,X_623),true),true),true) )],[refute_0_227,refute_0_245]) ).
cnf(refute_0_247,plain,
product(inverse(inverse(X_52)),multiplicative_identity,X_52) = true,
inference(subst,[],[refute_0_246:[bind(X_623,$fot(X_52))]]) ).
cnf(refute_0_248,plain,
( ifeq2(product(inverse(inverse(X_52)),multiplicative_identity,X_52),true,X_52,multiply(inverse(inverse(X_52)),multiplicative_identity)) != multiply(inverse(inverse(X_52)),multiplicative_identity)
| product(inverse(inverse(X_52)),multiplicative_identity,X_52) != true
| ifeq2(true,true,X_52,multiply(inverse(inverse(X_52)),multiplicative_identity)) = multiply(inverse(inverse(X_52)),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(inverse(inverse(X_52)),multiplicative_identity,X_52),true,X_52,multiply(inverse(inverse(X_52)),multiplicative_identity)),multiply(inverse(inverse(X_52)),multiplicative_identity)) ),[0,0],$fot(true)]]) ).
cnf(refute_0_249,plain,
( ifeq2(product(inverse(inverse(X_52)),multiplicative_identity,X_52),true,X_52,multiply(inverse(inverse(X_52)),multiplicative_identity)) != multiply(inverse(inverse(X_52)),multiplicative_identity)
| ifeq2(true,true,X_52,multiply(inverse(inverse(X_52)),multiplicative_identity)) = multiply(inverse(inverse(X_52)),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(product(inverse(inverse(X_52)),multiplicative_identity,X_52),true) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
ifeq2(true,true,X_52,multiply(inverse(inverse(X_52)),multiplicative_identity)) = multiply(inverse(inverse(X_52)),multiplicative_identity),
inference(resolve,[$cnf( $equal(ifeq2(product(inverse(inverse(X_52)),multiplicative_identity,X_52),true,X_52,multiply(inverse(inverse(X_52)),multiplicative_identity)),multiply(inverse(inverse(X_52)),multiplicative_identity)) )],[refute_0_100,refute_0_249]) ).
cnf(refute_0_251,plain,
ifeq2(true,true,X_52,multiply(inverse(inverse(X_52)),multiplicative_identity)) = X_52,
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(X_52)),bind(C,$fot(multiply(inverse(inverse(X_52)),multiplicative_identity)))]]) ).
cnf(refute_0_252,plain,
( ifeq2(true,true,X_52,multiply(inverse(inverse(X_52)),multiplicative_identity)) != X_52
| ifeq2(true,true,X_52,multiply(inverse(inverse(X_52)),multiplicative_identity)) != multiply(inverse(inverse(X_52)),multiplicative_identity)
| X_52 = multiply(inverse(inverse(X_52)),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(true,true,X_52,multiply(inverse(inverse(X_52)),multiplicative_identity)),multiply(inverse(inverse(X_52)),multiplicative_identity)) ),[0],$fot(X_52)]]) ).
cnf(refute_0_253,plain,
( ifeq2(true,true,X_52,multiply(inverse(inverse(X_52)),multiplicative_identity)) != multiply(inverse(inverse(X_52)),multiplicative_identity)
| X_52 = multiply(inverse(inverse(X_52)),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(ifeq2(true,true,X_52,multiply(inverse(inverse(X_52)),multiplicative_identity)),X_52) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
ifeq2(product(multiplicative_identity,X_56,multiply(multiplicative_identity,X_56)),true,X_56,multiply(multiplicative_identity,X_56)) = multiply(multiplicative_identity,X_56),
inference(subst,[],[refute_0_203:[bind(X_52,$fot(X_56)),bind(X_53,$fot(multiply(multiplicative_identity,X_56)))]]) ).
cnf(refute_0_255,plain,
product(multiplicative_identity,X_56,multiply(multiplicative_identity,X_56)) = true,
inference(subst,[],[closure_of_multiplication:[bind(X,$fot(multiplicative_identity)),bind(Y,$fot(X_56))]]) ).
cnf(refute_0_256,plain,
( ifeq2(product(multiplicative_identity,X_56,multiply(multiplicative_identity,X_56)),true,X_56,multiply(multiplicative_identity,X_56)) != multiply(multiplicative_identity,X_56)
| product(multiplicative_identity,X_56,multiply(multiplicative_identity,X_56)) != true
| ifeq2(true,true,X_56,multiply(multiplicative_identity,X_56)) = multiply(multiplicative_identity,X_56) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(multiplicative_identity,X_56,multiply(multiplicative_identity,X_56)),true,X_56,multiply(multiplicative_identity,X_56)),multiply(multiplicative_identity,X_56)) ),[0,0],$fot(true)]]) ).
cnf(refute_0_257,plain,
( ifeq2(product(multiplicative_identity,X_56,multiply(multiplicative_identity,X_56)),true,X_56,multiply(multiplicative_identity,X_56)) != multiply(multiplicative_identity,X_56)
| ifeq2(true,true,X_56,multiply(multiplicative_identity,X_56)) = multiply(multiplicative_identity,X_56) ),
inference(resolve,[$cnf( $equal(product(multiplicative_identity,X_56,multiply(multiplicative_identity,X_56)),true) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
ifeq2(true,true,X_56,multiply(multiplicative_identity,X_56)) = multiply(multiplicative_identity,X_56),
inference(resolve,[$cnf( $equal(ifeq2(product(multiplicative_identity,X_56,multiply(multiplicative_identity,X_56)),true,X_56,multiply(multiplicative_identity,X_56)),multiply(multiplicative_identity,X_56)) )],[refute_0_254,refute_0_257]) ).
cnf(refute_0_259,plain,
ifeq2(true,true,X_56,multiply(multiplicative_identity,X_56)) = X_56,
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(X_56)),bind(C,$fot(multiply(multiplicative_identity,X_56)))]]) ).
cnf(refute_0_260,plain,
( ifeq2(true,true,X_56,multiply(multiplicative_identity,X_56)) != X_56
| ifeq2(true,true,X_56,multiply(multiplicative_identity,X_56)) != multiply(multiplicative_identity,X_56)
| X_56 = multiply(multiplicative_identity,X_56) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(true,true,X_56,multiply(multiplicative_identity,X_56)),multiply(multiplicative_identity,X_56)) ),[0],$fot(X_56)]]) ).
cnf(refute_0_261,plain,
( ifeq2(true,true,X_56,multiply(multiplicative_identity,X_56)) != multiply(multiplicative_identity,X_56)
| X_56 = multiply(multiplicative_identity,X_56) ),
inference(resolve,[$cnf( $equal(ifeq2(true,true,X_56,multiply(multiplicative_identity,X_56)),X_56) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
X_56 = multiply(multiplicative_identity,X_56),
inference(resolve,[$cnf( $equal(ifeq2(true,true,X_56,multiply(multiplicative_identity,X_56)),multiply(multiplicative_identity,X_56)) )],[refute_0_258,refute_0_261]) ).
cnf(refute_0_263,plain,
( X_56 != multiply(multiplicative_identity,X_56)
| multiply(multiplicative_identity,X_56) = X_56 ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(X_56)),bind(Y0,$fot(multiply(multiplicative_identity,X_56)))]]) ).
cnf(refute_0_264,plain,
multiply(multiplicative_identity,X_56) = X_56,
inference(resolve,[$cnf( $equal(X_56,multiply(multiplicative_identity,X_56)) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
multiply(multiplicative_identity,inverse(inverse(X_52))) = inverse(inverse(X_52)),
inference(subst,[],[refute_0_264:[bind(X_56,$fot(inverse(inverse(X_52))))]]) ).
cnf(refute_0_266,plain,
multiply(inverse(inverse(X_52)),multiplicative_identity) = multiply(multiplicative_identity,inverse(inverse(X_52))),
inference(subst,[],[refute_0_169:[bind(X_85,$fot(inverse(inverse(X_52)))),bind(X_86,$fot(multiplicative_identity))]]) ).
cnf(refute_0_267,plain,
( multiply(inverse(inverse(X_52)),multiplicative_identity) != multiply(multiplicative_identity,inverse(inverse(X_52)))
| multiply(multiplicative_identity,inverse(inverse(X_52))) != inverse(inverse(X_52))
| multiply(inverse(inverse(X_52)),multiplicative_identity) = inverse(inverse(X_52)) ),
inference(subst,[],[refute_0_177:[bind(X0,$fot(multiply(inverse(inverse(X_52)),multiplicative_identity))),bind(Y0,$fot(multiply(multiplicative_identity,inverse(inverse(X_52))))),bind(Z0,$fot(inverse(inverse(X_52))))]]) ).
cnf(refute_0_268,plain,
( multiply(multiplicative_identity,inverse(inverse(X_52))) != inverse(inverse(X_52))
| multiply(inverse(inverse(X_52)),multiplicative_identity) = inverse(inverse(X_52)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_52)),multiplicative_identity),multiply(multiplicative_identity,inverse(inverse(X_52)))) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
multiply(inverse(inverse(X_52)),multiplicative_identity) = inverse(inverse(X_52)),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,inverse(inverse(X_52))),inverse(inverse(X_52))) )],[refute_0_265,refute_0_268]) ).
cnf(refute_0_270,plain,
( X_52 != multiply(inverse(inverse(X_52)),multiplicative_identity)
| multiply(inverse(inverse(X_52)),multiplicative_identity) != inverse(inverse(X_52))
| X_52 = inverse(inverse(X_52)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_52,inverse(inverse(X_52))) ),[0],$fot(multiply(inverse(inverse(X_52)),multiplicative_identity))]]) ).
cnf(refute_0_271,plain,
( X_52 != multiply(inverse(inverse(X_52)),multiplicative_identity)
| X_52 = inverse(inverse(X_52)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_52)),multiplicative_identity),inverse(inverse(X_52))) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
( ifeq2(true,true,X_52,multiply(inverse(inverse(X_52)),multiplicative_identity)) != multiply(inverse(inverse(X_52)),multiplicative_identity)
| X_52 = inverse(inverse(X_52)) ),
inference(resolve,[$cnf( $equal(X_52,multiply(inverse(inverse(X_52)),multiplicative_identity)) )],[refute_0_253,refute_0_271]) ).
cnf(refute_0_273,plain,
X_52 = inverse(inverse(X_52)),
inference(resolve,[$cnf( $equal(ifeq2(true,true,X_52,multiply(inverse(inverse(X_52)),multiplicative_identity)),multiply(inverse(inverse(X_52)),multiplicative_identity)) )],[refute_0_250,refute_0_272]) ).
cnf(refute_0_274,plain,
( X_52 != inverse(inverse(X_52))
| inverse(inverse(X_52)) = X_52 ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(X_52)),bind(Y0,$fot(inverse(inverse(X_52))))]]) ).
cnf(refute_0_275,plain,
inverse(inverse(X_52)) = X_52,
inference(resolve,[$cnf( $equal(X_52,inverse(inverse(X_52))) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
inverse(inverse(X_646)) = X_646,
inference(subst,[],[refute_0_275:[bind(X_52,$fot(X_646))]]) ).
cnf(refute_0_277,plain,
sum(inverse(inverse(X_646)),X_646,X_644) = sum(inverse(inverse(X_646)),X_646,X_644),
introduced(tautology,[refl,[$fot(sum(inverse(inverse(X_646)),X_646,X_644))]]) ).
cnf(refute_0_278,plain,
( inverse(inverse(X_646)) != X_646
| sum(inverse(inverse(X_646)),X_646,X_644) != sum(inverse(inverse(X_646)),X_646,X_644)
| sum(inverse(inverse(X_646)),X_646,X_644) = sum(X_646,X_646,X_644) ),
introduced(tautology,[equality,[$cnf( $equal(sum(inverse(inverse(X_646)),X_646,X_644),sum(inverse(inverse(X_646)),X_646,X_644)) ),[1,0],$fot(X_646)]]) ).
cnf(refute_0_279,plain,
( inverse(inverse(X_646)) != X_646
| sum(inverse(inverse(X_646)),X_646,X_644) = sum(X_646,X_646,X_644) ),
inference(resolve,[$cnf( $equal(sum(inverse(inverse(X_646)),X_646,X_644),sum(inverse(inverse(X_646)),X_646,X_644)) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
sum(inverse(inverse(X_646)),X_646,X_644) = sum(X_646,X_646,X_644),
inference(resolve,[$cnf( $equal(inverse(inverse(X_646)),X_646) )],[refute_0_276,refute_0_279]) ).
cnf(refute_0_281,plain,
ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true) = ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),
introduced(tautology,[refl,[$fot(ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true))]]) ).
cnf(refute_0_282,plain,
( ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true) != ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true)
| sum(inverse(inverse(X_646)),X_646,X_644) != sum(X_646,X_646,X_644)
| ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true) = ifeq(sum(X_646,X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true)) ),[1,0],$fot(sum(X_646,X_646,X_644))]]) ).
cnf(refute_0_283,plain,
( sum(inverse(inverse(X_646)),X_646,X_644) != sum(X_646,X_646,X_644)
| ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true) = ifeq(sum(X_646,X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true) ),
inference(resolve,[$cnf( $equal(ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true)) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true) = ifeq(sum(X_646,X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),
inference(resolve,[$cnf( $equal(sum(inverse(inverse(X_646)),X_646,X_644),sum(X_646,X_646,X_644)) )],[refute_0_280,refute_0_283]) ).
cnf(refute_0_285,plain,
ifeq(true,true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true) = ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_286,plain,
( ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true) != ifeq(sum(X_646,X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true)
| ifeq(true,true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true) != ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true)
| ifeq(true,true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true) = ifeq(sum(X_646,X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true) ),
inference(subst,[],[refute_0_177:[bind(X0,$fot(ifeq(true,true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true))),bind(Y0,$fot(ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true))),bind(Z0,$fot(ifeq(sum(X_646,X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true)))]]) ).
cnf(refute_0_287,plain,
( ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true) != ifeq(sum(X_646,X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true)
| ifeq(true,true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true) = ifeq(sum(X_646,X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true) ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true),ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true)) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
ifeq(true,true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true) = ifeq(sum(X_646,X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),
inference(resolve,[$cnf( $equal(ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),ifeq(sum(X_646,X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true)) )],[refute_0_284,refute_0_287]) ).
cnf(refute_0_289,plain,
( ifeq(true,true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true) != ifeq(sum(X_646,X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true)
| ifeq(true,true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true) != true
| ifeq(sum(X_646,X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true),true) ),[0],$fot(ifeq(sum(X_646,X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true))]]) ).
cnf(refute_0_290,plain,
( ifeq(true,true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true) != true
| ifeq(sum(X_646,X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true),ifeq(sum(X_646,X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true)) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
ifeq(sum(X_646,X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(sum(inverse(inverse(X_646)),X_646,X_644),true,product(inverse(X_646),X_644,additive_identity),true),true),true) )],[refute_0_99,refute_0_290]) ).
cnf(refute_0_292,plain,
ifeq(sum(X_652,X_652,add(X_652,X_652)),true,product(inverse(X_652),add(X_652,X_652),additive_identity),true) = true,
inference(subst,[],[refute_0_291:[bind(X_644,$fot(add(X_652,X_652))),bind(X_646,$fot(X_652))]]) ).
cnf(refute_0_293,plain,
sum(X_652,X_652,add(X_652,X_652)) = true,
inference(subst,[],[refute_0_8:[bind(X_18,$fot(X_652)),bind(X_19,$fot(X_652))]]) ).
cnf(refute_0_294,plain,
( ifeq(sum(X_652,X_652,add(X_652,X_652)),true,product(inverse(X_652),add(X_652,X_652),additive_identity),true) != true
| sum(X_652,X_652,add(X_652,X_652)) != true
| ifeq(true,true,product(inverse(X_652),add(X_652,X_652),additive_identity),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(sum(X_652,X_652,add(X_652,X_652)),true,product(inverse(X_652),add(X_652,X_652),additive_identity),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_295,plain,
( ifeq(sum(X_652,X_652,add(X_652,X_652)),true,product(inverse(X_652),add(X_652,X_652),additive_identity),true) != true
| ifeq(true,true,product(inverse(X_652),add(X_652,X_652),additive_identity),true) = true ),
inference(resolve,[$cnf( $equal(sum(X_652,X_652,add(X_652,X_652)),true) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
ifeq(true,true,product(inverse(X_652),add(X_652,X_652),additive_identity),true) = true,
inference(resolve,[$cnf( $equal(ifeq(sum(X_652,X_652,add(X_652,X_652)),true,product(inverse(X_652),add(X_652,X_652),additive_identity),true),true) )],[refute_0_292,refute_0_295]) ).
cnf(refute_0_297,plain,
ifeq(true,true,product(inverse(X_652),add(X_652,X_652),additive_identity),true) = product(inverse(X_652),add(X_652,X_652),additive_identity),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(product(inverse(X_652),add(X_652,X_652),additive_identity))),bind(C,$fot(true))]]) ).
cnf(refute_0_298,plain,
( ifeq(true,true,product(inverse(X_652),add(X_652,X_652),additive_identity),true) != product(inverse(X_652),add(X_652,X_652),additive_identity)
| ifeq(true,true,product(inverse(X_652),add(X_652,X_652),additive_identity),true) != true
| product(inverse(X_652),add(X_652,X_652),additive_identity) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,product(inverse(X_652),add(X_652,X_652),additive_identity),true),true) ),[0],$fot(product(inverse(X_652),add(X_652,X_652),additive_identity))]]) ).
cnf(refute_0_299,plain,
( ifeq(true,true,product(inverse(X_652),add(X_652,X_652),additive_identity),true) != true
| product(inverse(X_652),add(X_652,X_652),additive_identity) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,product(inverse(X_652),add(X_652,X_652),additive_identity),true),product(inverse(X_652),add(X_652,X_652),additive_identity)) )],[refute_0_297,refute_0_298]) ).
cnf(refute_0_300,plain,
product(inverse(X_652),add(X_652,X_652),additive_identity) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,product(inverse(X_652),add(X_652,X_652),additive_identity),true),true) )],[refute_0_296,refute_0_299]) ).
cnf(refute_0_301,plain,
product(inverse(X_653),add(X_653,X_653),additive_identity) = true,
inference(subst,[],[refute_0_300:[bind(X_652,$fot(X_653))]]) ).
cnf(refute_0_302,plain,
( ifeq(product(inverse(X_653),add(X_653,X_653),additive_identity),true,product(add(X_653,X_653),inverse(X_653),additive_identity),true) != true
| product(inverse(X_653),add(X_653,X_653),additive_identity) != true
| ifeq(true,true,product(add(X_653,X_653),inverse(X_653),additive_identity),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(inverse(X_653),add(X_653,X_653),additive_identity),true,product(add(X_653,X_653),inverse(X_653),additive_identity),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_303,plain,
( ifeq(product(inverse(X_653),add(X_653,X_653),additive_identity),true,product(add(X_653,X_653),inverse(X_653),additive_identity),true) != true
| ifeq(true,true,product(add(X_653,X_653),inverse(X_653),additive_identity),true) = true ),
inference(resolve,[$cnf( $equal(product(inverse(X_653),add(X_653,X_653),additive_identity),true) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
ifeq(true,true,product(add(X_653,X_653),inverse(X_653),additive_identity),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(inverse(X_653),add(X_653,X_653),additive_identity),true,product(add(X_653,X_653),inverse(X_653),additive_identity),true),true) )],[refute_0_81,refute_0_303]) ).
cnf(refute_0_305,plain,
ifeq(true,true,product(add(X_653,X_653),inverse(X_653),additive_identity),true) = product(add(X_653,X_653),inverse(X_653),additive_identity),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(product(add(X_653,X_653),inverse(X_653),additive_identity))),bind(C,$fot(true))]]) ).
cnf(refute_0_306,plain,
( ifeq(true,true,product(add(X_653,X_653),inverse(X_653),additive_identity),true) != product(add(X_653,X_653),inverse(X_653),additive_identity)
| ifeq(true,true,product(add(X_653,X_653),inverse(X_653),additive_identity),true) != true
| product(add(X_653,X_653),inverse(X_653),additive_identity) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,product(add(X_653,X_653),inverse(X_653),additive_identity),true),true) ),[0],$fot(product(add(X_653,X_653),inverse(X_653),additive_identity))]]) ).
cnf(refute_0_307,plain,
( ifeq(true,true,product(add(X_653,X_653),inverse(X_653),additive_identity),true) != true
| product(add(X_653,X_653),inverse(X_653),additive_identity) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,product(add(X_653,X_653),inverse(X_653),additive_identity),true),product(add(X_653,X_653),inverse(X_653),additive_identity)) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
product(add(X_653,X_653),inverse(X_653),additive_identity) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,product(add(X_653,X_653),inverse(X_653),additive_identity),true),true) )],[refute_0_304,refute_0_307]) ).
cnf(refute_0_309,plain,
product(add(X_654,X_654),inverse(X_654),additive_identity) = true,
inference(subst,[],[refute_0_308:[bind(X_653,$fot(X_654))]]) ).
cnf(refute_0_310,plain,
( ifeq(product(add(X_654,X_654),inverse(X_654),additive_identity),true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true) != true
| product(add(X_654,X_654),inverse(X_654),additive_identity) != true
| ifeq(true,true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(add(X_654,X_654),inverse(X_654),additive_identity),true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_311,plain,
( ifeq(product(add(X_654,X_654),inverse(X_654),additive_identity),true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true) != true
| ifeq(true,true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true) = true ),
inference(resolve,[$cnf( $equal(product(add(X_654,X_654),inverse(X_654),additive_identity),true) )],[refute_0_309,refute_0_310]) ).
cnf(refute_0_312,plain,
ifeq(true,true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(add(X_654,X_654),inverse(X_654),additive_identity),true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true),true) )],[refute_0_80,refute_0_311]) ).
cnf(refute_0_313,plain,
inverse(inverse(X_654)) = X_654,
inference(subst,[],[refute_0_275:[bind(X_52,$fot(X_654))]]) ).
cnf(refute_0_314,plain,
multiply(inverse(inverse(X_654)),add(X_654,X_654)) = multiply(inverse(inverse(X_654)),add(X_654,X_654)),
introduced(tautology,[refl,[$fot(multiply(inverse(inverse(X_654)),add(X_654,X_654)))]]) ).
cnf(refute_0_315,plain,
( multiply(inverse(inverse(X_654)),add(X_654,X_654)) != multiply(inverse(inverse(X_654)),add(X_654,X_654))
| inverse(inverse(X_654)) != X_654
| multiply(inverse(inverse(X_654)),add(X_654,X_654)) = multiply(X_654,add(X_654,X_654)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X_654)),add(X_654,X_654)),multiply(inverse(inverse(X_654)),add(X_654,X_654))) ),[1,0],$fot(X_654)]]) ).
cnf(refute_0_316,plain,
( inverse(inverse(X_654)) != X_654
| multiply(inverse(inverse(X_654)),add(X_654,X_654)) = multiply(X_654,add(X_654,X_654)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_654)),add(X_654,X_654)),multiply(inverse(inverse(X_654)),add(X_654,X_654))) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
multiply(inverse(inverse(X_654)),add(X_654,X_654)) = multiply(X_654,add(X_654,X_654)),
inference(resolve,[$cnf( $equal(inverse(inverse(X_654)),X_654) )],[refute_0_313,refute_0_316]) ).
cnf(refute_0_318,plain,
multiply(add(X_654,X_654),inverse(inverse(X_654))) = multiply(inverse(inverse(X_654)),add(X_654,X_654)),
inference(subst,[],[refute_0_169:[bind(X_85,$fot(add(X_654,X_654))),bind(X_86,$fot(inverse(inverse(X_654))))]]) ).
cnf(refute_0_319,plain,
( multiply(add(X_654,X_654),inverse(inverse(X_654))) != multiply(inverse(inverse(X_654)),add(X_654,X_654))
| multiply(inverse(inverse(X_654)),add(X_654,X_654)) != multiply(X_654,add(X_654,X_654))
| multiply(add(X_654,X_654),inverse(inverse(X_654))) = multiply(X_654,add(X_654,X_654)) ),
inference(subst,[],[refute_0_177:[bind(X0,$fot(multiply(add(X_654,X_654),inverse(inverse(X_654))))),bind(Y0,$fot(multiply(inverse(inverse(X_654)),add(X_654,X_654)))),bind(Z0,$fot(multiply(X_654,add(X_654,X_654))))]]) ).
cnf(refute_0_320,plain,
( multiply(inverse(inverse(X_654)),add(X_654,X_654)) != multiply(X_654,add(X_654,X_654))
| multiply(add(X_654,X_654),inverse(inverse(X_654))) = multiply(X_654,add(X_654,X_654)) ),
inference(resolve,[$cnf( $equal(multiply(add(X_654,X_654),inverse(inverse(X_654))),multiply(inverse(inverse(X_654)),add(X_654,X_654))) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
multiply(add(X_654,X_654),inverse(inverse(X_654))) = multiply(X_654,add(X_654,X_654)),
inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X_654)),add(X_654,X_654)),multiply(X_654,add(X_654,X_654))) )],[refute_0_317,refute_0_320]) ).
cnf(refute_0_322,plain,
product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))) = product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),
introduced(tautology,[refl,[$fot(product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))))]]) ).
cnf(refute_0_323,plain,
( multiply(add(X_654,X_654),inverse(inverse(X_654))) != multiply(X_654,add(X_654,X_654))
| product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))) != product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654))))
| product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))) = product(add(X_654,X_654),multiplicative_identity,multiply(X_654,add(X_654,X_654))) ),
introduced(tautology,[equality,[$cnf( $equal(product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654))))) ),[1,2],$fot(multiply(X_654,add(X_654,X_654)))]]) ).
cnf(refute_0_324,plain,
( multiply(add(X_654,X_654),inverse(inverse(X_654))) != multiply(X_654,add(X_654,X_654))
| product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))) = product(add(X_654,X_654),multiplicative_identity,multiply(X_654,add(X_654,X_654))) ),
inference(resolve,[$cnf( $equal(product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654))))) )],[refute_0_322,refute_0_323]) ).
cnf(refute_0_325,plain,
product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))) = product(add(X_654,X_654),multiplicative_identity,multiply(X_654,add(X_654,X_654))),
inference(resolve,[$cnf( $equal(multiply(add(X_654,X_654),inverse(inverse(X_654))),multiply(X_654,add(X_654,X_654))) )],[refute_0_321,refute_0_324]) ).
cnf(refute_0_326,plain,
ifeq(true,true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true) = product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))))),bind(C,$fot(true))]]) ).
cnf(refute_0_327,plain,
( ifeq(true,true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true) != product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654))))
| product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))) != product(add(X_654,X_654),multiplicative_identity,multiply(X_654,add(X_654,X_654)))
| ifeq(true,true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true) = product(add(X_654,X_654),multiplicative_identity,multiply(X_654,add(X_654,X_654))) ),
inference(subst,[],[refute_0_177:[bind(X0,$fot(ifeq(true,true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true))),bind(Y0,$fot(product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))))),bind(Z0,$fot(product(add(X_654,X_654),multiplicative_identity,multiply(X_654,add(X_654,X_654)))))]]) ).
cnf(refute_0_328,plain,
( product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))) != product(add(X_654,X_654),multiplicative_identity,multiply(X_654,add(X_654,X_654)))
| ifeq(true,true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true) = product(add(X_654,X_654),multiplicative_identity,multiply(X_654,add(X_654,X_654))) ),
inference(resolve,[$cnf( $equal(ifeq(true,true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true),product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654))))) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
ifeq(true,true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true) = product(add(X_654,X_654),multiplicative_identity,multiply(X_654,add(X_654,X_654))),
inference(resolve,[$cnf( $equal(product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),product(add(X_654,X_654),multiplicative_identity,multiply(X_654,add(X_654,X_654)))) )],[refute_0_325,refute_0_328]) ).
cnf(refute_0_330,plain,
( ifeq(true,true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true) != product(add(X_654,X_654),multiplicative_identity,multiply(X_654,add(X_654,X_654)))
| ifeq(true,true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true) != true
| product(add(X_654,X_654),multiplicative_identity,multiply(X_654,add(X_654,X_654))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true),true) ),[0],$fot(product(add(X_654,X_654),multiplicative_identity,multiply(X_654,add(X_654,X_654))))]]) ).
cnf(refute_0_331,plain,
( ifeq(true,true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true) != true
| product(add(X_654,X_654),multiplicative_identity,multiply(X_654,add(X_654,X_654))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true),product(add(X_654,X_654),multiplicative_identity,multiply(X_654,add(X_654,X_654)))) )],[refute_0_329,refute_0_330]) ).
cnf(refute_0_332,plain,
product(add(X_654,X_654),multiplicative_identity,multiply(X_654,add(X_654,X_654))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,product(add(X_654,X_654),multiplicative_identity,multiply(add(X_654,X_654),inverse(inverse(X_654)))),true),true) )],[refute_0_312,refute_0_331]) ).
cnf(refute_0_333,plain,
product(add(X_659,X_659),multiplicative_identity,multiply(X_659,add(X_659,X_659))) = true,
inference(subst,[],[refute_0_332:[bind(X_654,$fot(X_659))]]) ).
cnf(refute_0_334,plain,
( ifeq2(product(add(X_659,X_659),multiplicative_identity,multiply(X_659,add(X_659,X_659))),true,multiply(X_659,add(X_659,X_659)),multiply(add(X_659,X_659),multiplicative_identity)) != multiply(add(X_659,X_659),multiplicative_identity)
| product(add(X_659,X_659),multiplicative_identity,multiply(X_659,add(X_659,X_659))) != true
| ifeq2(true,true,multiply(X_659,add(X_659,X_659)),multiply(add(X_659,X_659),multiplicative_identity)) = multiply(add(X_659,X_659),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(add(X_659,X_659),multiplicative_identity,multiply(X_659,add(X_659,X_659))),true,multiply(X_659,add(X_659,X_659)),multiply(add(X_659,X_659),multiplicative_identity)),multiply(add(X_659,X_659),multiplicative_identity)) ),[0,0],$fot(true)]]) ).
cnf(refute_0_335,plain,
( ifeq2(product(add(X_659,X_659),multiplicative_identity,multiply(X_659,add(X_659,X_659))),true,multiply(X_659,add(X_659,X_659)),multiply(add(X_659,X_659),multiplicative_identity)) != multiply(add(X_659,X_659),multiplicative_identity)
| ifeq2(true,true,multiply(X_659,add(X_659,X_659)),multiply(add(X_659,X_659),multiplicative_identity)) = multiply(add(X_659,X_659),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(product(add(X_659,X_659),multiplicative_identity,multiply(X_659,add(X_659,X_659))),true) )],[refute_0_333,refute_0_334]) ).
cnf(refute_0_336,plain,
ifeq2(true,true,multiply(X_659,add(X_659,X_659)),multiply(add(X_659,X_659),multiplicative_identity)) = multiply(add(X_659,X_659),multiplicative_identity),
inference(resolve,[$cnf( $equal(ifeq2(product(add(X_659,X_659),multiplicative_identity,multiply(X_659,add(X_659,X_659))),true,multiply(X_659,add(X_659,X_659)),multiply(add(X_659,X_659),multiplicative_identity)),multiply(add(X_659,X_659),multiplicative_identity)) )],[refute_0_32,refute_0_335]) ).
cnf(refute_0_337,plain,
ifeq2(true,true,multiply(X_659,add(X_659,X_659)),multiply(add(X_659,X_659),multiplicative_identity)) = multiply(X_659,add(X_659,X_659)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(multiply(X_659,add(X_659,X_659)))),bind(C,$fot(multiply(add(X_659,X_659),multiplicative_identity)))]]) ).
cnf(refute_0_338,plain,
( ifeq2(true,true,multiply(X_659,add(X_659,X_659)),multiply(add(X_659,X_659),multiplicative_identity)) != multiply(X_659,add(X_659,X_659))
| ifeq2(true,true,multiply(X_659,add(X_659,X_659)),multiply(add(X_659,X_659),multiplicative_identity)) != multiply(add(X_659,X_659),multiplicative_identity)
| multiply(X_659,add(X_659,X_659)) = multiply(add(X_659,X_659),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(true,true,multiply(X_659,add(X_659,X_659)),multiply(add(X_659,X_659),multiplicative_identity)),multiply(add(X_659,X_659),multiplicative_identity)) ),[0],$fot(multiply(X_659,add(X_659,X_659)))]]) ).
cnf(refute_0_339,plain,
( ifeq2(true,true,multiply(X_659,add(X_659,X_659)),multiply(add(X_659,X_659),multiplicative_identity)) != multiply(add(X_659,X_659),multiplicative_identity)
| multiply(X_659,add(X_659,X_659)) = multiply(add(X_659,X_659),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(ifeq2(true,true,multiply(X_659,add(X_659,X_659)),multiply(add(X_659,X_659),multiplicative_identity)),multiply(X_659,add(X_659,X_659))) )],[refute_0_337,refute_0_338]) ).
cnf(refute_0_340,plain,
multiply(multiplicative_identity,add(X_659,X_659)) = add(X_659,X_659),
inference(subst,[],[refute_0_264:[bind(X_56,$fot(add(X_659,X_659)))]]) ).
cnf(refute_0_341,plain,
multiply(add(X_659,X_659),multiplicative_identity) = multiply(multiplicative_identity,add(X_659,X_659)),
inference(subst,[],[refute_0_169:[bind(X_85,$fot(add(X_659,X_659))),bind(X_86,$fot(multiplicative_identity))]]) ).
cnf(refute_0_342,plain,
( multiply(add(X_659,X_659),multiplicative_identity) != multiply(multiplicative_identity,add(X_659,X_659))
| multiply(multiplicative_identity,add(X_659,X_659)) != add(X_659,X_659)
| multiply(add(X_659,X_659),multiplicative_identity) = add(X_659,X_659) ),
inference(subst,[],[refute_0_177:[bind(X0,$fot(multiply(add(X_659,X_659),multiplicative_identity))),bind(Y0,$fot(multiply(multiplicative_identity,add(X_659,X_659)))),bind(Z0,$fot(add(X_659,X_659)))]]) ).
cnf(refute_0_343,plain,
( multiply(multiplicative_identity,add(X_659,X_659)) != add(X_659,X_659)
| multiply(add(X_659,X_659),multiplicative_identity) = add(X_659,X_659) ),
inference(resolve,[$cnf( $equal(multiply(add(X_659,X_659),multiplicative_identity),multiply(multiplicative_identity,add(X_659,X_659))) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
multiply(add(X_659,X_659),multiplicative_identity) = add(X_659,X_659),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,add(X_659,X_659)),add(X_659,X_659)) )],[refute_0_340,refute_0_343]) ).
cnf(refute_0_345,plain,
( multiply(X_659,add(X_659,X_659)) != multiply(add(X_659,X_659),multiplicative_identity)
| multiply(add(X_659,X_659),multiplicative_identity) != add(X_659,X_659)
| multiply(X_659,add(X_659,X_659)) = add(X_659,X_659) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_659,add(X_659,X_659)),add(X_659,X_659)) ),[0],$fot(multiply(add(X_659,X_659),multiplicative_identity))]]) ).
cnf(refute_0_346,plain,
( multiply(X_659,add(X_659,X_659)) != multiply(add(X_659,X_659),multiplicative_identity)
| multiply(X_659,add(X_659,X_659)) = add(X_659,X_659) ),
inference(resolve,[$cnf( $equal(multiply(add(X_659,X_659),multiplicative_identity),add(X_659,X_659)) )],[refute_0_344,refute_0_345]) ).
cnf(refute_0_347,plain,
( ifeq2(true,true,multiply(X_659,add(X_659,X_659)),multiply(add(X_659,X_659),multiplicative_identity)) != multiply(add(X_659,X_659),multiplicative_identity)
| multiply(X_659,add(X_659,X_659)) = add(X_659,X_659) ),
inference(resolve,[$cnf( $equal(multiply(X_659,add(X_659,X_659)),multiply(add(X_659,X_659),multiplicative_identity)) )],[refute_0_339,refute_0_346]) ).
cnf(refute_0_348,plain,
multiply(X_659,add(X_659,X_659)) = add(X_659,X_659),
inference(resolve,[$cnf( $equal(ifeq2(true,true,multiply(X_659,add(X_659,X_659)),multiply(add(X_659,X_659),multiplicative_identity)),multiply(add(X_659,X_659),multiplicative_identity)) )],[refute_0_336,refute_0_347]) ).
cnf(refute_0_349,plain,
multiply(X_54,add(X_54,X_54)) = add(X_54,X_54),
inference(subst,[],[refute_0_348:[bind(X_659,$fot(X_54))]]) ).
cnf(refute_0_350,plain,
( multiply(X_54,add(X_54,X_54)) != add(X_54,X_54)
| ifeq2(product(X_54,add(X_54,X_54),X_53),true,multiply(X_54,add(X_54,X_54)),X_53) != X_53
| ifeq2(product(X_54,add(X_54,X_54),X_53),true,add(X_54,X_54),X_53) = X_53 ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(X_54,add(X_54,X_54),X_53),true,multiply(X_54,add(X_54,X_54)),X_53),X_53) ),[0,2],$fot(add(X_54,X_54))]]) ).
cnf(refute_0_351,plain,
( ifeq2(product(X_54,add(X_54,X_54),X_53),true,multiply(X_54,add(X_54,X_54)),X_53) != X_53
| ifeq2(product(X_54,add(X_54,X_54),X_53),true,add(X_54,X_54),X_53) = X_53 ),
inference(resolve,[$cnf( $equal(multiply(X_54,add(X_54,X_54)),add(X_54,X_54)) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
ifeq2(product(X_54,add(X_54,X_54),X_53),true,add(X_54,X_54),X_53) = X_53,
inference(resolve,[$cnf( $equal(ifeq2(product(X_54,add(X_54,X_54),X_53),true,multiply(X_54,add(X_54,X_54)),X_53),X_53) )],[refute_0_23,refute_0_351]) ).
cnf(refute_0_353,plain,
ifeq2(product(X_53,add(X_53,X_53),X_53),true,add(X_53,X_53),X_53) = X_53,
inference(subst,[],[refute_0_352:[bind(X_54,$fot(X_53))]]) ).
cnf(refute_0_354,plain,
ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(sum(X_265,additive_identity,X_265),true,product(X_265,X_266,X_268),true),true),true),true) = true,
inference(subst,[],[distributivity5:[bind(V1,$fot(X_265)),bind(V2,$fot(X_266)),bind(V3,$fot(X_267)),bind(V4,$fot(X_268)),bind(X,$fot(X_265)),bind(Y,$fot(additive_identity)),bind(Z,$fot(X_271))]]) ).
cnf(refute_0_355,plain,
sum(X_265,additive_identity,X_265) = true,
inference(subst,[],[additive_identity2:[bind(X,$fot(X_265))]]) ).
cnf(refute_0_356,plain,
( ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(sum(X_265,additive_identity,X_265),true,product(X_265,X_266,X_268),true),true),true),true) != true
| sum(X_265,additive_identity,X_265) != true
| ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(sum(X_265,additive_identity,X_265),true,product(X_265,X_266,X_268),true),true),true),true),true) ),[0,2,2,2,0],$fot(true)]]) ).
cnf(refute_0_357,plain,
( ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(sum(X_265,additive_identity,X_265),true,product(X_265,X_266,X_268),true),true),true),true) != true
| ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true) = true ),
inference(resolve,[$cnf( $equal(sum(X_265,additive_identity,X_265),true) )],[refute_0_355,refute_0_356]) ).
cnf(refute_0_358,plain,
ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(sum(X_265,additive_identity,X_265),true,product(X_265,X_266,X_268),true),true),true),true),true) )],[refute_0_354,refute_0_357]) ).
cnf(refute_0_359,plain,
ifeq(true,true,product(X_265,X_266,X_268),true) = product(X_265,X_266,X_268),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(product(X_265,X_266,X_268))),bind(C,$fot(true))]]) ).
cnf(refute_0_360,plain,
ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true) = ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),
introduced(tautology,[refl,[$fot(ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true))]]) ).
cnf(refute_0_361,plain,
( ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true) != ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true)
| ifeq(true,true,product(X_265,X_266,X_268),true) != product(X_265,X_266,X_268)
| ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true) = ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true)) ),[1,2],$fot(product(X_265,X_266,X_268))]]) ).
cnf(refute_0_362,plain,
( ifeq(true,true,product(X_265,X_266,X_268),true) != product(X_265,X_266,X_268)
| ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true) = ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true) ),
inference(resolve,[$cnf( $equal(ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true)) )],[refute_0_360,refute_0_361]) ).
cnf(refute_0_363,plain,
ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true) = ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,product(X_265,X_266,X_268),true),product(X_265,X_266,X_268)) )],[refute_0_359,refute_0_362]) ).
cnf(refute_0_364,plain,
ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true) = ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),
introduced(tautology,[refl,[$fot(ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true))]]) ).
cnf(refute_0_365,plain,
( ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true) != ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true)
| ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true) != ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true)
| ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true) = ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true)) ),[1,2],$fot(ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true))]]) ).
cnf(refute_0_366,plain,
( ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true) != ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true)
| ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true) = ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true)) )],[refute_0_364,refute_0_365]) ).
cnf(refute_0_367,plain,
ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true) = ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true),true),
inference(resolve,[$cnf( $equal(ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true)) )],[refute_0_363,refute_0_366]) ).
cnf(refute_0_368,plain,
ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true) = ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true),
introduced(tautology,[refl,[$fot(ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true))]]) ).
cnf(refute_0_369,plain,
( ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true) != ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true)
| ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true) != ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true),true)
| ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true) = ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true),true),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true),ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true)) ),[1,2],$fot(ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true),true))]]) ).
cnf(refute_0_370,plain,
( ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true) != ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true),true)
| ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true) = ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true),ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true)) )],[refute_0_368,refute_0_369]) ).
cnf(refute_0_371,plain,
ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true) = ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true),true),true),
inference(resolve,[$cnf( $equal(ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true),true)) )],[refute_0_367,refute_0_370]) ).
cnf(refute_0_372,plain,
( ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true) != ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true),true),true)
| ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true) != true
| ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true),true) ),[0],$fot(ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true),true),true))]]) ).
cnf(refute_0_373,plain,
( ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true) != true
| ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true),true),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true),ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true),true),true)) )],[refute_0_371,refute_0_372]) ).
cnf(refute_0_374,plain,
ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,product(X_265,X_266,X_268),true),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(additive_identity,X_271,X_267),true,ifeq(sum(X_265,X_267,X_268),true,ifeq(sum(X_265,X_271,X_266),true,ifeq(true,true,product(X_265,X_266,X_268),true),true),true),true),true) )],[refute_0_358,refute_0_373]) ).
cnf(refute_0_375,plain,
ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(sum(X_3571,additive_identity,X_3571),true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) = true,
inference(subst,[],[refute_0_374:[bind(X_265,$fot(X_3571)),bind(X_266,$fot(X_3569)),bind(X_267,$fot(additive_identity)),bind(X_268,$fot(X_3571)),bind(X_271,$fot(X_3572))]]) ).
cnf(refute_0_376,plain,
sum(X_3571,additive_identity,X_3571) = true,
inference(subst,[],[additive_identity2:[bind(X,$fot(X_3571))]]) ).
cnf(refute_0_377,plain,
( ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(sum(X_3571,additive_identity,X_3571),true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) != true
| sum(X_3571,additive_identity,X_3571) != true
| ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(sum(X_3571,additive_identity,X_3571),true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_378,plain,
( ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(sum(X_3571,additive_identity,X_3571),true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) != true
| ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) = true ),
inference(resolve,[$cnf( $equal(sum(X_3571,additive_identity,X_3571),true) )],[refute_0_376,refute_0_377]) ).
cnf(refute_0_379,plain,
ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(sum(X_3571,additive_identity,X_3571),true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true),true) )],[refute_0_375,refute_0_378]) ).
cnf(refute_0_380,plain,
ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true) = ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_381,plain,
ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) = ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true),
introduced(tautology,[refl,[$fot(ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true))]]) ).
cnf(refute_0_382,plain,
( ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true) != ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true)
| ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) != ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true)
| ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) = ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true),ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true)) ),[1,2],$fot(ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true))]]) ).
cnf(refute_0_383,plain,
( ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true) != ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true)
| ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) = ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true),ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true)) )],[refute_0_381,refute_0_382]) ).
cnf(refute_0_384,plain,
ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) = ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true)) )],[refute_0_380,refute_0_383]) ).
cnf(refute_0_385,plain,
product(additive_identity,Y,multiply(additive_identity,Y)) = true,
inference(subst,[],[closure_of_multiplication:[bind(X,$fot(additive_identity))]]) ).
cnf(refute_0_386,plain,
ifeq2(product(X_54,inverse(X_54),multiply(additive_identity,X_54)),true,multiply(additive_identity,X_54),multiply(X_54,inverse(X_54))) = multiply(X_54,inverse(X_54)),
inference(subst,[],[refute_0_31:[bind(X_52,$fot(multiply(additive_identity,X_54))),bind(X_55,$fot(inverse(X_54)))]]) ).
cnf(refute_0_387,plain,
ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(sum(X_106,additive_identity,X_106),true,product(X_108,X_106,X_107),true),true),true),true) = true,
inference(subst,[],[distributivity2:[bind(V1,$fot(X_104)),bind(V2,$fot(X_105)),bind(V3,$fot(X_106)),bind(V4,$fot(X_107)),bind(X,$fot(X_108)),bind(Y,$fot(X_106)),bind(Z,$fot(additive_identity))]]) ).
cnf(refute_0_388,plain,
sum(X_106,additive_identity,X_106) = true,
inference(subst,[],[additive_identity2:[bind(X,$fot(X_106))]]) ).
cnf(refute_0_389,plain,
( ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(sum(X_106,additive_identity,X_106),true,product(X_108,X_106,X_107),true),true),true),true) != true
| sum(X_106,additive_identity,X_106) != true
| ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(sum(X_106,additive_identity,X_106),true,product(X_108,X_106,X_107),true),true),true),true),true) ),[0,2,2,2,0],$fot(true)]]) ).
cnf(refute_0_390,plain,
( ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(sum(X_106,additive_identity,X_106),true,product(X_108,X_106,X_107),true),true),true),true) != true
| ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true) = true ),
inference(resolve,[$cnf( $equal(sum(X_106,additive_identity,X_106),true) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(sum(X_106,additive_identity,X_106),true,product(X_108,X_106,X_107),true),true),true),true),true) )],[refute_0_387,refute_0_390]) ).
cnf(refute_0_392,plain,
ifeq(true,true,product(X_108,X_106,X_107),true) = product(X_108,X_106,X_107),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(product(X_108,X_106,X_107))),bind(C,$fot(true))]]) ).
cnf(refute_0_393,plain,
ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true) = ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),
introduced(tautology,[refl,[$fot(ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true))]]) ).
cnf(refute_0_394,plain,
( ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true) != ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true)
| ifeq(true,true,product(X_108,X_106,X_107),true) != product(X_108,X_106,X_107)
| ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true) = ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true)) ),[1,2],$fot(product(X_108,X_106,X_107))]]) ).
cnf(refute_0_395,plain,
( ifeq(true,true,product(X_108,X_106,X_107),true) != product(X_108,X_106,X_107)
| ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true) = ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true) ),
inference(resolve,[$cnf( $equal(ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true)) )],[refute_0_393,refute_0_394]) ).
cnf(refute_0_396,plain,
ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true) = ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,product(X_108,X_106,X_107),true),product(X_108,X_106,X_107)) )],[refute_0_392,refute_0_395]) ).
cnf(refute_0_397,plain,
ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true) = ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),
introduced(tautology,[refl,[$fot(ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true))]]) ).
cnf(refute_0_398,plain,
( ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true) != ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true)
| ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true) != ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true)
| ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true) = ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true)) ),[1,2],$fot(ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true))]]) ).
cnf(refute_0_399,plain,
( ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true) != ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true)
| ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true) = ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true)) )],[refute_0_397,refute_0_398]) ).
cnf(refute_0_400,plain,
ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true) = ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true),true),
inference(resolve,[$cnf( $equal(ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true)) )],[refute_0_396,refute_0_399]) ).
cnf(refute_0_401,plain,
ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true) = ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true),
introduced(tautology,[refl,[$fot(ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true))]]) ).
cnf(refute_0_402,plain,
( ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true) != ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true),true)
| ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true) != ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true)
| ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true) = ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true),true),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true),ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true)) ),[1,2],$fot(ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true),true))]]) ).
cnf(refute_0_403,plain,
( ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true) != ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true),true)
| ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true) = ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true),ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true)) )],[refute_0_401,refute_0_402]) ).
cnf(refute_0_404,plain,
ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true) = ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true),true),true),
inference(resolve,[$cnf( $equal(ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true),true)) )],[refute_0_400,refute_0_403]) ).
cnf(refute_0_405,plain,
( ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true) != ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true),true),true)
| ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true) != true
| ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true),true) ),[0],$fot(ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true),true),true))]]) ).
cnf(refute_0_406,plain,
( ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true) != true
| ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true),true),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true),ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true),true),true)) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,product(X_108,X_106,X_107),true),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(X_108,additive_identity,X_105),true,ifeq(product(X_108,X_106,X_104),true,ifeq(sum(X_104,X_105,X_107),true,ifeq(true,true,product(X_108,X_106,X_107),true),true),true),true),true) )],[refute_0_391,refute_0_406]) ).
cnf(refute_0_408,plain,
ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(sum(additive_identity,X_282,X_282),true,product(X_283,X_281,X_282),true),true),true) = true,
inference(subst,[],[refute_0_407:[bind(X_104,$fot(additive_identity)),bind(X_105,$fot(X_282)),bind(X_106,$fot(X_281)),bind(X_107,$fot(X_282)),bind(X_108,$fot(X_283))]]) ).
cnf(refute_0_409,plain,
sum(additive_identity,X_282,X_282) = true,
inference(subst,[],[additive_identity1:[bind(X,$fot(X_282))]]) ).
cnf(refute_0_410,plain,
( ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(sum(additive_identity,X_282,X_282),true,product(X_283,X_281,X_282),true),true),true) != true
| sum(additive_identity,X_282,X_282) != true
| ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(sum(additive_identity,X_282,X_282),true,product(X_283,X_281,X_282),true),true),true),true) ),[0,2,2,0],$fot(true)]]) ).
cnf(refute_0_411,plain,
( ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(sum(additive_identity,X_282,X_282),true,product(X_283,X_281,X_282),true),true),true) != true
| ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true) = true ),
inference(resolve,[$cnf( $equal(sum(additive_identity,X_282,X_282),true) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(sum(additive_identity,X_282,X_282),true,product(X_283,X_281,X_282),true),true),true),true) )],[refute_0_408,refute_0_411]) ).
cnf(refute_0_413,plain,
ifeq(true,true,product(X_283,X_281,X_282),true) = product(X_283,X_281,X_282),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(product(X_283,X_281,X_282))),bind(C,$fot(true))]]) ).
cnf(refute_0_414,plain,
ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true) = ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),
introduced(tautology,[refl,[$fot(ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true))]]) ).
cnf(refute_0_415,plain,
( ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true) != ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true)
| ifeq(true,true,product(X_283,X_281,X_282),true) != product(X_283,X_281,X_282)
| ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true) = ifeq(product(X_283,X_281,additive_identity),true,product(X_283,X_281,X_282),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true)) ),[1,2],$fot(product(X_283,X_281,X_282))]]) ).
cnf(refute_0_416,plain,
( ifeq(true,true,product(X_283,X_281,X_282),true) != product(X_283,X_281,X_282)
| ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true) = ifeq(product(X_283,X_281,additive_identity),true,product(X_283,X_281,X_282),true) ),
inference(resolve,[$cnf( $equal(ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true)) )],[refute_0_414,refute_0_415]) ).
cnf(refute_0_417,plain,
ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true) = ifeq(product(X_283,X_281,additive_identity),true,product(X_283,X_281,X_282),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,product(X_283,X_281,X_282),true),product(X_283,X_281,X_282)) )],[refute_0_413,refute_0_416]) ).
cnf(refute_0_418,plain,
ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true) = ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true),
introduced(tautology,[refl,[$fot(ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true))]]) ).
cnf(refute_0_419,plain,
( ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true) != ifeq(product(X_283,X_281,additive_identity),true,product(X_283,X_281,X_282),true)
| ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true) != ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true)
| ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true) = ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,product(X_283,X_281,X_282),true),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true),ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true)) ),[1,2],$fot(ifeq(product(X_283,X_281,additive_identity),true,product(X_283,X_281,X_282),true))]]) ).
cnf(refute_0_420,plain,
( ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true) != ifeq(product(X_283,X_281,additive_identity),true,product(X_283,X_281,X_282),true)
| ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true) = ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,product(X_283,X_281,X_282),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true),ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true)) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true) = ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,product(X_283,X_281,X_282),true),true),
inference(resolve,[$cnf( $equal(ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),ifeq(product(X_283,X_281,additive_identity),true,product(X_283,X_281,X_282),true)) )],[refute_0_417,refute_0_420]) ).
cnf(refute_0_422,plain,
( ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true) != ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,product(X_283,X_281,X_282),true),true)
| ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true) != true
| ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,product(X_283,X_281,X_282),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true),true) ),[0],$fot(ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,product(X_283,X_281,X_282),true),true))]]) ).
cnf(refute_0_423,plain,
( ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true) != true
| ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,product(X_283,X_281,X_282),true),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true),ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,product(X_283,X_281,X_282),true),true)) )],[refute_0_421,refute_0_422]) ).
cnf(refute_0_424,plain,
ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,product(X_283,X_281,X_282),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(X_283,additive_identity,X_282),true,ifeq(product(X_283,X_281,additive_identity),true,ifeq(true,true,product(X_283,X_281,X_282),true),true),true),true) )],[refute_0_412,refute_0_423]) ).
cnf(refute_0_425,plain,
ifeq(product(X_286,additive_identity,X_285),true,ifeq(product(X_286,inverse(X_286),additive_identity),true,product(X_286,inverse(X_286),X_285),true),true) = true,
inference(subst,[],[refute_0_424:[bind(X_281,$fot(inverse(X_286))),bind(X_282,$fot(X_285)),bind(X_283,$fot(X_286))]]) ).
cnf(refute_0_426,plain,
product(X_286,inverse(X_286),additive_identity) = true,
inference(subst,[],[multiplicative_inverse2:[bind(X,$fot(X_286))]]) ).
cnf(refute_0_427,plain,
( ifeq(product(X_286,additive_identity,X_285),true,ifeq(product(X_286,inverse(X_286),additive_identity),true,product(X_286,inverse(X_286),X_285),true),true) != true
| product(X_286,inverse(X_286),additive_identity) != true
| ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_286,additive_identity,X_285),true,ifeq(product(X_286,inverse(X_286),additive_identity),true,product(X_286,inverse(X_286),X_285),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_428,plain,
( ifeq(product(X_286,additive_identity,X_285),true,ifeq(product(X_286,inverse(X_286),additive_identity),true,product(X_286,inverse(X_286),X_285),true),true) != true
| ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true) = true ),
inference(resolve,[$cnf( $equal(product(X_286,inverse(X_286),additive_identity),true) )],[refute_0_426,refute_0_427]) ).
cnf(refute_0_429,plain,
ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(X_286,additive_identity,X_285),true,ifeq(product(X_286,inverse(X_286),additive_identity),true,product(X_286,inverse(X_286),X_285),true),true),true) )],[refute_0_425,refute_0_428]) ).
cnf(refute_0_430,plain,
ifeq(true,true,product(X_286,inverse(X_286),X_285),true) = product(X_286,inverse(X_286),X_285),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(product(X_286,inverse(X_286),X_285))),bind(C,$fot(true))]]) ).
cnf(refute_0_431,plain,
ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true) = ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true),
introduced(tautology,[refl,[$fot(ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true))]]) ).
cnf(refute_0_432,plain,
( ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true) != ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true)
| ifeq(true,true,product(X_286,inverse(X_286),X_285),true) != product(X_286,inverse(X_286),X_285)
| ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true) = ifeq(product(X_286,additive_identity,X_285),true,product(X_286,inverse(X_286),X_285),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true),ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true)) ),[1,2],$fot(product(X_286,inverse(X_286),X_285))]]) ).
cnf(refute_0_433,plain,
( ifeq(true,true,product(X_286,inverse(X_286),X_285),true) != product(X_286,inverse(X_286),X_285)
| ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true) = ifeq(product(X_286,additive_identity,X_285),true,product(X_286,inverse(X_286),X_285),true) ),
inference(resolve,[$cnf( $equal(ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true),ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true)) )],[refute_0_431,refute_0_432]) ).
cnf(refute_0_434,plain,
ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true) = ifeq(product(X_286,additive_identity,X_285),true,product(X_286,inverse(X_286),X_285),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,product(X_286,inverse(X_286),X_285),true),product(X_286,inverse(X_286),X_285)) )],[refute_0_430,refute_0_433]) ).
cnf(refute_0_435,plain,
( ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true) != ifeq(product(X_286,additive_identity,X_285),true,product(X_286,inverse(X_286),X_285),true)
| ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true) != true
| ifeq(product(X_286,additive_identity,X_285),true,product(X_286,inverse(X_286),X_285),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true),true) ),[0],$fot(ifeq(product(X_286,additive_identity,X_285),true,product(X_286,inverse(X_286),X_285),true))]]) ).
cnf(refute_0_436,plain,
( ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true) != true
| ifeq(product(X_286,additive_identity,X_285),true,product(X_286,inverse(X_286),X_285),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true),ifeq(product(X_286,additive_identity,X_285),true,product(X_286,inverse(X_286),X_285),true)) )],[refute_0_434,refute_0_435]) ).
cnf(refute_0_437,plain,
ifeq(product(X_286,additive_identity,X_285),true,product(X_286,inverse(X_286),X_285),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(X_286,additive_identity,X_285),true,ifeq(true,true,product(X_286,inverse(X_286),X_285),true),true),true) )],[refute_0_429,refute_0_436]) ).
cnf(refute_0_438,plain,
ifeq(product(X_301,additive_identity,multiply(additive_identity,X_301)),true,product(X_301,inverse(X_301),multiply(additive_identity,X_301)),true) = true,
inference(subst,[],[refute_0_437:[bind(X_285,$fot(multiply(additive_identity,X_301))),bind(X_286,$fot(X_301))]]) ).
cnf(refute_0_439,plain,
product(X_301,additive_identity,multiply(additive_identity,X_301)) = true,
inference(subst,[],[refute_0_126:[bind(X_23,$fot(additive_identity)),bind(X_24,$fot(X_301))]]) ).
cnf(refute_0_440,plain,
( ifeq(product(X_301,additive_identity,multiply(additive_identity,X_301)),true,product(X_301,inverse(X_301),multiply(additive_identity,X_301)),true) != true
| product(X_301,additive_identity,multiply(additive_identity,X_301)) != true
| ifeq(true,true,product(X_301,inverse(X_301),multiply(additive_identity,X_301)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(X_301,additive_identity,multiply(additive_identity,X_301)),true,product(X_301,inverse(X_301),multiply(additive_identity,X_301)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_441,plain,
( ifeq(product(X_301,additive_identity,multiply(additive_identity,X_301)),true,product(X_301,inverse(X_301),multiply(additive_identity,X_301)),true) != true
| ifeq(true,true,product(X_301,inverse(X_301),multiply(additive_identity,X_301)),true) = true ),
inference(resolve,[$cnf( $equal(product(X_301,additive_identity,multiply(additive_identity,X_301)),true) )],[refute_0_439,refute_0_440]) ).
cnf(refute_0_442,plain,
ifeq(true,true,product(X_301,inverse(X_301),multiply(additive_identity,X_301)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(X_301,additive_identity,multiply(additive_identity,X_301)),true,product(X_301,inverse(X_301),multiply(additive_identity,X_301)),true),true) )],[refute_0_438,refute_0_441]) ).
cnf(refute_0_443,plain,
ifeq(true,true,product(X_301,inverse(X_301),multiply(additive_identity,X_301)),true) = product(X_301,inverse(X_301),multiply(additive_identity,X_301)),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(product(X_301,inverse(X_301),multiply(additive_identity,X_301)))),bind(C,$fot(true))]]) ).
cnf(refute_0_444,plain,
( ifeq(true,true,product(X_301,inverse(X_301),multiply(additive_identity,X_301)),true) != product(X_301,inverse(X_301),multiply(additive_identity,X_301))
| ifeq(true,true,product(X_301,inverse(X_301),multiply(additive_identity,X_301)),true) != true
| product(X_301,inverse(X_301),multiply(additive_identity,X_301)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,product(X_301,inverse(X_301),multiply(additive_identity,X_301)),true),true) ),[0],$fot(product(X_301,inverse(X_301),multiply(additive_identity,X_301)))]]) ).
cnf(refute_0_445,plain,
( ifeq(true,true,product(X_301,inverse(X_301),multiply(additive_identity,X_301)),true) != true
| product(X_301,inverse(X_301),multiply(additive_identity,X_301)) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,product(X_301,inverse(X_301),multiply(additive_identity,X_301)),true),product(X_301,inverse(X_301),multiply(additive_identity,X_301))) )],[refute_0_443,refute_0_444]) ).
cnf(refute_0_446,plain,
product(X_301,inverse(X_301),multiply(additive_identity,X_301)) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,product(X_301,inverse(X_301),multiply(additive_identity,X_301)),true),true) )],[refute_0_442,refute_0_445]) ).
cnf(refute_0_447,plain,
product(X_54,inverse(X_54),multiply(additive_identity,X_54)) = true,
inference(subst,[],[refute_0_446:[bind(X_301,$fot(X_54))]]) ).
cnf(refute_0_448,plain,
( ifeq2(product(X_54,inverse(X_54),multiply(additive_identity,X_54)),true,multiply(additive_identity,X_54),multiply(X_54,inverse(X_54))) != multiply(X_54,inverse(X_54))
| product(X_54,inverse(X_54),multiply(additive_identity,X_54)) != true
| ifeq2(true,true,multiply(additive_identity,X_54),multiply(X_54,inverse(X_54))) = multiply(X_54,inverse(X_54)) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(X_54,inverse(X_54),multiply(additive_identity,X_54)),true,multiply(additive_identity,X_54),multiply(X_54,inverse(X_54))),multiply(X_54,inverse(X_54))) ),[0,0],$fot(true)]]) ).
cnf(refute_0_449,plain,
( ifeq2(product(X_54,inverse(X_54),multiply(additive_identity,X_54)),true,multiply(additive_identity,X_54),multiply(X_54,inverse(X_54))) != multiply(X_54,inverse(X_54))
| ifeq2(true,true,multiply(additive_identity,X_54),multiply(X_54,inverse(X_54))) = multiply(X_54,inverse(X_54)) ),
inference(resolve,[$cnf( $equal(product(X_54,inverse(X_54),multiply(additive_identity,X_54)),true) )],[refute_0_447,refute_0_448]) ).
cnf(refute_0_450,plain,
ifeq2(true,true,multiply(additive_identity,X_54),multiply(X_54,inverse(X_54))) = multiply(X_54,inverse(X_54)),
inference(resolve,[$cnf( $equal(ifeq2(product(X_54,inverse(X_54),multiply(additive_identity,X_54)),true,multiply(additive_identity,X_54),multiply(X_54,inverse(X_54))),multiply(X_54,inverse(X_54))) )],[refute_0_386,refute_0_449]) ).
cnf(refute_0_451,plain,
ifeq2(true,true,multiply(additive_identity,X_54),multiply(X_54,inverse(X_54))) = multiply(additive_identity,X_54),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(multiply(additive_identity,X_54))),bind(C,$fot(multiply(X_54,inverse(X_54))))]]) ).
cnf(refute_0_452,plain,
( ifeq2(true,true,multiply(additive_identity,X_54),multiply(X_54,inverse(X_54))) != multiply(X_54,inverse(X_54))
| ifeq2(true,true,multiply(additive_identity,X_54),multiply(X_54,inverse(X_54))) != multiply(additive_identity,X_54)
| multiply(additive_identity,X_54) = multiply(X_54,inverse(X_54)) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(true,true,multiply(additive_identity,X_54),multiply(X_54,inverse(X_54))),multiply(X_54,inverse(X_54))) ),[0],$fot(multiply(additive_identity,X_54))]]) ).
cnf(refute_0_453,plain,
( ifeq2(true,true,multiply(additive_identity,X_54),multiply(X_54,inverse(X_54))) != multiply(X_54,inverse(X_54))
| multiply(additive_identity,X_54) = multiply(X_54,inverse(X_54)) ),
inference(resolve,[$cnf( $equal(ifeq2(true,true,multiply(additive_identity,X_54),multiply(X_54,inverse(X_54))),multiply(additive_identity,X_54)) )],[refute_0_451,refute_0_452]) ).
cnf(refute_0_454,plain,
ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(product(inverse(X_55),X_55,additive_identity),true,additive_identity,X_53),X_53) = X_53,
inference(subst,[],[multiplication_is_well_defined:[bind(U,$fot(additive_identity)),bind(V,$fot(X_53)),bind(X,$fot(inverse(X_55))),bind(Y,$fot(X_55))]]) ).
cnf(refute_0_455,plain,
product(inverse(X_55),X_55,additive_identity) = true,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(X_55))]]) ).
cnf(refute_0_456,plain,
( ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(product(inverse(X_55),X_55,additive_identity),true,additive_identity,X_53),X_53) != X_53
| product(inverse(X_55),X_55,additive_identity) != true
| ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53) = X_53 ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(product(inverse(X_55),X_55,additive_identity),true,additive_identity,X_53),X_53),X_53) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_457,plain,
( ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(product(inverse(X_55),X_55,additive_identity),true,additive_identity,X_53),X_53) != X_53
| ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53) = X_53 ),
inference(resolve,[$cnf( $equal(product(inverse(X_55),X_55,additive_identity),true) )],[refute_0_455,refute_0_456]) ).
cnf(refute_0_458,plain,
ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53) = X_53,
inference(resolve,[$cnf( $equal(ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(product(inverse(X_55),X_55,additive_identity),true,additive_identity,X_53),X_53),X_53) )],[refute_0_454,refute_0_457]) ).
cnf(refute_0_459,plain,
ifeq2(true,true,additive_identity,X_53) = additive_identity,
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(additive_identity)),bind(C,$fot(X_53))]]) ).
cnf(refute_0_460,plain,
ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53) = ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53),
introduced(tautology,[refl,[$fot(ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53))]]) ).
cnf(refute_0_461,plain,
( ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53) != ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53)
| ifeq2(true,true,additive_identity,X_53) != additive_identity
| ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53) = ifeq2(product(inverse(X_55),X_55,X_53),true,additive_identity,X_53) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53),ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53)) ),[1,2],$fot(additive_identity)]]) ).
cnf(refute_0_462,plain,
( ifeq2(true,true,additive_identity,X_53) != additive_identity
| ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53) = ifeq2(product(inverse(X_55),X_55,X_53),true,additive_identity,X_53) ),
inference(resolve,[$cnf( $equal(ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53),ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53)) )],[refute_0_460,refute_0_461]) ).
cnf(refute_0_463,plain,
ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53) = ifeq2(product(inverse(X_55),X_55,X_53),true,additive_identity,X_53),
inference(resolve,[$cnf( $equal(ifeq2(true,true,additive_identity,X_53),additive_identity) )],[refute_0_459,refute_0_462]) ).
cnf(refute_0_464,plain,
( ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53) != X_53
| ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53) != ifeq2(product(inverse(X_55),X_55,X_53),true,additive_identity,X_53)
| ifeq2(product(inverse(X_55),X_55,X_53),true,additive_identity,X_53) = X_53 ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53),X_53) ),[0],$fot(ifeq2(product(inverse(X_55),X_55,X_53),true,additive_identity,X_53))]]) ).
cnf(refute_0_465,plain,
( ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53) != X_53
| ifeq2(product(inverse(X_55),X_55,X_53),true,additive_identity,X_53) = X_53 ),
inference(resolve,[$cnf( $equal(ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53),ifeq2(product(inverse(X_55),X_55,X_53),true,additive_identity,X_53)) )],[refute_0_463,refute_0_464]) ).
cnf(refute_0_466,plain,
ifeq2(product(inverse(X_55),X_55,X_53),true,additive_identity,X_53) = X_53,
inference(resolve,[$cnf( $equal(ifeq2(product(inverse(X_55),X_55,X_53),true,ifeq2(true,true,additive_identity,X_53),X_53),X_53) )],[refute_0_458,refute_0_465]) ).
cnf(refute_0_467,plain,
ifeq2(product(inverse(X_67),X_67,multiply(X_67,inverse(X_67))),true,additive_identity,multiply(X_67,inverse(X_67))) = multiply(X_67,inverse(X_67)),
inference(subst,[],[refute_0_466:[bind(X_53,$fot(multiply(X_67,inverse(X_67)))),bind(X_55,$fot(X_67))]]) ).
cnf(refute_0_468,plain,
product(inverse(X_67),X_67,multiply(X_67,inverse(X_67))) = true,
inference(subst,[],[refute_0_126:[bind(X_23,$fot(X_67)),bind(X_24,$fot(inverse(X_67)))]]) ).
cnf(refute_0_469,plain,
( ifeq2(product(inverse(X_67),X_67,multiply(X_67,inverse(X_67))),true,additive_identity,multiply(X_67,inverse(X_67))) != multiply(X_67,inverse(X_67))
| product(inverse(X_67),X_67,multiply(X_67,inverse(X_67))) != true
| ifeq2(true,true,additive_identity,multiply(X_67,inverse(X_67))) = multiply(X_67,inverse(X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(inverse(X_67),X_67,multiply(X_67,inverse(X_67))),true,additive_identity,multiply(X_67,inverse(X_67))),multiply(X_67,inverse(X_67))) ),[0,0],$fot(true)]]) ).
cnf(refute_0_470,plain,
( ifeq2(product(inverse(X_67),X_67,multiply(X_67,inverse(X_67))),true,additive_identity,multiply(X_67,inverse(X_67))) != multiply(X_67,inverse(X_67))
| ifeq2(true,true,additive_identity,multiply(X_67,inverse(X_67))) = multiply(X_67,inverse(X_67)) ),
inference(resolve,[$cnf( $equal(product(inverse(X_67),X_67,multiply(X_67,inverse(X_67))),true) )],[refute_0_468,refute_0_469]) ).
cnf(refute_0_471,plain,
ifeq2(true,true,additive_identity,multiply(X_67,inverse(X_67))) = multiply(X_67,inverse(X_67)),
inference(resolve,[$cnf( $equal(ifeq2(product(inverse(X_67),X_67,multiply(X_67,inverse(X_67))),true,additive_identity,multiply(X_67,inverse(X_67))),multiply(X_67,inverse(X_67))) )],[refute_0_467,refute_0_470]) ).
cnf(refute_0_472,plain,
ifeq2(true,true,additive_identity,multiply(X_67,inverse(X_67))) = additive_identity,
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(additive_identity)),bind(C,$fot(multiply(X_67,inverse(X_67))))]]) ).
cnf(refute_0_473,plain,
( ifeq2(true,true,additive_identity,multiply(X_67,inverse(X_67))) != multiply(X_67,inverse(X_67))
| ifeq2(true,true,additive_identity,multiply(X_67,inverse(X_67))) != additive_identity
| additive_identity = multiply(X_67,inverse(X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(true,true,additive_identity,multiply(X_67,inverse(X_67))),multiply(X_67,inverse(X_67))) ),[0],$fot(additive_identity)]]) ).
cnf(refute_0_474,plain,
( ifeq2(true,true,additive_identity,multiply(X_67,inverse(X_67))) != multiply(X_67,inverse(X_67))
| additive_identity = multiply(X_67,inverse(X_67)) ),
inference(resolve,[$cnf( $equal(ifeq2(true,true,additive_identity,multiply(X_67,inverse(X_67))),additive_identity) )],[refute_0_472,refute_0_473]) ).
cnf(refute_0_475,plain,
additive_identity = multiply(X_67,inverse(X_67)),
inference(resolve,[$cnf( $equal(ifeq2(true,true,additive_identity,multiply(X_67,inverse(X_67))),multiply(X_67,inverse(X_67))) )],[refute_0_471,refute_0_474]) ).
cnf(refute_0_476,plain,
( additive_identity != multiply(X_67,inverse(X_67))
| multiply(X_67,inverse(X_67)) = additive_identity ),
inference(subst,[],[refute_0_167:[bind(X0,$fot(additive_identity)),bind(Y0,$fot(multiply(X_67,inverse(X_67))))]]) ).
cnf(refute_0_477,plain,
multiply(X_67,inverse(X_67)) = additive_identity,
inference(resolve,[$cnf( $equal(additive_identity,multiply(X_67,inverse(X_67))) )],[refute_0_475,refute_0_476]) ).
cnf(refute_0_478,plain,
multiply(X_54,inverse(X_54)) = additive_identity,
inference(subst,[],[refute_0_477:[bind(X_67,$fot(X_54))]]) ).
cnf(refute_0_479,plain,
( multiply(X_54,inverse(X_54)) != additive_identity
| multiply(additive_identity,X_54) != multiply(X_54,inverse(X_54))
| multiply(additive_identity,X_54) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_identity,X_54),multiply(X_54,inverse(X_54))) ),[1],$fot(additive_identity)]]) ).
cnf(refute_0_480,plain,
( multiply(additive_identity,X_54) != multiply(X_54,inverse(X_54))
| multiply(additive_identity,X_54) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(X_54,inverse(X_54)),additive_identity) )],[refute_0_478,refute_0_479]) ).
cnf(refute_0_481,plain,
( ifeq2(true,true,multiply(additive_identity,X_54),multiply(X_54,inverse(X_54))) != multiply(X_54,inverse(X_54))
| multiply(additive_identity,X_54) = additive_identity ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_54),multiply(X_54,inverse(X_54))) )],[refute_0_453,refute_0_480]) ).
cnf(refute_0_482,plain,
multiply(additive_identity,X_54) = additive_identity,
inference(resolve,[$cnf( $equal(ifeq2(true,true,multiply(additive_identity,X_54),multiply(X_54,inverse(X_54))),multiply(X_54,inverse(X_54))) )],[refute_0_450,refute_0_481]) ).
cnf(refute_0_483,plain,
multiply(additive_identity,Y) = additive_identity,
inference(subst,[],[refute_0_482:[bind(X_54,$fot(Y))]]) ).
cnf(refute_0_484,plain,
( multiply(additive_identity,Y) != additive_identity
| product(additive_identity,Y,multiply(additive_identity,Y)) != true
| product(additive_identity,Y,additive_identity) = true ),
introduced(tautology,[equality,[$cnf( $equal(product(additive_identity,Y,multiply(additive_identity,Y)),true) ),[0,2],$fot(additive_identity)]]) ).
cnf(refute_0_485,plain,
( product(additive_identity,Y,multiply(additive_identity,Y)) != true
| product(additive_identity,Y,additive_identity) = true ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,Y),additive_identity) )],[refute_0_483,refute_0_484]) ).
cnf(refute_0_486,plain,
product(additive_identity,Y,additive_identity) = true,
inference(resolve,[$cnf( $equal(product(additive_identity,Y,multiply(additive_identity,Y)),true) )],[refute_0_385,refute_0_485]) ).
cnf(refute_0_487,plain,
product(additive_identity,X_3572,additive_identity) = true,
inference(subst,[],[refute_0_486:[bind(Y,$fot(X_3572))]]) ).
cnf(refute_0_488,plain,
ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) = ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true),
introduced(tautology,[refl,[$fot(ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true))]]) ).
cnf(refute_0_489,plain,
( ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) != ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true)
| product(additive_identity,X_3572,additive_identity) != true
| ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) = ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true),ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true)) ),[1,0],$fot(true)]]) ).
cnf(refute_0_490,plain,
( product(additive_identity,X_3572,additive_identity) != true
| ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) = ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true),ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true)) )],[refute_0_488,refute_0_489]) ).
cnf(refute_0_491,plain,
ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) = ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true),
inference(resolve,[$cnf( $equal(product(additive_identity,X_3572,additive_identity),true) )],[refute_0_487,refute_0_490]) ).
cnf(refute_0_492,plain,
( ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) != ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true)
| ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) != ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true)
| ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) = ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true) ),
inference(subst,[],[refute_0_177:[bind(X0,$fot(ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true))),bind(Y0,$fot(ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true))),bind(Z0,$fot(ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true)))]]) ).
cnf(refute_0_493,plain,
( ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) != ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true)
| ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) = ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true) ),
inference(resolve,[$cnf( $equal(ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true),ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true)) )],[refute_0_491,refute_0_492]) ).
cnf(refute_0_494,plain,
ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) = ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true),ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true)) )],[refute_0_384,refute_0_493]) ).
cnf(refute_0_495,plain,
( ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) != ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true)
| ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true) != ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true)
| ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) = ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true) ),
inference(subst,[],[refute_0_177:[bind(X0,$fot(ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true))),bind(Y0,$fot(ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true))),bind(Z0,$fot(ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true)))]]) ).
cnf(refute_0_496,plain,
( ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true) != ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true)
| ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) = ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true) ),
inference(resolve,[$cnf( $equal(ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true),ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true)) )],[refute_0_494,refute_0_495]) ).
cnf(refute_0_497,plain,
ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) = ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true)) )],[refute_0_380,refute_0_496]) ).
cnf(refute_0_498,plain,
( ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) != ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true)
| ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) != true
| ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true),true) ),[0],$fot(ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true))]]) ).
cnf(refute_0_499,plain,
( ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true) != true
| ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true),ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true)) )],[refute_0_497,refute_0_498]) ).
cnf(refute_0_500,plain,
ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true) = true,
inference(resolve,[$cnf( $equal(ifeq(product(additive_identity,X_3572,additive_identity),true,ifeq(true,true,ifeq(sum(X_3571,X_3572,X_3569),true,product(X_3571,X_3569,X_3571),true),true),true),true) )],[refute_0_379,refute_0_499]) ).
cnf(refute_0_501,plain,
ifeq(sum(X_3574,X_3575,add(X_3575,X_3574)),true,product(X_3574,add(X_3575,X_3574),X_3574),true) = true,
inference(subst,[],[refute_0_500:[bind(X_3569,$fot(add(X_3575,X_3574))),bind(X_3571,$fot(X_3574)),bind(X_3572,$fot(X_3575))]]) ).
cnf(refute_0_502,plain,
sum(X_3574,X_3575,add(X_3575,X_3574)) = true,
inference(subst,[],[refute_0_8:[bind(X_18,$fot(X_3575)),bind(X_19,$fot(X_3574))]]) ).
cnf(refute_0_503,plain,
( ifeq(sum(X_3574,X_3575,add(X_3575,X_3574)),true,product(X_3574,add(X_3575,X_3574),X_3574),true) != true
| sum(X_3574,X_3575,add(X_3575,X_3574)) != true
| ifeq(true,true,product(X_3574,add(X_3575,X_3574),X_3574),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(sum(X_3574,X_3575,add(X_3575,X_3574)),true,product(X_3574,add(X_3575,X_3574),X_3574),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_504,plain,
( ifeq(sum(X_3574,X_3575,add(X_3575,X_3574)),true,product(X_3574,add(X_3575,X_3574),X_3574),true) != true
| ifeq(true,true,product(X_3574,add(X_3575,X_3574),X_3574),true) = true ),
inference(resolve,[$cnf( $equal(sum(X_3574,X_3575,add(X_3575,X_3574)),true) )],[refute_0_502,refute_0_503]) ).
cnf(refute_0_505,plain,
ifeq(true,true,product(X_3574,add(X_3575,X_3574),X_3574),true) = true,
inference(resolve,[$cnf( $equal(ifeq(sum(X_3574,X_3575,add(X_3575,X_3574)),true,product(X_3574,add(X_3575,X_3574),X_3574),true),true) )],[refute_0_501,refute_0_504]) ).
cnf(refute_0_506,plain,
ifeq(true,true,product(X_3574,add(X_3575,X_3574),X_3574),true) = product(X_3574,add(X_3575,X_3574),X_3574),
inference(subst,[],[ifeq_axiom_001:[bind(A,$fot(true)),bind(B,$fot(product(X_3574,add(X_3575,X_3574),X_3574))),bind(C,$fot(true))]]) ).
cnf(refute_0_507,plain,
( ifeq(true,true,product(X_3574,add(X_3575,X_3574),X_3574),true) != product(X_3574,add(X_3575,X_3574),X_3574)
| ifeq(true,true,product(X_3574,add(X_3575,X_3574),X_3574),true) != true
| product(X_3574,add(X_3575,X_3574),X_3574) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,product(X_3574,add(X_3575,X_3574),X_3574),true),true) ),[0],$fot(product(X_3574,add(X_3575,X_3574),X_3574))]]) ).
cnf(refute_0_508,plain,
( ifeq(true,true,product(X_3574,add(X_3575,X_3574),X_3574),true) != true
| product(X_3574,add(X_3575,X_3574),X_3574) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,product(X_3574,add(X_3575,X_3574),X_3574),true),product(X_3574,add(X_3575,X_3574),X_3574)) )],[refute_0_506,refute_0_507]) ).
cnf(refute_0_509,plain,
product(X_3574,add(X_3575,X_3574),X_3574) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,product(X_3574,add(X_3575,X_3574),X_3574),true),true) )],[refute_0_505,refute_0_508]) ).
cnf(refute_0_510,plain,
product(X_53,add(X_53,X_53),X_53) = true,
inference(subst,[],[refute_0_509:[bind(X_3574,$fot(X_53)),bind(X_3575,$fot(X_53))]]) ).
cnf(refute_0_511,plain,
( ifeq2(product(X_53,add(X_53,X_53),X_53),true,add(X_53,X_53),X_53) != X_53
| product(X_53,add(X_53,X_53),X_53) != true
| ifeq2(true,true,add(X_53,X_53),X_53) = X_53 ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(product(X_53,add(X_53,X_53),X_53),true,add(X_53,X_53),X_53),X_53) ),[0,0],$fot(true)]]) ).
cnf(refute_0_512,plain,
( ifeq2(product(X_53,add(X_53,X_53),X_53),true,add(X_53,X_53),X_53) != X_53
| ifeq2(true,true,add(X_53,X_53),X_53) = X_53 ),
inference(resolve,[$cnf( $equal(product(X_53,add(X_53,X_53),X_53),true) )],[refute_0_510,refute_0_511]) ).
cnf(refute_0_513,plain,
ifeq2(true,true,add(X_53,X_53),X_53) = X_53,
inference(resolve,[$cnf( $equal(ifeq2(product(X_53,add(X_53,X_53),X_53),true,add(X_53,X_53),X_53),X_53) )],[refute_0_353,refute_0_512]) ).
cnf(refute_0_514,plain,
ifeq2(true,true,add(X_53,X_53),X_53) = add(X_53,X_53),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(add(X_53,X_53))),bind(C,$fot(X_53))]]) ).
cnf(refute_0_515,plain,
( ifeq2(true,true,add(X_53,X_53),X_53) != X_53
| ifeq2(true,true,add(X_53,X_53),X_53) != add(X_53,X_53)
| add(X_53,X_53) = X_53 ),
introduced(tautology,[equality,[$cnf( $equal(ifeq2(true,true,add(X_53,X_53),X_53),X_53) ),[0],$fot(add(X_53,X_53))]]) ).
cnf(refute_0_516,plain,
( ifeq2(true,true,add(X_53,X_53),X_53) != X_53
| add(X_53,X_53) = X_53 ),
inference(resolve,[$cnf( $equal(ifeq2(true,true,add(X_53,X_53),X_53),add(X_53,X_53)) )],[refute_0_514,refute_0_515]) ).
cnf(refute_0_517,plain,
add(X_53,X_53) = X_53,
inference(resolve,[$cnf( $equal(ifeq2(true,true,add(X_53,X_53),X_53),X_53) )],[refute_0_513,refute_0_516]) ).
cnf(refute_0_518,plain,
add(X_19,X_19) = X_19,
inference(subst,[],[refute_0_517:[bind(X_53,$fot(X_19))]]) ).
cnf(refute_0_519,plain,
( add(X_19,X_19) != X_19
| sum(X_19,X_19,add(X_19,X_19)) != true
| sum(X_19,X_19,X_19) = true ),
introduced(tautology,[equality,[$cnf( $equal(sum(X_19,X_19,add(X_19,X_19)),true) ),[0,2],$fot(X_19)]]) ).
cnf(refute_0_520,plain,
( sum(X_19,X_19,add(X_19,X_19)) != true
| sum(X_19,X_19,X_19) = true ),
inference(resolve,[$cnf( $equal(add(X_19,X_19),X_19) )],[refute_0_518,refute_0_519]) ).
cnf(refute_0_521,plain,
sum(X_19,X_19,X_19) = true,
inference(resolve,[$cnf( $equal(sum(X_19,X_19,add(X_19,X_19)),true) )],[refute_0_9,refute_0_520]) ).
cnf(refute_0_522,plain,
sum(x,x,x) = true,
inference(subst,[],[refute_0_521:[bind(X_19,$fot(x))]]) ).
cnf(refute_0_523,plain,
( sum(x,x,x) != true
| true != true
| sum(x,x,x) = true ),
introduced(tautology,[equality,[$cnf( ~ $equal(sum(x,x,x),true) ),[0],$fot(true)]]) ).
cnf(refute_0_524,plain,
( true != true
| sum(x,x,x) = true ),
inference(resolve,[$cnf( $equal(sum(x,x,x),true) )],[refute_0_522,refute_0_523]) ).
cnf(refute_0_525,plain,
true != true,
inference(resolve,[$cnf( $equal(sum(x,x,x),true) )],[refute_0_524,prove_both_equalities]) ).
cnf(refute_0_526,plain,
true = true,
introduced(tautology,[refl,[$fot(true)]]) ).
cnf(refute_0_527,plain,
$false,
inference(resolve,[$cnf( $equal(true,true) )],[refute_0_526,refute_0_525]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO004-10 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 1 23:22:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 131.63/131.85 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 131.63/131.85
% 131.63/131.85 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 131.72/131.91
%------------------------------------------------------------------------------