TSTP Solution File: RNG018-6 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : RNG018-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 20:35:47 EDT 2022
% Result : Unsatisfiable 137.73s 137.94s
% Output : CNFRefutation 137.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 77
% Syntax : Number of clauses : 337 ( 183 unt; 0 nHn; 164 RR)
% Number of literals : 556 ( 555 equ; 222 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 822 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_additive_identity,axiom,
add(additive_identity,X) = X ).
cnf(right_additive_identity,axiom,
add(X,additive_identity) = X ).
cnf(right_multiplicative_zero,axiom,
multiply(X,additive_identity) = additive_identity ).
cnf(right_additive_inverse,axiom,
add(X,additive_inverse(X)) = additive_identity ).
cnf(additive_inverse_additive_inverse,axiom,
additive_inverse(additive_inverse(X)) = X ).
cnf(distribute1,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ).
cnf(distribute2,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ).
cnf(commutativity_for_addition,axiom,
add(X,Y) = add(Y,X) ).
cnf(associativity_for_addition,axiom,
add(X,add(Y,Z)) = add(add(X,Y),Z) ).
cnf(commutator,axiom,
commutator(X,Y) = add(multiply(Y,X),additive_inverse(multiply(X,Y))) ).
cnf(prove_distributivity,negated_conjecture,
multiply(add(x,y),additive_inverse(z)) != add(additive_inverse(multiply(x,z)),additive_inverse(multiply(y,z))) ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( multiply(add(X,Y),Z) != add(multiply(X,Z),multiply(Y,Z))
| add(multiply(X,Z),multiply(Y,Z)) = multiply(add(X,Y),Z) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(add(X,Y),Z))),bind(Y0,$fot(add(multiply(X,Z),multiply(Y,Z))))]]) ).
cnf(refute_0_4,plain,
add(multiply(X,Z),multiply(Y,Z)) = multiply(add(X,Y),Z),
inference(resolve,[$cnf( $equal(multiply(add(X,Y),Z),add(multiply(X,Z),multiply(Y,Z))) )],[distribute2,refute_0_3]) ).
cnf(refute_0_5,plain,
add(multiply(x,z),multiply(y,z)) = multiply(add(x,y),z),
inference(subst,[],[refute_0_4:[bind(X,$fot(x)),bind(Y,$fot(y)),bind(Z,$fot(z))]]) ).
cnf(refute_0_6,plain,
( add(X,Y) != add(Y,X)
| add(Y,X) = add(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X,Y))),bind(Y0,$fot(add(Y,X)))]]) ).
cnf(refute_0_7,plain,
add(Y,X) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X,Y),add(Y,X)) )],[commutativity_for_addition,refute_0_6]) ).
cnf(refute_0_8,plain,
add(multiply(y,z),multiply(x,z)) = add(multiply(x,z),multiply(y,z)),
inference(subst,[],[refute_0_7:[bind(X,$fot(multiply(x,z))),bind(Y,$fot(multiply(y,z)))]]) ).
cnf(refute_0_9,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_10,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_9]) ).
cnf(refute_0_11,plain,
( add(multiply(x,z),multiply(y,z)) != multiply(add(x,y),z)
| add(multiply(y,z),multiply(x,z)) != add(multiply(x,z),multiply(y,z))
| add(multiply(y,z),multiply(x,z)) = multiply(add(x,y),z) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(add(multiply(y,z),multiply(x,z)))),bind(Y0,$fot(add(multiply(x,z),multiply(y,z)))),bind(Z0,$fot(multiply(add(x,y),z)))]]) ).
cnf(refute_0_12,plain,
( add(multiply(x,z),multiply(y,z)) != multiply(add(x,y),z)
| add(multiply(y,z),multiply(x,z)) = multiply(add(x,y),z) ),
inference(resolve,[$cnf( $equal(add(multiply(y,z),multiply(x,z)),add(multiply(x,z),multiply(y,z))) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
add(multiply(y,z),multiply(x,z)) = multiply(add(x,y),z),
inference(resolve,[$cnf( $equal(add(multiply(x,z),multiply(y,z)),multiply(add(x,y),z)) )],[refute_0_5,refute_0_12]) ).
cnf(refute_0_14,plain,
additive_inverse(add(multiply(y,z),multiply(x,z))) = additive_inverse(add(multiply(y,z),multiply(x,z))),
introduced(tautology,[refl,[$fot(additive_inverse(add(multiply(y,z),multiply(x,z))))]]) ).
cnf(refute_0_15,plain,
( add(multiply(y,z),multiply(x,z)) != multiply(add(x,y),z)
| additive_inverse(add(multiply(y,z),multiply(x,z))) != additive_inverse(add(multiply(y,z),multiply(x,z)))
| additive_inverse(add(multiply(y,z),multiply(x,z))) = additive_inverse(multiply(add(x,y),z)) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(multiply(y,z),multiply(x,z))),additive_inverse(add(multiply(y,z),multiply(x,z)))) ),[1,0],$fot(multiply(add(x,y),z))]]) ).
cnf(refute_0_16,plain,
( add(multiply(y,z),multiply(x,z)) != multiply(add(x,y),z)
| additive_inverse(add(multiply(y,z),multiply(x,z))) = additive_inverse(multiply(add(x,y),z)) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(multiply(y,z),multiply(x,z))),additive_inverse(add(multiply(y,z),multiply(x,z)))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
additive_inverse(add(multiply(y,z),multiply(x,z))) = additive_inverse(multiply(add(x,y),z)),
inference(resolve,[$cnf( $equal(add(multiply(y,z),multiply(x,z)),multiply(add(x,y),z)) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
add(X_36,add(additive_inverse(X_36),X_38)) = add(add(X_36,additive_inverse(X_36)),X_38),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(X_36)),bind(Y,$fot(additive_inverse(X_36))),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_19,plain,
add(X_36,additive_inverse(X_36)) = additive_identity,
inference(subst,[],[right_additive_inverse:[bind(X,$fot(X_36))]]) ).
cnf(refute_0_20,plain,
( add(X_36,add(additive_inverse(X_36),X_38)) != add(add(X_36,additive_inverse(X_36)),X_38)
| add(X_36,additive_inverse(X_36)) != additive_identity
| add(X_36,add(additive_inverse(X_36),X_38)) = add(additive_identity,X_38) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_36,add(additive_inverse(X_36),X_38)),add(add(X_36,additive_inverse(X_36)),X_38)) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_21,plain,
( add(X_36,add(additive_inverse(X_36),X_38)) != add(add(X_36,additive_inverse(X_36)),X_38)
| add(X_36,add(additive_inverse(X_36),X_38)) = add(additive_identity,X_38) ),
inference(resolve,[$cnf( $equal(add(X_36,additive_inverse(X_36)),additive_identity) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
add(X_36,add(additive_inverse(X_36),X_38)) = add(additive_identity,X_38),
inference(resolve,[$cnf( $equal(add(X_36,add(additive_inverse(X_36),X_38)),add(add(X_36,additive_inverse(X_36)),X_38)) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
add(additive_identity,X_38) = X_38,
inference(subst,[],[left_additive_identity:[bind(X,$fot(X_38))]]) ).
cnf(refute_0_24,plain,
( add(X_36,add(additive_inverse(X_36),X_38)) != add(additive_identity,X_38)
| add(additive_identity,X_38) != X_38
| add(X_36,add(additive_inverse(X_36),X_38)) = X_38 ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_36,add(additive_inverse(X_36),X_38)),X_38) ),[0],$fot(add(additive_identity,X_38))]]) ).
cnf(refute_0_25,plain,
( add(X_36,add(additive_inverse(X_36),X_38)) != add(additive_identity,X_38)
| add(X_36,add(additive_inverse(X_36),X_38)) = X_38 ),
inference(resolve,[$cnf( $equal(add(additive_identity,X_38),X_38) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
add(X_36,add(additive_inverse(X_36),X_38)) = X_38,
inference(resolve,[$cnf( $equal(add(X_36,add(additive_inverse(X_36),X_38)),add(additive_identity,X_38)) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
add(X_36,add(additive_inverse(X_36),additive_inverse(add(X_57,additive_inverse(X_36))))) = additive_inverse(add(X_57,additive_inverse(X_36))),
inference(subst,[],[refute_0_26:[bind(X_38,$fot(additive_inverse(add(X_57,additive_inverse(X_36)))))]]) ).
cnf(refute_0_28,plain,
add(X_36,add(additive_inverse(X_36),add(X_52,additive_inverse(add(additive_inverse(X_36),X_52))))) = add(X_52,additive_inverse(add(additive_inverse(X_36),X_52))),
inference(subst,[],[refute_0_26:[bind(X_38,$fot(add(X_52,additive_inverse(add(additive_inverse(X_36),X_52)))))]]) ).
cnf(refute_0_29,plain,
add(add(X_36,X_37),additive_inverse(add(X_36,X_37))) = additive_identity,
inference(subst,[],[right_additive_inverse:[bind(X,$fot(add(X_36,X_37)))]]) ).
cnf(refute_0_30,plain,
add(X_36,add(X_37,additive_inverse(add(X_36,X_37)))) = add(add(X_36,X_37),additive_inverse(add(X_36,X_37))),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(additive_inverse(add(X_36,X_37))))]]) ).
cnf(refute_0_31,plain,
( add(X_36,add(X_37,additive_inverse(add(X_36,X_37)))) != add(add(X_36,X_37),additive_inverse(add(X_36,X_37)))
| add(add(X_36,X_37),additive_inverse(add(X_36,X_37))) = add(X_36,add(X_37,additive_inverse(add(X_36,X_37)))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_36,add(X_37,additive_inverse(add(X_36,X_37)))))),bind(Y0,$fot(add(add(X_36,X_37),additive_inverse(add(X_36,X_37)))))]]) ).
cnf(refute_0_32,plain,
add(add(X_36,X_37),additive_inverse(add(X_36,X_37))) = add(X_36,add(X_37,additive_inverse(add(X_36,X_37)))),
inference(resolve,[$cnf( $equal(add(X_36,add(X_37,additive_inverse(add(X_36,X_37)))),add(add(X_36,X_37),additive_inverse(add(X_36,X_37)))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( add(add(X_36,X_37),additive_inverse(add(X_36,X_37))) != add(X_36,add(X_37,additive_inverse(add(X_36,X_37))))
| add(add(X_36,X_37),additive_inverse(add(X_36,X_37))) != additive_identity
| add(X_36,add(X_37,additive_inverse(add(X_36,X_37)))) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_36,X_37),additive_inverse(add(X_36,X_37))),additive_identity) ),[0],$fot(add(X_36,add(X_37,additive_inverse(add(X_36,X_37)))))]]) ).
cnf(refute_0_34,plain,
( add(add(X_36,X_37),additive_inverse(add(X_36,X_37))) != additive_identity
| add(X_36,add(X_37,additive_inverse(add(X_36,X_37)))) = additive_identity ),
inference(resolve,[$cnf( $equal(add(add(X_36,X_37),additive_inverse(add(X_36,X_37))),add(X_36,add(X_37,additive_inverse(add(X_36,X_37))))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
add(X_36,add(X_37,additive_inverse(add(X_36,X_37)))) = additive_identity,
inference(resolve,[$cnf( $equal(add(add(X_36,X_37),additive_inverse(add(X_36,X_37))),additive_identity) )],[refute_0_29,refute_0_34]) ).
cnf(refute_0_36,plain,
add(additive_inverse(X_36),add(X_52,additive_inverse(add(additive_inverse(X_36),X_52)))) = additive_identity,
inference(subst,[],[refute_0_35:[bind(X_36,$fot(additive_inverse(X_36))),bind(X_37,$fot(X_52))]]) ).
cnf(refute_0_37,plain,
( add(X_36,add(additive_inverse(X_36),add(X_52,additive_inverse(add(additive_inverse(X_36),X_52))))) != add(X_52,additive_inverse(add(additive_inverse(X_36),X_52)))
| add(additive_inverse(X_36),add(X_52,additive_inverse(add(additive_inverse(X_36),X_52)))) != additive_identity
| add(X_36,additive_identity) = add(X_52,additive_inverse(add(additive_inverse(X_36),X_52))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_36,add(additive_inverse(X_36),add(X_52,additive_inverse(add(additive_inverse(X_36),X_52))))),add(X_52,additive_inverse(add(additive_inverse(X_36),X_52)))) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_38,plain,
( add(X_36,add(additive_inverse(X_36),add(X_52,additive_inverse(add(additive_inverse(X_36),X_52))))) != add(X_52,additive_inverse(add(additive_inverse(X_36),X_52)))
| add(X_36,additive_identity) = add(X_52,additive_inverse(add(additive_inverse(X_36),X_52))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_36),add(X_52,additive_inverse(add(additive_inverse(X_36),X_52)))),additive_identity) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
add(X_36,additive_identity) = add(X_52,additive_inverse(add(additive_inverse(X_36),X_52))),
inference(resolve,[$cnf( $equal(add(X_36,add(additive_inverse(X_36),add(X_52,additive_inverse(add(additive_inverse(X_36),X_52))))),add(X_52,additive_inverse(add(additive_inverse(X_36),X_52)))) )],[refute_0_28,refute_0_38]) ).
cnf(refute_0_40,plain,
add(X_36,additive_identity) = X_36,
inference(subst,[],[right_additive_identity:[bind(X,$fot(X_36))]]) ).
cnf(refute_0_41,plain,
( add(X_36,additive_identity) != X_36
| add(X_36,additive_identity) != add(X_52,additive_inverse(add(additive_inverse(X_36),X_52)))
| X_36 = add(X_52,additive_inverse(add(additive_inverse(X_36),X_52))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_36,additive_identity),add(X_52,additive_inverse(add(additive_inverse(X_36),X_52)))) ),[0],$fot(X_36)]]) ).
cnf(refute_0_42,plain,
( add(X_36,additive_identity) != add(X_52,additive_inverse(add(additive_inverse(X_36),X_52)))
| X_36 = add(X_52,additive_inverse(add(additive_inverse(X_36),X_52))) ),
inference(resolve,[$cnf( $equal(add(X_36,additive_identity),X_36) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
X_36 = add(X_52,additive_inverse(add(additive_inverse(X_36),X_52))),
inference(resolve,[$cnf( $equal(add(X_36,additive_identity),add(X_52,additive_inverse(add(additive_inverse(X_36),X_52)))) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
additive_inverse(X) = add(X_54,additive_inverse(add(additive_inverse(additive_inverse(X)),X_54))),
inference(subst,[],[refute_0_43:[bind(X_36,$fot(additive_inverse(X))),bind(X_52,$fot(X_54))]]) ).
cnf(refute_0_45,plain,
( additive_inverse(X) != add(X_54,additive_inverse(add(additive_inverse(additive_inverse(X)),X_54)))
| additive_inverse(additive_inverse(X)) != X
| additive_inverse(X) = add(X_54,additive_inverse(add(X,X_54))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(X),add(X_54,additive_inverse(add(additive_inverse(additive_inverse(X)),X_54)))) ),[1,1,0,0],$fot(X)]]) ).
cnf(refute_0_46,plain,
( additive_inverse(X) != add(X_54,additive_inverse(add(additive_inverse(additive_inverse(X)),X_54)))
| additive_inverse(X) = add(X_54,additive_inverse(add(X,X_54))) ),
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(X)),X) )],[additive_inverse_additive_inverse,refute_0_45]) ).
cnf(refute_0_47,plain,
additive_inverse(X) = add(X_54,additive_inverse(add(X,X_54))),
inference(resolve,[$cnf( $equal(additive_inverse(X),add(X_54,additive_inverse(add(additive_inverse(additive_inverse(X)),X_54)))) )],[refute_0_44,refute_0_46]) ).
cnf(refute_0_48,plain,
additive_inverse(X_57) = add(additive_inverse(X_36),additive_inverse(add(X_57,additive_inverse(X_36)))),
inference(subst,[],[refute_0_47:[bind(X,$fot(X_57)),bind(X_54,$fot(additive_inverse(X_36)))]]) ).
cnf(refute_0_49,plain,
( additive_inverse(X_57) != add(additive_inverse(X_36),additive_inverse(add(X_57,additive_inverse(X_36))))
| add(additive_inverse(X_36),additive_inverse(add(X_57,additive_inverse(X_36)))) = additive_inverse(X_57) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(additive_inverse(X_57))),bind(Y0,$fot(add(additive_inverse(X_36),additive_inverse(add(X_57,additive_inverse(X_36))))))]]) ).
cnf(refute_0_50,plain,
add(additive_inverse(X_36),additive_inverse(add(X_57,additive_inverse(X_36)))) = additive_inverse(X_57),
inference(resolve,[$cnf( $equal(additive_inverse(X_57),add(additive_inverse(X_36),additive_inverse(add(X_57,additive_inverse(X_36))))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( add(X_36,add(additive_inverse(X_36),additive_inverse(add(X_57,additive_inverse(X_36))))) != additive_inverse(add(X_57,additive_inverse(X_36)))
| add(additive_inverse(X_36),additive_inverse(add(X_57,additive_inverse(X_36)))) != additive_inverse(X_57)
| add(X_36,additive_inverse(X_57)) = additive_inverse(add(X_57,additive_inverse(X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_36,add(additive_inverse(X_36),additive_inverse(add(X_57,additive_inverse(X_36))))),additive_inverse(add(X_57,additive_inverse(X_36)))) ),[0,1],$fot(additive_inverse(X_57))]]) ).
cnf(refute_0_52,plain,
( add(X_36,add(additive_inverse(X_36),additive_inverse(add(X_57,additive_inverse(X_36))))) != additive_inverse(add(X_57,additive_inverse(X_36)))
| add(X_36,additive_inverse(X_57)) = additive_inverse(add(X_57,additive_inverse(X_36))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_36),additive_inverse(add(X_57,additive_inverse(X_36)))),additive_inverse(X_57)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
add(X_36,additive_inverse(X_57)) = additive_inverse(add(X_57,additive_inverse(X_36))),
inference(resolve,[$cnf( $equal(add(X_36,add(additive_inverse(X_36),additive_inverse(add(X_57,additive_inverse(X_36))))),additive_inverse(add(X_57,additive_inverse(X_36)))) )],[refute_0_27,refute_0_52]) ).
cnf(refute_0_54,plain,
add(additive_inverse(X),additive_inverse(X_64)) = additive_inverse(add(X_64,additive_inverse(additive_inverse(X)))),
inference(subst,[],[refute_0_53:[bind(X_36,$fot(additive_inverse(X))),bind(X_57,$fot(X_64))]]) ).
cnf(refute_0_55,plain,
( add(additive_inverse(X),additive_inverse(X_64)) != additive_inverse(add(X_64,additive_inverse(additive_inverse(X))))
| additive_inverse(additive_inverse(X)) != X
| add(additive_inverse(X),additive_inverse(X_64)) = additive_inverse(add(X_64,X)) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(X),additive_inverse(X_64)),additive_inverse(add(X_64,additive_inverse(additive_inverse(X))))) ),[1,0,1],$fot(X)]]) ).
cnf(refute_0_56,plain,
( add(additive_inverse(X),additive_inverse(X_64)) != additive_inverse(add(X_64,additive_inverse(additive_inverse(X))))
| add(additive_inverse(X),additive_inverse(X_64)) = additive_inverse(add(X_64,X)) ),
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(X)),X) )],[additive_inverse_additive_inverse,refute_0_55]) ).
cnf(refute_0_57,plain,
add(additive_inverse(X),additive_inverse(X_64)) = additive_inverse(add(X_64,X)),
inference(resolve,[$cnf( $equal(add(additive_inverse(X),additive_inverse(X_64)),additive_inverse(add(X_64,additive_inverse(additive_inverse(X))))) )],[refute_0_54,refute_0_56]) ).
cnf(refute_0_58,plain,
add(additive_inverse(multiply(x,z)),additive_inverse(multiply(y,z))) = additive_inverse(add(multiply(y,z),multiply(x,z))),
inference(subst,[],[refute_0_57:[bind(X,$fot(multiply(x,z))),bind(X_64,$fot(multiply(y,z)))]]) ).
cnf(refute_0_59,plain,
( add(additive_inverse(multiply(x,z)),additive_inverse(multiply(y,z))) != additive_inverse(add(multiply(y,z),multiply(x,z)))
| additive_inverse(add(multiply(y,z),multiply(x,z))) != additive_inverse(multiply(add(x,y),z))
| add(additive_inverse(multiply(x,z)),additive_inverse(multiply(y,z))) = additive_inverse(multiply(add(x,y),z)) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(add(additive_inverse(multiply(x,z)),additive_inverse(multiply(y,z))))),bind(Y0,$fot(additive_inverse(add(multiply(y,z),multiply(x,z))))),bind(Z0,$fot(additive_inverse(multiply(add(x,y),z))))]]) ).
cnf(refute_0_60,plain,
( additive_inverse(add(multiply(y,z),multiply(x,z))) != additive_inverse(multiply(add(x,y),z))
| add(additive_inverse(multiply(x,z)),additive_inverse(multiply(y,z))) = additive_inverse(multiply(add(x,y),z)) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(multiply(x,z)),additive_inverse(multiply(y,z))),additive_inverse(add(multiply(y,z),multiply(x,z)))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
add(additive_inverse(multiply(x,z)),additive_inverse(multiply(y,z))) = additive_inverse(multiply(add(x,y),z)),
inference(resolve,[$cnf( $equal(additive_inverse(add(multiply(y,z),multiply(x,z))),additive_inverse(multiply(add(x,y),z))) )],[refute_0_17,refute_0_60]) ).
cnf(refute_0_62,plain,
( multiply(add(x,y),additive_inverse(z)) != additive_inverse(multiply(add(x,y),z))
| add(additive_inverse(multiply(x,z)),additive_inverse(multiply(y,z))) != additive_inverse(multiply(add(x,y),z))
| multiply(add(x,y),additive_inverse(z)) = add(additive_inverse(multiply(x,z)),additive_inverse(multiply(y,z))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(add(x,y),additive_inverse(z)),add(additive_inverse(multiply(x,z)),additive_inverse(multiply(y,z)))) ),[1],$fot(additive_inverse(multiply(add(x,y),z)))]]) ).
cnf(refute_0_63,plain,
( multiply(add(x,y),additive_inverse(z)) != additive_inverse(multiply(add(x,y),z))
| multiply(add(x,y),additive_inverse(z)) = add(additive_inverse(multiply(x,z)),additive_inverse(multiply(y,z))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(multiply(x,z)),additive_inverse(multiply(y,z))),additive_inverse(multiply(add(x,y),z))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
multiply(add(x,y),additive_inverse(z)) != additive_inverse(multiply(add(x,y),z)),
inference(resolve,[$cnf( $equal(multiply(add(x,y),additive_inverse(z)),add(additive_inverse(multiply(x,z)),additive_inverse(multiply(y,z)))) )],[refute_0_63,prove_distributivity]) ).
cnf(refute_0_65,plain,
add(commutator(X_61,X_62),add(additive_inverse(commutator(X_61,X_62)),X_38)) = X_38,
inference(subst,[],[refute_0_26:[bind(X_36,$fot(commutator(X_61,X_62)))]]) ).
cnf(refute_0_66,plain,
additive_inverse(X) = add(additive_inverse(add(X_57,X)),additive_inverse(add(X,additive_inverse(add(X_57,X))))),
inference(subst,[],[refute_0_47:[bind(X_54,$fot(additive_inverse(add(X_57,X))))]]) ).
cnf(refute_0_67,plain,
additive_inverse(X_57) = add(X,additive_inverse(add(X_57,X))),
inference(subst,[],[refute_0_47:[bind(X,$fot(X_57)),bind(X_54,$fot(X))]]) ).
cnf(refute_0_68,plain,
( additive_inverse(X_57) != add(X,additive_inverse(add(X_57,X)))
| add(X,additive_inverse(add(X_57,X))) = additive_inverse(X_57) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(additive_inverse(X_57))),bind(Y0,$fot(add(X,additive_inverse(add(X_57,X)))))]]) ).
cnf(refute_0_69,plain,
add(X,additive_inverse(add(X_57,X))) = additive_inverse(X_57),
inference(resolve,[$cnf( $equal(additive_inverse(X_57),add(X,additive_inverse(add(X_57,X)))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( add(X,additive_inverse(add(X_57,X))) != additive_inverse(X_57)
| additive_inverse(X) != add(additive_inverse(add(X_57,X)),additive_inverse(add(X,additive_inverse(add(X_57,X)))))
| additive_inverse(X) = add(additive_inverse(add(X_57,X)),additive_inverse(additive_inverse(X_57))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(X),add(additive_inverse(add(X_57,X)),additive_inverse(add(X,additive_inverse(add(X_57,X)))))) ),[1,1,0],$fot(additive_inverse(X_57))]]) ).
cnf(refute_0_71,plain,
( additive_inverse(X) != add(additive_inverse(add(X_57,X)),additive_inverse(add(X,additive_inverse(add(X_57,X)))))
| additive_inverse(X) = add(additive_inverse(add(X_57,X)),additive_inverse(additive_inverse(X_57))) ),
inference(resolve,[$cnf( $equal(add(X,additive_inverse(add(X_57,X))),additive_inverse(X_57)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
additive_inverse(X) = add(additive_inverse(add(X_57,X)),additive_inverse(additive_inverse(X_57))),
inference(resolve,[$cnf( $equal(additive_inverse(X),add(additive_inverse(add(X_57,X)),additive_inverse(add(X,additive_inverse(add(X_57,X)))))) )],[refute_0_66,refute_0_71]) ).
cnf(refute_0_73,plain,
additive_inverse(additive_inverse(X_57)) = X_57,
inference(subst,[],[additive_inverse_additive_inverse:[bind(X,$fot(X_57))]]) ).
cnf(refute_0_74,plain,
add(additive_inverse(additive_inverse(X_57)),additive_inverse(add(X_57,X))) = add(additive_inverse(additive_inverse(X_57)),additive_inverse(add(X_57,X))),
introduced(tautology,[refl,[$fot(add(additive_inverse(additive_inverse(X_57)),additive_inverse(add(X_57,X))))]]) ).
cnf(refute_0_75,plain,
( add(additive_inverse(additive_inverse(X_57)),additive_inverse(add(X_57,X))) != add(additive_inverse(additive_inverse(X_57)),additive_inverse(add(X_57,X)))
| additive_inverse(additive_inverse(X_57)) != X_57
| add(additive_inverse(additive_inverse(X_57)),additive_inverse(add(X_57,X))) = add(X_57,additive_inverse(add(X_57,X))) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(additive_inverse(X_57)),additive_inverse(add(X_57,X))),add(additive_inverse(additive_inverse(X_57)),additive_inverse(add(X_57,X)))) ),[1,0],$fot(X_57)]]) ).
cnf(refute_0_76,plain,
( additive_inverse(additive_inverse(X_57)) != X_57
| add(additive_inverse(additive_inverse(X_57)),additive_inverse(add(X_57,X))) = add(X_57,additive_inverse(add(X_57,X))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(additive_inverse(X_57)),additive_inverse(add(X_57,X))),add(additive_inverse(additive_inverse(X_57)),additive_inverse(add(X_57,X)))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
add(additive_inverse(additive_inverse(X_57)),additive_inverse(add(X_57,X))) = add(X_57,additive_inverse(add(X_57,X))),
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(X_57)),X_57) )],[refute_0_73,refute_0_76]) ).
cnf(refute_0_78,plain,
add(additive_inverse(add(X_57,X)),additive_inverse(additive_inverse(X_57))) = add(additive_inverse(additive_inverse(X_57)),additive_inverse(add(X_57,X))),
inference(subst,[],[refute_0_7:[bind(X,$fot(additive_inverse(additive_inverse(X_57)))),bind(Y,$fot(additive_inverse(add(X_57,X))))]]) ).
cnf(refute_0_79,plain,
( add(additive_inverse(add(X_57,X)),additive_inverse(additive_inverse(X_57))) != add(additive_inverse(additive_inverse(X_57)),additive_inverse(add(X_57,X)))
| add(additive_inverse(additive_inverse(X_57)),additive_inverse(add(X_57,X))) != add(X_57,additive_inverse(add(X_57,X)))
| add(additive_inverse(add(X_57,X)),additive_inverse(additive_inverse(X_57))) = add(X_57,additive_inverse(add(X_57,X))) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(add(additive_inverse(add(X_57,X)),additive_inverse(additive_inverse(X_57))))),bind(Y0,$fot(add(additive_inverse(additive_inverse(X_57)),additive_inverse(add(X_57,X))))),bind(Z0,$fot(add(X_57,additive_inverse(add(X_57,X)))))]]) ).
cnf(refute_0_80,plain,
( add(additive_inverse(additive_inverse(X_57)),additive_inverse(add(X_57,X))) != add(X_57,additive_inverse(add(X_57,X)))
| add(additive_inverse(add(X_57,X)),additive_inverse(additive_inverse(X_57))) = add(X_57,additive_inverse(add(X_57,X))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(add(X_57,X)),additive_inverse(additive_inverse(X_57))),add(additive_inverse(additive_inverse(X_57)),additive_inverse(add(X_57,X)))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
add(additive_inverse(add(X_57,X)),additive_inverse(additive_inverse(X_57))) = add(X_57,additive_inverse(add(X_57,X))),
inference(resolve,[$cnf( $equal(add(additive_inverse(additive_inverse(X_57)),additive_inverse(add(X_57,X))),add(X_57,additive_inverse(add(X_57,X)))) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
( add(additive_inverse(add(X_57,X)),additive_inverse(additive_inverse(X_57))) != add(X_57,additive_inverse(add(X_57,X)))
| additive_inverse(X) != add(additive_inverse(add(X_57,X)),additive_inverse(additive_inverse(X_57)))
| additive_inverse(X) = add(X_57,additive_inverse(add(X_57,X))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(X),add(additive_inverse(add(X_57,X)),additive_inverse(additive_inverse(X_57)))) ),[1],$fot(add(X_57,additive_inverse(add(X_57,X))))]]) ).
cnf(refute_0_83,plain,
( additive_inverse(X) != add(additive_inverse(add(X_57,X)),additive_inverse(additive_inverse(X_57)))
| additive_inverse(X) = add(X_57,additive_inverse(add(X_57,X))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(add(X_57,X)),additive_inverse(additive_inverse(X_57))),add(X_57,additive_inverse(add(X_57,X)))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
additive_inverse(X) = add(X_57,additive_inverse(add(X_57,X))),
inference(resolve,[$cnf( $equal(additive_inverse(X),add(additive_inverse(add(X_57,X)),additive_inverse(additive_inverse(X_57)))) )],[refute_0_72,refute_0_83]) ).
cnf(refute_0_85,plain,
additive_inverse(commutator(X,Y)) = add(multiply(X,Y),additive_inverse(add(multiply(X,Y),commutator(X,Y)))),
inference(subst,[],[refute_0_84:[bind(X,$fot(commutator(X,Y))),bind(X_57,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_86,plain,
add(X_39,add(additive_inverse(X_39),X_40)) = X_40,
inference(subst,[],[refute_0_26:[bind(X_36,$fot(X_39)),bind(X_38,$fot(X_40))]]) ).
cnf(refute_0_87,plain,
add(X_40,additive_inverse(X_39)) = add(additive_inverse(X_39),X_40),
inference(subst,[],[commutativity_for_addition:[bind(X,$fot(X_40)),bind(Y,$fot(additive_inverse(X_39)))]]) ).
cnf(refute_0_88,plain,
( add(X_40,additive_inverse(X_39)) != add(additive_inverse(X_39),X_40)
| add(additive_inverse(X_39),X_40) = add(X_40,additive_inverse(X_39)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_40,additive_inverse(X_39)))),bind(Y0,$fot(add(additive_inverse(X_39),X_40)))]]) ).
cnf(refute_0_89,plain,
add(additive_inverse(X_39),X_40) = add(X_40,additive_inverse(X_39)),
inference(resolve,[$cnf( $equal(add(X_40,additive_inverse(X_39)),add(additive_inverse(X_39),X_40)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( add(X_39,add(additive_inverse(X_39),X_40)) != X_40
| add(additive_inverse(X_39),X_40) != add(X_40,additive_inverse(X_39))
| add(X_39,add(X_40,additive_inverse(X_39))) = X_40 ),
introduced(tautology,[equality,[$cnf( $equal(add(X_39,add(additive_inverse(X_39),X_40)),X_40) ),[0,1],$fot(add(X_40,additive_inverse(X_39)))]]) ).
cnf(refute_0_91,plain,
( add(X_39,add(additive_inverse(X_39),X_40)) != X_40
| add(X_39,add(X_40,additive_inverse(X_39))) = X_40 ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_39),X_40),add(X_40,additive_inverse(X_39))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
add(X_39,add(X_40,additive_inverse(X_39))) = X_40,
inference(resolve,[$cnf( $equal(add(X_39,add(additive_inverse(X_39),X_40)),X_40) )],[refute_0_86,refute_0_91]) ).
cnf(refute_0_93,plain,
add(multiply(X,Y),add(multiply(Y,X),additive_inverse(multiply(X,Y)))) = multiply(Y,X),
inference(subst,[],[refute_0_92:[bind(X_39,$fot(multiply(X,Y))),bind(X_40,$fot(multiply(Y,X)))]]) ).
cnf(refute_0_94,plain,
( commutator(X,Y) != add(multiply(Y,X),additive_inverse(multiply(X,Y)))
| add(multiply(Y,X),additive_inverse(multiply(X,Y))) = commutator(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(commutator(X,Y))),bind(Y0,$fot(add(multiply(Y,X),additive_inverse(multiply(X,Y)))))]]) ).
cnf(refute_0_95,plain,
add(multiply(Y,X),additive_inverse(multiply(X,Y))) = commutator(X,Y),
inference(resolve,[$cnf( $equal(commutator(X,Y),add(multiply(Y,X),additive_inverse(multiply(X,Y)))) )],[commutator,refute_0_94]) ).
cnf(refute_0_96,plain,
( add(multiply(X,Y),add(multiply(Y,X),additive_inverse(multiply(X,Y)))) != multiply(Y,X)
| add(multiply(Y,X),additive_inverse(multiply(X,Y))) != commutator(X,Y)
| add(multiply(X,Y),commutator(X,Y)) = multiply(Y,X) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,Y),add(multiply(Y,X),additive_inverse(multiply(X,Y)))),multiply(Y,X)) ),[0,1],$fot(commutator(X,Y))]]) ).
cnf(refute_0_97,plain,
( add(multiply(X,Y),add(multiply(Y,X),additive_inverse(multiply(X,Y)))) != multiply(Y,X)
| add(multiply(X,Y),commutator(X,Y)) = multiply(Y,X) ),
inference(resolve,[$cnf( $equal(add(multiply(Y,X),additive_inverse(multiply(X,Y))),commutator(X,Y)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
add(multiply(X,Y),commutator(X,Y)) = multiply(Y,X),
inference(resolve,[$cnf( $equal(add(multiply(X,Y),add(multiply(Y,X),additive_inverse(multiply(X,Y)))),multiply(Y,X)) )],[refute_0_93,refute_0_97]) ).
cnf(refute_0_99,plain,
( add(multiply(X,Y),commutator(X,Y)) != multiply(Y,X)
| additive_inverse(commutator(X,Y)) != add(multiply(X,Y),additive_inverse(add(multiply(X,Y),commutator(X,Y))))
| additive_inverse(commutator(X,Y)) = add(multiply(X,Y),additive_inverse(multiply(Y,X))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(commutator(X,Y)),add(multiply(X,Y),additive_inverse(add(multiply(X,Y),commutator(X,Y))))) ),[1,1,0],$fot(multiply(Y,X))]]) ).
cnf(refute_0_100,plain,
( additive_inverse(commutator(X,Y)) != add(multiply(X,Y),additive_inverse(add(multiply(X,Y),commutator(X,Y))))
| additive_inverse(commutator(X,Y)) = add(multiply(X,Y),additive_inverse(multiply(Y,X))) ),
inference(resolve,[$cnf( $equal(add(multiply(X,Y),commutator(X,Y)),multiply(Y,X)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
additive_inverse(commutator(X,Y)) = add(multiply(X,Y),additive_inverse(multiply(Y,X))),
inference(resolve,[$cnf( $equal(additive_inverse(commutator(X,Y)),add(multiply(X,Y),additive_inverse(add(multiply(X,Y),commutator(X,Y))))) )],[refute_0_85,refute_0_100]) ).
cnf(refute_0_102,plain,
add(multiply(X,Y),additive_inverse(multiply(Y,X))) = commutator(Y,X),
inference(subst,[],[refute_0_95:[bind(X,$fot(Y)),bind(Y,$fot(X))]]) ).
cnf(refute_0_103,plain,
( add(multiply(X,Y),additive_inverse(multiply(Y,X))) != commutator(Y,X)
| additive_inverse(commutator(X,Y)) != add(multiply(X,Y),additive_inverse(multiply(Y,X)))
| additive_inverse(commutator(X,Y)) = commutator(Y,X) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(commutator(X,Y)),add(multiply(X,Y),additive_inverse(multiply(Y,X)))) ),[1],$fot(commutator(Y,X))]]) ).
cnf(refute_0_104,plain,
( additive_inverse(commutator(X,Y)) != add(multiply(X,Y),additive_inverse(multiply(Y,X)))
| additive_inverse(commutator(X,Y)) = commutator(Y,X) ),
inference(resolve,[$cnf( $equal(add(multiply(X,Y),additive_inverse(multiply(Y,X))),commutator(Y,X)) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
additive_inverse(commutator(X,Y)) = commutator(Y,X),
inference(resolve,[$cnf( $equal(additive_inverse(commutator(X,Y)),add(multiply(X,Y),additive_inverse(multiply(Y,X)))) )],[refute_0_101,refute_0_104]) ).
cnf(refute_0_106,plain,
additive_inverse(commutator(X_61,X_62)) = commutator(X_62,X_61),
inference(subst,[],[refute_0_105:[bind(X,$fot(X_61)),bind(Y,$fot(X_62))]]) ).
cnf(refute_0_107,plain,
( add(commutator(X_61,X_62),add(additive_inverse(commutator(X_61,X_62)),X_38)) != X_38
| additive_inverse(commutator(X_61,X_62)) != commutator(X_62,X_61)
| add(commutator(X_61,X_62),add(commutator(X_62,X_61),X_38)) = X_38 ),
introduced(tautology,[equality,[$cnf( $equal(add(commutator(X_61,X_62),add(additive_inverse(commutator(X_61,X_62)),X_38)),X_38) ),[0,1,0],$fot(commutator(X_62,X_61))]]) ).
cnf(refute_0_108,plain,
( add(commutator(X_61,X_62),add(additive_inverse(commutator(X_61,X_62)),X_38)) != X_38
| add(commutator(X_61,X_62),add(commutator(X_62,X_61),X_38)) = X_38 ),
inference(resolve,[$cnf( $equal(additive_inverse(commutator(X_61,X_62)),commutator(X_62,X_61)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
add(commutator(X_61,X_62),add(commutator(X_62,X_61),X_38)) = X_38,
inference(resolve,[$cnf( $equal(add(commutator(X_61,X_62),add(additive_inverse(commutator(X_61,X_62)),X_38)),X_38) )],[refute_0_65,refute_0_108]) ).
cnf(refute_0_110,plain,
add(commutator(X_61,X_62),add(commutator(X_62,X_61),multiply(X_61,additive_inverse(X_62)))) = multiply(X_61,additive_inverse(X_62)),
inference(subst,[],[refute_0_109:[bind(X_38,$fot(multiply(X_61,additive_inverse(X_62))))]]) ).
cnf(refute_0_111,plain,
add(multiply(X_45,X_46),add(multiply(X_45,X_47),Z)) = add(add(multiply(X_45,X_46),multiply(X_45,X_47)),Z),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(multiply(X_45,X_46))),bind(Y,$fot(multiply(X_45,X_47)))]]) ).
cnf(refute_0_112,plain,
multiply(X_45,add(X_46,X_47)) = add(multiply(X_45,X_46),multiply(X_45,X_47)),
inference(subst,[],[distribute1:[bind(X,$fot(X_45)),bind(Y,$fot(X_46)),bind(Z,$fot(X_47))]]) ).
cnf(refute_0_113,plain,
( multiply(X_45,add(X_46,X_47)) != add(multiply(X_45,X_46),multiply(X_45,X_47))
| add(multiply(X_45,X_46),multiply(X_45,X_47)) = multiply(X_45,add(X_46,X_47)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X_45,add(X_46,X_47)))),bind(Y0,$fot(add(multiply(X_45,X_46),multiply(X_45,X_47))))]]) ).
cnf(refute_0_114,plain,
add(multiply(X_45,X_46),multiply(X_45,X_47)) = multiply(X_45,add(X_46,X_47)),
inference(resolve,[$cnf( $equal(multiply(X_45,add(X_46,X_47)),add(multiply(X_45,X_46),multiply(X_45,X_47))) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
( add(multiply(X_45,X_46),multiply(X_45,X_47)) != multiply(X_45,add(X_46,X_47))
| add(multiply(X_45,X_46),add(multiply(X_45,X_47),Z)) != add(add(multiply(X_45,X_46),multiply(X_45,X_47)),Z)
| add(multiply(X_45,X_46),add(multiply(X_45,X_47),Z)) = add(multiply(X_45,add(X_46,X_47)),Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_45,X_46),add(multiply(X_45,X_47),Z)),add(add(multiply(X_45,X_46),multiply(X_45,X_47)),Z)) ),[1,0],$fot(multiply(X_45,add(X_46,X_47)))]]) ).
cnf(refute_0_116,plain,
( add(multiply(X_45,X_46),add(multiply(X_45,X_47),Z)) != add(add(multiply(X_45,X_46),multiply(X_45,X_47)),Z)
| add(multiply(X_45,X_46),add(multiply(X_45,X_47),Z)) = add(multiply(X_45,add(X_46,X_47)),Z) ),
inference(resolve,[$cnf( $equal(add(multiply(X_45,X_46),multiply(X_45,X_47)),multiply(X_45,add(X_46,X_47))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
add(multiply(X_45,X_46),add(multiply(X_45,X_47),Z)) = add(multiply(X_45,add(X_46,X_47)),Z),
inference(resolve,[$cnf( $equal(add(multiply(X_45,X_46),add(multiply(X_45,X_47),Z)),add(add(multiply(X_45,X_46),multiply(X_45,X_47)),Z)) )],[refute_0_111,refute_0_116]) ).
cnf(refute_0_118,plain,
add(multiply(X_774,X_775),add(multiply(X_774,X_776),additive_inverse(multiply(X_776,X_774)))) = add(multiply(X_774,add(X_775,X_776)),additive_inverse(multiply(X_776,X_774))),
inference(subst,[],[refute_0_117:[bind(Z,$fot(additive_inverse(multiply(X_776,X_774)))),bind(X_45,$fot(X_774)),bind(X_46,$fot(X_775)),bind(X_47,$fot(X_776))]]) ).
cnf(refute_0_119,plain,
commutator(X_776,X_774) = add(multiply(X_774,X_776),additive_inverse(multiply(X_776,X_774))),
inference(subst,[],[commutator:[bind(X,$fot(X_776)),bind(Y,$fot(X_774))]]) ).
cnf(refute_0_120,plain,
( commutator(X_776,X_774) != add(multiply(X_774,X_776),additive_inverse(multiply(X_776,X_774)))
| add(multiply(X_774,X_776),additive_inverse(multiply(X_776,X_774))) = commutator(X_776,X_774) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(commutator(X_776,X_774))),bind(Y0,$fot(add(multiply(X_774,X_776),additive_inverse(multiply(X_776,X_774)))))]]) ).
cnf(refute_0_121,plain,
add(multiply(X_774,X_776),additive_inverse(multiply(X_776,X_774))) = commutator(X_776,X_774),
inference(resolve,[$cnf( $equal(commutator(X_776,X_774),add(multiply(X_774,X_776),additive_inverse(multiply(X_776,X_774)))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
( add(multiply(X_774,X_775),add(multiply(X_774,X_776),additive_inverse(multiply(X_776,X_774)))) != add(multiply(X_774,add(X_775,X_776)),additive_inverse(multiply(X_776,X_774)))
| add(multiply(X_774,X_776),additive_inverse(multiply(X_776,X_774))) != commutator(X_776,X_774)
| add(multiply(X_774,X_775),commutator(X_776,X_774)) = add(multiply(X_774,add(X_775,X_776)),additive_inverse(multiply(X_776,X_774))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_774,X_775),add(multiply(X_774,X_776),additive_inverse(multiply(X_776,X_774)))),add(multiply(X_774,add(X_775,X_776)),additive_inverse(multiply(X_776,X_774)))) ),[0,1],$fot(commutator(X_776,X_774))]]) ).
cnf(refute_0_123,plain,
( add(multiply(X_774,X_775),add(multiply(X_774,X_776),additive_inverse(multiply(X_776,X_774)))) != add(multiply(X_774,add(X_775,X_776)),additive_inverse(multiply(X_776,X_774)))
| add(multiply(X_774,X_775),commutator(X_776,X_774)) = add(multiply(X_774,add(X_775,X_776)),additive_inverse(multiply(X_776,X_774))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_774,X_776),additive_inverse(multiply(X_776,X_774))),commutator(X_776,X_774)) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
add(multiply(X_774,X_775),commutator(X_776,X_774)) = add(multiply(X_774,add(X_775,X_776)),additive_inverse(multiply(X_776,X_774))),
inference(resolve,[$cnf( $equal(add(multiply(X_774,X_775),add(multiply(X_774,X_776),additive_inverse(multiply(X_776,X_774)))),add(multiply(X_774,add(X_775,X_776)),additive_inverse(multiply(X_776,X_774)))) )],[refute_0_118,refute_0_123]) ).
cnf(refute_0_125,plain,
add(X_36,add(X_37,X_38)) = add(add(X_36,X_37),X_38),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_126,plain,
add(X_38,X_37) = add(X_37,X_38),
inference(subst,[],[commutativity_for_addition:[bind(X,$fot(X_38)),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_127,plain,
( add(X_38,X_37) != add(X_37,X_38)
| add(X_37,X_38) = add(X_38,X_37) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_38,X_37))),bind(Y0,$fot(add(X_37,X_38)))]]) ).
cnf(refute_0_128,plain,
add(X_37,X_38) = add(X_38,X_37),
inference(resolve,[$cnf( $equal(add(X_38,X_37),add(X_37,X_38)) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
( add(X_36,add(X_37,X_38)) != add(add(X_36,X_37),X_38)
| add(X_37,X_38) != add(X_38,X_37)
| add(X_36,add(X_38,X_37)) = add(add(X_36,X_37),X_38) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_36,add(X_37,X_38)),add(add(X_36,X_37),X_38)) ),[0,1],$fot(add(X_38,X_37))]]) ).
cnf(refute_0_130,plain,
( add(X_36,add(X_37,X_38)) != add(add(X_36,X_37),X_38)
| add(X_36,add(X_38,X_37)) = add(add(X_36,X_37),X_38) ),
inference(resolve,[$cnf( $equal(add(X_37,X_38),add(X_38,X_37)) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
add(X_36,add(X_38,X_37)) = add(add(X_36,X_37),X_38),
inference(resolve,[$cnf( $equal(add(X_36,add(X_37,X_38)),add(add(X_36,X_37),X_38)) )],[refute_0_125,refute_0_130]) ).
cnf(refute_0_132,plain,
( add(X,add(Y,Z)) != add(add(X,Y),Z)
| add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X,add(Y,Z)))),bind(Y0,$fot(add(add(X,Y),Z)))]]) ).
cnf(refute_0_133,plain,
add(add(X,Y),Z) = add(X,add(Y,Z)),
inference(resolve,[$cnf( $equal(add(X,add(Y,Z)),add(add(X,Y),Z)) )],[associativity_for_addition,refute_0_132]) ).
cnf(refute_0_134,plain,
add(add(X_36,X_37),X_38) = add(X_36,add(X_37,X_38)),
inference(subst,[],[refute_0_133:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_135,plain,
( add(X_36,add(X_38,X_37)) != add(add(X_36,X_37),X_38)
| add(add(X_36,X_37),X_38) != add(X_36,add(X_37,X_38))
| add(X_36,add(X_38,X_37)) = add(X_36,add(X_37,X_38)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_36,add(X_38,X_37)),add(X_36,add(X_37,X_38))) ),[0],$fot(add(add(X_36,X_37),X_38))]]) ).
cnf(refute_0_136,plain,
( add(X_36,add(X_38,X_37)) != add(add(X_36,X_37),X_38)
| add(X_36,add(X_38,X_37)) = add(X_36,add(X_37,X_38)) ),
inference(resolve,[$cnf( $equal(add(add(X_36,X_37),X_38),add(X_36,add(X_37,X_38))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
add(X_36,add(X_38,X_37)) = add(X_36,add(X_37,X_38)),
inference(resolve,[$cnf( $equal(add(X_36,add(X_38,X_37)),add(add(X_36,X_37),X_38)) )],[refute_0_131,refute_0_136]) ).
cnf(refute_0_138,plain,
add(multiply(X_774,X_775),add(X_38,multiply(X_774,X_776))) = add(multiply(X_774,X_775),add(multiply(X_774,X_776),X_38)),
inference(subst,[],[refute_0_137:[bind(X_36,$fot(multiply(X_774,X_775))),bind(X_37,$fot(multiply(X_774,X_776)))]]) ).
cnf(refute_0_139,plain,
add(multiply(X_774,X_775),add(multiply(X_774,X_776),X_38)) = add(multiply(X_774,add(X_775,X_776)),X_38),
inference(subst,[],[refute_0_117:[bind(Z,$fot(X_38)),bind(X_45,$fot(X_774)),bind(X_46,$fot(X_775)),bind(X_47,$fot(X_776))]]) ).
cnf(refute_0_140,plain,
( add(multiply(X_774,X_775),add(X_38,multiply(X_774,X_776))) != add(multiply(X_774,X_775),add(multiply(X_774,X_776),X_38))
| add(multiply(X_774,X_775),add(multiply(X_774,X_776),X_38)) != add(multiply(X_774,add(X_775,X_776)),X_38)
| add(multiply(X_774,X_775),add(X_38,multiply(X_774,X_776))) = add(multiply(X_774,add(X_775,X_776)),X_38) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(multiply(X_774,X_775),add(X_38,multiply(X_774,X_776))),add(multiply(X_774,add(X_775,X_776)),X_38)) ),[0],$fot(add(multiply(X_774,X_775),add(multiply(X_774,X_776),X_38)))]]) ).
cnf(refute_0_141,plain,
( add(multiply(X_774,X_775),add(X_38,multiply(X_774,X_776))) != add(multiply(X_774,X_775),add(multiply(X_774,X_776),X_38))
| add(multiply(X_774,X_775),add(X_38,multiply(X_774,X_776))) = add(multiply(X_774,add(X_775,X_776)),X_38) ),
inference(resolve,[$cnf( $equal(add(multiply(X_774,X_775),add(multiply(X_774,X_776),X_38)),add(multiply(X_774,add(X_775,X_776)),X_38)) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
add(multiply(X_774,X_775),add(X_38,multiply(X_774,X_776))) = add(multiply(X_774,add(X_775,X_776)),X_38),
inference(resolve,[$cnf( $equal(add(multiply(X_774,X_775),add(X_38,multiply(X_774,X_776))),add(multiply(X_774,X_775),add(multiply(X_774,X_776),X_38))) )],[refute_0_138,refute_0_141]) ).
cnf(refute_0_143,plain,
add(X,add(X_36,X_37)) = add(add(X_36,X_37),X),
inference(subst,[],[commutativity_for_addition:[bind(Y,$fot(add(X_36,X_37)))]]) ).
cnf(refute_0_144,plain,
add(X_36,add(X_37,X)) = add(add(X_36,X_37),X),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(X_36)),bind(Y,$fot(X_37)),bind(Z,$fot(X))]]) ).
cnf(refute_0_145,plain,
( add(X_36,add(X_37,X)) != add(add(X_36,X_37),X)
| add(add(X_36,X_37),X) = add(X_36,add(X_37,X)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_36,add(X_37,X)))),bind(Y0,$fot(add(add(X_36,X_37),X)))]]) ).
cnf(refute_0_146,plain,
add(add(X_36,X_37),X) = add(X_36,add(X_37,X)),
inference(resolve,[$cnf( $equal(add(X_36,add(X_37,X)),add(add(X_36,X_37),X)) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
( add(X,add(X_36,X_37)) != add(add(X_36,X_37),X)
| add(add(X_36,X_37),X) != add(X_36,add(X_37,X))
| add(X,add(X_36,X_37)) = add(X_36,add(X_37,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X,add(X_36,X_37)),add(X_36,add(X_37,X))) ),[0],$fot(add(add(X_36,X_37),X))]]) ).
cnf(refute_0_148,plain,
( add(X,add(X_36,X_37)) != add(add(X_36,X_37),X)
| add(X,add(X_36,X_37)) = add(X_36,add(X_37,X)) ),
inference(resolve,[$cnf( $equal(add(add(X_36,X_37),X),add(X_36,add(X_37,X))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
add(X,add(X_36,X_37)) = add(X_36,add(X_37,X)),
inference(resolve,[$cnf( $equal(add(X,add(X_36,X_37)),add(add(X_36,X_37),X)) )],[refute_0_143,refute_0_148]) ).
cnf(refute_0_150,plain,
add(multiply(X,Z),add(X_142,multiply(X,Y))) = add(X_142,add(multiply(X,Y),multiply(X,Z))),
inference(subst,[],[refute_0_149:[bind(X,$fot(multiply(X,Z))),bind(X_36,$fot(X_142)),bind(X_37,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_151,plain,
( multiply(X,add(Y,Z)) != add(multiply(X,Y),multiply(X,Z))
| add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(multiply(X,add(Y,Z)))),bind(Y0,$fot(add(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_152,plain,
add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,add(Y,Z)),add(multiply(X,Y),multiply(X,Z))) )],[distribute1,refute_0_151]) ).
cnf(refute_0_153,plain,
( add(multiply(X,Y),multiply(X,Z)) != multiply(X,add(Y,Z))
| add(multiply(X,Z),add(X_142,multiply(X,Y))) != add(X_142,add(multiply(X,Y),multiply(X,Z)))
| add(multiply(X,Z),add(X_142,multiply(X,Y))) = add(X_142,multiply(X,add(Y,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,Z),add(X_142,multiply(X,Y))),add(X_142,add(multiply(X,Y),multiply(X,Z)))) ),[1,1],$fot(multiply(X,add(Y,Z)))]]) ).
cnf(refute_0_154,plain,
( add(multiply(X,Z),add(X_142,multiply(X,Y))) != add(X_142,add(multiply(X,Y),multiply(X,Z)))
| add(multiply(X,Z),add(X_142,multiply(X,Y))) = add(X_142,multiply(X,add(Y,Z))) ),
inference(resolve,[$cnf( $equal(add(multiply(X,Y),multiply(X,Z)),multiply(X,add(Y,Z))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
add(multiply(X,Z),add(X_142,multiply(X,Y))) = add(X_142,multiply(X,add(Y,Z))),
inference(resolve,[$cnf( $equal(add(multiply(X,Z),add(X_142,multiply(X,Y))),add(X_142,add(multiply(X,Y),multiply(X,Z)))) )],[refute_0_150,refute_0_154]) ).
cnf(refute_0_156,plain,
add(multiply(X_774,X_775),add(X_38,multiply(X_774,X_776))) = add(X_38,multiply(X_774,add(X_776,X_775))),
inference(subst,[],[refute_0_155:[bind(X,$fot(X_774)),bind(Y,$fot(X_776)),bind(Z,$fot(X_775)),bind(X_142,$fot(X_38))]]) ).
cnf(refute_0_157,plain,
( add(multiply(X_774,X_775),add(X_38,multiply(X_774,X_776))) != add(X_38,multiply(X_774,add(X_776,X_775)))
| add(multiply(X_774,X_775),add(X_38,multiply(X_774,X_776))) != add(multiply(X_774,add(X_775,X_776)),X_38)
| add(X_38,multiply(X_774,add(X_776,X_775))) = add(multiply(X_774,add(X_775,X_776)),X_38) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_774,X_775),add(X_38,multiply(X_774,X_776))),add(multiply(X_774,add(X_775,X_776)),X_38)) ),[0],$fot(add(X_38,multiply(X_774,add(X_776,X_775))))]]) ).
cnf(refute_0_158,plain,
( add(multiply(X_774,X_775),add(X_38,multiply(X_774,X_776))) != add(multiply(X_774,add(X_775,X_776)),X_38)
| add(X_38,multiply(X_774,add(X_776,X_775))) = add(multiply(X_774,add(X_775,X_776)),X_38) ),
inference(resolve,[$cnf( $equal(add(multiply(X_774,X_775),add(X_38,multiply(X_774,X_776))),add(X_38,multiply(X_774,add(X_776,X_775)))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
add(X_38,multiply(X_774,add(X_776,X_775))) = add(multiply(X_774,add(X_775,X_776)),X_38),
inference(resolve,[$cnf( $equal(add(multiply(X_774,X_775),add(X_38,multiply(X_774,X_776))),add(multiply(X_774,add(X_775,X_776)),X_38)) )],[refute_0_142,refute_0_158]) ).
cnf(refute_0_160,plain,
( add(X_38,multiply(X_774,add(X_776,X_775))) != add(multiply(X_774,add(X_775,X_776)),X_38)
| add(multiply(X_774,add(X_775,X_776)),X_38) = add(X_38,multiply(X_774,add(X_776,X_775))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_38,multiply(X_774,add(X_776,X_775))))),bind(Y0,$fot(add(multiply(X_774,add(X_775,X_776)),X_38)))]]) ).
cnf(refute_0_161,plain,
add(multiply(X_774,add(X_775,X_776)),X_38) = add(X_38,multiply(X_774,add(X_776,X_775))),
inference(resolve,[$cnf( $equal(add(X_38,multiply(X_774,add(X_776,X_775))),add(multiply(X_774,add(X_775,X_776)),X_38)) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
add(multiply(X_774,add(X_775,X_776)),additive_inverse(multiply(X_776,X_774))) = add(additive_inverse(multiply(X_776,X_774)),multiply(X_774,add(X_776,X_775))),
inference(subst,[],[refute_0_161:[bind(X_38,$fot(additive_inverse(multiply(X_776,X_774))))]]) ).
cnf(refute_0_163,plain,
( add(multiply(X_774,X_775),commutator(X_776,X_774)) != add(multiply(X_774,add(X_775,X_776)),additive_inverse(multiply(X_776,X_774)))
| add(multiply(X_774,add(X_775,X_776)),additive_inverse(multiply(X_776,X_774))) != add(additive_inverse(multiply(X_776,X_774)),multiply(X_774,add(X_776,X_775)))
| add(multiply(X_774,X_775),commutator(X_776,X_774)) = add(additive_inverse(multiply(X_776,X_774)),multiply(X_774,add(X_776,X_775))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(multiply(X_774,X_775),commutator(X_776,X_774)),add(additive_inverse(multiply(X_776,X_774)),multiply(X_774,add(X_776,X_775)))) ),[0],$fot(add(multiply(X_774,add(X_775,X_776)),additive_inverse(multiply(X_776,X_774))))]]) ).
cnf(refute_0_164,plain,
( add(multiply(X_774,X_775),commutator(X_776,X_774)) != add(multiply(X_774,add(X_775,X_776)),additive_inverse(multiply(X_776,X_774)))
| add(multiply(X_774,X_775),commutator(X_776,X_774)) = add(additive_inverse(multiply(X_776,X_774)),multiply(X_774,add(X_776,X_775))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_774,add(X_775,X_776)),additive_inverse(multiply(X_776,X_774))),add(additive_inverse(multiply(X_776,X_774)),multiply(X_774,add(X_776,X_775)))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
add(multiply(X_774,X_775),commutator(X_776,X_774)) = add(additive_inverse(multiply(X_776,X_774)),multiply(X_774,add(X_776,X_775))),
inference(resolve,[$cnf( $equal(add(multiply(X_774,X_775),commutator(X_776,X_774)),add(multiply(X_774,add(X_775,X_776)),additive_inverse(multiply(X_776,X_774)))) )],[refute_0_124,refute_0_164]) ).
cnf(refute_0_166,plain,
add(multiply(X_798,additive_inverse(X_800)),commutator(X_800,X_798)) = add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,add(X_800,additive_inverse(X_800)))),
inference(subst,[],[refute_0_165:[bind(X_774,$fot(X_798)),bind(X_775,$fot(additive_inverse(X_800))),bind(X_776,$fot(X_800))]]) ).
cnf(refute_0_167,plain,
add(X_800,additive_inverse(X_800)) = additive_identity,
inference(subst,[],[right_additive_inverse:[bind(X,$fot(X_800))]]) ).
cnf(refute_0_168,plain,
( add(X_800,additive_inverse(X_800)) != additive_identity
| add(multiply(X_798,additive_inverse(X_800)),commutator(X_800,X_798)) != add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,add(X_800,additive_inverse(X_800))))
| add(multiply(X_798,additive_inverse(X_800)),commutator(X_800,X_798)) = add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_798,additive_inverse(X_800)),commutator(X_800,X_798)),add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,add(X_800,additive_inverse(X_800))))) ),[1,1,1],$fot(additive_identity)]]) ).
cnf(refute_0_169,plain,
( add(multiply(X_798,additive_inverse(X_800)),commutator(X_800,X_798)) != add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,add(X_800,additive_inverse(X_800))))
| add(multiply(X_798,additive_inverse(X_800)),commutator(X_800,X_798)) = add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity)) ),
inference(resolve,[$cnf( $equal(add(X_800,additive_inverse(X_800)),additive_identity) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
add(multiply(X_798,additive_inverse(X_800)),commutator(X_800,X_798)) = add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(X_798,additive_inverse(X_800)),commutator(X_800,X_798)),add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,add(X_800,additive_inverse(X_800))))) )],[refute_0_166,refute_0_169]) ).
cnf(refute_0_171,plain,
add(X,add(add(X_42,additive_inverse(X)),Z)) = add(add(X,add(X_42,additive_inverse(X))),Z),
inference(subst,[],[associativity_for_addition:[bind(Y,$fot(add(X_42,additive_inverse(X))))]]) ).
cnf(refute_0_172,plain,
add(X,add(X_42,additive_inverse(X))) = X_42,
inference(subst,[],[refute_0_92:[bind(X_39,$fot(X)),bind(X_40,$fot(X_42))]]) ).
cnf(refute_0_173,plain,
( add(X,add(X_42,additive_inverse(X))) != X_42
| add(X,add(add(X_42,additive_inverse(X)),Z)) != add(add(X,add(X_42,additive_inverse(X))),Z)
| add(X,add(add(X_42,additive_inverse(X)),Z)) = add(X_42,Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,add(add(X_42,additive_inverse(X)),Z)),add(add(X,add(X_42,additive_inverse(X))),Z)) ),[1,0],$fot(X_42)]]) ).
cnf(refute_0_174,plain,
( add(X,add(add(X_42,additive_inverse(X)),Z)) != add(add(X,add(X_42,additive_inverse(X))),Z)
| add(X,add(add(X_42,additive_inverse(X)),Z)) = add(X_42,Z) ),
inference(resolve,[$cnf( $equal(add(X,add(X_42,additive_inverse(X))),X_42) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
add(X,add(add(X_42,additive_inverse(X)),Z)) = add(X_42,Z),
inference(resolve,[$cnf( $equal(add(X,add(add(X_42,additive_inverse(X)),Z)),add(add(X,add(X_42,additive_inverse(X))),Z)) )],[refute_0_171,refute_0_174]) ).
cnf(refute_0_176,plain,
add(add(X_42,additive_inverse(X)),Z) = add(X_42,add(additive_inverse(X),Z)),
inference(subst,[],[refute_0_133:[bind(X,$fot(X_42)),bind(Y,$fot(additive_inverse(X)))]]) ).
cnf(refute_0_177,plain,
add(X,add(add(X_42,additive_inverse(X)),Z)) = add(X,add(add(X_42,additive_inverse(X)),Z)),
introduced(tautology,[refl,[$fot(add(X,add(add(X_42,additive_inverse(X)),Z)))]]) ).
cnf(refute_0_178,plain,
( add(X,add(add(X_42,additive_inverse(X)),Z)) != add(X,add(add(X_42,additive_inverse(X)),Z))
| add(add(X_42,additive_inverse(X)),Z) != add(X_42,add(additive_inverse(X),Z))
| add(X,add(add(X_42,additive_inverse(X)),Z)) = add(X,add(X_42,add(additive_inverse(X),Z))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,add(add(X_42,additive_inverse(X)),Z)),add(X,add(add(X_42,additive_inverse(X)),Z))) ),[1,1],$fot(add(X_42,add(additive_inverse(X),Z)))]]) ).
cnf(refute_0_179,plain,
( add(add(X_42,additive_inverse(X)),Z) != add(X_42,add(additive_inverse(X),Z))
| add(X,add(add(X_42,additive_inverse(X)),Z)) = add(X,add(X_42,add(additive_inverse(X),Z))) ),
inference(resolve,[$cnf( $equal(add(X,add(add(X_42,additive_inverse(X)),Z)),add(X,add(add(X_42,additive_inverse(X)),Z))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
add(X,add(add(X_42,additive_inverse(X)),Z)) = add(X,add(X_42,add(additive_inverse(X),Z))),
inference(resolve,[$cnf( $equal(add(add(X_42,additive_inverse(X)),Z),add(X_42,add(additive_inverse(X),Z))) )],[refute_0_176,refute_0_179]) ).
cnf(refute_0_181,plain,
( add(X,add(add(X_42,additive_inverse(X)),Z)) != add(X,add(X_42,add(additive_inverse(X),Z)))
| add(X,add(add(X_42,additive_inverse(X)),Z)) != add(X_42,Z)
| add(X,add(X_42,add(additive_inverse(X),Z))) = add(X_42,Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,add(add(X_42,additive_inverse(X)),Z)),add(X_42,Z)) ),[0],$fot(add(X,add(X_42,add(additive_inverse(X),Z))))]]) ).
cnf(refute_0_182,plain,
( add(X,add(add(X_42,additive_inverse(X)),Z)) != add(X_42,Z)
| add(X,add(X_42,add(additive_inverse(X),Z))) = add(X_42,Z) ),
inference(resolve,[$cnf( $equal(add(X,add(add(X_42,additive_inverse(X)),Z)),add(X,add(X_42,add(additive_inverse(X),Z)))) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
add(X,add(X_42,add(additive_inverse(X),Z))) = add(X_42,Z),
inference(resolve,[$cnf( $equal(add(X,add(add(X_42,additive_inverse(X)),Z)),add(X_42,Z)) )],[refute_0_175,refute_0_182]) ).
cnf(refute_0_184,plain,
add(add(X_149,X_148),add(X_289,add(additive_inverse(add(X_149,X_148)),X_288))) = add(X_289,X_288),
inference(subst,[],[refute_0_183:[bind(X,$fot(add(X_149,X_148))),bind(Z,$fot(X_288)),bind(X_42,$fot(X_289))]]) ).
cnf(refute_0_185,plain,
additive_inverse(add(X_148,X_149)) = add(X_57,additive_inverse(add(X_57,add(X_148,X_149)))),
inference(subst,[],[refute_0_84:[bind(X,$fot(add(X_148,X_149)))]]) ).
cnf(refute_0_186,plain,
add(X_37,X_36) = add(X_36,X_37),
inference(subst,[],[commutativity_for_addition:[bind(X,$fot(X_37)),bind(Y,$fot(X_36))]]) ).
cnf(refute_0_187,plain,
( add(X_37,X_36) != add(X_36,X_37)
| add(X_36,X_37) = add(X_37,X_36) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_37,X_36))),bind(Y0,$fot(add(X_36,X_37)))]]) ).
cnf(refute_0_188,plain,
add(X_36,X_37) = add(X_37,X_36),
inference(resolve,[$cnf( $equal(add(X_37,X_36),add(X_36,X_37)) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
( add(X_36,X_37) != add(X_37,X_36)
| add(X_36,add(X_37,X_38)) != add(add(X_36,X_37),X_38)
| add(X_36,add(X_37,X_38)) = add(add(X_37,X_36),X_38) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_36,add(X_37,X_38)),add(add(X_36,X_37),X_38)) ),[1,0],$fot(add(X_37,X_36))]]) ).
cnf(refute_0_190,plain,
( add(X_36,add(X_37,X_38)) != add(add(X_36,X_37),X_38)
| add(X_36,add(X_37,X_38)) = add(add(X_37,X_36),X_38) ),
inference(resolve,[$cnf( $equal(add(X_36,X_37),add(X_37,X_36)) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
add(X_36,add(X_37,X_38)) = add(add(X_37,X_36),X_38),
inference(resolve,[$cnf( $equal(add(X_36,add(X_37,X_38)),add(add(X_36,X_37),X_38)) )],[refute_0_125,refute_0_190]) ).
cnf(refute_0_192,plain,
add(add(X_37,X_36),X_38) = add(X_37,add(X_36,X_38)),
inference(subst,[],[refute_0_133:[bind(X,$fot(X_37)),bind(Y,$fot(X_36)),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_193,plain,
( add(X_36,add(X_37,X_38)) != add(add(X_37,X_36),X_38)
| add(add(X_37,X_36),X_38) != add(X_37,add(X_36,X_38))
| add(X_36,add(X_37,X_38)) = add(X_37,add(X_36,X_38)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_36,add(X_37,X_38)),add(X_37,add(X_36,X_38))) ),[0],$fot(add(add(X_37,X_36),X_38))]]) ).
cnf(refute_0_194,plain,
( add(X_36,add(X_37,X_38)) != add(add(X_37,X_36),X_38)
| add(X_36,add(X_37,X_38)) = add(X_37,add(X_36,X_38)) ),
inference(resolve,[$cnf( $equal(add(add(X_37,X_36),X_38),add(X_37,add(X_36,X_38))) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
add(X_36,add(X_37,X_38)) = add(X_37,add(X_36,X_38)),
inference(resolve,[$cnf( $equal(add(X_36,add(X_37,X_38)),add(add(X_37,X_36),X_38)) )],[refute_0_191,refute_0_194]) ).
cnf(refute_0_196,plain,
add(X_57,add(X_148,X_149)) = add(X_148,add(X_57,X_149)),
inference(subst,[],[refute_0_195:[bind(X_36,$fot(X_57)),bind(X_37,$fot(X_148)),bind(X_38,$fot(X_149))]]) ).
cnf(refute_0_197,plain,
( add(X_57,add(X_148,X_149)) != add(X_148,add(X_57,X_149))
| additive_inverse(add(X_148,X_149)) != add(X_57,additive_inverse(add(X_57,add(X_148,X_149))))
| additive_inverse(add(X_148,X_149)) = add(X_57,additive_inverse(add(X_148,add(X_57,X_149)))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(X_148,X_149)),add(X_57,additive_inverse(add(X_57,add(X_148,X_149))))) ),[1,1,0],$fot(add(X_148,add(X_57,X_149)))]]) ).
cnf(refute_0_198,plain,
( additive_inverse(add(X_148,X_149)) != add(X_57,additive_inverse(add(X_57,add(X_148,X_149))))
| additive_inverse(add(X_148,X_149)) = add(X_57,additive_inverse(add(X_148,add(X_57,X_149)))) ),
inference(resolve,[$cnf( $equal(add(X_57,add(X_148,X_149)),add(X_148,add(X_57,X_149))) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
additive_inverse(add(X_148,X_149)) = add(X_57,additive_inverse(add(X_148,add(X_57,X_149)))),
inference(resolve,[$cnf( $equal(additive_inverse(add(X_148,X_149)),add(X_57,additive_inverse(add(X_57,add(X_148,X_149))))) )],[refute_0_185,refute_0_198]) ).
cnf(refute_0_200,plain,
additive_inverse(add(X_143,X_141)) = add(X_57,additive_inverse(add(X_57,add(X_143,X_141)))),
inference(subst,[],[refute_0_84:[bind(X,$fot(add(X_143,X_141)))]]) ).
cnf(refute_0_201,plain,
add(X_141,add(X_57,X_143)) = add(X_57,add(X_143,X_141)),
inference(subst,[],[refute_0_149:[bind(X,$fot(X_141)),bind(X_36,$fot(X_57)),bind(X_37,$fot(X_143))]]) ).
cnf(refute_0_202,plain,
( add(X_141,add(X_57,X_143)) != add(X_57,add(X_143,X_141))
| add(X_57,add(X_143,X_141)) = add(X_141,add(X_57,X_143)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_141,add(X_57,X_143)))),bind(Y0,$fot(add(X_57,add(X_143,X_141))))]]) ).
cnf(refute_0_203,plain,
add(X_57,add(X_143,X_141)) = add(X_141,add(X_57,X_143)),
inference(resolve,[$cnf( $equal(add(X_141,add(X_57,X_143)),add(X_57,add(X_143,X_141))) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
( add(X_57,add(X_143,X_141)) != add(X_141,add(X_57,X_143))
| additive_inverse(add(X_143,X_141)) != add(X_57,additive_inverse(add(X_57,add(X_143,X_141))))
| additive_inverse(add(X_143,X_141)) = add(X_57,additive_inverse(add(X_141,add(X_57,X_143)))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(X_143,X_141)),add(X_57,additive_inverse(add(X_57,add(X_143,X_141))))) ),[1,1,0],$fot(add(X_141,add(X_57,X_143)))]]) ).
cnf(refute_0_205,plain,
( additive_inverse(add(X_143,X_141)) != add(X_57,additive_inverse(add(X_57,add(X_143,X_141))))
| additive_inverse(add(X_143,X_141)) = add(X_57,additive_inverse(add(X_141,add(X_57,X_143)))) ),
inference(resolve,[$cnf( $equal(add(X_57,add(X_143,X_141)),add(X_141,add(X_57,X_143))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
additive_inverse(add(X_143,X_141)) = add(X_57,additive_inverse(add(X_141,add(X_57,X_143)))),
inference(resolve,[$cnf( $equal(additive_inverse(add(X_143,X_141)),add(X_57,additive_inverse(add(X_57,add(X_143,X_141))))) )],[refute_0_200,refute_0_205]) ).
cnf(refute_0_207,plain,
( additive_inverse(add(X_143,X_141)) != add(X_57,additive_inverse(add(X_141,add(X_57,X_143))))
| add(X_57,additive_inverse(add(X_141,add(X_57,X_143)))) = additive_inverse(add(X_143,X_141)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(additive_inverse(add(X_143,X_141)))),bind(Y0,$fot(add(X_57,additive_inverse(add(X_141,add(X_57,X_143))))))]]) ).
cnf(refute_0_208,plain,
add(X_57,additive_inverse(add(X_141,add(X_57,X_143)))) = additive_inverse(add(X_143,X_141)),
inference(resolve,[$cnf( $equal(additive_inverse(add(X_143,X_141)),add(X_57,additive_inverse(add(X_141,add(X_57,X_143))))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
add(X_57,additive_inverse(add(X_148,add(X_57,X_149)))) = additive_inverse(add(X_149,X_148)),
inference(subst,[],[refute_0_208:[bind(X_141,$fot(X_148)),bind(X_143,$fot(X_149))]]) ).
cnf(refute_0_210,plain,
( add(X_57,additive_inverse(add(X_148,add(X_57,X_149)))) != additive_inverse(add(X_149,X_148))
| additive_inverse(add(X_148,X_149)) != add(X_57,additive_inverse(add(X_148,add(X_57,X_149))))
| additive_inverse(add(X_148,X_149)) = additive_inverse(add(X_149,X_148)) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(X_148,X_149)),add(X_57,additive_inverse(add(X_148,add(X_57,X_149))))) ),[1],$fot(additive_inverse(add(X_149,X_148)))]]) ).
cnf(refute_0_211,plain,
( additive_inverse(add(X_148,X_149)) != add(X_57,additive_inverse(add(X_148,add(X_57,X_149))))
| additive_inverse(add(X_148,X_149)) = additive_inverse(add(X_149,X_148)) ),
inference(resolve,[$cnf( $equal(add(X_57,additive_inverse(add(X_148,add(X_57,X_149)))),additive_inverse(add(X_149,X_148))) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
additive_inverse(add(X_148,X_149)) = additive_inverse(add(X_149,X_148)),
inference(resolve,[$cnf( $equal(additive_inverse(add(X_148,X_149)),add(X_57,additive_inverse(add(X_148,add(X_57,X_149))))) )],[refute_0_199,refute_0_211]) ).
cnf(refute_0_213,plain,
( additive_inverse(add(X_148,X_149)) != additive_inverse(add(X_149,X_148))
| additive_inverse(add(X_149,X_148)) = additive_inverse(add(X_148,X_149)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(additive_inverse(add(X_148,X_149)))),bind(Y0,$fot(additive_inverse(add(X_149,X_148))))]]) ).
cnf(refute_0_214,plain,
additive_inverse(add(X_149,X_148)) = additive_inverse(add(X_148,X_149)),
inference(resolve,[$cnf( $equal(additive_inverse(add(X_148,X_149)),additive_inverse(add(X_149,X_148))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
( add(add(X_149,X_148),add(X_289,add(additive_inverse(add(X_149,X_148)),X_288))) != add(X_289,X_288)
| additive_inverse(add(X_149,X_148)) != additive_inverse(add(X_148,X_149))
| add(add(X_149,X_148),add(X_289,add(additive_inverse(add(X_148,X_149)),X_288))) = add(X_289,X_288) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_149,X_148),add(X_289,add(additive_inverse(add(X_149,X_148)),X_288))),add(X_289,X_288)) ),[0,1,1,0],$fot(additive_inverse(add(X_148,X_149)))]]) ).
cnf(refute_0_216,plain,
( add(add(X_149,X_148),add(X_289,add(additive_inverse(add(X_149,X_148)),X_288))) != add(X_289,X_288)
| add(add(X_149,X_148),add(X_289,add(additive_inverse(add(X_148,X_149)),X_288))) = add(X_289,X_288) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(X_149,X_148)),additive_inverse(add(X_148,X_149))) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
add(add(X_149,X_148),add(X_289,add(additive_inverse(add(X_148,X_149)),X_288))) = add(X_289,X_288),
inference(resolve,[$cnf( $equal(add(add(X_149,X_148),add(X_289,add(additive_inverse(add(X_149,X_148)),X_288))),add(X_289,X_288)) )],[refute_0_184,refute_0_216]) ).
cnf(refute_0_218,plain,
add(add(X_149,X_148),add(X_289,add(additive_inverse(add(X_148,X_149)),X_288))) = add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))),
inference(subst,[],[refute_0_133:[bind(X,$fot(X_149)),bind(Y,$fot(X_148)),bind(Z,$fot(add(X_289,add(additive_inverse(add(X_148,X_149)),X_288))))]]) ).
cnf(refute_0_219,plain,
( add(add(X_149,X_148),add(X_289,add(additive_inverse(add(X_148,X_149)),X_288))) != add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288))))
| add(add(X_149,X_148),add(X_289,add(additive_inverse(add(X_148,X_149)),X_288))) != add(X_289,X_288)
| add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))) = add(X_289,X_288) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_149,X_148),add(X_289,add(additive_inverse(add(X_148,X_149)),X_288))),add(X_289,X_288)) ),[0],$fot(add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))))]]) ).
cnf(refute_0_220,plain,
( add(add(X_149,X_148),add(X_289,add(additive_inverse(add(X_148,X_149)),X_288))) != add(X_289,X_288)
| add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))) = add(X_289,X_288) ),
inference(resolve,[$cnf( $equal(add(add(X_149,X_148),add(X_289,add(additive_inverse(add(X_148,X_149)),X_288))),add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288))))) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))) = add(X_289,X_288),
inference(resolve,[$cnf( $equal(add(add(X_149,X_148),add(X_289,add(additive_inverse(add(X_148,X_149)),X_288))),add(X_289,X_288)) )],[refute_0_217,refute_0_220]) ).
cnf(refute_0_222,plain,
add(X_41,add(add(X,Y),additive_inverse(X_41))) = add(X,Y),
inference(subst,[],[refute_0_92:[bind(X_39,$fot(X_41)),bind(X_40,$fot(add(X,Y)))]]) ).
cnf(refute_0_223,plain,
add(X,add(Y,additive_inverse(X_41))) = add(add(X,Y),additive_inverse(X_41)),
inference(subst,[],[associativity_for_addition:[bind(Z,$fot(additive_inverse(X_41)))]]) ).
cnf(refute_0_224,plain,
( add(X,add(Y,additive_inverse(X_41))) != add(add(X,Y),additive_inverse(X_41))
| add(add(X,Y),additive_inverse(X_41)) = add(X,add(Y,additive_inverse(X_41))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X,add(Y,additive_inverse(X_41))))),bind(Y0,$fot(add(add(X,Y),additive_inverse(X_41))))]]) ).
cnf(refute_0_225,plain,
add(add(X,Y),additive_inverse(X_41)) = add(X,add(Y,additive_inverse(X_41))),
inference(resolve,[$cnf( $equal(add(X,add(Y,additive_inverse(X_41))),add(add(X,Y),additive_inverse(X_41))) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
( add(X_41,add(add(X,Y),additive_inverse(X_41))) != add(X,Y)
| add(add(X,Y),additive_inverse(X_41)) != add(X,add(Y,additive_inverse(X_41)))
| add(X_41,add(X,add(Y,additive_inverse(X_41)))) = add(X,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_41,add(add(X,Y),additive_inverse(X_41))),add(X,Y)) ),[0,1],$fot(add(X,add(Y,additive_inverse(X_41))))]]) ).
cnf(refute_0_227,plain,
( add(X_41,add(add(X,Y),additive_inverse(X_41))) != add(X,Y)
| add(X_41,add(X,add(Y,additive_inverse(X_41)))) = add(X,Y) ),
inference(resolve,[$cnf( $equal(add(add(X,Y),additive_inverse(X_41)),add(X,add(Y,additive_inverse(X_41)))) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
add(X_41,add(X,add(Y,additive_inverse(X_41)))) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X_41,add(add(X,Y),additive_inverse(X_41))),add(X,Y)) )],[refute_0_222,refute_0_227]) ).
cnf(refute_0_229,plain,
add(X_149,add(X_288,add(X_289,additive_inverse(X_149)))) = add(X_288,X_289),
inference(subst,[],[refute_0_228:[bind(X,$fot(X_288)),bind(Y,$fot(X_289)),bind(X_41,$fot(X_149))]]) ).
cnf(refute_0_230,plain,
add(X,add(X_36,add(X_370,additive_inverse(add(X_36,X_369))))) = add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X)),
inference(subst,[],[refute_0_149:[bind(X_37,$fot(add(X_370,additive_inverse(add(X_36,X_369)))))]]) ).
cnf(refute_0_231,plain,
add(additive_inverse(add(X_143,X)),add(X_142,X_143)) = add(X_142,add(X_143,additive_inverse(add(X_143,X)))),
inference(subst,[],[refute_0_149:[bind(X,$fot(additive_inverse(add(X_143,X)))),bind(X_36,$fot(X_142)),bind(X_37,$fot(X_143))]]) ).
cnf(refute_0_232,plain,
additive_inverse(X) = add(X_143,additive_inverse(add(X_143,X))),
inference(subst,[],[refute_0_84:[bind(X_57,$fot(X_143))]]) ).
cnf(refute_0_233,plain,
( additive_inverse(X) != add(X_143,additive_inverse(add(X_143,X)))
| add(X_143,additive_inverse(add(X_143,X))) = additive_inverse(X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(additive_inverse(X))),bind(Y0,$fot(add(X_143,additive_inverse(add(X_143,X)))))]]) ).
cnf(refute_0_234,plain,
add(X_143,additive_inverse(add(X_143,X))) = additive_inverse(X),
inference(resolve,[$cnf( $equal(additive_inverse(X),add(X_143,additive_inverse(add(X_143,X)))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
( add(X_143,additive_inverse(add(X_143,X))) != additive_inverse(X)
| add(additive_inverse(add(X_143,X)),add(X_142,X_143)) != add(X_142,add(X_143,additive_inverse(add(X_143,X))))
| add(additive_inverse(add(X_143,X)),add(X_142,X_143)) = add(X_142,additive_inverse(X)) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(add(X_143,X)),add(X_142,X_143)),add(X_142,add(X_143,additive_inverse(add(X_143,X))))) ),[1,1],$fot(additive_inverse(X))]]) ).
cnf(refute_0_236,plain,
( add(additive_inverse(add(X_143,X)),add(X_142,X_143)) != add(X_142,add(X_143,additive_inverse(add(X_143,X))))
| add(additive_inverse(add(X_143,X)),add(X_142,X_143)) = add(X_142,additive_inverse(X)) ),
inference(resolve,[$cnf( $equal(add(X_143,additive_inverse(add(X_143,X))),additive_inverse(X)) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
add(additive_inverse(add(X_143,X)),add(X_142,X_143)) = add(X_142,additive_inverse(X)),
inference(resolve,[$cnf( $equal(add(additive_inverse(add(X_143,X)),add(X_142,X_143)),add(X_142,add(X_143,additive_inverse(add(X_143,X))))) )],[refute_0_231,refute_0_236]) ).
cnf(refute_0_238,plain,
add(X_141,add(X_142,X_143)) = add(X_142,add(X_143,X_141)),
inference(subst,[],[refute_0_149:[bind(X,$fot(X_141)),bind(X_36,$fot(X_142)),bind(X_37,$fot(X_143))]]) ).
cnf(refute_0_239,plain,
add(X_143,X_142) = add(X_142,X_143),
inference(subst,[],[commutativity_for_addition:[bind(X,$fot(X_143)),bind(Y,$fot(X_142))]]) ).
cnf(refute_0_240,plain,
( add(X_143,X_142) != add(X_142,X_143)
| add(X_142,X_143) = add(X_143,X_142) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_143,X_142))),bind(Y0,$fot(add(X_142,X_143)))]]) ).
cnf(refute_0_241,plain,
add(X_142,X_143) = add(X_143,X_142),
inference(resolve,[$cnf( $equal(add(X_143,X_142),add(X_142,X_143)) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
( add(X_141,add(X_142,X_143)) != add(X_142,add(X_143,X_141))
| add(X_142,X_143) != add(X_143,X_142)
| add(X_141,add(X_143,X_142)) = add(X_142,add(X_143,X_141)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_141,add(X_142,X_143)),add(X_142,add(X_143,X_141))) ),[0,1],$fot(add(X_143,X_142))]]) ).
cnf(refute_0_243,plain,
( add(X_141,add(X_142,X_143)) != add(X_142,add(X_143,X_141))
| add(X_141,add(X_143,X_142)) = add(X_142,add(X_143,X_141)) ),
inference(resolve,[$cnf( $equal(add(X_142,X_143),add(X_143,X_142)) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
add(X_141,add(X_143,X_142)) = add(X_142,add(X_143,X_141)),
inference(resolve,[$cnf( $equal(add(X_141,add(X_142,X_143)),add(X_142,add(X_143,X_141))) )],[refute_0_238,refute_0_243]) ).
cnf(refute_0_245,plain,
( add(X_141,add(X_143,X_142)) != add(X_142,add(X_143,X_141))
| add(X_142,add(X_143,X_141)) = add(X_141,add(X_143,X_142)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_141,add(X_143,X_142)))),bind(Y0,$fot(add(X_142,add(X_143,X_141))))]]) ).
cnf(refute_0_246,plain,
add(X_142,add(X_143,X_141)) = add(X_141,add(X_143,X_142)),
inference(resolve,[$cnf( $equal(add(X_141,add(X_143,X_142)),add(X_142,add(X_143,X_141))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
add(additive_inverse(add(X_143,X)),add(X_142,X_143)) = add(X_143,add(X_142,additive_inverse(add(X_143,X)))),
inference(subst,[],[refute_0_246:[bind(X_141,$fot(X_143)),bind(X_142,$fot(additive_inverse(add(X_143,X)))),bind(X_143,$fot(X_142))]]) ).
cnf(refute_0_248,plain,
( add(additive_inverse(add(X_143,X)),add(X_142,X_143)) != add(X_142,additive_inverse(X))
| add(additive_inverse(add(X_143,X)),add(X_142,X_143)) != add(X_143,add(X_142,additive_inverse(add(X_143,X))))
| add(X_143,add(X_142,additive_inverse(add(X_143,X)))) = add(X_142,additive_inverse(X)) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(add(X_143,X)),add(X_142,X_143)),add(X_142,additive_inverse(X))) ),[0],$fot(add(X_143,add(X_142,additive_inverse(add(X_143,X)))))]]) ).
cnf(refute_0_249,plain,
( add(additive_inverse(add(X_143,X)),add(X_142,X_143)) != add(X_142,additive_inverse(X))
| add(X_143,add(X_142,additive_inverse(add(X_143,X)))) = add(X_142,additive_inverse(X)) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(add(X_143,X)),add(X_142,X_143)),add(X_143,add(X_142,additive_inverse(add(X_143,X))))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
add(X_143,add(X_142,additive_inverse(add(X_143,X)))) = add(X_142,additive_inverse(X)),
inference(resolve,[$cnf( $equal(add(additive_inverse(add(X_143,X)),add(X_142,X_143)),add(X_142,additive_inverse(X))) )],[refute_0_237,refute_0_249]) ).
cnf(refute_0_251,plain,
add(X_36,add(X_370,additive_inverse(add(X_36,X_369)))) = add(X_370,additive_inverse(X_369)),
inference(subst,[],[refute_0_250:[bind(X,$fot(X_369)),bind(X_142,$fot(X_370)),bind(X_143,$fot(X_36))]]) ).
cnf(refute_0_252,plain,
( add(X,add(X_36,add(X_370,additive_inverse(add(X_36,X_369))))) != add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X))
| add(X_36,add(X_370,additive_inverse(add(X_36,X_369)))) != add(X_370,additive_inverse(X_369))
| add(X,add(X_370,additive_inverse(X_369))) = add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,add(X_36,add(X_370,additive_inverse(add(X_36,X_369))))),add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X))) ),[0,1],$fot(add(X_370,additive_inverse(X_369)))]]) ).
cnf(refute_0_253,plain,
( add(X,add(X_36,add(X_370,additive_inverse(add(X_36,X_369))))) != add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X))
| add(X,add(X_370,additive_inverse(X_369))) = add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X)) ),
inference(resolve,[$cnf( $equal(add(X_36,add(X_370,additive_inverse(add(X_36,X_369)))),add(X_370,additive_inverse(X_369))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
add(X,add(X_370,additive_inverse(X_369))) = add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X)),
inference(resolve,[$cnf( $equal(add(X,add(X_36,add(X_370,additive_inverse(add(X_36,X_369))))),add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X))) )],[refute_0_230,refute_0_253]) ).
cnf(refute_0_255,plain,
add(add(X_370,additive_inverse(add(X_36,X_369))),X) = add(X_370,add(additive_inverse(add(X_36,X_369)),X)),
inference(subst,[],[refute_0_133:[bind(X,$fot(X_370)),bind(Y,$fot(additive_inverse(add(X_36,X_369)))),bind(Z,$fot(X))]]) ).
cnf(refute_0_256,plain,
add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X)) = add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X)),
introduced(tautology,[refl,[$fot(add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X)))]]) ).
cnf(refute_0_257,plain,
( add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X)) != add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X))
| add(add(X_370,additive_inverse(add(X_36,X_369))),X) != add(X_370,add(additive_inverse(add(X_36,X_369)),X))
| add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X)) = add(X_36,add(X_370,add(additive_inverse(add(X_36,X_369)),X))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X)),add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X))) ),[1,1],$fot(add(X_370,add(additive_inverse(add(X_36,X_369)),X)))]]) ).
cnf(refute_0_258,plain,
( add(add(X_370,additive_inverse(add(X_36,X_369))),X) != add(X_370,add(additive_inverse(add(X_36,X_369)),X))
| add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X)) = add(X_36,add(X_370,add(additive_inverse(add(X_36,X_369)),X))) ),
inference(resolve,[$cnf( $equal(add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X)),add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X))) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X)) = add(X_36,add(X_370,add(additive_inverse(add(X_36,X_369)),X))),
inference(resolve,[$cnf( $equal(add(add(X_370,additive_inverse(add(X_36,X_369))),X),add(X_370,add(additive_inverse(add(X_36,X_369)),X))) )],[refute_0_255,refute_0_258]) ).
cnf(refute_0_260,plain,
( add(X,add(X_370,additive_inverse(X_369))) != add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X))
| add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X)) != add(X_36,add(X_370,add(additive_inverse(add(X_36,X_369)),X)))
| add(X,add(X_370,additive_inverse(X_369))) = add(X_36,add(X_370,add(additive_inverse(add(X_36,X_369)),X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X,add(X_370,additive_inverse(X_369))),add(X_36,add(X_370,add(additive_inverse(add(X_36,X_369)),X)))) ),[0],$fot(add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X)))]]) ).
cnf(refute_0_261,plain,
( add(X,add(X_370,additive_inverse(X_369))) != add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X))
| add(X,add(X_370,additive_inverse(X_369))) = add(X_36,add(X_370,add(additive_inverse(add(X_36,X_369)),X))) ),
inference(resolve,[$cnf( $equal(add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X)),add(X_36,add(X_370,add(additive_inverse(add(X_36,X_369)),X)))) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
add(X,add(X_370,additive_inverse(X_369))) = add(X_36,add(X_370,add(additive_inverse(add(X_36,X_369)),X))),
inference(resolve,[$cnf( $equal(add(X,add(X_370,additive_inverse(X_369))),add(X_36,add(add(X_370,additive_inverse(add(X_36,X_369))),X))) )],[refute_0_254,refute_0_261]) ).
cnf(refute_0_263,plain,
( add(X,add(X_370,additive_inverse(X_369))) != add(X_36,add(X_370,add(additive_inverse(add(X_36,X_369)),X)))
| add(X_36,add(X_370,add(additive_inverse(add(X_36,X_369)),X))) = add(X,add(X_370,additive_inverse(X_369))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X,add(X_370,additive_inverse(X_369))))),bind(Y0,$fot(add(X_36,add(X_370,add(additive_inverse(add(X_36,X_369)),X)))))]]) ).
cnf(refute_0_264,plain,
add(X_36,add(X_370,add(additive_inverse(add(X_36,X_369)),X))) = add(X,add(X_370,additive_inverse(X_369))),
inference(resolve,[$cnf( $equal(add(X,add(X_370,additive_inverse(X_369))),add(X_36,add(X_370,add(additive_inverse(add(X_36,X_369)),X)))) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288))) = add(X_288,add(X_289,additive_inverse(X_149))),
inference(subst,[],[refute_0_264:[bind(X,$fot(X_288)),bind(X_36,$fot(X_148)),bind(X_369,$fot(X_149)),bind(X_370,$fot(X_289))]]) ).
cnf(refute_0_266,plain,
add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))) = add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))),
introduced(tautology,[refl,[$fot(add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))))]]) ).
cnf(refute_0_267,plain,
( add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288))) != add(X_288,add(X_289,additive_inverse(X_149)))
| add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))) != add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288))))
| add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))) = add(X_149,add(X_288,add(X_289,additive_inverse(X_149)))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))),add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288))))) ),[1,1],$fot(add(X_288,add(X_289,additive_inverse(X_149))))]]) ).
cnf(refute_0_268,plain,
( add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288))) != add(X_288,add(X_289,additive_inverse(X_149)))
| add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))) = add(X_149,add(X_288,add(X_289,additive_inverse(X_149)))) ),
inference(resolve,[$cnf( $equal(add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))),add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288))))) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))) = add(X_149,add(X_288,add(X_289,additive_inverse(X_149)))),
inference(resolve,[$cnf( $equal(add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288))),add(X_288,add(X_289,additive_inverse(X_149)))) )],[refute_0_265,refute_0_268]) ).
cnf(refute_0_270,plain,
( add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))) != add(X_149,add(X_288,add(X_289,additive_inverse(X_149))))
| add(X_149,add(X_288,add(X_289,additive_inverse(X_149)))) != add(X_288,X_289)
| add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))) = add(X_288,X_289) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))))),bind(Y0,$fot(add(X_149,add(X_288,add(X_289,additive_inverse(X_149)))))),bind(Z0,$fot(add(X_288,X_289)))]]) ).
cnf(refute_0_271,plain,
( add(X_149,add(X_288,add(X_289,additive_inverse(X_149)))) != add(X_288,X_289)
| add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))) = add(X_288,X_289) ),
inference(resolve,[$cnf( $equal(add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))),add(X_149,add(X_288,add(X_289,additive_inverse(X_149))))) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))) = add(X_288,X_289),
inference(resolve,[$cnf( $equal(add(X_149,add(X_288,add(X_289,additive_inverse(X_149)))),add(X_288,X_289)) )],[refute_0_229,refute_0_271]) ).
cnf(refute_0_273,plain,
( add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))) != add(X_288,X_289)
| add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))) != add(X_289,X_288)
| add(X_288,X_289) = add(X_289,X_288) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))),add(X_289,X_288)) ),[0],$fot(add(X_288,X_289))]]) ).
cnf(refute_0_274,plain,
( add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))) != add(X_289,X_288)
| add(X_288,X_289) = add(X_289,X_288) ),
inference(resolve,[$cnf( $equal(add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))),add(X_288,X_289)) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
add(X_288,X_289) = add(X_289,X_288),
inference(resolve,[$cnf( $equal(add(X_149,add(X_148,add(X_289,add(additive_inverse(add(X_148,X_149)),X_288)))),add(X_289,X_288)) )],[refute_0_221,refute_0_274]) ).
cnf(refute_0_276,plain,
( add(X_288,X_289) != add(X_289,X_288)
| add(X_289,X_288) = add(X_288,X_289) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(add(X_288,X_289))),bind(Y0,$fot(add(X_289,X_288)))]]) ).
cnf(refute_0_277,plain,
add(X_289,X_288) = add(X_288,X_289),
inference(resolve,[$cnf( $equal(add(X_288,X_289),add(X_289,X_288)) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
add(multiply(X_798,additive_inverse(X_800)),commutator(X_800,X_798)) = add(commutator(X_800,X_798),multiply(X_798,additive_inverse(X_800))),
inference(subst,[],[refute_0_277:[bind(X_288,$fot(commutator(X_800,X_798))),bind(X_289,$fot(multiply(X_798,additive_inverse(X_800))))]]) ).
cnf(refute_0_279,plain,
( add(multiply(X_798,additive_inverse(X_800)),commutator(X_800,X_798)) != add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity))
| add(multiply(X_798,additive_inverse(X_800)),commutator(X_800,X_798)) != add(commutator(X_800,X_798),multiply(X_798,additive_inverse(X_800)))
| add(commutator(X_800,X_798),multiply(X_798,additive_inverse(X_800))) = add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_798,additive_inverse(X_800)),commutator(X_800,X_798)),add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity))) ),[0],$fot(add(commutator(X_800,X_798),multiply(X_798,additive_inverse(X_800))))]]) ).
cnf(refute_0_280,plain,
( add(multiply(X_798,additive_inverse(X_800)),commutator(X_800,X_798)) != add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity))
| add(commutator(X_800,X_798),multiply(X_798,additive_inverse(X_800))) = add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_798,additive_inverse(X_800)),commutator(X_800,X_798)),add(commutator(X_800,X_798),multiply(X_798,additive_inverse(X_800)))) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
add(additive_identity,additive_inverse(multiply(X_800,X_798))) = additive_inverse(multiply(X_800,X_798)),
inference(subst,[],[left_additive_identity:[bind(X,$fot(additive_inverse(multiply(X_800,X_798))))]]) ).
cnf(refute_0_282,plain,
multiply(X_798,additive_identity) = additive_identity,
inference(subst,[],[right_multiplicative_zero:[bind(X,$fot(X_798))]]) ).
cnf(refute_0_283,plain,
add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798))) = add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798))),
introduced(tautology,[refl,[$fot(add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798))))]]) ).
cnf(refute_0_284,plain,
( multiply(X_798,additive_identity) != additive_identity
| add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798))) != add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798)))
| add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798))) = add(additive_identity,additive_inverse(multiply(X_800,X_798))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798))),add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798)))) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_285,plain,
( multiply(X_798,additive_identity) != additive_identity
| add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798))) = add(additive_identity,additive_inverse(multiply(X_800,X_798))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798))),add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798)))) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798))) = add(additive_identity,additive_inverse(multiply(X_800,X_798))),
inference(resolve,[$cnf( $equal(multiply(X_798,additive_identity),additive_identity) )],[refute_0_282,refute_0_285]) ).
cnf(refute_0_287,plain,
( add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798))) != add(additive_identity,additive_inverse(multiply(X_800,X_798)))
| add(additive_identity,additive_inverse(multiply(X_800,X_798))) != additive_inverse(multiply(X_800,X_798))
| add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798))) = additive_inverse(multiply(X_800,X_798)) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798))))),bind(Y0,$fot(add(additive_identity,additive_inverse(multiply(X_800,X_798))))),bind(Z0,$fot(additive_inverse(multiply(X_800,X_798))))]]) ).
cnf(refute_0_288,plain,
( add(additive_identity,additive_inverse(multiply(X_800,X_798))) != additive_inverse(multiply(X_800,X_798))
| add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798))) = additive_inverse(multiply(X_800,X_798)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798))),add(additive_identity,additive_inverse(multiply(X_800,X_798)))) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798))) = additive_inverse(multiply(X_800,X_798)),
inference(resolve,[$cnf( $equal(add(additive_identity,additive_inverse(multiply(X_800,X_798))),additive_inverse(multiply(X_800,X_798))) )],[refute_0_281,refute_0_288]) ).
cnf(refute_0_290,plain,
add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity)) = add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798))),
inference(subst,[],[refute_0_277:[bind(X_288,$fot(multiply(X_798,additive_identity))),bind(X_289,$fot(additive_inverse(multiply(X_800,X_798))))]]) ).
cnf(refute_0_291,plain,
( add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798))) != additive_inverse(multiply(X_800,X_798))
| add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity)) != add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798)))
| add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity)) = additive_inverse(multiply(X_800,X_798)) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity)))),bind(Y0,$fot(add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798))))),bind(Z0,$fot(additive_inverse(multiply(X_800,X_798))))]]) ).
cnf(refute_0_292,plain,
( add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798))) != additive_inverse(multiply(X_800,X_798))
| add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity)) = additive_inverse(multiply(X_800,X_798)) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity)),add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798)))) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity)) = additive_inverse(multiply(X_800,X_798)),
inference(resolve,[$cnf( $equal(add(multiply(X_798,additive_identity),additive_inverse(multiply(X_800,X_798))),additive_inverse(multiply(X_800,X_798))) )],[refute_0_289,refute_0_292]) ).
cnf(refute_0_294,plain,
( add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity)) != additive_inverse(multiply(X_800,X_798))
| add(commutator(X_800,X_798),multiply(X_798,additive_inverse(X_800))) != add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity))
| add(commutator(X_800,X_798),multiply(X_798,additive_inverse(X_800))) = additive_inverse(multiply(X_800,X_798)) ),
introduced(tautology,[equality,[$cnf( $equal(add(commutator(X_800,X_798),multiply(X_798,additive_inverse(X_800))),add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity))) ),[1],$fot(additive_inverse(multiply(X_800,X_798)))]]) ).
cnf(refute_0_295,plain,
( add(commutator(X_800,X_798),multiply(X_798,additive_inverse(X_800))) != add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity))
| add(commutator(X_800,X_798),multiply(X_798,additive_inverse(X_800))) = additive_inverse(multiply(X_800,X_798)) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity)),additive_inverse(multiply(X_800,X_798))) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
( add(multiply(X_798,additive_inverse(X_800)),commutator(X_800,X_798)) != add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity))
| add(commutator(X_800,X_798),multiply(X_798,additive_inverse(X_800))) = additive_inverse(multiply(X_800,X_798)) ),
inference(resolve,[$cnf( $equal(add(commutator(X_800,X_798),multiply(X_798,additive_inverse(X_800))),add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity))) )],[refute_0_280,refute_0_295]) ).
cnf(refute_0_297,plain,
add(commutator(X_800,X_798),multiply(X_798,additive_inverse(X_800))) = additive_inverse(multiply(X_800,X_798)),
inference(resolve,[$cnf( $equal(add(multiply(X_798,additive_inverse(X_800)),commutator(X_800,X_798)),add(additive_inverse(multiply(X_800,X_798)),multiply(X_798,additive_identity))) )],[refute_0_170,refute_0_296]) ).
cnf(refute_0_298,plain,
add(commutator(X_62,X_61),multiply(X_61,additive_inverse(X_62))) = additive_inverse(multiply(X_62,X_61)),
inference(subst,[],[refute_0_297:[bind(X_798,$fot(X_61)),bind(X_800,$fot(X_62))]]) ).
cnf(refute_0_299,plain,
( add(commutator(X_61,X_62),add(commutator(X_62,X_61),multiply(X_61,additive_inverse(X_62)))) != multiply(X_61,additive_inverse(X_62))
| add(commutator(X_62,X_61),multiply(X_61,additive_inverse(X_62))) != additive_inverse(multiply(X_62,X_61))
| add(commutator(X_61,X_62),additive_inverse(multiply(X_62,X_61))) = multiply(X_61,additive_inverse(X_62)) ),
introduced(tautology,[equality,[$cnf( $equal(add(commutator(X_61,X_62),add(commutator(X_62,X_61),multiply(X_61,additive_inverse(X_62)))),multiply(X_61,additive_inverse(X_62))) ),[0,1],$fot(additive_inverse(multiply(X_62,X_61)))]]) ).
cnf(refute_0_300,plain,
( add(commutator(X_61,X_62),add(commutator(X_62,X_61),multiply(X_61,additive_inverse(X_62)))) != multiply(X_61,additive_inverse(X_62))
| add(commutator(X_61,X_62),additive_inverse(multiply(X_62,X_61))) = multiply(X_61,additive_inverse(X_62)) ),
inference(resolve,[$cnf( $equal(add(commutator(X_62,X_61),multiply(X_61,additive_inverse(X_62))),additive_inverse(multiply(X_62,X_61))) )],[refute_0_298,refute_0_299]) ).
cnf(refute_0_301,plain,
add(commutator(X_61,X_62),additive_inverse(multiply(X_62,X_61))) = multiply(X_61,additive_inverse(X_62)),
inference(resolve,[$cnf( $equal(add(commutator(X_61,X_62),add(commutator(X_62,X_61),multiply(X_61,additive_inverse(X_62)))),multiply(X_61,additive_inverse(X_62))) )],[refute_0_110,refute_0_300]) ).
cnf(refute_0_302,plain,
add(multiply(X_62,X_61),commutator(X_62,X_61)) = multiply(X_61,X_62),
inference(subst,[],[refute_0_98:[bind(X,$fot(X_62)),bind(Y,$fot(X_61))]]) ).
cnf(refute_0_303,plain,
additive_inverse(add(multiply(X_62,X_61),commutator(X_62,X_61))) = additive_inverse(add(multiply(X_62,X_61),commutator(X_62,X_61))),
introduced(tautology,[refl,[$fot(additive_inverse(add(multiply(X_62,X_61),commutator(X_62,X_61))))]]) ).
cnf(refute_0_304,plain,
( add(multiply(X_62,X_61),commutator(X_62,X_61)) != multiply(X_61,X_62)
| additive_inverse(add(multiply(X_62,X_61),commutator(X_62,X_61))) != additive_inverse(add(multiply(X_62,X_61),commutator(X_62,X_61)))
| additive_inverse(add(multiply(X_62,X_61),commutator(X_62,X_61))) = additive_inverse(multiply(X_61,X_62)) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(add(multiply(X_62,X_61),commutator(X_62,X_61))),additive_inverse(add(multiply(X_62,X_61),commutator(X_62,X_61)))) ),[1,0],$fot(multiply(X_61,X_62))]]) ).
cnf(refute_0_305,plain,
( add(multiply(X_62,X_61),commutator(X_62,X_61)) != multiply(X_61,X_62)
| additive_inverse(add(multiply(X_62,X_61),commutator(X_62,X_61))) = additive_inverse(multiply(X_61,X_62)) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(multiply(X_62,X_61),commutator(X_62,X_61))),additive_inverse(add(multiply(X_62,X_61),commutator(X_62,X_61)))) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
additive_inverse(add(multiply(X_62,X_61),commutator(X_62,X_61))) = additive_inverse(multiply(X_61,X_62)),
inference(resolve,[$cnf( $equal(add(multiply(X_62,X_61),commutator(X_62,X_61)),multiply(X_61,X_62)) )],[refute_0_302,refute_0_305]) ).
cnf(refute_0_307,plain,
add(commutator(X,Y),additive_inverse(X_64)) = additive_inverse(add(X_64,additive_inverse(commutator(X,Y)))),
inference(subst,[],[refute_0_53:[bind(X_36,$fot(commutator(X,Y))),bind(X_57,$fot(X_64))]]) ).
cnf(refute_0_308,plain,
( add(commutator(X,Y),additive_inverse(X_64)) != additive_inverse(add(X_64,additive_inverse(commutator(X,Y))))
| additive_inverse(commutator(X,Y)) != commutator(Y,X)
| add(commutator(X,Y),additive_inverse(X_64)) = additive_inverse(add(X_64,commutator(Y,X))) ),
introduced(tautology,[equality,[$cnf( $equal(add(commutator(X,Y),additive_inverse(X_64)),additive_inverse(add(X_64,additive_inverse(commutator(X,Y))))) ),[1,0,1],$fot(commutator(Y,X))]]) ).
cnf(refute_0_309,plain,
( add(commutator(X,Y),additive_inverse(X_64)) != additive_inverse(add(X_64,additive_inverse(commutator(X,Y))))
| add(commutator(X,Y),additive_inverse(X_64)) = additive_inverse(add(X_64,commutator(Y,X))) ),
inference(resolve,[$cnf( $equal(additive_inverse(commutator(X,Y)),commutator(Y,X)) )],[refute_0_105,refute_0_308]) ).
cnf(refute_0_310,plain,
add(commutator(X,Y),additive_inverse(X_64)) = additive_inverse(add(X_64,commutator(Y,X))),
inference(resolve,[$cnf( $equal(add(commutator(X,Y),additive_inverse(X_64)),additive_inverse(add(X_64,additive_inverse(commutator(X,Y))))) )],[refute_0_307,refute_0_309]) ).
cnf(refute_0_311,plain,
add(commutator(X_61,X_62),additive_inverse(multiply(X_62,X_61))) = additive_inverse(add(multiply(X_62,X_61),commutator(X_62,X_61))),
inference(subst,[],[refute_0_310:[bind(X,$fot(X_61)),bind(Y,$fot(X_62)),bind(X_64,$fot(multiply(X_62,X_61)))]]) ).
cnf(refute_0_312,plain,
( add(commutator(X_61,X_62),additive_inverse(multiply(X_62,X_61))) != additive_inverse(add(multiply(X_62,X_61),commutator(X_62,X_61)))
| additive_inverse(add(multiply(X_62,X_61),commutator(X_62,X_61))) != additive_inverse(multiply(X_61,X_62))
| add(commutator(X_61,X_62),additive_inverse(multiply(X_62,X_61))) = additive_inverse(multiply(X_61,X_62)) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(add(commutator(X_61,X_62),additive_inverse(multiply(X_62,X_61))))),bind(Y0,$fot(additive_inverse(add(multiply(X_62,X_61),commutator(X_62,X_61))))),bind(Z0,$fot(additive_inverse(multiply(X_61,X_62))))]]) ).
cnf(refute_0_313,plain,
( additive_inverse(add(multiply(X_62,X_61),commutator(X_62,X_61))) != additive_inverse(multiply(X_61,X_62))
| add(commutator(X_61,X_62),additive_inverse(multiply(X_62,X_61))) = additive_inverse(multiply(X_61,X_62)) ),
inference(resolve,[$cnf( $equal(add(commutator(X_61,X_62),additive_inverse(multiply(X_62,X_61))),additive_inverse(add(multiply(X_62,X_61),commutator(X_62,X_61)))) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
add(commutator(X_61,X_62),additive_inverse(multiply(X_62,X_61))) = additive_inverse(multiply(X_61,X_62)),
inference(resolve,[$cnf( $equal(additive_inverse(add(multiply(X_62,X_61),commutator(X_62,X_61))),additive_inverse(multiply(X_61,X_62))) )],[refute_0_306,refute_0_313]) ).
cnf(refute_0_315,plain,
( add(commutator(X_61,X_62),additive_inverse(multiply(X_62,X_61))) != multiply(X_61,additive_inverse(X_62))
| add(commutator(X_61,X_62),additive_inverse(multiply(X_62,X_61))) != additive_inverse(multiply(X_61,X_62))
| additive_inverse(multiply(X_61,X_62)) = multiply(X_61,additive_inverse(X_62)) ),
introduced(tautology,[equality,[$cnf( $equal(add(commutator(X_61,X_62),additive_inverse(multiply(X_62,X_61))),multiply(X_61,additive_inverse(X_62))) ),[0],$fot(additive_inverse(multiply(X_61,X_62)))]]) ).
cnf(refute_0_316,plain,
( add(commutator(X_61,X_62),additive_inverse(multiply(X_62,X_61))) != multiply(X_61,additive_inverse(X_62))
| additive_inverse(multiply(X_61,X_62)) = multiply(X_61,additive_inverse(X_62)) ),
inference(resolve,[$cnf( $equal(add(commutator(X_61,X_62),additive_inverse(multiply(X_62,X_61))),additive_inverse(multiply(X_61,X_62))) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
additive_inverse(multiply(X_61,X_62)) = multiply(X_61,additive_inverse(X_62)),
inference(resolve,[$cnf( $equal(add(commutator(X_61,X_62),additive_inverse(multiply(X_62,X_61))),multiply(X_61,additive_inverse(X_62))) )],[refute_0_301,refute_0_316]) ).
cnf(refute_0_318,plain,
( additive_inverse(multiply(X_61,X_62)) != multiply(X_61,additive_inverse(X_62))
| multiply(X_61,additive_inverse(X_62)) = additive_inverse(multiply(X_61,X_62)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(additive_inverse(multiply(X_61,X_62)))),bind(Y0,$fot(multiply(X_61,additive_inverse(X_62))))]]) ).
cnf(refute_0_319,plain,
multiply(X_61,additive_inverse(X_62)) = additive_inverse(multiply(X_61,X_62)),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X_61,X_62)),multiply(X_61,additive_inverse(X_62))) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
multiply(add(x,y),additive_inverse(z)) = additive_inverse(multiply(add(x,y),z)),
inference(subst,[],[refute_0_319:[bind(X_61,$fot(add(x,y))),bind(X_62,$fot(z))]]) ).
cnf(refute_0_321,plain,
( multiply(add(x,y),additive_inverse(z)) != additive_inverse(multiply(add(x,y),z))
| additive_inverse(multiply(add(x,y),z)) != additive_inverse(multiply(add(x,y),z))
| multiply(add(x,y),additive_inverse(z)) = additive_inverse(multiply(add(x,y),z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(add(x,y),additive_inverse(z)),additive_inverse(multiply(add(x,y),z))) ),[0],$fot(additive_inverse(multiply(add(x,y),z)))]]) ).
cnf(refute_0_322,plain,
( additive_inverse(multiply(add(x,y),z)) != additive_inverse(multiply(add(x,y),z))
| multiply(add(x,y),additive_inverse(z)) = additive_inverse(multiply(add(x,y),z)) ),
inference(resolve,[$cnf( $equal(multiply(add(x,y),additive_inverse(z)),additive_inverse(multiply(add(x,y),z))) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
additive_inverse(multiply(add(x,y),z)) != additive_inverse(multiply(add(x,y),z)),
inference(resolve,[$cnf( $equal(multiply(add(x,y),additive_inverse(z)),additive_inverse(multiply(add(x,y),z))) )],[refute_0_322,refute_0_64]) ).
cnf(refute_0_324,plain,
additive_inverse(multiply(add(x,y),z)) = additive_inverse(multiply(add(x,y),z)),
introduced(tautology,[refl,[$fot(additive_inverse(multiply(add(x,y),z)))]]) ).
cnf(refute_0_325,plain,
$false,
inference(resolve,[$cnf( $equal(additive_inverse(multiply(add(x,y),z)),additive_inverse(multiply(add(x,y),z))) )],[refute_0_324,refute_0_323]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG018-6 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon May 30 13:31:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 137.73/137.94 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 137.73/137.94
% 137.73/137.94 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 137.83/137.98
%------------------------------------------------------------------------------