TSTP Solution File: RNG014-6 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : RNG014-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 20:35:46 EDT 2022
% Result : Timeout 291.75s 291.93s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 69
% Syntax : Number of clauses : 303 ( 166 unt; 0 nHn; 140 RR)
% Number of literals : 498 ( 497 equ; 197 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 776 ( 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_equation,negated_conjecture,
multiply(a,additive_inverse(b)) != additive_inverse(multiply(a,b)) ).
cnf(refute_0_0,plain,
add(X_42,add(additive_inverse(X_42),X_44)) = add(add(X_42,additive_inverse(X_42)),X_44),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(X_42)),bind(Y,$fot(additive_inverse(X_42))),bind(Z,$fot(X_44))]]) ).
cnf(refute_0_1,plain,
add(X_42,additive_inverse(X_42)) = additive_identity,
inference(subst,[],[right_additive_inverse:[bind(X,$fot(X_42))]]) ).
cnf(refute_0_2,plain,
( add(X_42,add(additive_inverse(X_42),X_44)) != add(add(X_42,additive_inverse(X_42)),X_44)
| add(X_42,additive_inverse(X_42)) != additive_identity
| add(X_42,add(additive_inverse(X_42),X_44)) = add(additive_identity,X_44) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_42,add(additive_inverse(X_42),X_44)),add(add(X_42,additive_inverse(X_42)),X_44)) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_3,plain,
( add(X_42,add(additive_inverse(X_42),X_44)) != add(add(X_42,additive_inverse(X_42)),X_44)
| add(X_42,add(additive_inverse(X_42),X_44)) = add(additive_identity,X_44) ),
inference(resolve,[$cnf( $equal(add(X_42,additive_inverse(X_42)),additive_identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
add(X_42,add(additive_inverse(X_42),X_44)) = add(additive_identity,X_44),
inference(resolve,[$cnf( $equal(add(X_42,add(additive_inverse(X_42),X_44)),add(add(X_42,additive_inverse(X_42)),X_44)) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
add(additive_identity,X_44) = X_44,
inference(subst,[],[left_additive_identity:[bind(X,$fot(X_44))]]) ).
cnf(refute_0_6,plain,
( add(X_42,add(additive_inverse(X_42),X_44)) != add(additive_identity,X_44)
| add(additive_identity,X_44) != X_44
| add(X_42,add(additive_inverse(X_42),X_44)) = X_44 ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_42,add(additive_inverse(X_42),X_44)),X_44) ),[0],$fot(add(additive_identity,X_44))]]) ).
cnf(refute_0_7,plain,
( add(X_42,add(additive_inverse(X_42),X_44)) != add(additive_identity,X_44)
| add(X_42,add(additive_inverse(X_42),X_44)) = X_44 ),
inference(resolve,[$cnf( $equal(add(additive_identity,X_44),X_44) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
add(X_42,add(additive_inverse(X_42),X_44)) = X_44,
inference(resolve,[$cnf( $equal(add(X_42,add(additive_inverse(X_42),X_44)),add(additive_identity,X_44)) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
add(X_42,add(additive_inverse(X_42),add(X_56,additive_inverse(add(additive_inverse(X_42),X_56))))) = add(X_56,additive_inverse(add(additive_inverse(X_42),X_56))),
inference(subst,[],[refute_0_8:[bind(X_44,$fot(add(X_56,additive_inverse(add(additive_inverse(X_42),X_56)))))]]) ).
cnf(refute_0_10,plain,
add(add(X_42,X_43),additive_inverse(add(X_42,X_43))) = additive_identity,
inference(subst,[],[right_additive_inverse:[bind(X,$fot(add(X_42,X_43)))]]) ).
cnf(refute_0_11,plain,
add(X_42,add(X_43,additive_inverse(add(X_42,X_43)))) = add(add(X_42,X_43),additive_inverse(add(X_42,X_43))),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(X_42)),bind(Y,$fot(X_43)),bind(Z,$fot(additive_inverse(add(X_42,X_43))))]]) ).
cnf(refute_0_12,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_13,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_14,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( add(X_42,add(X_43,additive_inverse(add(X_42,X_43)))) != add(add(X_42,X_43),additive_inverse(add(X_42,X_43)))
| add(add(X_42,X_43),additive_inverse(add(X_42,X_43))) = add(X_42,add(X_43,additive_inverse(add(X_42,X_43)))) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_42,add(X_43,additive_inverse(add(X_42,X_43)))))),bind(Y0,$fot(add(add(X_42,X_43),additive_inverse(add(X_42,X_43)))))]]) ).
cnf(refute_0_16,plain,
add(add(X_42,X_43),additive_inverse(add(X_42,X_43))) = add(X_42,add(X_43,additive_inverse(add(X_42,X_43)))),
inference(resolve,[$cnf( $equal(add(X_42,add(X_43,additive_inverse(add(X_42,X_43)))),add(add(X_42,X_43),additive_inverse(add(X_42,X_43)))) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
( add(add(X_42,X_43),additive_inverse(add(X_42,X_43))) != add(X_42,add(X_43,additive_inverse(add(X_42,X_43))))
| add(add(X_42,X_43),additive_inverse(add(X_42,X_43))) != additive_identity
| add(X_42,add(X_43,additive_inverse(add(X_42,X_43)))) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_42,X_43),additive_inverse(add(X_42,X_43))),additive_identity) ),[0],$fot(add(X_42,add(X_43,additive_inverse(add(X_42,X_43)))))]]) ).
cnf(refute_0_18,plain,
( add(add(X_42,X_43),additive_inverse(add(X_42,X_43))) != additive_identity
| add(X_42,add(X_43,additive_inverse(add(X_42,X_43)))) = additive_identity ),
inference(resolve,[$cnf( $equal(add(add(X_42,X_43),additive_inverse(add(X_42,X_43))),add(X_42,add(X_43,additive_inverse(add(X_42,X_43))))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
add(X_42,add(X_43,additive_inverse(add(X_42,X_43)))) = additive_identity,
inference(resolve,[$cnf( $equal(add(add(X_42,X_43),additive_inverse(add(X_42,X_43))),additive_identity) )],[refute_0_10,refute_0_18]) ).
cnf(refute_0_20,plain,
add(additive_inverse(X_42),add(X_56,additive_inverse(add(additive_inverse(X_42),X_56)))) = additive_identity,
inference(subst,[],[refute_0_19:[bind(X_42,$fot(additive_inverse(X_42))),bind(X_43,$fot(X_56))]]) ).
cnf(refute_0_21,plain,
( add(X_42,add(additive_inverse(X_42),add(X_56,additive_inverse(add(additive_inverse(X_42),X_56))))) != add(X_56,additive_inverse(add(additive_inverse(X_42),X_56)))
| add(additive_inverse(X_42),add(X_56,additive_inverse(add(additive_inverse(X_42),X_56)))) != additive_identity
| add(X_42,additive_identity) = add(X_56,additive_inverse(add(additive_inverse(X_42),X_56))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_42,add(additive_inverse(X_42),add(X_56,additive_inverse(add(additive_inverse(X_42),X_56))))),add(X_56,additive_inverse(add(additive_inverse(X_42),X_56)))) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_22,plain,
( add(X_42,add(additive_inverse(X_42),add(X_56,additive_inverse(add(additive_inverse(X_42),X_56))))) != add(X_56,additive_inverse(add(additive_inverse(X_42),X_56)))
| add(X_42,additive_identity) = add(X_56,additive_inverse(add(additive_inverse(X_42),X_56))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_42),add(X_56,additive_inverse(add(additive_inverse(X_42),X_56)))),additive_identity) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
add(X_42,additive_identity) = add(X_56,additive_inverse(add(additive_inverse(X_42),X_56))),
inference(resolve,[$cnf( $equal(add(X_42,add(additive_inverse(X_42),add(X_56,additive_inverse(add(additive_inverse(X_42),X_56))))),add(X_56,additive_inverse(add(additive_inverse(X_42),X_56)))) )],[refute_0_9,refute_0_22]) ).
cnf(refute_0_24,plain,
add(X_42,additive_identity) = X_42,
inference(subst,[],[right_additive_identity:[bind(X,$fot(X_42))]]) ).
cnf(refute_0_25,plain,
( add(X_42,additive_identity) != X_42
| add(X_42,additive_identity) != add(X_56,additive_inverse(add(additive_inverse(X_42),X_56)))
| X_42 = add(X_56,additive_inverse(add(additive_inverse(X_42),X_56))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_42,additive_identity),add(X_56,additive_inverse(add(additive_inverse(X_42),X_56)))) ),[0],$fot(X_42)]]) ).
cnf(refute_0_26,plain,
( add(X_42,additive_identity) != add(X_56,additive_inverse(add(additive_inverse(X_42),X_56)))
| X_42 = add(X_56,additive_inverse(add(additive_inverse(X_42),X_56))) ),
inference(resolve,[$cnf( $equal(add(X_42,additive_identity),X_42) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
X_42 = add(X_56,additive_inverse(add(additive_inverse(X_42),X_56))),
inference(resolve,[$cnf( $equal(add(X_42,additive_identity),add(X_56,additive_inverse(add(additive_inverse(X_42),X_56)))) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
additive_inverse(X) = add(X_64,additive_inverse(add(additive_inverse(additive_inverse(X)),X_64))),
inference(subst,[],[refute_0_27:[bind(X_42,$fot(additive_inverse(X))),bind(X_56,$fot(X_64))]]) ).
cnf(refute_0_29,plain,
( additive_inverse(X) != add(X_64,additive_inverse(add(additive_inverse(additive_inverse(X)),X_64)))
| additive_inverse(additive_inverse(X)) != X
| additive_inverse(X) = add(X_64,additive_inverse(add(X,X_64))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(X),add(X_64,additive_inverse(add(additive_inverse(additive_inverse(X)),X_64)))) ),[1,1,0,0],$fot(X)]]) ).
cnf(refute_0_30,plain,
( additive_inverse(X) != add(X_64,additive_inverse(add(additive_inverse(additive_inverse(X)),X_64)))
| additive_inverse(X) = add(X_64,additive_inverse(add(X,X_64))) ),
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(X)),X) )],[additive_inverse_additive_inverse,refute_0_29]) ).
cnf(refute_0_31,plain,
additive_inverse(X) = add(X_64,additive_inverse(add(X,X_64))),
inference(resolve,[$cnf( $equal(additive_inverse(X),add(X_64,additive_inverse(add(additive_inverse(additive_inverse(X)),X_64)))) )],[refute_0_28,refute_0_30]) ).
cnf(refute_0_32,plain,
additive_inverse(multiply(X_1009,X_1008)) = add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(add(multiply(X_1009,X_1008),multiply(additive_inverse(X_1008),X_1009)))),
inference(subst,[],[refute_0_31:[bind(X,$fot(multiply(X_1009,X_1008))),bind(X_64,$fot(multiply(additive_inverse(X_1008),X_1009)))]]) ).
cnf(refute_0_33,plain,
add(multiply(X_47,X_48),add(multiply(X_47,X_49),Z)) = add(add(multiply(X_47,X_48),multiply(X_47,X_49)),Z),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(multiply(X_47,X_48))),bind(Y,$fot(multiply(X_47,X_49)))]]) ).
cnf(refute_0_34,plain,
multiply(X_47,add(X_48,X_49)) = add(multiply(X_47,X_48),multiply(X_47,X_49)),
inference(subst,[],[distribute1:[bind(X,$fot(X_47)),bind(Y,$fot(X_48)),bind(Z,$fot(X_49))]]) ).
cnf(refute_0_35,plain,
( multiply(X_47,add(X_48,X_49)) != add(multiply(X_47,X_48),multiply(X_47,X_49))
| add(multiply(X_47,X_48),multiply(X_47,X_49)) = multiply(X_47,add(X_48,X_49)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(multiply(X_47,add(X_48,X_49)))),bind(Y0,$fot(add(multiply(X_47,X_48),multiply(X_47,X_49))))]]) ).
cnf(refute_0_36,plain,
add(multiply(X_47,X_48),multiply(X_47,X_49)) = multiply(X_47,add(X_48,X_49)),
inference(resolve,[$cnf( $equal(multiply(X_47,add(X_48,X_49)),add(multiply(X_47,X_48),multiply(X_47,X_49))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( add(multiply(X_47,X_48),multiply(X_47,X_49)) != multiply(X_47,add(X_48,X_49))
| add(multiply(X_47,X_48),add(multiply(X_47,X_49),Z)) != add(add(multiply(X_47,X_48),multiply(X_47,X_49)),Z)
| add(multiply(X_47,X_48),add(multiply(X_47,X_49),Z)) = add(multiply(X_47,add(X_48,X_49)),Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_47,X_48),add(multiply(X_47,X_49),Z)),add(add(multiply(X_47,X_48),multiply(X_47,X_49)),Z)) ),[1,0],$fot(multiply(X_47,add(X_48,X_49)))]]) ).
cnf(refute_0_38,plain,
( add(multiply(X_47,X_48),add(multiply(X_47,X_49),Z)) != add(add(multiply(X_47,X_48),multiply(X_47,X_49)),Z)
| add(multiply(X_47,X_48),add(multiply(X_47,X_49),Z)) = add(multiply(X_47,add(X_48,X_49)),Z) ),
inference(resolve,[$cnf( $equal(add(multiply(X_47,X_48),multiply(X_47,X_49)),multiply(X_47,add(X_48,X_49))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
add(multiply(X_47,X_48),add(multiply(X_47,X_49),Z)) = add(multiply(X_47,add(X_48,X_49)),Z),
inference(resolve,[$cnf( $equal(add(multiply(X_47,X_48),add(multiply(X_47,X_49),Z)),add(add(multiply(X_47,X_48),multiply(X_47,X_49)),Z)) )],[refute_0_33,refute_0_38]) ).
cnf(refute_0_40,plain,
add(multiply(X_556,X_557),add(multiply(X_556,X_558),commutator(X_556,X_558))) = add(multiply(X_556,add(X_557,X_558)),commutator(X_556,X_558)),
inference(subst,[],[refute_0_39:[bind(Z,$fot(commutator(X_556,X_558))),bind(X_47,$fot(X_556)),bind(X_48,$fot(X_557)),bind(X_49,$fot(X_558))]]) ).
cnf(refute_0_41,plain,
add(X_45,add(additive_inverse(X_45),X_46)) = X_46,
inference(subst,[],[refute_0_8:[bind(X_42,$fot(X_45)),bind(X_44,$fot(X_46))]]) ).
cnf(refute_0_42,plain,
add(X_46,additive_inverse(X_45)) = add(additive_inverse(X_45),X_46),
inference(subst,[],[commutativity_for_addition:[bind(X,$fot(X_46)),bind(Y,$fot(additive_inverse(X_45)))]]) ).
cnf(refute_0_43,plain,
( add(X_46,additive_inverse(X_45)) != add(additive_inverse(X_45),X_46)
| add(additive_inverse(X_45),X_46) = add(X_46,additive_inverse(X_45)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_46,additive_inverse(X_45)))),bind(Y0,$fot(add(additive_inverse(X_45),X_46)))]]) ).
cnf(refute_0_44,plain,
add(additive_inverse(X_45),X_46) = add(X_46,additive_inverse(X_45)),
inference(resolve,[$cnf( $equal(add(X_46,additive_inverse(X_45)),add(additive_inverse(X_45),X_46)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( add(X_45,add(additive_inverse(X_45),X_46)) != X_46
| add(additive_inverse(X_45),X_46) != add(X_46,additive_inverse(X_45))
| add(X_45,add(X_46,additive_inverse(X_45))) = X_46 ),
introduced(tautology,[equality,[$cnf( $equal(add(X_45,add(additive_inverse(X_45),X_46)),X_46) ),[0,1],$fot(add(X_46,additive_inverse(X_45)))]]) ).
cnf(refute_0_46,plain,
( add(X_45,add(additive_inverse(X_45),X_46)) != X_46
| add(X_45,add(X_46,additive_inverse(X_45))) = X_46 ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_45),X_46),add(X_46,additive_inverse(X_45))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
add(X_45,add(X_46,additive_inverse(X_45))) = X_46,
inference(resolve,[$cnf( $equal(add(X_45,add(additive_inverse(X_45),X_46)),X_46) )],[refute_0_41,refute_0_46]) ).
cnf(refute_0_48,plain,
add(multiply(X,Y),add(multiply(Y,X),additive_inverse(multiply(X,Y)))) = multiply(Y,X),
inference(subst,[],[refute_0_47:[bind(X_45,$fot(multiply(X,Y))),bind(X_46,$fot(multiply(Y,X)))]]) ).
cnf(refute_0_49,plain,
( commutator(X,Y) != add(multiply(Y,X),additive_inverse(multiply(X,Y)))
| add(multiply(Y,X),additive_inverse(multiply(X,Y))) = commutator(X,Y) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(commutator(X,Y))),bind(Y0,$fot(add(multiply(Y,X),additive_inverse(multiply(X,Y)))))]]) ).
cnf(refute_0_50,plain,
add(multiply(Y,X),additive_inverse(multiply(X,Y))) = commutator(X,Y),
inference(resolve,[$cnf( $equal(commutator(X,Y),add(multiply(Y,X),additive_inverse(multiply(X,Y)))) )],[commutator,refute_0_49]) ).
cnf(refute_0_51,plain,
( add(multiply(X,Y),add(multiply(Y,X),additive_inverse(multiply(X,Y)))) != multiply(Y,X)
| add(multiply(Y,X),additive_inverse(multiply(X,Y))) != commutator(X,Y)
| add(multiply(X,Y),commutator(X,Y)) = multiply(Y,X) ),
introduced(tautology,[equality,[$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_52,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( $equal(add(multiply(Y,X),additive_inverse(multiply(X,Y))),commutator(X,Y)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
add(multiply(X,Y),commutator(X,Y)) = multiply(Y,X),
inference(resolve,[$cnf( $equal(add(multiply(X,Y),add(multiply(Y,X),additive_inverse(multiply(X,Y)))),multiply(Y,X)) )],[refute_0_48,refute_0_52]) ).
cnf(refute_0_54,plain,
add(multiply(X_556,X_558),commutator(X_556,X_558)) = multiply(X_558,X_556),
inference(subst,[],[refute_0_53:[bind(X,$fot(X_556)),bind(Y,$fot(X_558))]]) ).
cnf(refute_0_55,plain,
( add(multiply(X_556,X_557),add(multiply(X_556,X_558),commutator(X_556,X_558))) != add(multiply(X_556,add(X_557,X_558)),commutator(X_556,X_558))
| add(multiply(X_556,X_558),commutator(X_556,X_558)) != multiply(X_558,X_556)
| add(multiply(X_556,X_557),multiply(X_558,X_556)) = add(multiply(X_556,add(X_557,X_558)),commutator(X_556,X_558)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_556,X_557),add(multiply(X_556,X_558),commutator(X_556,X_558))),add(multiply(X_556,add(X_557,X_558)),commutator(X_556,X_558))) ),[0,1],$fot(multiply(X_558,X_556))]]) ).
cnf(refute_0_56,plain,
( add(multiply(X_556,X_557),add(multiply(X_556,X_558),commutator(X_556,X_558))) != add(multiply(X_556,add(X_557,X_558)),commutator(X_556,X_558))
| add(multiply(X_556,X_557),multiply(X_558,X_556)) = add(multiply(X_556,add(X_557,X_558)),commutator(X_556,X_558)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_556,X_558),commutator(X_556,X_558)),multiply(X_558,X_556)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
add(multiply(X_556,X_557),multiply(X_558,X_556)) = add(multiply(X_556,add(X_557,X_558)),commutator(X_556,X_558)),
inference(resolve,[$cnf( $equal(add(multiply(X_556,X_557),add(multiply(X_556,X_558),commutator(X_556,X_558))),add(multiply(X_556,add(X_557,X_558)),commutator(X_556,X_558))) )],[refute_0_40,refute_0_56]) ).
cnf(refute_0_58,plain,
add(X_42,add(X_43,X_44)) = add(add(X_42,X_43),X_44),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(X_42)),bind(Y,$fot(X_43)),bind(Z,$fot(X_44))]]) ).
cnf(refute_0_59,plain,
add(X_44,X_43) = add(X_43,X_44),
inference(subst,[],[commutativity_for_addition:[bind(X,$fot(X_44)),bind(Y,$fot(X_43))]]) ).
cnf(refute_0_60,plain,
( add(X_44,X_43) != add(X_43,X_44)
| add(X_43,X_44) = add(X_44,X_43) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_44,X_43))),bind(Y0,$fot(add(X_43,X_44)))]]) ).
cnf(refute_0_61,plain,
add(X_43,X_44) = add(X_44,X_43),
inference(resolve,[$cnf( $equal(add(X_44,X_43),add(X_43,X_44)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( add(X_42,add(X_43,X_44)) != add(add(X_42,X_43),X_44)
| add(X_43,X_44) != add(X_44,X_43)
| add(X_42,add(X_44,X_43)) = add(add(X_42,X_43),X_44) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_42,add(X_43,X_44)),add(add(X_42,X_43),X_44)) ),[0,1],$fot(add(X_44,X_43))]]) ).
cnf(refute_0_63,plain,
( add(X_42,add(X_43,X_44)) != add(add(X_42,X_43),X_44)
| add(X_42,add(X_44,X_43)) = add(add(X_42,X_43),X_44) ),
inference(resolve,[$cnf( $equal(add(X_43,X_44),add(X_44,X_43)) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
add(X_42,add(X_44,X_43)) = add(add(X_42,X_43),X_44),
inference(resolve,[$cnf( $equal(add(X_42,add(X_43,X_44)),add(add(X_42,X_43),X_44)) )],[refute_0_58,refute_0_63]) ).
cnf(refute_0_65,plain,
( add(X,add(Y,Z)) != add(add(X,Y),Z)
| add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X,add(Y,Z)))),bind(Y0,$fot(add(add(X,Y),Z)))]]) ).
cnf(refute_0_66,plain,
add(add(X,Y),Z) = add(X,add(Y,Z)),
inference(resolve,[$cnf( $equal(add(X,add(Y,Z)),add(add(X,Y),Z)) )],[associativity_for_addition,refute_0_65]) ).
cnf(refute_0_67,plain,
add(add(X_42,X_43),X_44) = add(X_42,add(X_43,X_44)),
inference(subst,[],[refute_0_66:[bind(X,$fot(X_42)),bind(Y,$fot(X_43)),bind(Z,$fot(X_44))]]) ).
cnf(refute_0_68,plain,
( add(X_42,add(X_44,X_43)) != add(add(X_42,X_43),X_44)
| add(add(X_42,X_43),X_44) != add(X_42,add(X_43,X_44))
| add(X_42,add(X_44,X_43)) = add(X_42,add(X_43,X_44)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_42,add(X_44,X_43)),add(X_42,add(X_43,X_44))) ),[0],$fot(add(add(X_42,X_43),X_44))]]) ).
cnf(refute_0_69,plain,
( add(X_42,add(X_44,X_43)) != add(add(X_42,X_43),X_44)
| add(X_42,add(X_44,X_43)) = add(X_42,add(X_43,X_44)) ),
inference(resolve,[$cnf( $equal(add(add(X_42,X_43),X_44),add(X_42,add(X_43,X_44))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
add(X_42,add(X_44,X_43)) = add(X_42,add(X_43,X_44)),
inference(resolve,[$cnf( $equal(add(X_42,add(X_44,X_43)),add(add(X_42,X_43),X_44)) )],[refute_0_64,refute_0_69]) ).
cnf(refute_0_71,plain,
add(multiply(X_556,X_557),add(X_44,multiply(X_556,X_558))) = add(multiply(X_556,X_557),add(multiply(X_556,X_558),X_44)),
inference(subst,[],[refute_0_70:[bind(X_42,$fot(multiply(X_556,X_557))),bind(X_43,$fot(multiply(X_556,X_558)))]]) ).
cnf(refute_0_72,plain,
add(multiply(X_556,X_557),add(multiply(X_556,X_558),X_44)) = add(multiply(X_556,add(X_557,X_558)),X_44),
inference(subst,[],[refute_0_39:[bind(Z,$fot(X_44)),bind(X_47,$fot(X_556)),bind(X_48,$fot(X_557)),bind(X_49,$fot(X_558))]]) ).
cnf(refute_0_73,plain,
( add(multiply(X_556,X_557),add(X_44,multiply(X_556,X_558))) != add(multiply(X_556,X_557),add(multiply(X_556,X_558),X_44))
| add(multiply(X_556,X_557),add(multiply(X_556,X_558),X_44)) != add(multiply(X_556,add(X_557,X_558)),X_44)
| add(multiply(X_556,X_557),add(X_44,multiply(X_556,X_558))) = add(multiply(X_556,add(X_557,X_558)),X_44) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(multiply(X_556,X_557),add(X_44,multiply(X_556,X_558))),add(multiply(X_556,add(X_557,X_558)),X_44)) ),[0],$fot(add(multiply(X_556,X_557),add(multiply(X_556,X_558),X_44)))]]) ).
cnf(refute_0_74,plain,
( add(multiply(X_556,X_557),add(X_44,multiply(X_556,X_558))) != add(multiply(X_556,X_557),add(multiply(X_556,X_558),X_44))
| add(multiply(X_556,X_557),add(X_44,multiply(X_556,X_558))) = add(multiply(X_556,add(X_557,X_558)),X_44) ),
inference(resolve,[$cnf( $equal(add(multiply(X_556,X_557),add(multiply(X_556,X_558),X_44)),add(multiply(X_556,add(X_557,X_558)),X_44)) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
add(multiply(X_556,X_557),add(X_44,multiply(X_556,X_558))) = add(multiply(X_556,add(X_557,X_558)),X_44),
inference(resolve,[$cnf( $equal(add(multiply(X_556,X_557),add(X_44,multiply(X_556,X_558))),add(multiply(X_556,X_557),add(multiply(X_556,X_558),X_44))) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
add(X,add(X_42,X_43)) = add(add(X_42,X_43),X),
inference(subst,[],[commutativity_for_addition:[bind(Y,$fot(add(X_42,X_43)))]]) ).
cnf(refute_0_77,plain,
add(X_42,add(X_43,X)) = add(add(X_42,X_43),X),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(X_42)),bind(Y,$fot(X_43)),bind(Z,$fot(X))]]) ).
cnf(refute_0_78,plain,
( add(X_42,add(X_43,X)) != add(add(X_42,X_43),X)
| add(add(X_42,X_43),X) = add(X_42,add(X_43,X)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_42,add(X_43,X)))),bind(Y0,$fot(add(add(X_42,X_43),X)))]]) ).
cnf(refute_0_79,plain,
add(add(X_42,X_43),X) = add(X_42,add(X_43,X)),
inference(resolve,[$cnf( $equal(add(X_42,add(X_43,X)),add(add(X_42,X_43),X)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
( add(X,add(X_42,X_43)) != add(add(X_42,X_43),X)
| add(add(X_42,X_43),X) != add(X_42,add(X_43,X))
| add(X,add(X_42,X_43)) = add(X_42,add(X_43,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X,add(X_42,X_43)),add(X_42,add(X_43,X))) ),[0],$fot(add(add(X_42,X_43),X))]]) ).
cnf(refute_0_81,plain,
( add(X,add(X_42,X_43)) != add(add(X_42,X_43),X)
| add(X,add(X_42,X_43)) = add(X_42,add(X_43,X)) ),
inference(resolve,[$cnf( $equal(add(add(X_42,X_43),X),add(X_42,add(X_43,X))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
add(X,add(X_42,X_43)) = add(X_42,add(X_43,X)),
inference(resolve,[$cnf( $equal(add(X,add(X_42,X_43)),add(add(X_42,X_43),X)) )],[refute_0_76,refute_0_81]) ).
cnf(refute_0_83,plain,
add(multiply(X,Z),add(X_130,multiply(X,Y))) = add(X_130,add(multiply(X,Y),multiply(X,Z))),
inference(subst,[],[refute_0_82:[bind(X,$fot(multiply(X,Z))),bind(X_42,$fot(X_130)),bind(X_43,$fot(multiply(X,Y)))]]) ).
cnf(refute_0_84,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_14:[bind(X0,$fot(multiply(X,add(Y,Z)))),bind(Y0,$fot(add(multiply(X,Y),multiply(X,Z))))]]) ).
cnf(refute_0_85,plain,
add(multiply(X,Y),multiply(X,Z)) = multiply(X,add(Y,Z)),
inference(resolve,[$cnf( $equal(multiply(X,add(Y,Z)),add(multiply(X,Y),multiply(X,Z))) )],[distribute1,refute_0_84]) ).
cnf(refute_0_86,plain,
( add(multiply(X,Y),multiply(X,Z)) != multiply(X,add(Y,Z))
| add(multiply(X,Z),add(X_130,multiply(X,Y))) != add(X_130,add(multiply(X,Y),multiply(X,Z)))
| add(multiply(X,Z),add(X_130,multiply(X,Y))) = add(X_130,multiply(X,add(Y,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X,Z),add(X_130,multiply(X,Y))),add(X_130,add(multiply(X,Y),multiply(X,Z)))) ),[1,1],$fot(multiply(X,add(Y,Z)))]]) ).
cnf(refute_0_87,plain,
( add(multiply(X,Z),add(X_130,multiply(X,Y))) != add(X_130,add(multiply(X,Y),multiply(X,Z)))
| add(multiply(X,Z),add(X_130,multiply(X,Y))) = add(X_130,multiply(X,add(Y,Z))) ),
inference(resolve,[$cnf( $equal(add(multiply(X,Y),multiply(X,Z)),multiply(X,add(Y,Z))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
add(multiply(X,Z),add(X_130,multiply(X,Y))) = add(X_130,multiply(X,add(Y,Z))),
inference(resolve,[$cnf( $equal(add(multiply(X,Z),add(X_130,multiply(X,Y))),add(X_130,add(multiply(X,Y),multiply(X,Z)))) )],[refute_0_83,refute_0_87]) ).
cnf(refute_0_89,plain,
add(multiply(X_556,X_557),add(X_44,multiply(X_556,X_558))) = add(X_44,multiply(X_556,add(X_558,X_557))),
inference(subst,[],[refute_0_88:[bind(X,$fot(X_556)),bind(Y,$fot(X_558)),bind(Z,$fot(X_557)),bind(X_130,$fot(X_44))]]) ).
cnf(refute_0_90,plain,
( add(multiply(X_556,X_557),add(X_44,multiply(X_556,X_558))) != add(X_44,multiply(X_556,add(X_558,X_557)))
| add(multiply(X_556,X_557),add(X_44,multiply(X_556,X_558))) != add(multiply(X_556,add(X_557,X_558)),X_44)
| add(X_44,multiply(X_556,add(X_558,X_557))) = add(multiply(X_556,add(X_557,X_558)),X_44) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_556,X_557),add(X_44,multiply(X_556,X_558))),add(multiply(X_556,add(X_557,X_558)),X_44)) ),[0],$fot(add(X_44,multiply(X_556,add(X_558,X_557))))]]) ).
cnf(refute_0_91,plain,
( add(multiply(X_556,X_557),add(X_44,multiply(X_556,X_558))) != add(multiply(X_556,add(X_557,X_558)),X_44)
| add(X_44,multiply(X_556,add(X_558,X_557))) = add(multiply(X_556,add(X_557,X_558)),X_44) ),
inference(resolve,[$cnf( $equal(add(multiply(X_556,X_557),add(X_44,multiply(X_556,X_558))),add(X_44,multiply(X_556,add(X_558,X_557)))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
add(X_44,multiply(X_556,add(X_558,X_557))) = add(multiply(X_556,add(X_557,X_558)),X_44),
inference(resolve,[$cnf( $equal(add(multiply(X_556,X_557),add(X_44,multiply(X_556,X_558))),add(multiply(X_556,add(X_557,X_558)),X_44)) )],[refute_0_75,refute_0_91]) ).
cnf(refute_0_93,plain,
( add(X_44,multiply(X_556,add(X_558,X_557))) != add(multiply(X_556,add(X_557,X_558)),X_44)
| add(multiply(X_556,add(X_557,X_558)),X_44) = add(X_44,multiply(X_556,add(X_558,X_557))) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_44,multiply(X_556,add(X_558,X_557))))),bind(Y0,$fot(add(multiply(X_556,add(X_557,X_558)),X_44)))]]) ).
cnf(refute_0_94,plain,
add(multiply(X_556,add(X_557,X_558)),X_44) = add(X_44,multiply(X_556,add(X_558,X_557))),
inference(resolve,[$cnf( $equal(add(X_44,multiply(X_556,add(X_558,X_557))),add(multiply(X_556,add(X_557,X_558)),X_44)) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
add(multiply(X_556,add(X_557,X_558)),commutator(X_556,X_558)) = add(commutator(X_556,X_558),multiply(X_556,add(X_558,X_557))),
inference(subst,[],[refute_0_94:[bind(X_44,$fot(commutator(X_556,X_558)))]]) ).
cnf(refute_0_96,plain,
( add(multiply(X_556,X_557),multiply(X_558,X_556)) != add(multiply(X_556,add(X_557,X_558)),commutator(X_556,X_558))
| add(multiply(X_556,add(X_557,X_558)),commutator(X_556,X_558)) != add(commutator(X_556,X_558),multiply(X_556,add(X_558,X_557)))
| add(multiply(X_556,X_557),multiply(X_558,X_556)) = add(commutator(X_556,X_558),multiply(X_556,add(X_558,X_557))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(multiply(X_556,X_557),multiply(X_558,X_556)),add(commutator(X_556,X_558),multiply(X_556,add(X_558,X_557)))) ),[0],$fot(add(multiply(X_556,add(X_557,X_558)),commutator(X_556,X_558)))]]) ).
cnf(refute_0_97,plain,
( add(multiply(X_556,X_557),multiply(X_558,X_556)) != add(multiply(X_556,add(X_557,X_558)),commutator(X_556,X_558))
| add(multiply(X_556,X_557),multiply(X_558,X_556)) = add(commutator(X_556,X_558),multiply(X_556,add(X_558,X_557))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_556,add(X_557,X_558)),commutator(X_556,X_558)),add(commutator(X_556,X_558),multiply(X_556,add(X_558,X_557)))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
add(multiply(X_556,X_557),multiply(X_558,X_556)) = add(commutator(X_556,X_558),multiply(X_556,add(X_558,X_557))),
inference(resolve,[$cnf( $equal(add(multiply(X_556,X_557),multiply(X_558,X_556)),add(multiply(X_556,add(X_557,X_558)),commutator(X_556,X_558))) )],[refute_0_57,refute_0_97]) ).
cnf(refute_0_99,plain,
add(multiply(X_848,additive_inverse(X_850)),multiply(X_850,X_848)) = add(commutator(X_848,X_850),multiply(X_848,add(X_850,additive_inverse(X_850)))),
inference(subst,[],[refute_0_98:[bind(X_556,$fot(X_848)),bind(X_557,$fot(additive_inverse(X_850))),bind(X_558,$fot(X_850))]]) ).
cnf(refute_0_100,plain,
add(X_850,additive_inverse(X_850)) = additive_identity,
inference(subst,[],[right_additive_inverse:[bind(X,$fot(X_850))]]) ).
cnf(refute_0_101,plain,
( add(X_850,additive_inverse(X_850)) != additive_identity
| add(multiply(X_848,additive_inverse(X_850)),multiply(X_850,X_848)) != add(commutator(X_848,X_850),multiply(X_848,add(X_850,additive_inverse(X_850))))
| add(multiply(X_848,additive_inverse(X_850)),multiply(X_850,X_848)) = add(commutator(X_848,X_850),multiply(X_848,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_848,additive_inverse(X_850)),multiply(X_850,X_848)),add(commutator(X_848,X_850),multiply(X_848,add(X_850,additive_inverse(X_850))))) ),[1,1,1],$fot(additive_identity)]]) ).
cnf(refute_0_102,plain,
( add(multiply(X_848,additive_inverse(X_850)),multiply(X_850,X_848)) != add(commutator(X_848,X_850),multiply(X_848,add(X_850,additive_inverse(X_850))))
| add(multiply(X_848,additive_inverse(X_850)),multiply(X_850,X_848)) = add(commutator(X_848,X_850),multiply(X_848,additive_identity)) ),
inference(resolve,[$cnf( $equal(add(X_850,additive_inverse(X_850)),additive_identity) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
add(multiply(X_848,additive_inverse(X_850)),multiply(X_850,X_848)) = add(commutator(X_848,X_850),multiply(X_848,additive_identity)),
inference(resolve,[$cnf( $equal(add(multiply(X_848,additive_inverse(X_850)),multiply(X_850,X_848)),add(commutator(X_848,X_850),multiply(X_848,add(X_850,additive_inverse(X_850))))) )],[refute_0_99,refute_0_102]) ).
cnf(refute_0_104,plain,
add(X,add(Y,add(additive_inverse(Y),X_46))) = add(add(X,Y),add(additive_inverse(Y),X_46)),
inference(subst,[],[associativity_for_addition:[bind(Z,$fot(add(additive_inverse(Y),X_46)))]]) ).
cnf(refute_0_105,plain,
add(Y,add(additive_inverse(Y),X_46)) = X_46,
inference(subst,[],[refute_0_8:[bind(X_42,$fot(Y)),bind(X_44,$fot(X_46))]]) ).
cnf(refute_0_106,plain,
( add(X,add(Y,add(additive_inverse(Y),X_46))) != add(add(X,Y),add(additive_inverse(Y),X_46))
| add(Y,add(additive_inverse(Y),X_46)) != X_46
| add(X,X_46) = add(add(X,Y),add(additive_inverse(Y),X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,add(Y,add(additive_inverse(Y),X_46))),add(add(X,Y),add(additive_inverse(Y),X_46))) ),[0,1],$fot(X_46)]]) ).
cnf(refute_0_107,plain,
( add(X,add(Y,add(additive_inverse(Y),X_46))) != add(add(X,Y),add(additive_inverse(Y),X_46))
| add(X,X_46) = add(add(X,Y),add(additive_inverse(Y),X_46)) ),
inference(resolve,[$cnf( $equal(add(Y,add(additive_inverse(Y),X_46)),X_46) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
add(X,X_46) = add(add(X,Y),add(additive_inverse(Y),X_46)),
inference(resolve,[$cnf( $equal(add(X,add(Y,add(additive_inverse(Y),X_46))),add(add(X,Y),add(additive_inverse(Y),X_46))) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
add(add(X,Y),X_46) = add(X,add(Y,X_46)),
inference(subst,[],[refute_0_66:[bind(Z,$fot(X_46))]]) ).
cnf(refute_0_110,plain,
add(additive_inverse(Y),add(add(X,Y),X_46)) = add(additive_inverse(Y),add(add(X,Y),X_46)),
introduced(tautology,[refl,[$fot(add(additive_inverse(Y),add(add(X,Y),X_46)))]]) ).
cnf(refute_0_111,plain,
( add(add(X,Y),X_46) != add(X,add(Y,X_46))
| add(additive_inverse(Y),add(add(X,Y),X_46)) != add(additive_inverse(Y),add(add(X,Y),X_46))
| add(additive_inverse(Y),add(add(X,Y),X_46)) = add(additive_inverse(Y),add(X,add(Y,X_46))) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(Y),add(add(X,Y),X_46)),add(additive_inverse(Y),add(add(X,Y),X_46))) ),[1,1],$fot(add(X,add(Y,X_46)))]]) ).
cnf(refute_0_112,plain,
( add(add(X,Y),X_46) != add(X,add(Y,X_46))
| add(additive_inverse(Y),add(add(X,Y),X_46)) = add(additive_inverse(Y),add(X,add(Y,X_46))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(Y),add(add(X,Y),X_46)),add(additive_inverse(Y),add(add(X,Y),X_46))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
add(additive_inverse(Y),add(add(X,Y),X_46)) = add(additive_inverse(Y),add(X,add(Y,X_46))),
inference(resolve,[$cnf( $equal(add(add(X,Y),X_46),add(X,add(Y,X_46))) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
add(X_43,X_42) = add(X_42,X_43),
inference(subst,[],[commutativity_for_addition:[bind(X,$fot(X_43)),bind(Y,$fot(X_42))]]) ).
cnf(refute_0_115,plain,
( add(X_43,X_42) != add(X_42,X_43)
| add(X_42,X_43) = add(X_43,X_42) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_43,X_42))),bind(Y0,$fot(add(X_42,X_43)))]]) ).
cnf(refute_0_116,plain,
add(X_42,X_43) = add(X_43,X_42),
inference(resolve,[$cnf( $equal(add(X_43,X_42),add(X_42,X_43)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
( add(X_42,X_43) != add(X_43,X_42)
| add(X_42,add(X_43,X_44)) != add(add(X_42,X_43),X_44)
| add(X_42,add(X_43,X_44)) = add(add(X_43,X_42),X_44) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_42,add(X_43,X_44)),add(add(X_42,X_43),X_44)) ),[1,0],$fot(add(X_43,X_42))]]) ).
cnf(refute_0_118,plain,
( add(X_42,add(X_43,X_44)) != add(add(X_42,X_43),X_44)
| add(X_42,add(X_43,X_44)) = add(add(X_43,X_42),X_44) ),
inference(resolve,[$cnf( $equal(add(X_42,X_43),add(X_43,X_42)) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
add(X_42,add(X_43,X_44)) = add(add(X_43,X_42),X_44),
inference(resolve,[$cnf( $equal(add(X_42,add(X_43,X_44)),add(add(X_42,X_43),X_44)) )],[refute_0_58,refute_0_118]) ).
cnf(refute_0_120,plain,
add(add(X_43,X_42),X_44) = add(X_43,add(X_42,X_44)),
inference(subst,[],[refute_0_66:[bind(X,$fot(X_43)),bind(Y,$fot(X_42)),bind(Z,$fot(X_44))]]) ).
cnf(refute_0_121,plain,
( add(X_42,add(X_43,X_44)) != add(add(X_43,X_42),X_44)
| add(add(X_43,X_42),X_44) != add(X_43,add(X_42,X_44))
| add(X_42,add(X_43,X_44)) = add(X_43,add(X_42,X_44)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_42,add(X_43,X_44)),add(X_43,add(X_42,X_44))) ),[0],$fot(add(add(X_43,X_42),X_44))]]) ).
cnf(refute_0_122,plain,
( add(X_42,add(X_43,X_44)) != add(add(X_43,X_42),X_44)
| add(X_42,add(X_43,X_44)) = add(X_43,add(X_42,X_44)) ),
inference(resolve,[$cnf( $equal(add(add(X_43,X_42),X_44),add(X_43,add(X_42,X_44))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
add(X_42,add(X_43,X_44)) = add(X_43,add(X_42,X_44)),
inference(resolve,[$cnf( $equal(add(X_42,add(X_43,X_44)),add(add(X_43,X_42),X_44)) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
( add(X_42,add(X_43,X_44)) != add(X_43,add(X_42,X_44))
| add(X_43,add(X_42,X_44)) = add(X_42,add(X_43,X_44)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_42,add(X_43,X_44)))),bind(Y0,$fot(add(X_43,add(X_42,X_44))))]]) ).
cnf(refute_0_125,plain,
add(X_43,add(X_42,X_44)) = add(X_42,add(X_43,X_44)),
inference(resolve,[$cnf( $equal(add(X_42,add(X_43,X_44)),add(X_43,add(X_42,X_44))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
add(add(X,Y),add(additive_inverse(Y),X_46)) = add(additive_inverse(Y),add(add(X,Y),X_46)),
inference(subst,[],[refute_0_125:[bind(X_42,$fot(additive_inverse(Y))),bind(X_43,$fot(add(X,Y))),bind(X_44,$fot(X_46))]]) ).
cnf(refute_0_127,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_128,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_14,refute_0_127]) ).
cnf(refute_0_129,plain,
( add(add(X,Y),add(additive_inverse(Y),X_46)) != add(additive_inverse(Y),add(add(X,Y),X_46))
| add(additive_inverse(Y),add(add(X,Y),X_46)) != add(additive_inverse(Y),add(X,add(Y,X_46)))
| add(add(X,Y),add(additive_inverse(Y),X_46)) = add(additive_inverse(Y),add(X,add(Y,X_46))) ),
inference(subst,[],[refute_0_128:[bind(X0,$fot(add(add(X,Y),add(additive_inverse(Y),X_46)))),bind(Y0,$fot(add(additive_inverse(Y),add(add(X,Y),X_46)))),bind(Z0,$fot(add(additive_inverse(Y),add(X,add(Y,X_46)))))]]) ).
cnf(refute_0_130,plain,
( add(additive_inverse(Y),add(add(X,Y),X_46)) != add(additive_inverse(Y),add(X,add(Y,X_46)))
| add(add(X,Y),add(additive_inverse(Y),X_46)) = add(additive_inverse(Y),add(X,add(Y,X_46))) ),
inference(resolve,[$cnf( $equal(add(add(X,Y),add(additive_inverse(Y),X_46)),add(additive_inverse(Y),add(add(X,Y),X_46))) )],[refute_0_126,refute_0_129]) ).
cnf(refute_0_131,plain,
add(add(X,Y),add(additive_inverse(Y),X_46)) = add(additive_inverse(Y),add(X,add(Y,X_46))),
inference(resolve,[$cnf( $equal(add(additive_inverse(Y),add(add(X,Y),X_46)),add(additive_inverse(Y),add(X,add(Y,X_46)))) )],[refute_0_113,refute_0_130]) ).
cnf(refute_0_132,plain,
( add(X,X_46) != add(add(X,Y),add(additive_inverse(Y),X_46))
| add(add(X,Y),add(additive_inverse(Y),X_46)) != add(additive_inverse(Y),add(X,add(Y,X_46)))
| add(X,X_46) = add(additive_inverse(Y),add(X,add(Y,X_46))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X,X_46),add(additive_inverse(Y),add(X,add(Y,X_46)))) ),[0],$fot(add(add(X,Y),add(additive_inverse(Y),X_46)))]]) ).
cnf(refute_0_133,plain,
( add(X,X_46) != add(add(X,Y),add(additive_inverse(Y),X_46))
| add(X,X_46) = add(additive_inverse(Y),add(X,add(Y,X_46))) ),
inference(resolve,[$cnf( $equal(add(add(X,Y),add(additive_inverse(Y),X_46)),add(additive_inverse(Y),add(X,add(Y,X_46)))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
add(X,X_46) = add(additive_inverse(Y),add(X,add(Y,X_46))),
inference(resolve,[$cnf( $equal(add(X,X_46),add(add(X,Y),add(additive_inverse(Y),X_46))) )],[refute_0_108,refute_0_133]) ).
cnf(refute_0_135,plain,
add(X_53,add(add(X,Y),additive_inverse(X_53))) = add(X,Y),
inference(subst,[],[refute_0_47:[bind(X_45,$fot(X_53)),bind(X_46,$fot(add(X,Y)))]]) ).
cnf(refute_0_136,plain,
add(X,add(Y,additive_inverse(X_53))) = add(add(X,Y),additive_inverse(X_53)),
inference(subst,[],[associativity_for_addition:[bind(Z,$fot(additive_inverse(X_53)))]]) ).
cnf(refute_0_137,plain,
( add(X,add(Y,additive_inverse(X_53))) != add(add(X,Y),additive_inverse(X_53))
| add(add(X,Y),additive_inverse(X_53)) = add(X,add(Y,additive_inverse(X_53))) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X,add(Y,additive_inverse(X_53))))),bind(Y0,$fot(add(add(X,Y),additive_inverse(X_53))))]]) ).
cnf(refute_0_138,plain,
add(add(X,Y),additive_inverse(X_53)) = add(X,add(Y,additive_inverse(X_53))),
inference(resolve,[$cnf( $equal(add(X,add(Y,additive_inverse(X_53))),add(add(X,Y),additive_inverse(X_53))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
( add(X_53,add(add(X,Y),additive_inverse(X_53))) != add(X,Y)
| add(add(X,Y),additive_inverse(X_53)) != add(X,add(Y,additive_inverse(X_53)))
| add(X_53,add(X,add(Y,additive_inverse(X_53)))) = add(X,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_53,add(add(X,Y),additive_inverse(X_53))),add(X,Y)) ),[0,1],$fot(add(X,add(Y,additive_inverse(X_53))))]]) ).
cnf(refute_0_140,plain,
( add(X_53,add(add(X,Y),additive_inverse(X_53))) != add(X,Y)
| add(X_53,add(X,add(Y,additive_inverse(X_53)))) = add(X,Y) ),
inference(resolve,[$cnf( $equal(add(add(X,Y),additive_inverse(X_53)),add(X,add(Y,additive_inverse(X_53)))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
add(X_53,add(X,add(Y,additive_inverse(X_53)))) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X_53,add(add(X,Y),additive_inverse(X_53))),add(X,Y)) )],[refute_0_135,refute_0_140]) ).
cnf(refute_0_142,plain,
add(Y,add(X_46,add(X,additive_inverse(Y)))) = add(X_46,X),
inference(subst,[],[refute_0_141:[bind(X,$fot(X_46)),bind(Y,$fot(X)),bind(X_53,$fot(Y))]]) ).
cnf(refute_0_143,plain,
add(X,add(X_42,add(X_131,X_129))) = add(X_42,add(add(X_131,X_129),X)),
inference(subst,[],[refute_0_82:[bind(X_43,$fot(add(X_131,X_129)))]]) ).
cnf(refute_0_144,plain,
add(X_129,add(X_42,X_131)) = add(X_42,add(X_131,X_129)),
inference(subst,[],[refute_0_82:[bind(X,$fot(X_129)),bind(X_43,$fot(X_131))]]) ).
cnf(refute_0_145,plain,
( add(X_129,add(X_42,X_131)) != add(X_42,add(X_131,X_129))
| add(X_42,add(X_131,X_129)) = add(X_129,add(X_42,X_131)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X_129,add(X_42,X_131)))),bind(Y0,$fot(add(X_42,add(X_131,X_129))))]]) ).
cnf(refute_0_146,plain,
add(X_42,add(X_131,X_129)) = add(X_129,add(X_42,X_131)),
inference(resolve,[$cnf( $equal(add(X_129,add(X_42,X_131)),add(X_42,add(X_131,X_129))) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
( add(X,add(X_42,add(X_131,X_129))) != add(X_42,add(add(X_131,X_129),X))
| add(X_42,add(X_131,X_129)) != add(X_129,add(X_42,X_131))
| add(X,add(X_129,add(X_42,X_131))) = add(X_42,add(add(X_131,X_129),X)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,add(X_42,add(X_131,X_129))),add(X_42,add(add(X_131,X_129),X))) ),[0,1],$fot(add(X_129,add(X_42,X_131)))]]) ).
cnf(refute_0_148,plain,
( add(X,add(X_42,add(X_131,X_129))) != add(X_42,add(add(X_131,X_129),X))
| add(X,add(X_129,add(X_42,X_131))) = add(X_42,add(add(X_131,X_129),X)) ),
inference(resolve,[$cnf( $equal(add(X_42,add(X_131,X_129)),add(X_129,add(X_42,X_131))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
add(X,add(X_129,add(X_42,X_131))) = add(X_42,add(add(X_131,X_129),X)),
inference(resolve,[$cnf( $equal(add(X,add(X_42,add(X_131,X_129))),add(X_42,add(add(X_131,X_129),X))) )],[refute_0_143,refute_0_148]) ).
cnf(refute_0_150,plain,
add(add(X_131,X_129),X) = add(X_131,add(X_129,X)),
inference(subst,[],[refute_0_66:[bind(X,$fot(X_131)),bind(Y,$fot(X_129)),bind(Z,$fot(X))]]) ).
cnf(refute_0_151,plain,
add(X_42,add(add(X_131,X_129),X)) = add(X_42,add(add(X_131,X_129),X)),
introduced(tautology,[refl,[$fot(add(X_42,add(add(X_131,X_129),X)))]]) ).
cnf(refute_0_152,plain,
( add(X_42,add(add(X_131,X_129),X)) != add(X_42,add(add(X_131,X_129),X))
| add(add(X_131,X_129),X) != add(X_131,add(X_129,X))
| add(X_42,add(add(X_131,X_129),X)) = add(X_42,add(X_131,add(X_129,X))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_42,add(add(X_131,X_129),X)),add(X_42,add(add(X_131,X_129),X))) ),[1,1],$fot(add(X_131,add(X_129,X)))]]) ).
cnf(refute_0_153,plain,
( add(add(X_131,X_129),X) != add(X_131,add(X_129,X))
| add(X_42,add(add(X_131,X_129),X)) = add(X_42,add(X_131,add(X_129,X))) ),
inference(resolve,[$cnf( $equal(add(X_42,add(add(X_131,X_129),X)),add(X_42,add(add(X_131,X_129),X))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
add(X_42,add(add(X_131,X_129),X)) = add(X_42,add(X_131,add(X_129,X))),
inference(resolve,[$cnf( $equal(add(add(X_131,X_129),X),add(X_131,add(X_129,X))) )],[refute_0_150,refute_0_153]) ).
cnf(refute_0_155,plain,
( add(X,add(X_129,add(X_42,X_131))) != add(X_42,add(add(X_131,X_129),X))
| add(X_42,add(add(X_131,X_129),X)) != add(X_42,add(X_131,add(X_129,X)))
| add(X,add(X_129,add(X_42,X_131))) = add(X_42,add(X_131,add(X_129,X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X,add(X_129,add(X_42,X_131))),add(X_42,add(X_131,add(X_129,X)))) ),[0],$fot(add(X_42,add(add(X_131,X_129),X)))]]) ).
cnf(refute_0_156,plain,
( add(X,add(X_129,add(X_42,X_131))) != add(X_42,add(add(X_131,X_129),X))
| add(X,add(X_129,add(X_42,X_131))) = add(X_42,add(X_131,add(X_129,X))) ),
inference(resolve,[$cnf( $equal(add(X_42,add(add(X_131,X_129),X)),add(X_42,add(X_131,add(X_129,X)))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
add(X,add(X_129,add(X_42,X_131))) = add(X_42,add(X_131,add(X_129,X))),
inference(resolve,[$cnf( $equal(add(X,add(X_129,add(X_42,X_131))),add(X_42,add(add(X_131,X_129),X))) )],[refute_0_149,refute_0_156]) ).
cnf(refute_0_158,plain,
add(additive_inverse(Y),add(X,add(Y,X_46))) = add(Y,add(X_46,add(X,additive_inverse(Y)))),
inference(subst,[],[refute_0_157:[bind(X,$fot(additive_inverse(Y))),bind(X_129,$fot(X)),bind(X_131,$fot(X_46)),bind(X_42,$fot(Y))]]) ).
cnf(refute_0_159,plain,
( add(Y,add(X_46,add(X,additive_inverse(Y)))) != add(X_46,X)
| add(additive_inverse(Y),add(X,add(Y,X_46))) != add(Y,add(X_46,add(X,additive_inverse(Y))))
| add(additive_inverse(Y),add(X,add(Y,X_46))) = add(X_46,X) ),
inference(subst,[],[refute_0_128:[bind(X0,$fot(add(additive_inverse(Y),add(X,add(Y,X_46))))),bind(Y0,$fot(add(Y,add(X_46,add(X,additive_inverse(Y)))))),bind(Z0,$fot(add(X_46,X)))]]) ).
cnf(refute_0_160,plain,
( add(Y,add(X_46,add(X,additive_inverse(Y)))) != add(X_46,X)
| add(additive_inverse(Y),add(X,add(Y,X_46))) = add(X_46,X) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(Y),add(X,add(Y,X_46))),add(Y,add(X_46,add(X,additive_inverse(Y))))) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
add(additive_inverse(Y),add(X,add(Y,X_46))) = add(X_46,X),
inference(resolve,[$cnf( $equal(add(Y,add(X_46,add(X,additive_inverse(Y)))),add(X_46,X)) )],[refute_0_142,refute_0_160]) ).
cnf(refute_0_162,plain,
( add(X,X_46) != add(additive_inverse(Y),add(X,add(Y,X_46)))
| add(additive_inverse(Y),add(X,add(Y,X_46))) != add(X_46,X)
| add(X,X_46) = add(X_46,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X,X_46),add(X_46,X)) ),[0],$fot(add(additive_inverse(Y),add(X,add(Y,X_46))))]]) ).
cnf(refute_0_163,plain,
( add(X,X_46) != add(additive_inverse(Y),add(X,add(Y,X_46)))
| add(X,X_46) = add(X_46,X) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(Y),add(X,add(Y,X_46))),add(X_46,X)) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
add(X,X_46) = add(X_46,X),
inference(resolve,[$cnf( $equal(add(X,X_46),add(additive_inverse(Y),add(X,add(Y,X_46)))) )],[refute_0_134,refute_0_163]) ).
cnf(refute_0_165,plain,
( add(X,X_46) != add(X_46,X)
| add(X_46,X) = add(X,X_46) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X,X_46))),bind(Y0,$fot(add(X_46,X)))]]) ).
cnf(refute_0_166,plain,
add(X_46,X) = add(X,X_46),
inference(resolve,[$cnf( $equal(add(X,X_46),add(X_46,X)) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
add(multiply(X_848,additive_inverse(X_850)),multiply(X_850,X_848)) = add(multiply(X_850,X_848),multiply(X_848,additive_inverse(X_850))),
inference(subst,[],[refute_0_166:[bind(X,$fot(multiply(X_850,X_848))),bind(X_46,$fot(multiply(X_848,additive_inverse(X_850))))]]) ).
cnf(refute_0_168,plain,
( add(multiply(X_848,additive_inverse(X_850)),multiply(X_850,X_848)) != add(multiply(X_850,X_848),multiply(X_848,additive_inverse(X_850)))
| add(multiply(X_848,additive_inverse(X_850)),multiply(X_850,X_848)) != add(commutator(X_848,X_850),multiply(X_848,additive_identity))
| add(multiply(X_850,X_848),multiply(X_848,additive_inverse(X_850))) = add(commutator(X_848,X_850),multiply(X_848,additive_identity)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_848,additive_inverse(X_850)),multiply(X_850,X_848)),add(commutator(X_848,X_850),multiply(X_848,additive_identity))) ),[0],$fot(add(multiply(X_850,X_848),multiply(X_848,additive_inverse(X_850))))]]) ).
cnf(refute_0_169,plain,
( add(multiply(X_848,additive_inverse(X_850)),multiply(X_850,X_848)) != add(commutator(X_848,X_850),multiply(X_848,additive_identity))
| add(multiply(X_850,X_848),multiply(X_848,additive_inverse(X_850))) = add(commutator(X_848,X_850),multiply(X_848,additive_identity)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_848,additive_inverse(X_850)),multiply(X_850,X_848)),add(multiply(X_850,X_848),multiply(X_848,additive_inverse(X_850)))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
add(additive_identity,commutator(X_848,X_850)) = commutator(X_848,X_850),
inference(subst,[],[left_additive_identity:[bind(X,$fot(commutator(X_848,X_850)))]]) ).
cnf(refute_0_171,plain,
multiply(X_848,additive_identity) = additive_identity,
inference(subst,[],[right_multiplicative_zero:[bind(X,$fot(X_848))]]) ).
cnf(refute_0_172,plain,
add(multiply(X_848,additive_identity),commutator(X_848,X_850)) = add(multiply(X_848,additive_identity),commutator(X_848,X_850)),
introduced(tautology,[refl,[$fot(add(multiply(X_848,additive_identity),commutator(X_848,X_850)))]]) ).
cnf(refute_0_173,plain,
( multiply(X_848,additive_identity) != additive_identity
| add(multiply(X_848,additive_identity),commutator(X_848,X_850)) != add(multiply(X_848,additive_identity),commutator(X_848,X_850))
| add(multiply(X_848,additive_identity),commutator(X_848,X_850)) = add(additive_identity,commutator(X_848,X_850)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_848,additive_identity),commutator(X_848,X_850)),add(multiply(X_848,additive_identity),commutator(X_848,X_850))) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_174,plain,
( multiply(X_848,additive_identity) != additive_identity
| add(multiply(X_848,additive_identity),commutator(X_848,X_850)) = add(additive_identity,commutator(X_848,X_850)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_848,additive_identity),commutator(X_848,X_850)),add(multiply(X_848,additive_identity),commutator(X_848,X_850))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
add(multiply(X_848,additive_identity),commutator(X_848,X_850)) = add(additive_identity,commutator(X_848,X_850)),
inference(resolve,[$cnf( $equal(multiply(X_848,additive_identity),additive_identity) )],[refute_0_171,refute_0_174]) ).
cnf(refute_0_176,plain,
( add(multiply(X_848,additive_identity),commutator(X_848,X_850)) != add(additive_identity,commutator(X_848,X_850))
| add(additive_identity,commutator(X_848,X_850)) != commutator(X_848,X_850)
| add(multiply(X_848,additive_identity),commutator(X_848,X_850)) = commutator(X_848,X_850) ),
inference(subst,[],[refute_0_128:[bind(X0,$fot(add(multiply(X_848,additive_identity),commutator(X_848,X_850)))),bind(Y0,$fot(add(additive_identity,commutator(X_848,X_850)))),bind(Z0,$fot(commutator(X_848,X_850)))]]) ).
cnf(refute_0_177,plain,
( add(additive_identity,commutator(X_848,X_850)) != commutator(X_848,X_850)
| add(multiply(X_848,additive_identity),commutator(X_848,X_850)) = commutator(X_848,X_850) ),
inference(resolve,[$cnf( $equal(add(multiply(X_848,additive_identity),commutator(X_848,X_850)),add(additive_identity,commutator(X_848,X_850))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
add(multiply(X_848,additive_identity),commutator(X_848,X_850)) = commutator(X_848,X_850),
inference(resolve,[$cnf( $equal(add(additive_identity,commutator(X_848,X_850)),commutator(X_848,X_850)) )],[refute_0_170,refute_0_177]) ).
cnf(refute_0_179,plain,
add(commutator(X_848,X_850),multiply(X_848,additive_identity)) = add(multiply(X_848,additive_identity),commutator(X_848,X_850)),
inference(subst,[],[refute_0_166:[bind(X,$fot(multiply(X_848,additive_identity))),bind(X_46,$fot(commutator(X_848,X_850)))]]) ).
cnf(refute_0_180,plain,
( add(multiply(X_848,additive_identity),commutator(X_848,X_850)) != commutator(X_848,X_850)
| add(commutator(X_848,X_850),multiply(X_848,additive_identity)) != add(multiply(X_848,additive_identity),commutator(X_848,X_850))
| add(commutator(X_848,X_850),multiply(X_848,additive_identity)) = commutator(X_848,X_850) ),
inference(subst,[],[refute_0_128:[bind(X0,$fot(add(commutator(X_848,X_850),multiply(X_848,additive_identity)))),bind(Y0,$fot(add(multiply(X_848,additive_identity),commutator(X_848,X_850)))),bind(Z0,$fot(commutator(X_848,X_850)))]]) ).
cnf(refute_0_181,plain,
( add(multiply(X_848,additive_identity),commutator(X_848,X_850)) != commutator(X_848,X_850)
| add(commutator(X_848,X_850),multiply(X_848,additive_identity)) = commutator(X_848,X_850) ),
inference(resolve,[$cnf( $equal(add(commutator(X_848,X_850),multiply(X_848,additive_identity)),add(multiply(X_848,additive_identity),commutator(X_848,X_850))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
add(commutator(X_848,X_850),multiply(X_848,additive_identity)) = commutator(X_848,X_850),
inference(resolve,[$cnf( $equal(add(multiply(X_848,additive_identity),commutator(X_848,X_850)),commutator(X_848,X_850)) )],[refute_0_178,refute_0_181]) ).
cnf(refute_0_183,plain,
( add(multiply(X_850,X_848),multiply(X_848,additive_inverse(X_850))) != add(commutator(X_848,X_850),multiply(X_848,additive_identity))
| add(commutator(X_848,X_850),multiply(X_848,additive_identity)) != commutator(X_848,X_850)
| add(multiply(X_850,X_848),multiply(X_848,additive_inverse(X_850))) = commutator(X_848,X_850) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(multiply(X_850,X_848),multiply(X_848,additive_inverse(X_850))),commutator(X_848,X_850)) ),[0],$fot(add(commutator(X_848,X_850),multiply(X_848,additive_identity)))]]) ).
cnf(refute_0_184,plain,
( add(multiply(X_850,X_848),multiply(X_848,additive_inverse(X_850))) != add(commutator(X_848,X_850),multiply(X_848,additive_identity))
| add(multiply(X_850,X_848),multiply(X_848,additive_inverse(X_850))) = commutator(X_848,X_850) ),
inference(resolve,[$cnf( $equal(add(commutator(X_848,X_850),multiply(X_848,additive_identity)),commutator(X_848,X_850)) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
( add(multiply(X_848,additive_inverse(X_850)),multiply(X_850,X_848)) != add(commutator(X_848,X_850),multiply(X_848,additive_identity))
| add(multiply(X_850,X_848),multiply(X_848,additive_inverse(X_850))) = commutator(X_848,X_850) ),
inference(resolve,[$cnf( $equal(add(multiply(X_850,X_848),multiply(X_848,additive_inverse(X_850))),add(commutator(X_848,X_850),multiply(X_848,additive_identity))) )],[refute_0_169,refute_0_184]) ).
cnf(refute_0_186,plain,
add(multiply(X_850,X_848),multiply(X_848,additive_inverse(X_850))) = commutator(X_848,X_850),
inference(resolve,[$cnf( $equal(add(multiply(X_848,additive_inverse(X_850)),multiply(X_850,X_848)),add(commutator(X_848,X_850),multiply(X_848,additive_identity))) )],[refute_0_103,refute_0_185]) ).
cnf(refute_0_187,plain,
add(multiply(additive_inverse(X),X_986),multiply(X_986,additive_inverse(additive_inverse(X)))) = commutator(X_986,additive_inverse(X)),
inference(subst,[],[refute_0_186:[bind(X_848,$fot(X_986)),bind(X_850,$fot(additive_inverse(X)))]]) ).
cnf(refute_0_188,plain,
( add(multiply(additive_inverse(X),X_986),multiply(X_986,additive_inverse(additive_inverse(X)))) != commutator(X_986,additive_inverse(X))
| additive_inverse(additive_inverse(X)) != X
| add(multiply(additive_inverse(X),X_986),multiply(X_986,X)) = commutator(X_986,additive_inverse(X)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_inverse(X),X_986),multiply(X_986,additive_inverse(additive_inverse(X)))),commutator(X_986,additive_inverse(X))) ),[0,1,1],$fot(X)]]) ).
cnf(refute_0_189,plain,
( add(multiply(additive_inverse(X),X_986),multiply(X_986,additive_inverse(additive_inverse(X)))) != commutator(X_986,additive_inverse(X))
| add(multiply(additive_inverse(X),X_986),multiply(X_986,X)) = commutator(X_986,additive_inverse(X)) ),
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(X)),X) )],[additive_inverse_additive_inverse,refute_0_188]) ).
cnf(refute_0_190,plain,
add(multiply(additive_inverse(X),X_986),multiply(X_986,X)) = commutator(X_986,additive_inverse(X)),
inference(resolve,[$cnf( $equal(add(multiply(additive_inverse(X),X_986),multiply(X_986,additive_inverse(additive_inverse(X)))),commutator(X_986,additive_inverse(X))) )],[refute_0_187,refute_0_189]) ).
cnf(refute_0_191,plain,
add(additive_inverse(multiply(X_562,X_563)),add(X_43,multiply(add(X_562,X_562),X_563))) = add(X_43,add(additive_inverse(multiply(X_562,X_563)),multiply(add(X_562,X_562),X_563))),
inference(subst,[],[refute_0_123:[bind(X_42,$fot(additive_inverse(multiply(X_562,X_563)))),bind(X_44,$fot(multiply(add(X_562,X_562),X_563)))]]) ).
cnf(refute_0_192,plain,
add(multiply(X_556,X_557),add(multiply(X_556,X_558),additive_inverse(multiply(X_556,X_557)))) = multiply(X_556,X_558),
inference(subst,[],[refute_0_47:[bind(X_45,$fot(multiply(X_556,X_557))),bind(X_46,$fot(multiply(X_556,X_558)))]]) ).
cnf(refute_0_193,plain,
add(multiply(X_556,X_557),add(multiply(X_556,X_558),additive_inverse(multiply(X_556,X_557)))) = add(multiply(X_556,add(X_557,X_558)),additive_inverse(multiply(X_556,X_557))),
inference(subst,[],[refute_0_39:[bind(Z,$fot(additive_inverse(multiply(X_556,X_557)))),bind(X_47,$fot(X_556)),bind(X_48,$fot(X_557)),bind(X_49,$fot(X_558))]]) ).
cnf(refute_0_194,plain,
( add(multiply(X_556,X_557),add(multiply(X_556,X_558),additive_inverse(multiply(X_556,X_557)))) != multiply(X_556,X_558)
| add(multiply(X_556,X_557),add(multiply(X_556,X_558),additive_inverse(multiply(X_556,X_557)))) != add(multiply(X_556,add(X_557,X_558)),additive_inverse(multiply(X_556,X_557)))
| add(multiply(X_556,add(X_557,X_558)),additive_inverse(multiply(X_556,X_557))) = multiply(X_556,X_558) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_556,X_557),add(multiply(X_556,X_558),additive_inverse(multiply(X_556,X_557)))),multiply(X_556,X_558)) ),[0],$fot(add(multiply(X_556,add(X_557,X_558)),additive_inverse(multiply(X_556,X_557))))]]) ).
cnf(refute_0_195,plain,
( add(multiply(X_556,X_557),add(multiply(X_556,X_558),additive_inverse(multiply(X_556,X_557)))) != multiply(X_556,X_558)
| add(multiply(X_556,add(X_557,X_558)),additive_inverse(multiply(X_556,X_557))) = multiply(X_556,X_558) ),
inference(resolve,[$cnf( $equal(add(multiply(X_556,X_557),add(multiply(X_556,X_558),additive_inverse(multiply(X_556,X_557)))),add(multiply(X_556,add(X_557,X_558)),additive_inverse(multiply(X_556,X_557)))) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
add(multiply(X_556,add(X_557,X_558)),additive_inverse(multiply(X_556,X_557))) = multiply(X_556,X_558),
inference(resolve,[$cnf( $equal(add(multiply(X_556,X_557),add(multiply(X_556,X_558),additive_inverse(multiply(X_556,X_557)))),multiply(X_556,X_558)) )],[refute_0_192,refute_0_195]) ).
cnf(refute_0_197,plain,
add(multiply(X_556,add(X_557,X_558)),additive_inverse(multiply(X_556,X_557))) = add(additive_inverse(multiply(X_556,X_557)),multiply(X_556,add(X_557,X_558))),
inference(subst,[],[refute_0_166:[bind(X,$fot(additive_inverse(multiply(X_556,X_557)))),bind(X_46,$fot(multiply(X_556,add(X_557,X_558))))]]) ).
cnf(refute_0_198,plain,
( add(multiply(X_556,add(X_557,X_558)),additive_inverse(multiply(X_556,X_557))) != multiply(X_556,X_558)
| add(multiply(X_556,add(X_557,X_558)),additive_inverse(multiply(X_556,X_557))) != add(additive_inverse(multiply(X_556,X_557)),multiply(X_556,add(X_557,X_558)))
| add(additive_inverse(multiply(X_556,X_557)),multiply(X_556,add(X_557,X_558))) = multiply(X_556,X_558) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_556,add(X_557,X_558)),additive_inverse(multiply(X_556,X_557))),multiply(X_556,X_558)) ),[0],$fot(add(additive_inverse(multiply(X_556,X_557)),multiply(X_556,add(X_557,X_558))))]]) ).
cnf(refute_0_199,plain,
( add(multiply(X_556,add(X_557,X_558)),additive_inverse(multiply(X_556,X_557))) != multiply(X_556,X_558)
| add(additive_inverse(multiply(X_556,X_557)),multiply(X_556,add(X_557,X_558))) = multiply(X_556,X_558) ),
inference(resolve,[$cnf( $equal(add(multiply(X_556,add(X_557,X_558)),additive_inverse(multiply(X_556,X_557))),add(additive_inverse(multiply(X_556,X_557)),multiply(X_556,add(X_557,X_558)))) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
add(additive_inverse(multiply(X_556,X_557)),multiply(X_556,add(X_557,X_558))) = multiply(X_556,X_558),
inference(resolve,[$cnf( $equal(add(multiply(X_556,add(X_557,X_558)),additive_inverse(multiply(X_556,X_557))),multiply(X_556,X_558)) )],[refute_0_196,refute_0_199]) ).
cnf(refute_0_201,plain,
add(additive_inverse(multiply(X_559,X_561)),multiply(X_559,add(X_561,X_561))) = multiply(X_559,X_561),
inference(subst,[],[refute_0_200:[bind(X_556,$fot(X_559)),bind(X_557,$fot(X_561)),bind(X_558,$fot(X_561))]]) ).
cnf(refute_0_202,plain,
multiply(X,add(Z,Z)) = add(multiply(X,Z),multiply(X,Z)),
inference(subst,[],[distribute1:[bind(Y,$fot(Z))]]) ).
cnf(refute_0_203,plain,
multiply(add(X,X),Z) = add(multiply(X,Z),multiply(X,Z)),
inference(subst,[],[distribute2:[bind(Y,$fot(X))]]) ).
cnf(refute_0_204,plain,
( multiply(add(X,X),Z) != add(multiply(X,Z),multiply(X,Z))
| add(multiply(X,Z),multiply(X,Z)) = multiply(add(X,X),Z) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(multiply(add(X,X),Z))),bind(Y0,$fot(add(multiply(X,Z),multiply(X,Z))))]]) ).
cnf(refute_0_205,plain,
add(multiply(X,Z),multiply(X,Z)) = multiply(add(X,X),Z),
inference(resolve,[$cnf( $equal(multiply(add(X,X),Z),add(multiply(X,Z),multiply(X,Z))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
( multiply(X,add(Z,Z)) != add(multiply(X,Z),multiply(X,Z))
| add(multiply(X,Z),multiply(X,Z)) != multiply(add(X,X),Z)
| multiply(X,add(Z,Z)) = multiply(add(X,X),Z) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X,add(Z,Z)),multiply(add(X,X),Z)) ),[0],$fot(add(multiply(X,Z),multiply(X,Z)))]]) ).
cnf(refute_0_207,plain,
( multiply(X,add(Z,Z)) != add(multiply(X,Z),multiply(X,Z))
| multiply(X,add(Z,Z)) = multiply(add(X,X),Z) ),
inference(resolve,[$cnf( $equal(add(multiply(X,Z),multiply(X,Z)),multiply(add(X,X),Z)) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
multiply(X,add(Z,Z)) = multiply(add(X,X),Z),
inference(resolve,[$cnf( $equal(multiply(X,add(Z,Z)),add(multiply(X,Z),multiply(X,Z))) )],[refute_0_202,refute_0_207]) ).
cnf(refute_0_209,plain,
multiply(X_559,add(X_561,X_561)) = multiply(add(X_559,X_559),X_561),
inference(subst,[],[refute_0_208:[bind(X,$fot(X_559)),bind(Z,$fot(X_561))]]) ).
cnf(refute_0_210,plain,
( multiply(X_559,add(X_561,X_561)) != multiply(add(X_559,X_559),X_561)
| add(additive_inverse(multiply(X_559,X_561)),multiply(X_559,add(X_561,X_561))) != multiply(X_559,X_561)
| add(additive_inverse(multiply(X_559,X_561)),multiply(add(X_559,X_559),X_561)) = multiply(X_559,X_561) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(multiply(X_559,X_561)),multiply(X_559,add(X_561,X_561))),multiply(X_559,X_561)) ),[0,1],$fot(multiply(add(X_559,X_559),X_561))]]) ).
cnf(refute_0_211,plain,
( add(additive_inverse(multiply(X_559,X_561)),multiply(X_559,add(X_561,X_561))) != multiply(X_559,X_561)
| add(additive_inverse(multiply(X_559,X_561)),multiply(add(X_559,X_559),X_561)) = multiply(X_559,X_561) ),
inference(resolve,[$cnf( $equal(multiply(X_559,add(X_561,X_561)),multiply(add(X_559,X_559),X_561)) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
add(additive_inverse(multiply(X_559,X_561)),multiply(add(X_559,X_559),X_561)) = multiply(X_559,X_561),
inference(resolve,[$cnf( $equal(add(additive_inverse(multiply(X_559,X_561)),multiply(X_559,add(X_561,X_561))),multiply(X_559,X_561)) )],[refute_0_201,refute_0_211]) ).
cnf(refute_0_213,plain,
add(additive_inverse(multiply(X_562,X_563)),multiply(add(X_562,X_562),X_563)) = multiply(X_562,X_563),
inference(subst,[],[refute_0_212:[bind(X_559,$fot(X_562)),bind(X_561,$fot(X_563))]]) ).
cnf(refute_0_214,plain,
( add(additive_inverse(multiply(X_562,X_563)),multiply(add(X_562,X_562),X_563)) != multiply(X_562,X_563)
| add(additive_inverse(multiply(X_562,X_563)),add(X_43,multiply(add(X_562,X_562),X_563))) != add(X_43,add(additive_inverse(multiply(X_562,X_563)),multiply(add(X_562,X_562),X_563)))
| add(additive_inverse(multiply(X_562,X_563)),add(X_43,multiply(add(X_562,X_562),X_563))) = add(X_43,multiply(X_562,X_563)) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(multiply(X_562,X_563)),add(X_43,multiply(add(X_562,X_562),X_563))),add(X_43,add(additive_inverse(multiply(X_562,X_563)),multiply(add(X_562,X_562),X_563)))) ),[1,1],$fot(multiply(X_562,X_563))]]) ).
cnf(refute_0_215,plain,
( add(additive_inverse(multiply(X_562,X_563)),add(X_43,multiply(add(X_562,X_562),X_563))) != add(X_43,add(additive_inverse(multiply(X_562,X_563)),multiply(add(X_562,X_562),X_563)))
| add(additive_inverse(multiply(X_562,X_563)),add(X_43,multiply(add(X_562,X_562),X_563))) = add(X_43,multiply(X_562,X_563)) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(multiply(X_562,X_563)),multiply(add(X_562,X_562),X_563)),multiply(X_562,X_563)) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
add(additive_inverse(multiply(X_562,X_563)),add(X_43,multiply(add(X_562,X_562),X_563))) = add(X_43,multiply(X_562,X_563)),
inference(resolve,[$cnf( $equal(add(additive_inverse(multiply(X_562,X_563)),add(X_43,multiply(add(X_562,X_562),X_563))),add(X_43,add(additive_inverse(multiply(X_562,X_563)),multiply(add(X_562,X_562),X_563)))) )],[refute_0_191,refute_0_215]) ).
cnf(refute_0_217,plain,
add(multiply(X_50,X_52),add(multiply(X_51,X_52),Z)) = add(add(multiply(X_50,X_52),multiply(X_51,X_52)),Z),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(multiply(X_50,X_52))),bind(Y,$fot(multiply(X_51,X_52)))]]) ).
cnf(refute_0_218,plain,
multiply(add(X_50,X_51),X_52) = add(multiply(X_50,X_52),multiply(X_51,X_52)),
inference(subst,[],[distribute2:[bind(X,$fot(X_50)),bind(Y,$fot(X_51)),bind(Z,$fot(X_52))]]) ).
cnf(refute_0_219,plain,
( multiply(add(X_50,X_51),X_52) != add(multiply(X_50,X_52),multiply(X_51,X_52))
| add(multiply(X_50,X_52),multiply(X_51,X_52)) = multiply(add(X_50,X_51),X_52) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(multiply(add(X_50,X_51),X_52))),bind(Y0,$fot(add(multiply(X_50,X_52),multiply(X_51,X_52))))]]) ).
cnf(refute_0_220,plain,
add(multiply(X_50,X_52),multiply(X_51,X_52)) = multiply(add(X_50,X_51),X_52),
inference(resolve,[$cnf( $equal(multiply(add(X_50,X_51),X_52),add(multiply(X_50,X_52),multiply(X_51,X_52))) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
( add(multiply(X_50,X_52),multiply(X_51,X_52)) != multiply(add(X_50,X_51),X_52)
| add(multiply(X_50,X_52),add(multiply(X_51,X_52),Z)) != add(add(multiply(X_50,X_52),multiply(X_51,X_52)),Z)
| add(multiply(X_50,X_52),add(multiply(X_51,X_52),Z)) = add(multiply(add(X_50,X_51),X_52),Z) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_50,X_52),add(multiply(X_51,X_52),Z)),add(add(multiply(X_50,X_52),multiply(X_51,X_52)),Z)) ),[1,0],$fot(multiply(add(X_50,X_51),X_52))]]) ).
cnf(refute_0_222,plain,
( add(multiply(X_50,X_52),add(multiply(X_51,X_52),Z)) != add(add(multiply(X_50,X_52),multiply(X_51,X_52)),Z)
| add(multiply(X_50,X_52),add(multiply(X_51,X_52),Z)) = add(multiply(add(X_50,X_51),X_52),Z) ),
inference(resolve,[$cnf( $equal(add(multiply(X_50,X_52),multiply(X_51,X_52)),multiply(add(X_50,X_51),X_52)) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
add(multiply(X_50,X_52),add(multiply(X_51,X_52),Z)) = add(multiply(add(X_50,X_51),X_52),Z),
inference(resolve,[$cnf( $equal(add(multiply(X_50,X_52),add(multiply(X_51,X_52),Z)),add(add(multiply(X_50,X_52),multiply(X_51,X_52)),Z)) )],[refute_0_217,refute_0_222]) ).
cnf(refute_0_224,plain,
add(multiply(X_954,X_956),add(multiply(X_955,X_956),add(X_46,additive_inverse(multiply(X_955,X_956))))) = add(multiply(add(X_954,X_955),X_956),add(X_46,additive_inverse(multiply(X_955,X_956)))),
inference(subst,[],[refute_0_223:[bind(Z,$fot(add(X_46,additive_inverse(multiply(X_955,X_956))))),bind(X_50,$fot(X_954)),bind(X_51,$fot(X_955)),bind(X_52,$fot(X_956))]]) ).
cnf(refute_0_225,plain,
add(multiply(X_955,X_956),add(X_46,additive_inverse(multiply(X_955,X_956)))) = X_46,
inference(subst,[],[refute_0_47:[bind(X_45,$fot(multiply(X_955,X_956)))]]) ).
cnf(refute_0_226,plain,
( add(multiply(X_954,X_956),add(multiply(X_955,X_956),add(X_46,additive_inverse(multiply(X_955,X_956))))) != add(multiply(add(X_954,X_955),X_956),add(X_46,additive_inverse(multiply(X_955,X_956))))
| add(multiply(X_955,X_956),add(X_46,additive_inverse(multiply(X_955,X_956)))) != X_46
| add(multiply(X_954,X_956),X_46) = add(multiply(add(X_954,X_955),X_956),add(X_46,additive_inverse(multiply(X_955,X_956)))) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_954,X_956),add(multiply(X_955,X_956),add(X_46,additive_inverse(multiply(X_955,X_956))))),add(multiply(add(X_954,X_955),X_956),add(X_46,additive_inverse(multiply(X_955,X_956))))) ),[0,1],$fot(X_46)]]) ).
cnf(refute_0_227,plain,
( add(multiply(X_954,X_956),add(multiply(X_955,X_956),add(X_46,additive_inverse(multiply(X_955,X_956))))) != add(multiply(add(X_954,X_955),X_956),add(X_46,additive_inverse(multiply(X_955,X_956))))
| add(multiply(X_954,X_956),X_46) = add(multiply(add(X_954,X_955),X_956),add(X_46,additive_inverse(multiply(X_955,X_956)))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_955,X_956),add(X_46,additive_inverse(multiply(X_955,X_956)))),X_46) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
add(multiply(X_954,X_956),X_46) = add(multiply(add(X_954,X_955),X_956),add(X_46,additive_inverse(multiply(X_955,X_956)))),
inference(resolve,[$cnf( $equal(add(multiply(X_954,X_956),add(multiply(X_955,X_956),add(X_46,additive_inverse(multiply(X_955,X_956))))),add(multiply(add(X_954,X_955),X_956),add(X_46,additive_inverse(multiply(X_955,X_956))))) )],[refute_0_224,refute_0_227]) ).
cnf(refute_0_229,plain,
add(X_42,add(X_43,X)) = add(X_43,add(X_42,X)),
inference(subst,[],[refute_0_123:[bind(X_44,$fot(X))]]) ).
cnf(refute_0_230,plain,
( add(X,add(X_42,X_43)) != add(X_42,add(X_43,X))
| add(X_42,add(X_43,X)) != add(X_43,add(X_42,X))
| add(X,add(X_42,X_43)) = add(X_43,add(X_42,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X,add(X_42,X_43)),add(X_43,add(X_42,X))) ),[0],$fot(add(X_42,add(X_43,X)))]]) ).
cnf(refute_0_231,plain,
( add(X,add(X_42,X_43)) != add(X_42,add(X_43,X))
| add(X,add(X_42,X_43)) = add(X_43,add(X_42,X)) ),
inference(resolve,[$cnf( $equal(add(X_42,add(X_43,X)),add(X_43,add(X_42,X))) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
add(X,add(X_42,X_43)) = add(X_43,add(X_42,X)),
inference(resolve,[$cnf( $equal(add(X,add(X_42,X_43)),add(X_42,add(X_43,X))) )],[refute_0_82,refute_0_231]) ).
cnf(refute_0_233,plain,
( add(X,add(X_42,X_43)) != add(X_43,add(X_42,X))
| add(X_43,add(X_42,X)) = add(X,add(X_42,X_43)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(X,add(X_42,X_43)))),bind(Y0,$fot(add(X_43,add(X_42,X))))]]) ).
cnf(refute_0_234,plain,
add(X_43,add(X_42,X)) = add(X,add(X_42,X_43)),
inference(resolve,[$cnf( $equal(add(X,add(X_42,X_43)),add(X_43,add(X_42,X))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
add(multiply(add(X_954,X_955),X_956),add(X_46,additive_inverse(multiply(X_955,X_956)))) = add(additive_inverse(multiply(X_955,X_956)),add(X_46,multiply(add(X_954,X_955),X_956))),
inference(subst,[],[refute_0_234:[bind(X,$fot(additive_inverse(multiply(X_955,X_956)))),bind(X_42,$fot(X_46)),bind(X_43,$fot(multiply(add(X_954,X_955),X_956)))]]) ).
cnf(refute_0_236,plain,
( add(multiply(X_954,X_956),X_46) != add(multiply(add(X_954,X_955),X_956),add(X_46,additive_inverse(multiply(X_955,X_956))))
| add(multiply(add(X_954,X_955),X_956),add(X_46,additive_inverse(multiply(X_955,X_956)))) != add(additive_inverse(multiply(X_955,X_956)),add(X_46,multiply(add(X_954,X_955),X_956)))
| add(multiply(X_954,X_956),X_46) = add(additive_inverse(multiply(X_955,X_956)),add(X_46,multiply(add(X_954,X_955),X_956))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(multiply(X_954,X_956),X_46),add(additive_inverse(multiply(X_955,X_956)),add(X_46,multiply(add(X_954,X_955),X_956)))) ),[0],$fot(add(multiply(add(X_954,X_955),X_956),add(X_46,additive_inverse(multiply(X_955,X_956)))))]]) ).
cnf(refute_0_237,plain,
( add(multiply(X_954,X_956),X_46) != add(multiply(add(X_954,X_955),X_956),add(X_46,additive_inverse(multiply(X_955,X_956))))
| add(multiply(X_954,X_956),X_46) = add(additive_inverse(multiply(X_955,X_956)),add(X_46,multiply(add(X_954,X_955),X_956))) ),
inference(resolve,[$cnf( $equal(add(multiply(add(X_954,X_955),X_956),add(X_46,additive_inverse(multiply(X_955,X_956)))),add(additive_inverse(multiply(X_955,X_956)),add(X_46,multiply(add(X_954,X_955),X_956)))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
add(multiply(X_954,X_956),X_46) = add(additive_inverse(multiply(X_955,X_956)),add(X_46,multiply(add(X_954,X_955),X_956))),
inference(resolve,[$cnf( $equal(add(multiply(X_954,X_956),X_46),add(multiply(add(X_954,X_955),X_956),add(X_46,additive_inverse(multiply(X_955,X_956))))) )],[refute_0_228,refute_0_237]) ).
cnf(refute_0_239,plain,
( add(multiply(X_954,X_956),X_46) != add(additive_inverse(multiply(X_955,X_956)),add(X_46,multiply(add(X_954,X_955),X_956)))
| add(additive_inverse(multiply(X_955,X_956)),add(X_46,multiply(add(X_954,X_955),X_956))) = add(multiply(X_954,X_956),X_46) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(multiply(X_954,X_956),X_46))),bind(Y0,$fot(add(additive_inverse(multiply(X_955,X_956)),add(X_46,multiply(add(X_954,X_955),X_956)))))]]) ).
cnf(refute_0_240,plain,
add(additive_inverse(multiply(X_955,X_956)),add(X_46,multiply(add(X_954,X_955),X_956))) = add(multiply(X_954,X_956),X_46),
inference(resolve,[$cnf( $equal(add(multiply(X_954,X_956),X_46),add(additive_inverse(multiply(X_955,X_956)),add(X_46,multiply(add(X_954,X_955),X_956)))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
add(additive_inverse(multiply(X_562,X_563)),add(X_43,multiply(add(X_562,X_562),X_563))) = add(multiply(X_562,X_563),X_43),
inference(subst,[],[refute_0_240:[bind(X_46,$fot(X_43)),bind(X_954,$fot(X_562)),bind(X_955,$fot(X_562)),bind(X_956,$fot(X_563))]]) ).
cnf(refute_0_242,plain,
( add(additive_inverse(multiply(X_562,X_563)),add(X_43,multiply(add(X_562,X_562),X_563))) != add(X_43,multiply(X_562,X_563))
| add(additive_inverse(multiply(X_562,X_563)),add(X_43,multiply(add(X_562,X_562),X_563))) != add(multiply(X_562,X_563),X_43)
| add(multiply(X_562,X_563),X_43) = add(X_43,multiply(X_562,X_563)) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(multiply(X_562,X_563)),add(X_43,multiply(add(X_562,X_562),X_563))),add(X_43,multiply(X_562,X_563))) ),[0],$fot(add(multiply(X_562,X_563),X_43))]]) ).
cnf(refute_0_243,plain,
( add(additive_inverse(multiply(X_562,X_563)),add(X_43,multiply(add(X_562,X_562),X_563))) != add(X_43,multiply(X_562,X_563))
| add(multiply(X_562,X_563),X_43) = add(X_43,multiply(X_562,X_563)) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(multiply(X_562,X_563)),add(X_43,multiply(add(X_562,X_562),X_563))),add(multiply(X_562,X_563),X_43)) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
add(multiply(X_562,X_563),X_43) = add(X_43,multiply(X_562,X_563)),
inference(resolve,[$cnf( $equal(add(additive_inverse(multiply(X_562,X_563)),add(X_43,multiply(add(X_562,X_562),X_563))),add(X_43,multiply(X_562,X_563))) )],[refute_0_216,refute_0_243]) ).
cnf(refute_0_245,plain,
( add(multiply(X_562,X_563),X_43) != add(X_43,multiply(X_562,X_563))
| add(X_43,multiply(X_562,X_563)) = add(multiply(X_562,X_563),X_43) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(add(multiply(X_562,X_563),X_43))),bind(Y0,$fot(add(X_43,multiply(X_562,X_563))))]]) ).
cnf(refute_0_246,plain,
add(X_43,multiply(X_562,X_563)) = add(multiply(X_562,X_563),X_43),
inference(resolve,[$cnf( $equal(add(multiply(X_562,X_563),X_43),add(X_43,multiply(X_562,X_563))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
add(multiply(additive_inverse(X),X_986),multiply(X_986,X)) = add(multiply(X_986,X),multiply(additive_inverse(X),X_986)),
inference(subst,[],[refute_0_246:[bind(X_43,$fot(multiply(additive_inverse(X),X_986))),bind(X_562,$fot(X_986)),bind(X_563,$fot(X))]]) ).
cnf(refute_0_248,plain,
( add(multiply(additive_inverse(X),X_986),multiply(X_986,X)) != add(multiply(X_986,X),multiply(additive_inverse(X),X_986))
| add(multiply(additive_inverse(X),X_986),multiply(X_986,X)) != commutator(X_986,additive_inverse(X))
| add(multiply(X_986,X),multiply(additive_inverse(X),X_986)) = commutator(X_986,additive_inverse(X)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_inverse(X),X_986),multiply(X_986,X)),commutator(X_986,additive_inverse(X))) ),[0],$fot(add(multiply(X_986,X),multiply(additive_inverse(X),X_986)))]]) ).
cnf(refute_0_249,plain,
( add(multiply(additive_inverse(X),X_986),multiply(X_986,X)) != commutator(X_986,additive_inverse(X))
| add(multiply(X_986,X),multiply(additive_inverse(X),X_986)) = commutator(X_986,additive_inverse(X)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_inverse(X),X_986),multiply(X_986,X)),add(multiply(X_986,X),multiply(additive_inverse(X),X_986))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
add(multiply(X_986,X),multiply(additive_inverse(X),X_986)) = commutator(X_986,additive_inverse(X)),
inference(resolve,[$cnf( $equal(add(multiply(additive_inverse(X),X_986),multiply(X_986,X)),commutator(X_986,additive_inverse(X))) )],[refute_0_190,refute_0_249]) ).
cnf(refute_0_251,plain,
add(multiply(X_1009,X_1008),multiply(additive_inverse(X_1008),X_1009)) = commutator(X_1009,additive_inverse(X_1008)),
inference(subst,[],[refute_0_250:[bind(X,$fot(X_1008)),bind(X_986,$fot(X_1009))]]) ).
cnf(refute_0_252,plain,
( add(multiply(X_1009,X_1008),multiply(additive_inverse(X_1008),X_1009)) != commutator(X_1009,additive_inverse(X_1008))
| additive_inverse(multiply(X_1009,X_1008)) != add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(add(multiply(X_1009,X_1008),multiply(additive_inverse(X_1008),X_1009))))
| additive_inverse(multiply(X_1009,X_1008)) = add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008)))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(X_1009,X_1008)),add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(add(multiply(X_1009,X_1008),multiply(additive_inverse(X_1008),X_1009))))) ),[1,1,0],$fot(commutator(X_1009,additive_inverse(X_1008)))]]) ).
cnf(refute_0_253,plain,
( additive_inverse(multiply(X_1009,X_1008)) != add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(add(multiply(X_1009,X_1008),multiply(additive_inverse(X_1008),X_1009))))
| additive_inverse(multiply(X_1009,X_1008)) = add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008)))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_1009,X_1008),multiply(additive_inverse(X_1008),X_1009)),commutator(X_1009,additive_inverse(X_1008))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
additive_inverse(multiply(X_1009,X_1008)) = add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008)))),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X_1009,X_1008)),add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(add(multiply(X_1009,X_1008),multiply(additive_inverse(X_1008),X_1009))))) )],[refute_0_32,refute_0_253]) ).
cnf(refute_0_255,plain,
add(multiply(additive_inverse(X_1008),X_1009),commutator(additive_inverse(X_1008),X_1009)) = multiply(X_1009,additive_inverse(X_1008)),
inference(subst,[],[refute_0_53:[bind(X,$fot(additive_inverse(X_1008))),bind(Y,$fot(X_1009))]]) ).
cnf(refute_0_256,plain,
add(multiply(X_123,X_124),add(additive_inverse(multiply(X_123,X_124)),additive_inverse(commutator(X_123,X_124)))) = additive_inverse(commutator(X_123,X_124)),
inference(subst,[],[refute_0_8:[bind(X_42,$fot(multiply(X_123,X_124))),bind(X_44,$fot(additive_inverse(commutator(X_123,X_124))))]]) ).
cnf(refute_0_257,plain,
additive_inverse(multiply(Y,X)) = add(additive_inverse(multiply(X,Y)),additive_inverse(add(multiply(Y,X),additive_inverse(multiply(X,Y))))),
inference(subst,[],[refute_0_31:[bind(X,$fot(multiply(Y,X))),bind(X_64,$fot(additive_inverse(multiply(X,Y))))]]) ).
cnf(refute_0_258,plain,
( add(multiply(Y,X),additive_inverse(multiply(X,Y))) != commutator(X,Y)
| additive_inverse(multiply(Y,X)) != add(additive_inverse(multiply(X,Y)),additive_inverse(add(multiply(Y,X),additive_inverse(multiply(X,Y)))))
| additive_inverse(multiply(Y,X)) = add(additive_inverse(multiply(X,Y)),additive_inverse(commutator(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(Y,X)),add(additive_inverse(multiply(X,Y)),additive_inverse(add(multiply(Y,X),additive_inverse(multiply(X,Y)))))) ),[1,1,0],$fot(commutator(X,Y))]]) ).
cnf(refute_0_259,plain,
( additive_inverse(multiply(Y,X)) != add(additive_inverse(multiply(X,Y)),additive_inverse(add(multiply(Y,X),additive_inverse(multiply(X,Y)))))
| additive_inverse(multiply(Y,X)) = add(additive_inverse(multiply(X,Y)),additive_inverse(commutator(X,Y))) ),
inference(resolve,[$cnf( $equal(add(multiply(Y,X),additive_inverse(multiply(X,Y))),commutator(X,Y)) )],[refute_0_50,refute_0_258]) ).
cnf(refute_0_260,plain,
additive_inverse(multiply(Y,X)) = add(additive_inverse(multiply(X,Y)),additive_inverse(commutator(X,Y))),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(Y,X)),add(additive_inverse(multiply(X,Y)),additive_inverse(add(multiply(Y,X),additive_inverse(multiply(X,Y)))))) )],[refute_0_257,refute_0_259]) ).
cnf(refute_0_261,plain,
additive_inverse(multiply(X_124,X_123)) = add(additive_inverse(multiply(X_123,X_124)),additive_inverse(commutator(X_123,X_124))),
inference(subst,[],[refute_0_260:[bind(X,$fot(X_123)),bind(Y,$fot(X_124))]]) ).
cnf(refute_0_262,plain,
( additive_inverse(multiply(X_124,X_123)) != add(additive_inverse(multiply(X_123,X_124)),additive_inverse(commutator(X_123,X_124)))
| add(additive_inverse(multiply(X_123,X_124)),additive_inverse(commutator(X_123,X_124))) = additive_inverse(multiply(X_124,X_123)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(additive_inverse(multiply(X_124,X_123)))),bind(Y0,$fot(add(additive_inverse(multiply(X_123,X_124)),additive_inverse(commutator(X_123,X_124)))))]]) ).
cnf(refute_0_263,plain,
add(additive_inverse(multiply(X_123,X_124)),additive_inverse(commutator(X_123,X_124))) = additive_inverse(multiply(X_124,X_123)),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X_124,X_123)),add(additive_inverse(multiply(X_123,X_124)),additive_inverse(commutator(X_123,X_124)))) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
( add(multiply(X_123,X_124),add(additive_inverse(multiply(X_123,X_124)),additive_inverse(commutator(X_123,X_124)))) != additive_inverse(commutator(X_123,X_124))
| add(additive_inverse(multiply(X_123,X_124)),additive_inverse(commutator(X_123,X_124))) != additive_inverse(multiply(X_124,X_123))
| add(multiply(X_123,X_124),additive_inverse(multiply(X_124,X_123))) = additive_inverse(commutator(X_123,X_124)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_123,X_124),add(additive_inverse(multiply(X_123,X_124)),additive_inverse(commutator(X_123,X_124)))),additive_inverse(commutator(X_123,X_124))) ),[0,1],$fot(additive_inverse(multiply(X_124,X_123)))]]) ).
cnf(refute_0_265,plain,
( add(multiply(X_123,X_124),add(additive_inverse(multiply(X_123,X_124)),additive_inverse(commutator(X_123,X_124)))) != additive_inverse(commutator(X_123,X_124))
| add(multiply(X_123,X_124),additive_inverse(multiply(X_124,X_123))) = additive_inverse(commutator(X_123,X_124)) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(multiply(X_123,X_124)),additive_inverse(commutator(X_123,X_124))),additive_inverse(multiply(X_124,X_123))) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
add(multiply(X_123,X_124),additive_inverse(multiply(X_124,X_123))) = additive_inverse(commutator(X_123,X_124)),
inference(resolve,[$cnf( $equal(add(multiply(X_123,X_124),add(additive_inverse(multiply(X_123,X_124)),additive_inverse(commutator(X_123,X_124)))),additive_inverse(commutator(X_123,X_124))) )],[refute_0_256,refute_0_265]) ).
cnf(refute_0_267,plain,
add(multiply(X_123,X_124),additive_inverse(multiply(X_124,X_123))) = commutator(X_124,X_123),
inference(subst,[],[refute_0_50:[bind(X,$fot(X_124)),bind(Y,$fot(X_123))]]) ).
cnf(refute_0_268,plain,
( add(multiply(X_123,X_124),additive_inverse(multiply(X_124,X_123))) != additive_inverse(commutator(X_123,X_124))
| add(multiply(X_123,X_124),additive_inverse(multiply(X_124,X_123))) != commutator(X_124,X_123)
| commutator(X_124,X_123) = additive_inverse(commutator(X_123,X_124)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_123,X_124),additive_inverse(multiply(X_124,X_123))),additive_inverse(commutator(X_123,X_124))) ),[0],$fot(commutator(X_124,X_123))]]) ).
cnf(refute_0_269,plain,
( add(multiply(X_123,X_124),additive_inverse(multiply(X_124,X_123))) != additive_inverse(commutator(X_123,X_124))
| commutator(X_124,X_123) = additive_inverse(commutator(X_123,X_124)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_123,X_124),additive_inverse(multiply(X_124,X_123))),commutator(X_124,X_123)) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
commutator(X_124,X_123) = additive_inverse(commutator(X_123,X_124)),
inference(resolve,[$cnf( $equal(add(multiply(X_123,X_124),additive_inverse(multiply(X_124,X_123))),additive_inverse(commutator(X_123,X_124))) )],[refute_0_266,refute_0_269]) ).
cnf(refute_0_271,plain,
( commutator(X_124,X_123) != additive_inverse(commutator(X_123,X_124))
| additive_inverse(commutator(X_123,X_124)) = commutator(X_124,X_123) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(commutator(X_124,X_123))),bind(Y0,$fot(additive_inverse(commutator(X_123,X_124))))]]) ).
cnf(refute_0_272,plain,
additive_inverse(commutator(X_123,X_124)) = commutator(X_124,X_123),
inference(resolve,[$cnf( $equal(commutator(X_124,X_123),additive_inverse(commutator(X_123,X_124))) )],[refute_0_270,refute_0_271]) ).
cnf(refute_0_273,plain,
additive_inverse(commutator(X_1009,additive_inverse(X_1008))) = commutator(additive_inverse(X_1008),X_1009),
inference(subst,[],[refute_0_272:[bind(X_123,$fot(X_1009)),bind(X_124,$fot(additive_inverse(X_1008)))]]) ).
cnf(refute_0_274,plain,
add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008)))) = add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008)))),
introduced(tautology,[refl,[$fot(add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008)))))]]) ).
cnf(refute_0_275,plain,
( add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008)))) != add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008))))
| additive_inverse(commutator(X_1009,additive_inverse(X_1008))) != commutator(additive_inverse(X_1008),X_1009)
| add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008)))) = add(multiply(additive_inverse(X_1008),X_1009),commutator(additive_inverse(X_1008),X_1009)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008)))),add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008))))) ),[1,1],$fot(commutator(additive_inverse(X_1008),X_1009))]]) ).
cnf(refute_0_276,plain,
( additive_inverse(commutator(X_1009,additive_inverse(X_1008))) != commutator(additive_inverse(X_1008),X_1009)
| add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008)))) = add(multiply(additive_inverse(X_1008),X_1009),commutator(additive_inverse(X_1008),X_1009)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008)))),add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008))))) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008)))) = add(multiply(additive_inverse(X_1008),X_1009),commutator(additive_inverse(X_1008),X_1009)),
inference(resolve,[$cnf( $equal(additive_inverse(commutator(X_1009,additive_inverse(X_1008))),commutator(additive_inverse(X_1008),X_1009)) )],[refute_0_273,refute_0_276]) ).
cnf(refute_0_278,plain,
( add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008)))) != add(multiply(additive_inverse(X_1008),X_1009),commutator(additive_inverse(X_1008),X_1009))
| add(multiply(additive_inverse(X_1008),X_1009),commutator(additive_inverse(X_1008),X_1009)) != multiply(X_1009,additive_inverse(X_1008))
| add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008)))) = multiply(X_1009,additive_inverse(X_1008)) ),
inference(subst,[],[refute_0_128:[bind(X0,$fot(add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008)))))),bind(Y0,$fot(add(multiply(additive_inverse(X_1008),X_1009),commutator(additive_inverse(X_1008),X_1009)))),bind(Z0,$fot(multiply(X_1009,additive_inverse(X_1008))))]]) ).
cnf(refute_0_279,plain,
( add(multiply(additive_inverse(X_1008),X_1009),commutator(additive_inverse(X_1008),X_1009)) != multiply(X_1009,additive_inverse(X_1008))
| add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008)))) = multiply(X_1009,additive_inverse(X_1008)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008)))),add(multiply(additive_inverse(X_1008),X_1009),commutator(additive_inverse(X_1008),X_1009))) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008)))) = multiply(X_1009,additive_inverse(X_1008)),
inference(resolve,[$cnf( $equal(add(multiply(additive_inverse(X_1008),X_1009),commutator(additive_inverse(X_1008),X_1009)),multiply(X_1009,additive_inverse(X_1008))) )],[refute_0_255,refute_0_279]) ).
cnf(refute_0_281,plain,
( add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008)))) != multiply(X_1009,additive_inverse(X_1008))
| additive_inverse(multiply(X_1009,X_1008)) != add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008))))
| additive_inverse(multiply(X_1009,X_1008)) = multiply(X_1009,additive_inverse(X_1008)) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(X_1009,X_1008)),add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008))))) ),[1],$fot(multiply(X_1009,additive_inverse(X_1008)))]]) ).
cnf(refute_0_282,plain,
( additive_inverse(multiply(X_1009,X_1008)) != add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008))))
| additive_inverse(multiply(X_1009,X_1008)) = multiply(X_1009,additive_inverse(X_1008)) ),
inference(resolve,[$cnf( $equal(add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008)))),multiply(X_1009,additive_inverse(X_1008))) )],[refute_0_280,refute_0_281]) ).
cnf(refute_0_283,plain,
additive_inverse(multiply(X_1009,X_1008)) = multiply(X_1009,additive_inverse(X_1008)),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X_1009,X_1008)),add(multiply(additive_inverse(X_1008),X_1009),additive_inverse(commutator(X_1009,additive_inverse(X_1008))))) )],[refute_0_254,refute_0_282]) ).
cnf(refute_0_284,plain,
( additive_inverse(multiply(X_1009,X_1008)) != multiply(X_1009,additive_inverse(X_1008))
| multiply(X_1009,additive_inverse(X_1008)) = additive_inverse(multiply(X_1009,X_1008)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(additive_inverse(multiply(X_1009,X_1008)))),bind(Y0,$fot(multiply(X_1009,additive_inverse(X_1008))))]]) ).
cnf(refute_0_285,plain,
multiply(X_1009,additive_inverse(X_1008)) = additive_inverse(multiply(X_1009,X_1008)),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X_1009,X_1008)),multiply(X_1009,additive_inverse(X_1008))) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
multiply(a,additive_inverse(b)) = additive_inverse(multiply(a,b)),
inference(subst,[],[refute_0_285:[bind(X_1008,$fot(b)),bind(X_1009,$fot(a))]]) ).
cnf(refute_0_287,plain,
( multiply(a,additive_inverse(b)) != additive_inverse(multiply(a,b))
| additive_inverse(multiply(a,b)) != additive_inverse(multiply(a,b))
| multiply(a,additive_inverse(b)) = additive_inverse(multiply(a,b)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,b))) ),[0],$fot(additive_inverse(multiply(a,b)))]]) ).
cnf(refute_0_288,plain,
( additive_inverse(multiply(a,b)) != additive_inverse(multiply(a,b))
| multiply(a,additive_inverse(b)) = additive_inverse(multiply(a,b)) ),
inference(resolve,[$cnf( $equal(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,b))) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
additive_inverse(multiply(a,b)) != additive_inverse(multiply(a,b)),
inference(resolve,[$cnf( $equal(multiply(a,additive_inverse(b)),additive_inverse(multiply(a,b))) )],[refute_0_288,prove_equation]) ).
cnf(refute_0_290,plain,
additive_inverse(multiply(a,b)) = additive_inverse(multiply(a,b)),
introduced(tautology,[refl,[$fot(additive_inverse(multiply(a,b)))]]) ).
cnf(refute_0_291,plain,
$false,
inference(resolve,[$cnf( $equal(additive_inverse(multiply(a,b)),additive_inverse(multiply(a,b))) )],[refute_0_290,refute_0_289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : RNG014-6 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon May 30 06:58:13 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 291.75/291.93 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 291.75/291.93
% 291.75/291.93 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 291.75/291.96
%------------------------------------------------------------------------------