TSTP Solution File: RNG015-6 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : RNG015-6 : 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 : Unsatisfiable 1.07s 1.27s
% Output : CNFRefutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 42
% Syntax : Number of clauses : 190 ( 104 unt; 0 nHn; 90 RR)
% Number of literals : 312 ( 311 equ; 124 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; 4 con; 0-2 aty)
% Number of variables : 482 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_additive_identity,axiom,
add(additive_identity,X) = X ).
cnf(right_additive_identity,axiom,
add(X,additive_identity) = X ).
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(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(prove_distributivity,negated_conjecture,
multiply(x,add(y,additive_inverse(z))) != add(multiply(x,y),additive_inverse(multiply(x,z))) ).
cnf(refute_0_0,plain,
multiply(X,add(Y,additive_inverse(X_129))) = add(multiply(X,Y),multiply(X,additive_inverse(X_129))),
inference(subst,[],[distribute1:[bind(Z,$fot(additive_inverse(X_129)))]]) ).
cnf(refute_0_1,plain,
add(X_32,add(additive_inverse(X_32),X_34)) = add(add(X_32,additive_inverse(X_32)),X_34),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(X_32)),bind(Y,$fot(additive_inverse(X_32))),bind(Z,$fot(X_34))]]) ).
cnf(refute_0_2,plain,
add(X_32,additive_inverse(X_32)) = additive_identity,
inference(subst,[],[right_additive_inverse:[bind(X,$fot(X_32))]]) ).
cnf(refute_0_3,plain,
( add(X_32,add(additive_inverse(X_32),X_34)) != add(add(X_32,additive_inverse(X_32)),X_34)
| add(X_32,additive_inverse(X_32)) != additive_identity
| add(X_32,add(additive_inverse(X_32),X_34)) = add(additive_identity,X_34) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_32,add(additive_inverse(X_32),X_34)),add(add(X_32,additive_inverse(X_32)),X_34)) ),[1,0],$fot(additive_identity)]]) ).
cnf(refute_0_4,plain,
( add(X_32,add(additive_inverse(X_32),X_34)) != add(add(X_32,additive_inverse(X_32)),X_34)
| add(X_32,add(additive_inverse(X_32),X_34)) = add(additive_identity,X_34) ),
inference(resolve,[$cnf( $equal(add(X_32,additive_inverse(X_32)),additive_identity) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
add(X_32,add(additive_inverse(X_32),X_34)) = add(additive_identity,X_34),
inference(resolve,[$cnf( $equal(add(X_32,add(additive_inverse(X_32),X_34)),add(add(X_32,additive_inverse(X_32)),X_34)) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
add(additive_identity,X_34) = X_34,
inference(subst,[],[left_additive_identity:[bind(X,$fot(X_34))]]) ).
cnf(refute_0_7,plain,
( add(X_32,add(additive_inverse(X_32),X_34)) != add(additive_identity,X_34)
| add(additive_identity,X_34) != X_34
| add(X_32,add(additive_inverse(X_32),X_34)) = X_34 ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_32,add(additive_inverse(X_32),X_34)),X_34) ),[0],$fot(add(additive_identity,X_34))]]) ).
cnf(refute_0_8,plain,
( add(X_32,add(additive_inverse(X_32),X_34)) != add(additive_identity,X_34)
| add(X_32,add(additive_inverse(X_32),X_34)) = X_34 ),
inference(resolve,[$cnf( $equal(add(additive_identity,X_34),X_34) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
add(X_32,add(additive_inverse(X_32),X_34)) = X_34,
inference(resolve,[$cnf( $equal(add(X_32,add(additive_inverse(X_32),X_34)),add(additive_identity,X_34)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
add(X_32,add(additive_inverse(X_32),add(X_60,additive_inverse(add(additive_inverse(X_32),X_60))))) = add(X_60,additive_inverse(add(additive_inverse(X_32),X_60))),
inference(subst,[],[refute_0_9:[bind(X_34,$fot(add(X_60,additive_inverse(add(additive_inverse(X_32),X_60)))))]]) ).
cnf(refute_0_11,plain,
add(add(X_32,X_33),additive_inverse(add(X_32,X_33))) = additive_identity,
inference(subst,[],[right_additive_inverse:[bind(X,$fot(add(X_32,X_33)))]]) ).
cnf(refute_0_12,plain,
add(X_32,add(X_33,additive_inverse(add(X_32,X_33)))) = add(add(X_32,X_33),additive_inverse(add(X_32,X_33))),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(X_32)),bind(Y,$fot(X_33)),bind(Z,$fot(additive_inverse(add(X_32,X_33))))]]) ).
cnf(refute_0_13,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_14,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_15,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( add(X_32,add(X_33,additive_inverse(add(X_32,X_33)))) != add(add(X_32,X_33),additive_inverse(add(X_32,X_33)))
| add(add(X_32,X_33),additive_inverse(add(X_32,X_33))) = add(X_32,add(X_33,additive_inverse(add(X_32,X_33)))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(add(X_32,add(X_33,additive_inverse(add(X_32,X_33)))))),bind(Y0,$fot(add(add(X_32,X_33),additive_inverse(add(X_32,X_33)))))]]) ).
cnf(refute_0_17,plain,
add(add(X_32,X_33),additive_inverse(add(X_32,X_33))) = add(X_32,add(X_33,additive_inverse(add(X_32,X_33)))),
inference(resolve,[$cnf( $equal(add(X_32,add(X_33,additive_inverse(add(X_32,X_33)))),add(add(X_32,X_33),additive_inverse(add(X_32,X_33)))) )],[refute_0_12,refute_0_16]) ).
cnf(refute_0_18,plain,
( add(add(X_32,X_33),additive_inverse(add(X_32,X_33))) != add(X_32,add(X_33,additive_inverse(add(X_32,X_33))))
| add(add(X_32,X_33),additive_inverse(add(X_32,X_33))) != additive_identity
| add(X_32,add(X_33,additive_inverse(add(X_32,X_33)))) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_32,X_33),additive_inverse(add(X_32,X_33))),additive_identity) ),[0],$fot(add(X_32,add(X_33,additive_inverse(add(X_32,X_33)))))]]) ).
cnf(refute_0_19,plain,
( add(add(X_32,X_33),additive_inverse(add(X_32,X_33))) != additive_identity
| add(X_32,add(X_33,additive_inverse(add(X_32,X_33)))) = additive_identity ),
inference(resolve,[$cnf( $equal(add(add(X_32,X_33),additive_inverse(add(X_32,X_33))),add(X_32,add(X_33,additive_inverse(add(X_32,X_33))))) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
add(X_32,add(X_33,additive_inverse(add(X_32,X_33)))) = additive_identity,
inference(resolve,[$cnf( $equal(add(add(X_32,X_33),additive_inverse(add(X_32,X_33))),additive_identity) )],[refute_0_11,refute_0_19]) ).
cnf(refute_0_21,plain,
add(additive_inverse(X_32),add(X_60,additive_inverse(add(additive_inverse(X_32),X_60)))) = additive_identity,
inference(subst,[],[refute_0_20:[bind(X_32,$fot(additive_inverse(X_32))),bind(X_33,$fot(X_60))]]) ).
cnf(refute_0_22,plain,
( add(X_32,add(additive_inverse(X_32),add(X_60,additive_inverse(add(additive_inverse(X_32),X_60))))) != add(X_60,additive_inverse(add(additive_inverse(X_32),X_60)))
| add(additive_inverse(X_32),add(X_60,additive_inverse(add(additive_inverse(X_32),X_60)))) != additive_identity
| add(X_32,additive_identity) = add(X_60,additive_inverse(add(additive_inverse(X_32),X_60))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_32,add(additive_inverse(X_32),add(X_60,additive_inverse(add(additive_inverse(X_32),X_60))))),add(X_60,additive_inverse(add(additive_inverse(X_32),X_60)))) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_23,plain,
( add(X_32,add(additive_inverse(X_32),add(X_60,additive_inverse(add(additive_inverse(X_32),X_60))))) != add(X_60,additive_inverse(add(additive_inverse(X_32),X_60)))
| add(X_32,additive_identity) = add(X_60,additive_inverse(add(additive_inverse(X_32),X_60))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_32),add(X_60,additive_inverse(add(additive_inverse(X_32),X_60)))),additive_identity) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
add(X_32,additive_identity) = add(X_60,additive_inverse(add(additive_inverse(X_32),X_60))),
inference(resolve,[$cnf( $equal(add(X_32,add(additive_inverse(X_32),add(X_60,additive_inverse(add(additive_inverse(X_32),X_60))))),add(X_60,additive_inverse(add(additive_inverse(X_32),X_60)))) )],[refute_0_10,refute_0_23]) ).
cnf(refute_0_25,plain,
add(X_32,additive_identity) = X_32,
inference(subst,[],[right_additive_identity:[bind(X,$fot(X_32))]]) ).
cnf(refute_0_26,plain,
( add(X_32,additive_identity) != X_32
| add(X_32,additive_identity) != add(X_60,additive_inverse(add(additive_inverse(X_32),X_60)))
| X_32 = add(X_60,additive_inverse(add(additive_inverse(X_32),X_60))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_32,additive_identity),add(X_60,additive_inverse(add(additive_inverse(X_32),X_60)))) ),[0],$fot(X_32)]]) ).
cnf(refute_0_27,plain,
( add(X_32,additive_identity) != add(X_60,additive_inverse(add(additive_inverse(X_32),X_60)))
| X_32 = add(X_60,additive_inverse(add(additive_inverse(X_32),X_60))) ),
inference(resolve,[$cnf( $equal(add(X_32,additive_identity),X_32) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
X_32 = add(X_60,additive_inverse(add(additive_inverse(X_32),X_60))),
inference(resolve,[$cnf( $equal(add(X_32,additive_identity),add(X_60,additive_inverse(add(additive_inverse(X_32),X_60)))) )],[refute_0_24,refute_0_27]) ).
cnf(refute_0_29,plain,
additive_inverse(X) = add(X_62,additive_inverse(add(additive_inverse(additive_inverse(X)),X_62))),
inference(subst,[],[refute_0_28:[bind(X_32,$fot(additive_inverse(X))),bind(X_60,$fot(X_62))]]) ).
cnf(refute_0_30,plain,
( additive_inverse(X) != add(X_62,additive_inverse(add(additive_inverse(additive_inverse(X)),X_62)))
| additive_inverse(additive_inverse(X)) != X
| additive_inverse(X) = add(X_62,additive_inverse(add(X,X_62))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(X),add(X_62,additive_inverse(add(additive_inverse(additive_inverse(X)),X_62)))) ),[1,1,0,0],$fot(X)]]) ).
cnf(refute_0_31,plain,
( additive_inverse(X) != add(X_62,additive_inverse(add(additive_inverse(additive_inverse(X)),X_62)))
| additive_inverse(X) = add(X_62,additive_inverse(add(X,X_62))) ),
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(X)),X) )],[additive_inverse_additive_inverse,refute_0_30]) ).
cnf(refute_0_32,plain,
additive_inverse(X) = add(X_62,additive_inverse(add(X,X_62))),
inference(resolve,[$cnf( $equal(additive_inverse(X),add(X_62,additive_inverse(add(additive_inverse(additive_inverse(X)),X_62)))) )],[refute_0_29,refute_0_31]) ).
cnf(refute_0_33,plain,
additive_inverse(multiply(X_67,X_68)) = add(multiply(X_67,X_69),additive_inverse(add(multiply(X_67,X_68),multiply(X_67,X_69)))),
inference(subst,[],[refute_0_32:[bind(X,$fot(multiply(X_67,X_68))),bind(X_62,$fot(multiply(X_67,X_69)))]]) ).
cnf(refute_0_34,plain,
multiply(X_67,add(X_68,X_69)) = add(multiply(X_67,X_68),multiply(X_67,X_69)),
inference(subst,[],[distribute1:[bind(X,$fot(X_67)),bind(Y,$fot(X_68)),bind(Z,$fot(X_69))]]) ).
cnf(refute_0_35,plain,
( multiply(X_67,add(X_68,X_69)) != add(multiply(X_67,X_68),multiply(X_67,X_69))
| add(multiply(X_67,X_68),multiply(X_67,X_69)) = multiply(X_67,add(X_68,X_69)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(multiply(X_67,add(X_68,X_69)))),bind(Y0,$fot(add(multiply(X_67,X_68),multiply(X_67,X_69))))]]) ).
cnf(refute_0_36,plain,
add(multiply(X_67,X_68),multiply(X_67,X_69)) = multiply(X_67,add(X_68,X_69)),
inference(resolve,[$cnf( $equal(multiply(X_67,add(X_68,X_69)),add(multiply(X_67,X_68),multiply(X_67,X_69))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( add(multiply(X_67,X_68),multiply(X_67,X_69)) != multiply(X_67,add(X_68,X_69))
| additive_inverse(multiply(X_67,X_68)) != add(multiply(X_67,X_69),additive_inverse(add(multiply(X_67,X_68),multiply(X_67,X_69))))
| additive_inverse(multiply(X_67,X_68)) = add(multiply(X_67,X_69),additive_inverse(multiply(X_67,add(X_68,X_69)))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(X_67,X_68)),add(multiply(X_67,X_69),additive_inverse(add(multiply(X_67,X_68),multiply(X_67,X_69))))) ),[1,1,0],$fot(multiply(X_67,add(X_68,X_69)))]]) ).
cnf(refute_0_38,plain,
( additive_inverse(multiply(X_67,X_68)) != add(multiply(X_67,X_69),additive_inverse(add(multiply(X_67,X_68),multiply(X_67,X_69))))
| additive_inverse(multiply(X_67,X_68)) = add(multiply(X_67,X_69),additive_inverse(multiply(X_67,add(X_68,X_69)))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_67,X_68),multiply(X_67,X_69)),multiply(X_67,add(X_68,X_69))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
additive_inverse(multiply(X_67,X_68)) = add(multiply(X_67,X_69),additive_inverse(multiply(X_67,add(X_68,X_69)))),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X_67,X_68)),add(multiply(X_67,X_69),additive_inverse(add(multiply(X_67,X_68),multiply(X_67,X_69))))) )],[refute_0_33,refute_0_38]) ).
cnf(refute_0_40,plain,
additive_inverse(multiply(X_125,X_126)) = add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,add(X_126,add(additive_inverse(X_126),X_34))))),
inference(subst,[],[refute_0_39:[bind(X_67,$fot(X_125)),bind(X_68,$fot(X_126)),bind(X_69,$fot(add(additive_inverse(X_126),X_34)))]]) ).
cnf(refute_0_41,plain,
add(X_126,add(additive_inverse(X_126),X_34)) = X_34,
inference(subst,[],[refute_0_9:[bind(X_32,$fot(X_126))]]) ).
cnf(refute_0_42,plain,
( add(X_126,add(additive_inverse(X_126),X_34)) != X_34
| additive_inverse(multiply(X_125,X_126)) != add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,add(X_126,add(additive_inverse(X_126),X_34)))))
| additive_inverse(multiply(X_125,X_126)) = add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,X_34))) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(X_125,X_126)),add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,add(X_126,add(additive_inverse(X_126),X_34)))))) ),[1,1,0,1],$fot(X_34)]]) ).
cnf(refute_0_43,plain,
( additive_inverse(multiply(X_125,X_126)) != add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,add(X_126,add(additive_inverse(X_126),X_34)))))
| additive_inverse(multiply(X_125,X_126)) = add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,X_34))) ),
inference(resolve,[$cnf( $equal(add(X_126,add(additive_inverse(X_126),X_34)),X_34) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
additive_inverse(multiply(X_125,X_126)) = add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,X_34))),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X_125,X_126)),add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,add(X_126,add(additive_inverse(X_126),X_34)))))) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
add(X_32,add(additive_inverse(X_32),additive_inverse(add(X_65,additive_inverse(X_32))))) = additive_inverse(add(X_65,additive_inverse(X_32))),
inference(subst,[],[refute_0_9:[bind(X_34,$fot(additive_inverse(add(X_65,additive_inverse(X_32)))))]]) ).
cnf(refute_0_46,plain,
additive_inverse(X_65) = add(additive_inverse(X_32),additive_inverse(add(X_65,additive_inverse(X_32)))),
inference(subst,[],[refute_0_32:[bind(X,$fot(X_65)),bind(X_62,$fot(additive_inverse(X_32)))]]) ).
cnf(refute_0_47,plain,
( additive_inverse(X_65) != add(additive_inverse(X_32),additive_inverse(add(X_65,additive_inverse(X_32))))
| add(additive_inverse(X_32),additive_inverse(add(X_65,additive_inverse(X_32)))) = additive_inverse(X_65) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(additive_inverse(X_65))),bind(Y0,$fot(add(additive_inverse(X_32),additive_inverse(add(X_65,additive_inverse(X_32))))))]]) ).
cnf(refute_0_48,plain,
add(additive_inverse(X_32),additive_inverse(add(X_65,additive_inverse(X_32)))) = additive_inverse(X_65),
inference(resolve,[$cnf( $equal(additive_inverse(X_65),add(additive_inverse(X_32),additive_inverse(add(X_65,additive_inverse(X_32))))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( add(X_32,add(additive_inverse(X_32),additive_inverse(add(X_65,additive_inverse(X_32))))) != additive_inverse(add(X_65,additive_inverse(X_32)))
| add(additive_inverse(X_32),additive_inverse(add(X_65,additive_inverse(X_32)))) != additive_inverse(X_65)
| add(X_32,additive_inverse(X_65)) = additive_inverse(add(X_65,additive_inverse(X_32))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_32,add(additive_inverse(X_32),additive_inverse(add(X_65,additive_inverse(X_32))))),additive_inverse(add(X_65,additive_inverse(X_32)))) ),[0,1],$fot(additive_inverse(X_65))]]) ).
cnf(refute_0_50,plain,
( add(X_32,add(additive_inverse(X_32),additive_inverse(add(X_65,additive_inverse(X_32))))) != additive_inverse(add(X_65,additive_inverse(X_32)))
| add(X_32,additive_inverse(X_65)) = additive_inverse(add(X_65,additive_inverse(X_32))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_32),additive_inverse(add(X_65,additive_inverse(X_32)))),additive_inverse(X_65)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
add(X_32,additive_inverse(X_65)) = additive_inverse(add(X_65,additive_inverse(X_32))),
inference(resolve,[$cnf( $equal(add(X_32,add(additive_inverse(X_32),additive_inverse(add(X_65,additive_inverse(X_32))))),additive_inverse(add(X_65,additive_inverse(X_32)))) )],[refute_0_45,refute_0_50]) ).
cnf(refute_0_52,plain,
add(additive_inverse(X),additive_inverse(X_74)) = additive_inverse(add(X_74,additive_inverse(additive_inverse(X)))),
inference(subst,[],[refute_0_51:[bind(X_32,$fot(additive_inverse(X))),bind(X_65,$fot(X_74))]]) ).
cnf(refute_0_53,plain,
( add(additive_inverse(X),additive_inverse(X_74)) != additive_inverse(add(X_74,additive_inverse(additive_inverse(X))))
| additive_inverse(additive_inverse(X)) != X
| add(additive_inverse(X),additive_inverse(X_74)) = additive_inverse(add(X_74,X)) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(X),additive_inverse(X_74)),additive_inverse(add(X_74,additive_inverse(additive_inverse(X))))) ),[1,0,1],$fot(X)]]) ).
cnf(refute_0_54,plain,
( add(additive_inverse(X),additive_inverse(X_74)) != additive_inverse(add(X_74,additive_inverse(additive_inverse(X))))
| add(additive_inverse(X),additive_inverse(X_74)) = additive_inverse(add(X_74,X)) ),
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(X)),X) )],[additive_inverse_additive_inverse,refute_0_53]) ).
cnf(refute_0_55,plain,
add(additive_inverse(X),additive_inverse(X_74)) = additive_inverse(add(X_74,X)),
inference(resolve,[$cnf( $equal(add(additive_inverse(X),additive_inverse(X_74)),additive_inverse(add(X_74,additive_inverse(additive_inverse(X))))) )],[refute_0_52,refute_0_54]) ).
cnf(refute_0_56,plain,
add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))) = additive_inverse(add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127))))),
inference(subst,[],[refute_0_55:[bind(X,$fot(additive_inverse(multiply(X_125,add(X_126,X_127))))),bind(X_74,$fot(multiply(X_125,X_127)))]]) ).
cnf(refute_0_57,plain,
additive_inverse(multiply(X_125,X_126)) = add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127)))),
inference(subst,[],[refute_0_39:[bind(X_67,$fot(X_125)),bind(X_68,$fot(X_126)),bind(X_69,$fot(X_127))]]) ).
cnf(refute_0_58,plain,
( additive_inverse(multiply(X_125,X_126)) != add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127))))
| add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127)))) = additive_inverse(multiply(X_125,X_126)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(additive_inverse(multiply(X_125,X_126)))),bind(Y0,$fot(add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127))))))]]) ).
cnf(refute_0_59,plain,
add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127)))) = additive_inverse(multiply(X_125,X_126)),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X_125,X_126)),add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127))))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127)))) != additive_inverse(multiply(X_125,X_126))
| add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))) != additive_inverse(add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127)))))
| add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))) = additive_inverse(additive_inverse(multiply(X_125,X_126))) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))),additive_inverse(add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127)))))) ),[1,0],$fot(additive_inverse(multiply(X_125,X_126)))]]) ).
cnf(refute_0_61,plain,
( add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))) != additive_inverse(add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127)))))
| add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))) = additive_inverse(additive_inverse(multiply(X_125,X_126))) ),
inference(resolve,[$cnf( $equal(add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_126))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))) = additive_inverse(additive_inverse(multiply(X_125,X_126))),
inference(resolve,[$cnf( $equal(add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))),additive_inverse(add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127)))))) )],[refute_0_56,refute_0_61]) ).
cnf(refute_0_63,plain,
add(X,add(Y,add(additive_inverse(Y),X_36))) = add(add(X,Y),add(additive_inverse(Y),X_36)),
inference(subst,[],[associativity_for_addition:[bind(Z,$fot(add(additive_inverse(Y),X_36)))]]) ).
cnf(refute_0_64,plain,
add(Y,add(additive_inverse(Y),X_36)) = X_36,
inference(subst,[],[refute_0_9:[bind(X_32,$fot(Y)),bind(X_34,$fot(X_36))]]) ).
cnf(refute_0_65,plain,
( add(X,add(Y,add(additive_inverse(Y),X_36))) != add(add(X,Y),add(additive_inverse(Y),X_36))
| add(Y,add(additive_inverse(Y),X_36)) != X_36
| add(X,X_36) = add(add(X,Y),add(additive_inverse(Y),X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,add(Y,add(additive_inverse(Y),X_36))),add(add(X,Y),add(additive_inverse(Y),X_36))) ),[0,1],$fot(X_36)]]) ).
cnf(refute_0_66,plain,
( add(X,add(Y,add(additive_inverse(Y),X_36))) != add(add(X,Y),add(additive_inverse(Y),X_36))
| add(X,X_36) = add(add(X,Y),add(additive_inverse(Y),X_36)) ),
inference(resolve,[$cnf( $equal(add(Y,add(additive_inverse(Y),X_36)),X_36) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
add(X,X_36) = add(add(X,Y),add(additive_inverse(Y),X_36)),
inference(resolve,[$cnf( $equal(add(X,add(Y,add(additive_inverse(Y),X_36))),add(add(X,Y),add(additive_inverse(Y),X_36))) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
( add(X,add(Y,Z)) != add(add(X,Y),Z)
| add(add(X,Y),Z) = add(X,add(Y,Z)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(add(X,add(Y,Z)))),bind(Y0,$fot(add(add(X,Y),Z)))]]) ).
cnf(refute_0_69,plain,
add(add(X,Y),Z) = add(X,add(Y,Z)),
inference(resolve,[$cnf( $equal(add(X,add(Y,Z)),add(add(X,Y),Z)) )],[associativity_for_addition,refute_0_68]) ).
cnf(refute_0_70,plain,
add(add(X,Y),X_36) = add(X,add(Y,X_36)),
inference(subst,[],[refute_0_69:[bind(Z,$fot(X_36))]]) ).
cnf(refute_0_71,plain,
add(additive_inverse(Y),add(add(X,Y),X_36)) = add(additive_inverse(Y),add(add(X,Y),X_36)),
introduced(tautology,[refl,[$fot(add(additive_inverse(Y),add(add(X,Y),X_36)))]]) ).
cnf(refute_0_72,plain,
( add(add(X,Y),X_36) != add(X,add(Y,X_36))
| add(additive_inverse(Y),add(add(X,Y),X_36)) != add(additive_inverse(Y),add(add(X,Y),X_36))
| add(additive_inverse(Y),add(add(X,Y),X_36)) = add(additive_inverse(Y),add(X,add(Y,X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(Y),add(add(X,Y),X_36)),add(additive_inverse(Y),add(add(X,Y),X_36))) ),[1,1],$fot(add(X,add(Y,X_36)))]]) ).
cnf(refute_0_73,plain,
( add(add(X,Y),X_36) != add(X,add(Y,X_36))
| add(additive_inverse(Y),add(add(X,Y),X_36)) = add(additive_inverse(Y),add(X,add(Y,X_36))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(Y),add(add(X,Y),X_36)),add(additive_inverse(Y),add(add(X,Y),X_36))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
add(additive_inverse(Y),add(add(X,Y),X_36)) = add(additive_inverse(Y),add(X,add(Y,X_36))),
inference(resolve,[$cnf( $equal(add(add(X,Y),X_36),add(X,add(Y,X_36))) )],[refute_0_70,refute_0_73]) ).
cnf(refute_0_75,plain,
add(X_32,add(X_33,X_34)) = add(add(X_32,X_33),X_34),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(X_32)),bind(Y,$fot(X_33)),bind(Z,$fot(X_34))]]) ).
cnf(refute_0_76,plain,
add(X_33,X_32) = add(X_32,X_33),
inference(subst,[],[commutativity_for_addition:[bind(X,$fot(X_33)),bind(Y,$fot(X_32))]]) ).
cnf(refute_0_77,plain,
( add(X_33,X_32) != add(X_32,X_33)
| add(X_32,X_33) = add(X_33,X_32) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(add(X_33,X_32))),bind(Y0,$fot(add(X_32,X_33)))]]) ).
cnf(refute_0_78,plain,
add(X_32,X_33) = add(X_33,X_32),
inference(resolve,[$cnf( $equal(add(X_33,X_32),add(X_32,X_33)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
( add(X_32,X_33) != add(X_33,X_32)
| add(X_32,add(X_33,X_34)) != add(add(X_32,X_33),X_34)
| add(X_32,add(X_33,X_34)) = add(add(X_33,X_32),X_34) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_32,add(X_33,X_34)),add(add(X_32,X_33),X_34)) ),[1,0],$fot(add(X_33,X_32))]]) ).
cnf(refute_0_80,plain,
( add(X_32,add(X_33,X_34)) != add(add(X_32,X_33),X_34)
| add(X_32,add(X_33,X_34)) = add(add(X_33,X_32),X_34) ),
inference(resolve,[$cnf( $equal(add(X_32,X_33),add(X_33,X_32)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
add(X_32,add(X_33,X_34)) = add(add(X_33,X_32),X_34),
inference(resolve,[$cnf( $equal(add(X_32,add(X_33,X_34)),add(add(X_32,X_33),X_34)) )],[refute_0_75,refute_0_80]) ).
cnf(refute_0_82,plain,
add(add(X_33,X_32),X_34) = add(X_33,add(X_32,X_34)),
inference(subst,[],[refute_0_69:[bind(X,$fot(X_33)),bind(Y,$fot(X_32)),bind(Z,$fot(X_34))]]) ).
cnf(refute_0_83,plain,
( add(X_32,add(X_33,X_34)) != add(add(X_33,X_32),X_34)
| add(add(X_33,X_32),X_34) != add(X_33,add(X_32,X_34))
| add(X_32,add(X_33,X_34)) = add(X_33,add(X_32,X_34)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_32,add(X_33,X_34)),add(X_33,add(X_32,X_34))) ),[0],$fot(add(add(X_33,X_32),X_34))]]) ).
cnf(refute_0_84,plain,
( add(X_32,add(X_33,X_34)) != add(add(X_33,X_32),X_34)
| add(X_32,add(X_33,X_34)) = add(X_33,add(X_32,X_34)) ),
inference(resolve,[$cnf( $equal(add(add(X_33,X_32),X_34),add(X_33,add(X_32,X_34))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
add(X_32,add(X_33,X_34)) = add(X_33,add(X_32,X_34)),
inference(resolve,[$cnf( $equal(add(X_32,add(X_33,X_34)),add(add(X_33,X_32),X_34)) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
( add(X_32,add(X_33,X_34)) != add(X_33,add(X_32,X_34))
| add(X_33,add(X_32,X_34)) = add(X_32,add(X_33,X_34)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(add(X_32,add(X_33,X_34)))),bind(Y0,$fot(add(X_33,add(X_32,X_34))))]]) ).
cnf(refute_0_87,plain,
add(X_33,add(X_32,X_34)) = add(X_32,add(X_33,X_34)),
inference(resolve,[$cnf( $equal(add(X_32,add(X_33,X_34)),add(X_33,add(X_32,X_34))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
add(add(X,Y),add(additive_inverse(Y),X_36)) = add(additive_inverse(Y),add(add(X,Y),X_36)),
inference(subst,[],[refute_0_87:[bind(X_32,$fot(additive_inverse(Y))),bind(X_33,$fot(add(X,Y))),bind(X_34,$fot(X_36))]]) ).
cnf(refute_0_89,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_90,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_15,refute_0_89]) ).
cnf(refute_0_91,plain,
( add(add(X,Y),add(additive_inverse(Y),X_36)) != add(additive_inverse(Y),add(add(X,Y),X_36))
| add(additive_inverse(Y),add(add(X,Y),X_36)) != add(additive_inverse(Y),add(X,add(Y,X_36)))
| add(add(X,Y),add(additive_inverse(Y),X_36)) = add(additive_inverse(Y),add(X,add(Y,X_36))) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(add(add(X,Y),add(additive_inverse(Y),X_36)))),bind(Y0,$fot(add(additive_inverse(Y),add(add(X,Y),X_36)))),bind(Z0,$fot(add(additive_inverse(Y),add(X,add(Y,X_36)))))]]) ).
cnf(refute_0_92,plain,
( add(additive_inverse(Y),add(add(X,Y),X_36)) != add(additive_inverse(Y),add(X,add(Y,X_36)))
| add(add(X,Y),add(additive_inverse(Y),X_36)) = add(additive_inverse(Y),add(X,add(Y,X_36))) ),
inference(resolve,[$cnf( $equal(add(add(X,Y),add(additive_inverse(Y),X_36)),add(additive_inverse(Y),add(add(X,Y),X_36))) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
add(add(X,Y),add(additive_inverse(Y),X_36)) = add(additive_inverse(Y),add(X,add(Y,X_36))),
inference(resolve,[$cnf( $equal(add(additive_inverse(Y),add(add(X,Y),X_36)),add(additive_inverse(Y),add(X,add(Y,X_36)))) )],[refute_0_74,refute_0_92]) ).
cnf(refute_0_94,plain,
( add(X,X_36) != add(add(X,Y),add(additive_inverse(Y),X_36))
| add(add(X,Y),add(additive_inverse(Y),X_36)) != add(additive_inverse(Y),add(X,add(Y,X_36)))
| add(X,X_36) = add(additive_inverse(Y),add(X,add(Y,X_36))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X,X_36),add(additive_inverse(Y),add(X,add(Y,X_36)))) ),[0],$fot(add(add(X,Y),add(additive_inverse(Y),X_36)))]]) ).
cnf(refute_0_95,plain,
( add(X,X_36) != add(add(X,Y),add(additive_inverse(Y),X_36))
| add(X,X_36) = add(additive_inverse(Y),add(X,add(Y,X_36))) ),
inference(resolve,[$cnf( $equal(add(add(X,Y),add(additive_inverse(Y),X_36)),add(additive_inverse(Y),add(X,add(Y,X_36)))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
add(X,X_36) = add(additive_inverse(Y),add(X,add(Y,X_36))),
inference(resolve,[$cnf( $equal(add(X,X_36),add(add(X,Y),add(additive_inverse(Y),X_36))) )],[refute_0_67,refute_0_95]) ).
cnf(refute_0_97,plain,
add(X_35,add(additive_inverse(X_35),X_36)) = X_36,
inference(subst,[],[refute_0_9:[bind(X_32,$fot(X_35)),bind(X_34,$fot(X_36))]]) ).
cnf(refute_0_98,plain,
add(X_36,additive_inverse(X_35)) = add(additive_inverse(X_35),X_36),
inference(subst,[],[commutativity_for_addition:[bind(X,$fot(X_36)),bind(Y,$fot(additive_inverse(X_35)))]]) ).
cnf(refute_0_99,plain,
( add(X_36,additive_inverse(X_35)) != add(additive_inverse(X_35),X_36)
| add(additive_inverse(X_35),X_36) = add(X_36,additive_inverse(X_35)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(add(X_36,additive_inverse(X_35)))),bind(Y0,$fot(add(additive_inverse(X_35),X_36)))]]) ).
cnf(refute_0_100,plain,
add(additive_inverse(X_35),X_36) = add(X_36,additive_inverse(X_35)),
inference(resolve,[$cnf( $equal(add(X_36,additive_inverse(X_35)),add(additive_inverse(X_35),X_36)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
( add(X_35,add(additive_inverse(X_35),X_36)) != X_36
| add(additive_inverse(X_35),X_36) != add(X_36,additive_inverse(X_35))
| add(X_35,add(X_36,additive_inverse(X_35))) = X_36 ),
introduced(tautology,[equality,[$cnf( $equal(add(X_35,add(additive_inverse(X_35),X_36)),X_36) ),[0,1],$fot(add(X_36,additive_inverse(X_35)))]]) ).
cnf(refute_0_102,plain,
( add(X_35,add(additive_inverse(X_35),X_36)) != X_36
| add(X_35,add(X_36,additive_inverse(X_35))) = X_36 ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X_35),X_36),add(X_36,additive_inverse(X_35))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
add(X_35,add(X_36,additive_inverse(X_35))) = X_36,
inference(resolve,[$cnf( $equal(add(X_35,add(additive_inverse(X_35),X_36)),X_36) )],[refute_0_97,refute_0_102]) ).
cnf(refute_0_104,plain,
add(X_37,add(add(X,Y),additive_inverse(X_37))) = add(X,Y),
inference(subst,[],[refute_0_103:[bind(X_35,$fot(X_37)),bind(X_36,$fot(add(X,Y)))]]) ).
cnf(refute_0_105,plain,
add(X,add(Y,additive_inverse(X_37))) = add(add(X,Y),additive_inverse(X_37)),
inference(subst,[],[associativity_for_addition:[bind(Z,$fot(additive_inverse(X_37)))]]) ).
cnf(refute_0_106,plain,
( add(X,add(Y,additive_inverse(X_37))) != add(add(X,Y),additive_inverse(X_37))
| add(add(X,Y),additive_inverse(X_37)) = add(X,add(Y,additive_inverse(X_37))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(add(X,add(Y,additive_inverse(X_37))))),bind(Y0,$fot(add(add(X,Y),additive_inverse(X_37))))]]) ).
cnf(refute_0_107,plain,
add(add(X,Y),additive_inverse(X_37)) = add(X,add(Y,additive_inverse(X_37))),
inference(resolve,[$cnf( $equal(add(X,add(Y,additive_inverse(X_37))),add(add(X,Y),additive_inverse(X_37))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
( add(X_37,add(add(X,Y),additive_inverse(X_37))) != add(X,Y)
| add(add(X,Y),additive_inverse(X_37)) != add(X,add(Y,additive_inverse(X_37)))
| add(X_37,add(X,add(Y,additive_inverse(X_37)))) = add(X,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_37,add(add(X,Y),additive_inverse(X_37))),add(X,Y)) ),[0,1],$fot(add(X,add(Y,additive_inverse(X_37))))]]) ).
cnf(refute_0_109,plain,
( add(X_37,add(add(X,Y),additive_inverse(X_37))) != add(X,Y)
| add(X_37,add(X,add(Y,additive_inverse(X_37)))) = add(X,Y) ),
inference(resolve,[$cnf( $equal(add(add(X,Y),additive_inverse(X_37)),add(X,add(Y,additive_inverse(X_37)))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
add(X_37,add(X,add(Y,additive_inverse(X_37)))) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X_37,add(add(X,Y),additive_inverse(X_37))),add(X,Y)) )],[refute_0_104,refute_0_109]) ).
cnf(refute_0_111,plain,
add(Y,add(X_36,add(X,additive_inverse(Y)))) = add(X_36,X),
inference(subst,[],[refute_0_110:[bind(X,$fot(X_36)),bind(Y,$fot(X)),bind(X_37,$fot(Y))]]) ).
cnf(refute_0_112,plain,
add(X,add(X_32,X_33)) = add(add(X_32,X_33),X),
inference(subst,[],[commutativity_for_addition:[bind(Y,$fot(add(X_32,X_33)))]]) ).
cnf(refute_0_113,plain,
add(X_32,add(X_33,X)) = add(add(X_32,X_33),X),
inference(subst,[],[associativity_for_addition:[bind(X,$fot(X_32)),bind(Y,$fot(X_33)),bind(Z,$fot(X))]]) ).
cnf(refute_0_114,plain,
( add(X_32,add(X_33,X)) != add(add(X_32,X_33),X)
| add(add(X_32,X_33),X) = add(X_32,add(X_33,X)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(add(X_32,add(X_33,X)))),bind(Y0,$fot(add(add(X_32,X_33),X)))]]) ).
cnf(refute_0_115,plain,
add(add(X_32,X_33),X) = add(X_32,add(X_33,X)),
inference(resolve,[$cnf( $equal(add(X_32,add(X_33,X)),add(add(X_32,X_33),X)) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
( add(X,add(X_32,X_33)) != add(add(X_32,X_33),X)
| add(add(X_32,X_33),X) != add(X_32,add(X_33,X))
| add(X,add(X_32,X_33)) = add(X_32,add(X_33,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X,add(X_32,X_33)),add(X_32,add(X_33,X))) ),[0],$fot(add(add(X_32,X_33),X))]]) ).
cnf(refute_0_117,plain,
( add(X,add(X_32,X_33)) != add(add(X_32,X_33),X)
| add(X,add(X_32,X_33)) = add(X_32,add(X_33,X)) ),
inference(resolve,[$cnf( $equal(add(add(X_32,X_33),X),add(X_32,add(X_33,X))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
add(X,add(X_32,X_33)) = add(X_32,add(X_33,X)),
inference(resolve,[$cnf( $equal(add(X,add(X_32,X_33)),add(add(X_32,X_33),X)) )],[refute_0_112,refute_0_117]) ).
cnf(refute_0_119,plain,
add(X,add(X_32,add(X_111,X_109))) = add(X_32,add(add(X_111,X_109),X)),
inference(subst,[],[refute_0_118:[bind(X_33,$fot(add(X_111,X_109)))]]) ).
cnf(refute_0_120,plain,
add(X_109,add(X_32,X_111)) = add(X_32,add(X_111,X_109)),
inference(subst,[],[refute_0_118:[bind(X,$fot(X_109)),bind(X_33,$fot(X_111))]]) ).
cnf(refute_0_121,plain,
( add(X_109,add(X_32,X_111)) != add(X_32,add(X_111,X_109))
| add(X_32,add(X_111,X_109)) = add(X_109,add(X_32,X_111)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(add(X_109,add(X_32,X_111)))),bind(Y0,$fot(add(X_32,add(X_111,X_109))))]]) ).
cnf(refute_0_122,plain,
add(X_32,add(X_111,X_109)) = add(X_109,add(X_32,X_111)),
inference(resolve,[$cnf( $equal(add(X_109,add(X_32,X_111)),add(X_32,add(X_111,X_109))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
( add(X,add(X_32,add(X_111,X_109))) != add(X_32,add(add(X_111,X_109),X))
| add(X_32,add(X_111,X_109)) != add(X_109,add(X_32,X_111))
| add(X,add(X_109,add(X_32,X_111))) = add(X_32,add(add(X_111,X_109),X)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,add(X_32,add(X_111,X_109))),add(X_32,add(add(X_111,X_109),X))) ),[0,1],$fot(add(X_109,add(X_32,X_111)))]]) ).
cnf(refute_0_124,plain,
( add(X,add(X_32,add(X_111,X_109))) != add(X_32,add(add(X_111,X_109),X))
| add(X,add(X_109,add(X_32,X_111))) = add(X_32,add(add(X_111,X_109),X)) ),
inference(resolve,[$cnf( $equal(add(X_32,add(X_111,X_109)),add(X_109,add(X_32,X_111))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
add(X,add(X_109,add(X_32,X_111))) = add(X_32,add(add(X_111,X_109),X)),
inference(resolve,[$cnf( $equal(add(X,add(X_32,add(X_111,X_109))),add(X_32,add(add(X_111,X_109),X))) )],[refute_0_119,refute_0_124]) ).
cnf(refute_0_126,plain,
add(add(X_111,X_109),X) = add(X_111,add(X_109,X)),
inference(subst,[],[refute_0_69:[bind(X,$fot(X_111)),bind(Y,$fot(X_109)),bind(Z,$fot(X))]]) ).
cnf(refute_0_127,plain,
add(X_32,add(add(X_111,X_109),X)) = add(X_32,add(add(X_111,X_109),X)),
introduced(tautology,[refl,[$fot(add(X_32,add(add(X_111,X_109),X)))]]) ).
cnf(refute_0_128,plain,
( add(X_32,add(add(X_111,X_109),X)) != add(X_32,add(add(X_111,X_109),X))
| add(add(X_111,X_109),X) != add(X_111,add(X_109,X))
| add(X_32,add(add(X_111,X_109),X)) = add(X_32,add(X_111,add(X_109,X))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_32,add(add(X_111,X_109),X)),add(X_32,add(add(X_111,X_109),X))) ),[1,1],$fot(add(X_111,add(X_109,X)))]]) ).
cnf(refute_0_129,plain,
( add(add(X_111,X_109),X) != add(X_111,add(X_109,X))
| add(X_32,add(add(X_111,X_109),X)) = add(X_32,add(X_111,add(X_109,X))) ),
inference(resolve,[$cnf( $equal(add(X_32,add(add(X_111,X_109),X)),add(X_32,add(add(X_111,X_109),X))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
add(X_32,add(add(X_111,X_109),X)) = add(X_32,add(X_111,add(X_109,X))),
inference(resolve,[$cnf( $equal(add(add(X_111,X_109),X),add(X_111,add(X_109,X))) )],[refute_0_126,refute_0_129]) ).
cnf(refute_0_131,plain,
( add(X,add(X_109,add(X_32,X_111))) != add(X_32,add(add(X_111,X_109),X))
| add(X_32,add(add(X_111,X_109),X)) != add(X_32,add(X_111,add(X_109,X)))
| add(X,add(X_109,add(X_32,X_111))) = add(X_32,add(X_111,add(X_109,X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X,add(X_109,add(X_32,X_111))),add(X_32,add(X_111,add(X_109,X)))) ),[0],$fot(add(X_32,add(add(X_111,X_109),X)))]]) ).
cnf(refute_0_132,plain,
( add(X,add(X_109,add(X_32,X_111))) != add(X_32,add(add(X_111,X_109),X))
| add(X,add(X_109,add(X_32,X_111))) = add(X_32,add(X_111,add(X_109,X))) ),
inference(resolve,[$cnf( $equal(add(X_32,add(add(X_111,X_109),X)),add(X_32,add(X_111,add(X_109,X)))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
add(X,add(X_109,add(X_32,X_111))) = add(X_32,add(X_111,add(X_109,X))),
inference(resolve,[$cnf( $equal(add(X,add(X_109,add(X_32,X_111))),add(X_32,add(add(X_111,X_109),X))) )],[refute_0_125,refute_0_132]) ).
cnf(refute_0_134,plain,
add(additive_inverse(Y),add(X,add(Y,X_36))) = add(Y,add(X_36,add(X,additive_inverse(Y)))),
inference(subst,[],[refute_0_133:[bind(X,$fot(additive_inverse(Y))),bind(X_109,$fot(X)),bind(X_111,$fot(X_36)),bind(X_32,$fot(Y))]]) ).
cnf(refute_0_135,plain,
( add(Y,add(X_36,add(X,additive_inverse(Y)))) != add(X_36,X)
| add(additive_inverse(Y),add(X,add(Y,X_36))) != add(Y,add(X_36,add(X,additive_inverse(Y))))
| add(additive_inverse(Y),add(X,add(Y,X_36))) = add(X_36,X) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(add(additive_inverse(Y),add(X,add(Y,X_36))))),bind(Y0,$fot(add(Y,add(X_36,add(X,additive_inverse(Y)))))),bind(Z0,$fot(add(X_36,X)))]]) ).
cnf(refute_0_136,plain,
( add(Y,add(X_36,add(X,additive_inverse(Y)))) != add(X_36,X)
| add(additive_inverse(Y),add(X,add(Y,X_36))) = add(X_36,X) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(Y),add(X,add(Y,X_36))),add(Y,add(X_36,add(X,additive_inverse(Y))))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
add(additive_inverse(Y),add(X,add(Y,X_36))) = add(X_36,X),
inference(resolve,[$cnf( $equal(add(Y,add(X_36,add(X,additive_inverse(Y)))),add(X_36,X)) )],[refute_0_111,refute_0_136]) ).
cnf(refute_0_138,plain,
( add(X,X_36) != add(additive_inverse(Y),add(X,add(Y,X_36)))
| add(additive_inverse(Y),add(X,add(Y,X_36))) != add(X_36,X)
| add(X,X_36) = add(X_36,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X,X_36),add(X_36,X)) ),[0],$fot(add(additive_inverse(Y),add(X,add(Y,X_36))))]]) ).
cnf(refute_0_139,plain,
( add(X,X_36) != add(additive_inverse(Y),add(X,add(Y,X_36)))
| add(X,X_36) = add(X_36,X) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(Y),add(X,add(Y,X_36))),add(X_36,X)) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
add(X,X_36) = add(X_36,X),
inference(resolve,[$cnf( $equal(add(X,X_36),add(additive_inverse(Y),add(X,add(Y,X_36)))) )],[refute_0_96,refute_0_139]) ).
cnf(refute_0_141,plain,
( add(X,X_36) != add(X_36,X)
| add(X_36,X) = add(X,X_36) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(add(X,X_36))),bind(Y0,$fot(add(X_36,X)))]]) ).
cnf(refute_0_142,plain,
add(X_36,X) = add(X,X_36),
inference(resolve,[$cnf( $equal(add(X,X_36),add(X_36,X)) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
add(multiply(X_125,add(X_126,X_127)),additive_inverse(multiply(X_125,X_127))) = add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127))),
inference(subst,[],[refute_0_142:[bind(X,$fot(additive_inverse(multiply(X_125,X_127)))),bind(X_36,$fot(multiply(X_125,add(X_126,X_127))))]]) ).
cnf(refute_0_144,plain,
( add(X_32,additive_inverse(X_65)) != additive_inverse(add(X_65,additive_inverse(X_32)))
| additive_inverse(add(X_65,additive_inverse(X_32))) = add(X_32,additive_inverse(X_65)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(add(X_32,additive_inverse(X_65)))),bind(Y0,$fot(additive_inverse(add(X_65,additive_inverse(X_32)))))]]) ).
cnf(refute_0_145,plain,
additive_inverse(add(X_65,additive_inverse(X_32))) = add(X_32,additive_inverse(X_65)),
inference(resolve,[$cnf( $equal(add(X_32,additive_inverse(X_65)),additive_inverse(add(X_65,additive_inverse(X_32)))) )],[refute_0_51,refute_0_144]) ).
cnf(refute_0_146,plain,
additive_inverse(add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127))))) = add(multiply(X_125,add(X_126,X_127)),additive_inverse(multiply(X_125,X_127))),
inference(subst,[],[refute_0_145:[bind(X_32,$fot(multiply(X_125,add(X_126,X_127)))),bind(X_65,$fot(multiply(X_125,X_127)))]]) ).
cnf(refute_0_147,plain,
( add(multiply(X_125,add(X_126,X_127)),additive_inverse(multiply(X_125,X_127))) != add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127)))
| additive_inverse(add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127))))) != add(multiply(X_125,add(X_126,X_127)),additive_inverse(multiply(X_125,X_127)))
| additive_inverse(add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127))))) = add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127))) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(additive_inverse(add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127))))))),bind(Y0,$fot(add(multiply(X_125,add(X_126,X_127)),additive_inverse(multiply(X_125,X_127))))),bind(Z0,$fot(add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127)))))]]) ).
cnf(refute_0_148,plain,
( add(multiply(X_125,add(X_126,X_127)),additive_inverse(multiply(X_125,X_127))) != add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127)))
| additive_inverse(add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127))))) = add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127))) ),
inference(resolve,[$cnf( $equal(additive_inverse(add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127))))),add(multiply(X_125,add(X_126,X_127)),additive_inverse(multiply(X_125,X_127)))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
additive_inverse(add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127))))) = add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127))),
inference(resolve,[$cnf( $equal(add(multiply(X_125,add(X_126,X_127)),additive_inverse(multiply(X_125,X_127))),add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127)))) )],[refute_0_143,refute_0_148]) ).
cnf(refute_0_150,plain,
( add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))) != additive_inverse(add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127)))))
| additive_inverse(add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127))))) != add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127)))
| add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))) = add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127))) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))))),bind(Y0,$fot(additive_inverse(add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127))))))),bind(Z0,$fot(add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127)))))]]) ).
cnf(refute_0_151,plain,
( additive_inverse(add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127))))) != add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127)))
| add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))) = add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))),additive_inverse(add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127)))))) )],[refute_0_56,refute_0_150]) ).
cnf(refute_0_152,plain,
add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))) = add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127))),
inference(resolve,[$cnf( $equal(additive_inverse(add(multiply(X_125,X_127),additive_inverse(multiply(X_125,add(X_126,X_127))))),add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127)))) )],[refute_0_149,refute_0_151]) ).
cnf(refute_0_153,plain,
( add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))) != add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127)))
| add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))) != additive_inverse(additive_inverse(multiply(X_125,X_126)))
| add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127))) = additive_inverse(additive_inverse(multiply(X_125,X_126))) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))),additive_inverse(additive_inverse(multiply(X_125,X_126)))) ),[0],$fot(add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127))))]]) ).
cnf(refute_0_154,plain,
( add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))) != additive_inverse(additive_inverse(multiply(X_125,X_126)))
| add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127))) = additive_inverse(additive_inverse(multiply(X_125,X_126))) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))),add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127)))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
additive_inverse(additive_inverse(multiply(X_125,X_126))) = multiply(X_125,X_126),
inference(subst,[],[additive_inverse_additive_inverse:[bind(X,$fot(multiply(X_125,X_126)))]]) ).
cnf(refute_0_156,plain,
( add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127))) != additive_inverse(additive_inverse(multiply(X_125,X_126)))
| additive_inverse(additive_inverse(multiply(X_125,X_126))) != multiply(X_125,X_126)
| add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127))) = multiply(X_125,X_126) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127))),multiply(X_125,X_126)) ),[0],$fot(additive_inverse(additive_inverse(multiply(X_125,X_126))))]]) ).
cnf(refute_0_157,plain,
( add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127))) != additive_inverse(additive_inverse(multiply(X_125,X_126)))
| add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127))) = multiply(X_125,X_126) ),
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(multiply(X_125,X_126))),multiply(X_125,X_126)) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
( add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))) != additive_inverse(additive_inverse(multiply(X_125,X_126)))
| add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127))) = multiply(X_125,X_126) ),
inference(resolve,[$cnf( $equal(add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127))),additive_inverse(additive_inverse(multiply(X_125,X_126)))) )],[refute_0_154,refute_0_157]) ).
cnf(refute_0_159,plain,
add(additive_inverse(multiply(X_125,X_127)),multiply(X_125,add(X_126,X_127))) = multiply(X_125,X_126),
inference(resolve,[$cnf( $equal(add(additive_inverse(additive_inverse(multiply(X_125,add(X_126,X_127)))),additive_inverse(multiply(X_125,X_127))),additive_inverse(additive_inverse(multiply(X_125,X_126)))) )],[refute_0_62,refute_0_158]) ).
cnf(refute_0_160,plain,
add(additive_inverse(multiply(X_125,X_34)),multiply(X_125,add(additive_inverse(X_126),X_34))) = multiply(X_125,additive_inverse(X_126)),
inference(subst,[],[refute_0_159:[bind(X_126,$fot(additive_inverse(X_126))),bind(X_127,$fot(X_34))]]) ).
cnf(refute_0_161,plain,
add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,X_34))) = add(additive_inverse(multiply(X_125,X_34)),multiply(X_125,add(additive_inverse(X_126),X_34))),
inference(subst,[],[refute_0_142:[bind(X,$fot(additive_inverse(multiply(X_125,X_34)))),bind(X_36,$fot(multiply(X_125,add(additive_inverse(X_126),X_34))))]]) ).
cnf(refute_0_162,plain,
( add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,X_34))) != add(additive_inverse(multiply(X_125,X_34)),multiply(X_125,add(additive_inverse(X_126),X_34)))
| add(additive_inverse(multiply(X_125,X_34)),multiply(X_125,add(additive_inverse(X_126),X_34))) != multiply(X_125,additive_inverse(X_126))
| add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,X_34))) = multiply(X_125,additive_inverse(X_126)) ),
inference(subst,[],[refute_0_90:[bind(X0,$fot(add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,X_34))))),bind(Y0,$fot(add(additive_inverse(multiply(X_125,X_34)),multiply(X_125,add(additive_inverse(X_126),X_34))))),bind(Z0,$fot(multiply(X_125,additive_inverse(X_126))))]]) ).
cnf(refute_0_163,plain,
( add(additive_inverse(multiply(X_125,X_34)),multiply(X_125,add(additive_inverse(X_126),X_34))) != multiply(X_125,additive_inverse(X_126))
| add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,X_34))) = multiply(X_125,additive_inverse(X_126)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,X_34))),add(additive_inverse(multiply(X_125,X_34)),multiply(X_125,add(additive_inverse(X_126),X_34)))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,X_34))) = multiply(X_125,additive_inverse(X_126)),
inference(resolve,[$cnf( $equal(add(additive_inverse(multiply(X_125,X_34)),multiply(X_125,add(additive_inverse(X_126),X_34))),multiply(X_125,additive_inverse(X_126))) )],[refute_0_160,refute_0_163]) ).
cnf(refute_0_165,plain,
( add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,X_34))) != multiply(X_125,additive_inverse(X_126))
| additive_inverse(multiply(X_125,X_126)) != add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,X_34)))
| additive_inverse(multiply(X_125,X_126)) = multiply(X_125,additive_inverse(X_126)) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(X_125,X_126)),add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,X_34)))) ),[1],$fot(multiply(X_125,additive_inverse(X_126)))]]) ).
cnf(refute_0_166,plain,
( additive_inverse(multiply(X_125,X_126)) != add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,X_34)))
| additive_inverse(multiply(X_125,X_126)) = multiply(X_125,additive_inverse(X_126)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,X_34))),multiply(X_125,additive_inverse(X_126))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
additive_inverse(multiply(X_125,X_126)) = multiply(X_125,additive_inverse(X_126)),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X_125,X_126)),add(multiply(X_125,add(additive_inverse(X_126),X_34)),additive_inverse(multiply(X_125,X_34)))) )],[refute_0_44,refute_0_166]) ).
cnf(refute_0_168,plain,
additive_inverse(multiply(X,X_129)) = multiply(X,additive_inverse(X_129)),
inference(subst,[],[refute_0_167:[bind(X_125,$fot(X)),bind(X_126,$fot(X_129))]]) ).
cnf(refute_0_169,plain,
( additive_inverse(multiply(X,X_129)) != multiply(X,additive_inverse(X_129))
| multiply(X,additive_inverse(X_129)) = additive_inverse(multiply(X,X_129)) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(additive_inverse(multiply(X,X_129)))),bind(Y0,$fot(multiply(X,additive_inverse(X_129))))]]) ).
cnf(refute_0_170,plain,
multiply(X,additive_inverse(X_129)) = additive_inverse(multiply(X,X_129)),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X,X_129)),multiply(X,additive_inverse(X_129))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
( multiply(X,add(Y,additive_inverse(X_129))) != add(multiply(X,Y),multiply(X,additive_inverse(X_129)))
| multiply(X,additive_inverse(X_129)) != additive_inverse(multiply(X,X_129))
| multiply(X,add(Y,additive_inverse(X_129))) = add(multiply(X,Y),additive_inverse(multiply(X,X_129))) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X,add(Y,additive_inverse(X_129))),add(multiply(X,Y),multiply(X,additive_inverse(X_129)))) ),[1,1],$fot(additive_inverse(multiply(X,X_129)))]]) ).
cnf(refute_0_172,plain,
( multiply(X,add(Y,additive_inverse(X_129))) != add(multiply(X,Y),multiply(X,additive_inverse(X_129)))
| multiply(X,add(Y,additive_inverse(X_129))) = add(multiply(X,Y),additive_inverse(multiply(X,X_129))) ),
inference(resolve,[$cnf( $equal(multiply(X,additive_inverse(X_129)),additive_inverse(multiply(X,X_129))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
multiply(X,add(Y,additive_inverse(X_129))) = add(multiply(X,Y),additive_inverse(multiply(X,X_129))),
inference(resolve,[$cnf( $equal(multiply(X,add(Y,additive_inverse(X_129))),add(multiply(X,Y),multiply(X,additive_inverse(X_129)))) )],[refute_0_0,refute_0_172]) ).
cnf(refute_0_174,plain,
( multiply(X,add(Y,additive_inverse(X_129))) != add(multiply(X,Y),additive_inverse(multiply(X,X_129)))
| add(multiply(X,Y),additive_inverse(multiply(X,X_129))) = multiply(X,add(Y,additive_inverse(X_129))) ),
inference(subst,[],[refute_0_15:[bind(X0,$fot(multiply(X,add(Y,additive_inverse(X_129))))),bind(Y0,$fot(add(multiply(X,Y),additive_inverse(multiply(X,X_129)))))]]) ).
cnf(refute_0_175,plain,
add(multiply(X,Y),additive_inverse(multiply(X,X_129))) = multiply(X,add(Y,additive_inverse(X_129))),
inference(resolve,[$cnf( $equal(multiply(X,add(Y,additive_inverse(X_129))),add(multiply(X,Y),additive_inverse(multiply(X,X_129)))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
add(multiply(x,y),additive_inverse(multiply(x,z))) = multiply(x,add(y,additive_inverse(z))),
inference(subst,[],[refute_0_175:[bind(X,$fot(x)),bind(Y,$fot(y)),bind(X_129,$fot(z))]]) ).
cnf(refute_0_177,plain,
( multiply(x,add(y,additive_inverse(z))) != multiply(x,add(y,additive_inverse(z)))
| add(multiply(x,y),additive_inverse(multiply(x,z))) != multiply(x,add(y,additive_inverse(z)))
| multiply(x,add(y,additive_inverse(z))) = add(multiply(x,y),additive_inverse(multiply(x,z))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(x,add(y,additive_inverse(z))),add(multiply(x,y),additive_inverse(multiply(x,z)))) ),[1],$fot(multiply(x,add(y,additive_inverse(z))))]]) ).
cnf(refute_0_178,plain,
( multiply(x,add(y,additive_inverse(z))) != multiply(x,add(y,additive_inverse(z)))
| multiply(x,add(y,additive_inverse(z))) = add(multiply(x,y),additive_inverse(multiply(x,z))) ),
inference(resolve,[$cnf( $equal(add(multiply(x,y),additive_inverse(multiply(x,z))),multiply(x,add(y,additive_inverse(z)))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
multiply(x,add(y,additive_inverse(z))) != multiply(x,add(y,additive_inverse(z))),
inference(resolve,[$cnf( $equal(multiply(x,add(y,additive_inverse(z))),add(multiply(x,y),additive_inverse(multiply(x,z)))) )],[refute_0_178,prove_distributivity]) ).
cnf(refute_0_180,plain,
multiply(x,add(y,additive_inverse(z))) = multiply(x,add(y,additive_inverse(z))),
introduced(tautology,[refl,[$fot(multiply(x,add(y,additive_inverse(z))))]]) ).
cnf(refute_0_181,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(x,add(y,additive_inverse(z))),multiply(x,add(y,additive_inverse(z)))) )],[refute_0_180,refute_0_179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG015-6 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon May 30 14:14:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.07/1.27 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.07/1.27
% 1.07/1.27 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.13/1.29
%------------------------------------------------------------------------------