TSTP Solution File: RNG008-4 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : RNG008-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 20:35:43 EDT 2022
% Result : Unsatisfiable 0.52s 0.75s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 67
% Syntax : Number of clauses : 271 ( 143 unt; 0 nHn; 167 RR)
% Number of literals : 455 ( 454 equ; 185 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 361 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
add(additive_identity,X) = X ).
cnf(left_additive_inverse,axiom,
add(additive_inverse(X),X) = additive_identity ).
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(additive_inverse_additive_inverse,axiom,
additive_inverse(additive_inverse(X)) = X ).
cnf(multiply_additive_inverse1,axiom,
multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)) ).
cnf(multiply_additive_inverse2,axiom,
multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)) ).
cnf(associative_addition,axiom,
add(add(X,Y),Z) = add(X,add(Y,Z)) ).
cnf(commutative_addition,axiom,
add(X,Y) = add(Y,X) ).
cnf(boolean_ring,hypothesis,
multiply(X,X) = X ).
cnf(a_times_b_is_c,negated_conjecture,
multiply(a,b) = c ).
cnf(prove_commutativity,negated_conjecture,
multiply(b,a) != c ).
cnf(refute_0_0,plain,
multiply(add(X_57,X_59),X_59) = add(multiply(X_57,X_59),multiply(X_59,X_59)),
inference(subst,[],[distribute2:[bind(X,$fot(X_57)),bind(Y,$fot(X_59)),bind(Z,$fot(X_59))]]) ).
cnf(refute_0_1,plain,
multiply(X_59,X_59) = X_59,
inference(subst,[],[boolean_ring:[bind(X,$fot(X_59))]]) ).
cnf(refute_0_2,plain,
( multiply(X_59,X_59) != X_59
| multiply(add(X_57,X_59),X_59) != add(multiply(X_57,X_59),multiply(X_59,X_59))
| multiply(add(X_57,X_59),X_59) = add(multiply(X_57,X_59),X_59) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_57,X_59),X_59),add(multiply(X_57,X_59),multiply(X_59,X_59))) ),[1,1],$fot(X_59)]]) ).
cnf(refute_0_3,plain,
( multiply(add(X_57,X_59),X_59) != add(multiply(X_57,X_59),multiply(X_59,X_59))
| multiply(add(X_57,X_59),X_59) = add(multiply(X_57,X_59),X_59) ),
inference(resolve,[$cnf( $equal(multiply(X_59,X_59),X_59) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(add(X_57,X_59),X_59) = add(multiply(X_57,X_59),X_59),
inference(resolve,[$cnf( $equal(multiply(add(X_57,X_59),X_59),add(multiply(X_57,X_59),multiply(X_59,X_59))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( add(X,Y) != add(Y,X)
| add(Y,X) = add(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(add(X,Y))),bind(Y0,$fot(add(Y,X)))]]) ).
cnf(refute_0_9,plain,
add(Y,X) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X,Y),add(Y,X)) )],[commutative_addition,refute_0_8]) ).
cnf(refute_0_10,plain,
add(multiply(X_57,X_59),X_59) = add(X_59,multiply(X_57,X_59)),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_59)),bind(Y,$fot(multiply(X_57,X_59)))]]) ).
cnf(refute_0_11,plain,
( multiply(add(X_57,X_59),X_59) != add(multiply(X_57,X_59),X_59)
| add(multiply(X_57,X_59),X_59) != add(X_59,multiply(X_57,X_59))
| multiply(add(X_57,X_59),X_59) = add(X_59,multiply(X_57,X_59)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(add(X_57,X_59),X_59),add(X_59,multiply(X_57,X_59))) ),[0],$fot(add(multiply(X_57,X_59),X_59))]]) ).
cnf(refute_0_12,plain,
( multiply(add(X_57,X_59),X_59) != add(multiply(X_57,X_59),X_59)
| multiply(add(X_57,X_59),X_59) = add(X_59,multiply(X_57,X_59)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_57,X_59),X_59),add(X_59,multiply(X_57,X_59))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(add(X_57,X_59),X_59) = add(X_59,multiply(X_57,X_59)),
inference(resolve,[$cnf( $equal(multiply(add(X_57,X_59),X_59),add(multiply(X_57,X_59),X_59)) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
multiply(add(add(a,b),a),a) = add(a,multiply(add(a,b),a)),
inference(subst,[],[refute_0_13:[bind(X_57,$fot(add(a,b))),bind(X_59,$fot(a))]]) ).
cnf(refute_0_15,plain,
multiply(X_40,add(X_39,X_40)) = add(multiply(X_40,X_39),multiply(X_40,X_40)),
inference(subst,[],[distribute1:[bind(X,$fot(X_40)),bind(Y,$fot(X_39)),bind(Z,$fot(X_40))]]) ).
cnf(refute_0_16,plain,
multiply(X_40,X_40) = X_40,
inference(subst,[],[boolean_ring:[bind(X,$fot(X_40))]]) ).
cnf(refute_0_17,plain,
( multiply(X_40,X_40) != X_40
| multiply(X_40,add(X_39,X_40)) != add(multiply(X_40,X_39),multiply(X_40,X_40))
| multiply(X_40,add(X_39,X_40)) = add(multiply(X_40,X_39),X_40) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_40,add(X_39,X_40)),add(multiply(X_40,X_39),multiply(X_40,X_40))) ),[1,1],$fot(X_40)]]) ).
cnf(refute_0_18,plain,
( multiply(X_40,add(X_39,X_40)) != add(multiply(X_40,X_39),multiply(X_40,X_40))
| multiply(X_40,add(X_39,X_40)) = add(multiply(X_40,X_39),X_40) ),
inference(resolve,[$cnf( $equal(multiply(X_40,X_40),X_40) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
multiply(X_40,add(X_39,X_40)) = add(multiply(X_40,X_39),X_40),
inference(resolve,[$cnf( $equal(multiply(X_40,add(X_39,X_40)),add(multiply(X_40,X_39),multiply(X_40,X_40))) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
add(multiply(X_40,X_39),X_40) = add(X_40,multiply(X_40,X_39)),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_40)),bind(Y,$fot(multiply(X_40,X_39)))]]) ).
cnf(refute_0_21,plain,
( multiply(X_40,add(X_39,X_40)) != add(multiply(X_40,X_39),X_40)
| add(multiply(X_40,X_39),X_40) != add(X_40,multiply(X_40,X_39))
| multiply(X_40,add(X_39,X_40)) = add(X_40,multiply(X_40,X_39)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_40,add(X_39,X_40)),add(X_40,multiply(X_40,X_39))) ),[0],$fot(add(multiply(X_40,X_39),X_40))]]) ).
cnf(refute_0_22,plain,
( multiply(X_40,add(X_39,X_40)) != add(multiply(X_40,X_39),X_40)
| multiply(X_40,add(X_39,X_40)) = add(X_40,multiply(X_40,X_39)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_40,X_39),X_40),add(X_40,multiply(X_40,X_39))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
multiply(X_40,add(X_39,X_40)) = add(X_40,multiply(X_40,X_39)),
inference(resolve,[$cnf( $equal(multiply(X_40,add(X_39,X_40)),add(multiply(X_40,X_39),X_40)) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(add(a,b),add(b,add(a,b))) = add(add(a,b),multiply(add(a,b),b)),
inference(subst,[],[refute_0_23:[bind(X_39,$fot(b)),bind(X_40,$fot(add(a,b)))]]) ).
cnf(refute_0_25,plain,
multiply(add(X_57,a),b) = add(multiply(X_57,b),multiply(a,b)),
inference(subst,[],[distribute2:[bind(X,$fot(X_57)),bind(Y,$fot(a)),bind(Z,$fot(b))]]) ).
cnf(refute_0_26,plain,
( multiply(add(X_57,a),b) != add(multiply(X_57,b),multiply(a,b))
| multiply(a,b) != c
| multiply(add(X_57,a),b) = add(multiply(X_57,b),c) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_57,a),b),add(multiply(X_57,b),multiply(a,b))) ),[1,1],$fot(c)]]) ).
cnf(refute_0_27,plain,
( multiply(add(X_57,a),b) != add(multiply(X_57,b),multiply(a,b))
| multiply(add(X_57,a),b) = add(multiply(X_57,b),c) ),
inference(resolve,[$cnf( $equal(multiply(a,b),c) )],[a_times_b_is_c,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(add(X_57,a),b) = add(multiply(X_57,b),c),
inference(resolve,[$cnf( $equal(multiply(add(X_57,a),b),add(multiply(X_57,b),multiply(a,b))) )],[refute_0_25,refute_0_27]) ).
cnf(refute_0_29,plain,
add(multiply(X_57,b),c) = add(c,multiply(X_57,b)),
inference(subst,[],[refute_0_9:[bind(X,$fot(c)),bind(Y,$fot(multiply(X_57,b)))]]) ).
cnf(refute_0_30,plain,
( multiply(add(X_57,a),b) != add(multiply(X_57,b),c)
| add(multiply(X_57,b),c) != add(c,multiply(X_57,b))
| multiply(add(X_57,a),b) = add(c,multiply(X_57,b)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(add(X_57,a),b),add(c,multiply(X_57,b))) ),[0],$fot(add(multiply(X_57,b),c))]]) ).
cnf(refute_0_31,plain,
( multiply(add(X_57,a),b) != add(multiply(X_57,b),c)
| multiply(add(X_57,a),b) = add(c,multiply(X_57,b)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_57,b),c),add(c,multiply(X_57,b))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
multiply(add(X_57,a),b) = add(c,multiply(X_57,b)),
inference(resolve,[$cnf( $equal(multiply(add(X_57,a),b),add(multiply(X_57,b),c)) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
multiply(add(b,a),b) = add(c,multiply(b,b)),
inference(subst,[],[refute_0_32:[bind(X_57,$fot(b))]]) ).
cnf(refute_0_34,plain,
multiply(b,b) = b,
inference(subst,[],[boolean_ring:[bind(X,$fot(b))]]) ).
cnf(refute_0_35,plain,
( multiply(add(b,a),b) != add(c,multiply(b,b))
| multiply(b,b) != b
| multiply(add(b,a),b) = add(c,b) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(b,a),b),add(c,multiply(b,b))) ),[1,1],$fot(b)]]) ).
cnf(refute_0_36,plain,
( multiply(add(b,a),b) != add(c,multiply(b,b))
| multiply(add(b,a),b) = add(c,b) ),
inference(resolve,[$cnf( $equal(multiply(b,b),b) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
multiply(add(b,a),b) = add(c,b),
inference(resolve,[$cnf( $equal(multiply(add(b,a),b),add(c,multiply(b,b))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
multiply(add(X_60,a),b) = add(c,multiply(X_60,b)),
inference(subst,[],[refute_0_32:[bind(X_57,$fot(X_60))]]) ).
cnf(refute_0_39,plain,
add(a,X_60) = add(X_60,a),
inference(subst,[],[commutative_addition:[bind(X,$fot(a)),bind(Y,$fot(X_60))]]) ).
cnf(refute_0_40,plain,
( add(a,X_60) != add(X_60,a)
| add(X_60,a) = add(a,X_60) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(add(a,X_60))),bind(Y0,$fot(add(X_60,a)))]]) ).
cnf(refute_0_41,plain,
add(X_60,a) = add(a,X_60),
inference(resolve,[$cnf( $equal(add(a,X_60),add(X_60,a)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( multiply(add(X_60,a),b) != add(c,multiply(X_60,b))
| add(X_60,a) != add(a,X_60)
| multiply(add(a,X_60),b) = add(c,multiply(X_60,b)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_60,a),b),add(c,multiply(X_60,b))) ),[0,0],$fot(add(a,X_60))]]) ).
cnf(refute_0_43,plain,
( multiply(add(X_60,a),b) != add(c,multiply(X_60,b))
| multiply(add(a,X_60),b) = add(c,multiply(X_60,b)) ),
inference(resolve,[$cnf( $equal(add(X_60,a),add(a,X_60)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
multiply(add(a,X_60),b) = add(c,multiply(X_60,b)),
inference(resolve,[$cnf( $equal(multiply(add(X_60,a),b),add(c,multiply(X_60,b))) )],[refute_0_38,refute_0_43]) ).
cnf(refute_0_45,plain,
( multiply(add(X_57,a),b) != add(c,multiply(X_57,b))
| add(c,multiply(X_57,b)) = multiply(add(X_57,a),b) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(add(X_57,a),b))),bind(Y0,$fot(add(c,multiply(X_57,b))))]]) ).
cnf(refute_0_46,plain,
add(c,multiply(X_57,b)) = multiply(add(X_57,a),b),
inference(resolve,[$cnf( $equal(multiply(add(X_57,a),b),add(c,multiply(X_57,b))) )],[refute_0_32,refute_0_45]) ).
cnf(refute_0_47,plain,
add(c,multiply(X_60,b)) = multiply(add(X_60,a),b),
inference(subst,[],[refute_0_46:[bind(X_57,$fot(X_60))]]) ).
cnf(refute_0_48,plain,
( multiply(add(a,X_60),b) != add(c,multiply(X_60,b))
| add(c,multiply(X_60,b)) != multiply(add(X_60,a),b)
| multiply(add(a,X_60),b) = multiply(add(X_60,a),b) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(add(a,X_60),b),multiply(add(X_60,a),b)) ),[0],$fot(add(c,multiply(X_60,b)))]]) ).
cnf(refute_0_49,plain,
( multiply(add(a,X_60),b) != add(c,multiply(X_60,b))
| multiply(add(a,X_60),b) = multiply(add(X_60,a),b) ),
inference(resolve,[$cnf( $equal(add(c,multiply(X_60,b)),multiply(add(X_60,a),b)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
multiply(add(a,X_60),b) = multiply(add(X_60,a),b),
inference(resolve,[$cnf( $equal(multiply(add(a,X_60),b),add(c,multiply(X_60,b))) )],[refute_0_44,refute_0_49]) ).
cnf(refute_0_51,plain,
( multiply(add(a,X_60),b) != multiply(add(X_60,a),b)
| multiply(add(X_60,a),b) = multiply(add(a,X_60),b) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(add(a,X_60),b))),bind(Y0,$fot(multiply(add(X_60,a),b)))]]) ).
cnf(refute_0_52,plain,
multiply(add(X_60,a),b) = multiply(add(a,X_60),b),
inference(resolve,[$cnf( $equal(multiply(add(a,X_60),b),multiply(add(X_60,a),b)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
multiply(add(b,a),b) = multiply(add(a,b),b),
inference(subst,[],[refute_0_52:[bind(X_60,$fot(b))]]) ).
cnf(refute_0_54,plain,
( multiply(add(b,a),b) != multiply(add(a,b),b)
| multiply(add(b,a),b) != add(c,b)
| multiply(add(a,b),b) = add(c,b) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(b,a),b),add(c,b)) ),[0],$fot(multiply(add(a,b),b))]]) ).
cnf(refute_0_55,plain,
( multiply(add(b,a),b) != add(c,b)
| multiply(add(a,b),b) = add(c,b) ),
inference(resolve,[$cnf( $equal(multiply(add(b,a),b),multiply(add(a,b),b)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
add(c,b) = add(b,c),
inference(subst,[],[refute_0_9:[bind(X,$fot(b)),bind(Y,$fot(c))]]) ).
cnf(refute_0_57,plain,
( multiply(add(a,b),b) != add(c,b)
| add(c,b) != add(b,c)
| multiply(add(a,b),b) = add(b,c) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(add(a,b),b),add(b,c)) ),[0],$fot(add(c,b))]]) ).
cnf(refute_0_58,plain,
( multiply(add(a,b),b) != add(c,b)
| multiply(add(a,b),b) = add(b,c) ),
inference(resolve,[$cnf( $equal(add(c,b),add(b,c)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( multiply(add(b,a),b) != add(c,b)
| multiply(add(a,b),b) = add(b,c) ),
inference(resolve,[$cnf( $equal(multiply(add(a,b),b),add(c,b)) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
multiply(add(a,b),b) = add(b,c),
inference(resolve,[$cnf( $equal(multiply(add(b,a),b),add(c,b)) )],[refute_0_37,refute_0_59]) ).
cnf(refute_0_61,plain,
( multiply(add(a,b),add(b,add(a,b))) != add(add(a,b),multiply(add(a,b),b))
| multiply(add(a,b),b) != add(b,c)
| multiply(add(a,b),add(b,add(a,b))) = add(add(a,b),add(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(a,b),add(b,add(a,b))),add(add(a,b),multiply(add(a,b),b))) ),[1,1],$fot(add(b,c))]]) ).
cnf(refute_0_62,plain,
( multiply(add(a,b),add(b,add(a,b))) != add(add(a,b),multiply(add(a,b),b))
| multiply(add(a,b),add(b,add(a,b))) = add(add(a,b),add(b,c)) ),
inference(resolve,[$cnf( $equal(multiply(add(a,b),b),add(b,c)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
multiply(add(a,b),add(b,add(a,b))) = add(add(a,b),add(b,c)),
inference(resolve,[$cnf( $equal(multiply(add(a,b),add(b,add(a,b))),add(add(a,b),multiply(add(a,b),b))) )],[refute_0_24,refute_0_62]) ).
cnf(refute_0_64,plain,
add(additive_identity,X) = add(X,additive_identity),
inference(subst,[],[commutative_addition:[bind(X,$fot(additive_identity)),bind(Y,$fot(X))]]) ).
cnf(refute_0_65,plain,
( add(additive_identity,X) != X
| add(additive_identity,X) != add(X,additive_identity)
| add(X,additive_identity) = X ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_identity,X),X) ),[0],$fot(add(X,additive_identity))]]) ).
cnf(refute_0_66,plain,
( add(additive_identity,X) != X
| add(X,additive_identity) = X ),
inference(resolve,[$cnf( $equal(add(additive_identity,X),add(X,additive_identity)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
add(X,additive_identity) = X,
inference(resolve,[$cnf( $equal(add(additive_identity,X),X) )],[left_identity,refute_0_66]) ).
cnf(refute_0_68,plain,
add(a,additive_identity) = a,
inference(subst,[],[refute_0_67:[bind(X,$fot(a))]]) ).
cnf(refute_0_69,plain,
add(additive_inverse(X),X) = add(X,additive_inverse(X)),
inference(subst,[],[refute_0_9:[bind(Y,$fot(additive_inverse(X)))]]) ).
cnf(refute_0_70,plain,
( add(additive_inverse(X),X) != add(X,additive_inverse(X))
| add(additive_inverse(X),X) != additive_identity
| add(X,additive_inverse(X)) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_inverse(X),X),additive_identity) ),[0],$fot(add(X,additive_inverse(X)))]]) ).
cnf(refute_0_71,plain,
( add(additive_inverse(X),X) != additive_identity
| add(X,additive_inverse(X)) = additive_identity ),
inference(resolve,[$cnf( $equal(add(additive_inverse(X),X),add(X,additive_inverse(X))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
add(X,additive_inverse(X)) = additive_identity,
inference(resolve,[$cnf( $equal(add(additive_inverse(X),X),additive_identity) )],[left_additive_inverse,refute_0_71]) ).
cnf(refute_0_73,plain,
multiply(additive_inverse(X_10),additive_inverse(X_10)) = additive_inverse(X_10),
inference(subst,[],[boolean_ring:[bind(X,$fot(additive_inverse(X_10)))]]) ).
cnf(refute_0_74,plain,
multiply(additive_inverse(X_10),additive_inverse(X_10)) = additive_inverse(multiply(additive_inverse(X_10),X_10)),
inference(subst,[],[multiply_additive_inverse1:[bind(X,$fot(additive_inverse(X_10))),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_75,plain,
( multiply(additive_inverse(X_10),additive_inverse(X_10)) != additive_inverse(X_10)
| multiply(additive_inverse(X_10),additive_inverse(X_10)) != additive_inverse(multiply(additive_inverse(X_10),X_10))
| additive_inverse(multiply(additive_inverse(X_10),X_10)) = additive_inverse(X_10) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_inverse(X_10),additive_inverse(X_10)),additive_inverse(X_10)) ),[0],$fot(additive_inverse(multiply(additive_inverse(X_10),X_10)))]]) ).
cnf(refute_0_76,plain,
( multiply(additive_inverse(X_10),additive_inverse(X_10)) != additive_inverse(X_10)
| additive_inverse(multiply(additive_inverse(X_10),X_10)) = additive_inverse(X_10) ),
inference(resolve,[$cnf( $equal(multiply(additive_inverse(X_10),additive_inverse(X_10)),additive_inverse(multiply(additive_inverse(X_10),X_10))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
additive_inverse(multiply(additive_inverse(X_10),X_10)) = additive_inverse(X_10),
inference(resolve,[$cnf( $equal(multiply(additive_inverse(X_10),additive_inverse(X_10)),additive_inverse(X_10)) )],[refute_0_73,refute_0_76]) ).
cnf(refute_0_78,plain,
additive_inverse(additive_inverse(X_10)) = X_10,
inference(subst,[],[additive_inverse_additive_inverse:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_79,plain,
multiply(X_10,X_10) = X_10,
inference(subst,[],[boolean_ring:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_80,plain,
additive_inverse(multiply(X_10,X_10)) = additive_inverse(multiply(X_10,X_10)),
introduced(tautology,[refl,[$fot(additive_inverse(multiply(X_10,X_10)))]]) ).
cnf(refute_0_81,plain,
( multiply(X_10,X_10) != X_10
| additive_inverse(multiply(X_10,X_10)) != additive_inverse(multiply(X_10,X_10))
| additive_inverse(multiply(X_10,X_10)) = additive_inverse(X_10) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(X_10,X_10)),additive_inverse(multiply(X_10,X_10))) ),[1,0],$fot(X_10)]]) ).
cnf(refute_0_82,plain,
( multiply(X_10,X_10) != X_10
| additive_inverse(multiply(X_10,X_10)) = additive_inverse(X_10) ),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X_10,X_10)),additive_inverse(multiply(X_10,X_10))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
additive_inverse(multiply(X_10,X_10)) = additive_inverse(X_10),
inference(resolve,[$cnf( $equal(multiply(X_10,X_10),X_10) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
multiply(additive_inverse(X_10),X_10) = additive_inverse(multiply(X_10,X_10)),
inference(subst,[],[multiply_additive_inverse2:[bind(X,$fot(X_10)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_85,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_86,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_7,refute_0_85]) ).
cnf(refute_0_87,plain,
( multiply(additive_inverse(X_10),X_10) != additive_inverse(multiply(X_10,X_10))
| additive_inverse(multiply(X_10,X_10)) != additive_inverse(X_10)
| multiply(additive_inverse(X_10),X_10) = additive_inverse(X_10) ),
inference(subst,[],[refute_0_86:[bind(X0,$fot(multiply(additive_inverse(X_10),X_10))),bind(Y0,$fot(additive_inverse(multiply(X_10,X_10)))),bind(Z0,$fot(additive_inverse(X_10)))]]) ).
cnf(refute_0_88,plain,
( additive_inverse(multiply(X_10,X_10)) != additive_inverse(X_10)
| multiply(additive_inverse(X_10),X_10) = additive_inverse(X_10) ),
inference(resolve,[$cnf( $equal(multiply(additive_inverse(X_10),X_10),additive_inverse(multiply(X_10,X_10))) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
multiply(additive_inverse(X_10),X_10) = additive_inverse(X_10),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X_10,X_10)),additive_inverse(X_10)) )],[refute_0_83,refute_0_88]) ).
cnf(refute_0_90,plain,
additive_inverse(multiply(additive_inverse(X_10),X_10)) = additive_inverse(multiply(additive_inverse(X_10),X_10)),
introduced(tautology,[refl,[$fot(additive_inverse(multiply(additive_inverse(X_10),X_10)))]]) ).
cnf(refute_0_91,plain,
( multiply(additive_inverse(X_10),X_10) != additive_inverse(X_10)
| additive_inverse(multiply(additive_inverse(X_10),X_10)) != additive_inverse(multiply(additive_inverse(X_10),X_10))
| additive_inverse(multiply(additive_inverse(X_10),X_10)) = additive_inverse(additive_inverse(X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_10),X_10)),additive_inverse(multiply(additive_inverse(X_10),X_10))) ),[1,0],$fot(additive_inverse(X_10))]]) ).
cnf(refute_0_92,plain,
( multiply(additive_inverse(X_10),X_10) != additive_inverse(X_10)
| additive_inverse(multiply(additive_inverse(X_10),X_10)) = additive_inverse(additive_inverse(X_10)) ),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_10),X_10)),additive_inverse(multiply(additive_inverse(X_10),X_10))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
additive_inverse(multiply(additive_inverse(X_10),X_10)) = additive_inverse(additive_inverse(X_10)),
inference(resolve,[$cnf( $equal(multiply(additive_inverse(X_10),X_10),additive_inverse(X_10)) )],[refute_0_89,refute_0_92]) ).
cnf(refute_0_94,plain,
( additive_inverse(multiply(additive_inverse(X_10),X_10)) != additive_inverse(additive_inverse(X_10))
| additive_inverse(additive_inverse(X_10)) != X_10
| additive_inverse(multiply(additive_inverse(X_10),X_10)) = X_10 ),
inference(subst,[],[refute_0_86:[bind(X0,$fot(additive_inverse(multiply(additive_inverse(X_10),X_10)))),bind(Y0,$fot(additive_inverse(additive_inverse(X_10)))),bind(Z0,$fot(X_10))]]) ).
cnf(refute_0_95,plain,
( additive_inverse(additive_inverse(X_10)) != X_10
| additive_inverse(multiply(additive_inverse(X_10),X_10)) = X_10 ),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_10),X_10)),additive_inverse(additive_inverse(X_10))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
additive_inverse(multiply(additive_inverse(X_10),X_10)) = X_10,
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(X_10)),X_10) )],[refute_0_78,refute_0_95]) ).
cnf(refute_0_97,plain,
( additive_inverse(multiply(additive_inverse(X_10),X_10)) != X_10
| additive_inverse(multiply(additive_inverse(X_10),X_10)) != additive_inverse(X_10)
| X_10 = additive_inverse(X_10) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_10),X_10)),additive_inverse(X_10)) ),[0],$fot(X_10)]]) ).
cnf(refute_0_98,plain,
( additive_inverse(multiply(additive_inverse(X_10),X_10)) != additive_inverse(X_10)
| X_10 = additive_inverse(X_10) ),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_10),X_10)),X_10) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
X_10 = additive_inverse(X_10),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_10),X_10)),additive_inverse(X_10)) )],[refute_0_77,refute_0_98]) ).
cnf(refute_0_100,plain,
( X_10 != additive_inverse(X_10)
| additive_inverse(X_10) = X_10 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(X_10)),bind(Y0,$fot(additive_inverse(X_10)))]]) ).
cnf(refute_0_101,plain,
additive_inverse(X_10) = X_10,
inference(resolve,[$cnf( $equal(X_10,additive_inverse(X_10)) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
additive_inverse(X) = X,
inference(subst,[],[refute_0_101:[bind(X_10,$fot(X))]]) ).
cnf(refute_0_103,plain,
add(X,additive_inverse(X)) = add(X,additive_inverse(X)),
introduced(tautology,[refl,[$fot(add(X,additive_inverse(X)))]]) ).
cnf(refute_0_104,plain,
( add(X,additive_inverse(X)) != add(X,additive_inverse(X))
| additive_inverse(X) != X
| add(X,additive_inverse(X)) = add(X,X) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,additive_inverse(X)),add(X,additive_inverse(X))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_105,plain,
( additive_inverse(X) != X
| add(X,additive_inverse(X)) = add(X,X) ),
inference(resolve,[$cnf( $equal(add(X,additive_inverse(X)),add(X,additive_inverse(X))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
add(X,additive_inverse(X)) = add(X,X),
inference(resolve,[$cnf( $equal(additive_inverse(X),X) )],[refute_0_102,refute_0_105]) ).
cnf(refute_0_107,plain,
( add(X,additive_inverse(X)) != add(X,X)
| add(X,additive_inverse(X)) != additive_identity
| add(X,X) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(add(X,additive_inverse(X)),additive_identity) ),[0],$fot(add(X,X))]]) ).
cnf(refute_0_108,plain,
( add(X,additive_inverse(X)) != additive_identity
| add(X,X) = additive_identity ),
inference(resolve,[$cnf( $equal(add(X,additive_inverse(X)),add(X,X)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
add(X,X) = additive_identity,
inference(resolve,[$cnf( $equal(add(X,additive_inverse(X)),additive_identity) )],[refute_0_72,refute_0_108]) ).
cnf(refute_0_110,plain,
add(b,b) = additive_identity,
inference(subst,[],[refute_0_109:[bind(X,$fot(b))]]) ).
cnf(refute_0_111,plain,
add(a,add(b,b)) = add(a,add(b,b)),
introduced(tautology,[refl,[$fot(add(a,add(b,b)))]]) ).
cnf(refute_0_112,plain,
( add(a,add(b,b)) != add(a,add(b,b))
| add(b,b) != additive_identity
| add(a,add(b,b)) = add(a,additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(a,add(b,b)),add(a,add(b,b))) ),[1,1],$fot(additive_identity)]]) ).
cnf(refute_0_113,plain,
( add(b,b) != additive_identity
| add(a,add(b,b)) = add(a,additive_identity) ),
inference(resolve,[$cnf( $equal(add(a,add(b,b)),add(a,add(b,b))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
add(a,add(b,b)) = add(a,additive_identity),
inference(resolve,[$cnf( $equal(add(b,b),additive_identity) )],[refute_0_110,refute_0_113]) ).
cnf(refute_0_115,plain,
( add(a,add(b,b)) != add(a,additive_identity)
| add(a,additive_identity) != a
| add(a,add(b,b)) = a ),
inference(subst,[],[refute_0_86:[bind(X0,$fot(add(a,add(b,b)))),bind(Y0,$fot(add(a,additive_identity))),bind(Z0,$fot(a))]]) ).
cnf(refute_0_116,plain,
( add(a,additive_identity) != a
| add(a,add(b,b)) = a ),
inference(resolve,[$cnf( $equal(add(a,add(b,b)),add(a,additive_identity)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
add(a,add(b,b)) = a,
inference(resolve,[$cnf( $equal(add(a,additive_identity),a) )],[refute_0_68,refute_0_116]) ).
cnf(refute_0_118,plain,
add(add(X_14,X_14),X_15) = add(X_14,add(X_14,X_15)),
inference(subst,[],[associative_addition:[bind(X,$fot(X_14)),bind(Y,$fot(X_14)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_119,plain,
add(X_14,X_14) = additive_identity,
inference(subst,[],[refute_0_109:[bind(X,$fot(X_14))]]) ).
cnf(refute_0_120,plain,
( add(X_14,X_14) != additive_identity
| add(add(X_14,X_14),X_15) != add(X_14,add(X_14,X_15))
| add(additive_identity,X_15) = add(X_14,add(X_14,X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_14,X_14),X_15),add(X_14,add(X_14,X_15))) ),[0,0],$fot(additive_identity)]]) ).
cnf(refute_0_121,plain,
( add(add(X_14,X_14),X_15) != add(X_14,add(X_14,X_15))
| add(additive_identity,X_15) = add(X_14,add(X_14,X_15)) ),
inference(resolve,[$cnf( $equal(add(X_14,X_14),additive_identity) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
add(additive_identity,X_15) = add(X_14,add(X_14,X_15)),
inference(resolve,[$cnf( $equal(add(add(X_14,X_14),X_15),add(X_14,add(X_14,X_15))) )],[refute_0_118,refute_0_121]) ).
cnf(refute_0_123,plain,
add(additive_identity,X_15) = X_15,
inference(subst,[],[left_identity:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_124,plain,
( add(additive_identity,X_15) != X_15
| add(additive_identity,X_15) != add(X_14,add(X_14,X_15))
| X_15 = add(X_14,add(X_14,X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_identity,X_15),add(X_14,add(X_14,X_15))) ),[0],$fot(X_15)]]) ).
cnf(refute_0_125,plain,
( add(additive_identity,X_15) != add(X_14,add(X_14,X_15))
| X_15 = add(X_14,add(X_14,X_15)) ),
inference(resolve,[$cnf( $equal(add(additive_identity,X_15),X_15) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
X_15 = add(X_14,add(X_14,X_15)),
inference(resolve,[$cnf( $equal(add(additive_identity,X_15),add(X_14,add(X_14,X_15))) )],[refute_0_122,refute_0_125]) ).
cnf(refute_0_127,plain,
add(X_23,add(X_24,X_14)) = add(X_14,add(X_14,add(X_23,add(X_24,X_14)))),
inference(subst,[],[refute_0_126:[bind(X_15,$fot(add(X_23,add(X_24,X_14))))]]) ).
cnf(refute_0_128,plain,
add(add(X_13,X_15),X_15) = add(X_13,add(X_15,X_15)),
inference(subst,[],[associative_addition:[bind(X,$fot(X_13)),bind(Y,$fot(X_15)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_129,plain,
add(X_15,X_15) = additive_identity,
inference(subst,[],[refute_0_109:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_130,plain,
( add(X_15,X_15) != additive_identity
| add(add(X_13,X_15),X_15) != add(X_13,add(X_15,X_15))
| add(add(X_13,X_15),X_15) = add(X_13,additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_13,X_15),X_15),add(X_13,add(X_15,X_15))) ),[1,1],$fot(additive_identity)]]) ).
cnf(refute_0_131,plain,
( add(add(X_13,X_15),X_15) != add(X_13,add(X_15,X_15))
| add(add(X_13,X_15),X_15) = add(X_13,additive_identity) ),
inference(resolve,[$cnf( $equal(add(X_15,X_15),additive_identity) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
add(add(X_13,X_15),X_15) = add(X_13,additive_identity),
inference(resolve,[$cnf( $equal(add(add(X_13,X_15),X_15),add(X_13,add(X_15,X_15))) )],[refute_0_128,refute_0_131]) ).
cnf(refute_0_133,plain,
add(add(X_13,X_15),X_15) = add(X_15,add(X_13,X_15)),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_15)),bind(Y,$fot(add(X_13,X_15)))]]) ).
cnf(refute_0_134,plain,
( add(add(X_13,X_15),X_15) != add(X_13,additive_identity)
| add(add(X_13,X_15),X_15) != add(X_15,add(X_13,X_15))
| add(X_15,add(X_13,X_15)) = add(X_13,additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_13,X_15),X_15),add(X_13,additive_identity)) ),[0],$fot(add(X_15,add(X_13,X_15)))]]) ).
cnf(refute_0_135,plain,
( add(add(X_13,X_15),X_15) != add(X_13,additive_identity)
| add(X_15,add(X_13,X_15)) = add(X_13,additive_identity) ),
inference(resolve,[$cnf( $equal(add(add(X_13,X_15),X_15),add(X_15,add(X_13,X_15))) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
add(X_13,additive_identity) = X_13,
inference(subst,[],[refute_0_67:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_137,plain,
( add(X_13,additive_identity) != X_13
| add(X_15,add(X_13,X_15)) != add(X_13,additive_identity)
| add(X_15,add(X_13,X_15)) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(add(X_15,add(X_13,X_15)),add(X_13,additive_identity)) ),[1],$fot(X_13)]]) ).
cnf(refute_0_138,plain,
( add(X_15,add(X_13,X_15)) != add(X_13,additive_identity)
| add(X_15,add(X_13,X_15)) = X_13 ),
inference(resolve,[$cnf( $equal(add(X_13,additive_identity),X_13) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
( add(add(X_13,X_15),X_15) != add(X_13,additive_identity)
| add(X_15,add(X_13,X_15)) = X_13 ),
inference(resolve,[$cnf( $equal(add(X_15,add(X_13,X_15)),add(X_13,additive_identity)) )],[refute_0_135,refute_0_138]) ).
cnf(refute_0_140,plain,
add(X_15,add(X_13,X_15)) = X_13,
inference(resolve,[$cnf( $equal(add(add(X_13,X_15),X_15),add(X_13,additive_identity)) )],[refute_0_132,refute_0_139]) ).
cnf(refute_0_141,plain,
add(X_19,add(add(X,Y),X_19)) = add(X,Y),
inference(subst,[],[refute_0_140:[bind(X_13,$fot(add(X,Y))),bind(X_15,$fot(X_19))]]) ).
cnf(refute_0_142,plain,
add(add(X,Y),X_19) = add(X,add(Y,X_19)),
inference(subst,[],[associative_addition:[bind(Z,$fot(X_19))]]) ).
cnf(refute_0_143,plain,
( add(X_19,add(add(X,Y),X_19)) != add(X,Y)
| add(add(X,Y),X_19) != add(X,add(Y,X_19))
| add(X_19,add(X,add(Y,X_19))) = add(X,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_19,add(add(X,Y),X_19)),add(X,Y)) ),[0,1],$fot(add(X,add(Y,X_19)))]]) ).
cnf(refute_0_144,plain,
( add(X_19,add(add(X,Y),X_19)) != add(X,Y)
| add(X_19,add(X,add(Y,X_19))) = add(X,Y) ),
inference(resolve,[$cnf( $equal(add(add(X,Y),X_19),add(X,add(Y,X_19))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
add(X_19,add(X,add(Y,X_19))) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X_19,add(add(X,Y),X_19)),add(X,Y)) )],[refute_0_141,refute_0_144]) ).
cnf(refute_0_146,plain,
add(X_14,add(X_23,add(X_24,X_14))) = add(X_23,X_24),
inference(subst,[],[refute_0_145:[bind(X,$fot(X_23)),bind(Y,$fot(X_24)),bind(X_19,$fot(X_14))]]) ).
cnf(refute_0_147,plain,
( add(X_14,add(X_23,add(X_24,X_14))) != add(X_23,X_24)
| add(X_23,add(X_24,X_14)) != add(X_14,add(X_14,add(X_23,add(X_24,X_14))))
| add(X_23,add(X_24,X_14)) = add(X_14,add(X_23,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_23,add(X_24,X_14)),add(X_14,add(X_14,add(X_23,add(X_24,X_14))))) ),[1,1],$fot(add(X_23,X_24))]]) ).
cnf(refute_0_148,plain,
( add(X_23,add(X_24,X_14)) != add(X_14,add(X_14,add(X_23,add(X_24,X_14))))
| add(X_23,add(X_24,X_14)) = add(X_14,add(X_23,X_24)) ),
inference(resolve,[$cnf( $equal(add(X_14,add(X_23,add(X_24,X_14))),add(X_23,X_24)) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
add(X_23,add(X_24,X_14)) = add(X_14,add(X_23,X_24)),
inference(resolve,[$cnf( $equal(add(X_23,add(X_24,X_14)),add(X_14,add(X_14,add(X_23,add(X_24,X_14))))) )],[refute_0_127,refute_0_148]) ).
cnf(refute_0_150,plain,
( add(X_23,add(X_24,X_14)) != add(X_14,add(X_23,X_24))
| add(X_14,add(X_23,X_24)) = add(X_23,add(X_24,X_14)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(add(X_23,add(X_24,X_14)))),bind(Y0,$fot(add(X_14,add(X_23,X_24))))]]) ).
cnf(refute_0_151,plain,
add(X_14,add(X_23,X_24)) = add(X_23,add(X_24,X_14)),
inference(resolve,[$cnf( $equal(add(X_23,add(X_24,X_14)),add(X_14,add(X_23,X_24))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
add(b,add(a,b)) = add(a,add(b,b)),
inference(subst,[],[refute_0_151:[bind(X_14,$fot(b)),bind(X_23,$fot(a)),bind(X_24,$fot(b))]]) ).
cnf(refute_0_153,plain,
( add(a,add(b,b)) != a
| add(b,add(a,b)) != add(a,add(b,b))
| add(b,add(a,b)) = a ),
inference(subst,[],[refute_0_86:[bind(X0,$fot(add(b,add(a,b)))),bind(Y0,$fot(add(a,add(b,b)))),bind(Z0,$fot(a))]]) ).
cnf(refute_0_154,plain,
( add(a,add(b,b)) != a
| add(b,add(a,b)) = a ),
inference(resolve,[$cnf( $equal(add(b,add(a,b)),add(a,add(b,b))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
add(b,add(a,b)) = a,
inference(resolve,[$cnf( $equal(add(a,add(b,b)),a) )],[refute_0_117,refute_0_154]) ).
cnf(refute_0_156,plain,
multiply(add(a,b),add(b,add(a,b))) = multiply(add(a,b),add(b,add(a,b))),
introduced(tautology,[refl,[$fot(multiply(add(a,b),add(b,add(a,b))))]]) ).
cnf(refute_0_157,plain,
( multiply(add(a,b),add(b,add(a,b))) != multiply(add(a,b),add(b,add(a,b)))
| add(b,add(a,b)) != a
| multiply(add(a,b),add(b,add(a,b))) = multiply(add(a,b),a) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(a,b),add(b,add(a,b))),multiply(add(a,b),add(b,add(a,b)))) ),[1,1],$fot(a)]]) ).
cnf(refute_0_158,plain,
( add(b,add(a,b)) != a
| multiply(add(a,b),add(b,add(a,b))) = multiply(add(a,b),a) ),
inference(resolve,[$cnf( $equal(multiply(add(a,b),add(b,add(a,b))),multiply(add(a,b),add(b,add(a,b)))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
multiply(add(a,b),add(b,add(a,b))) = multiply(add(a,b),a),
inference(resolve,[$cnf( $equal(add(b,add(a,b)),a) )],[refute_0_155,refute_0_158]) ).
cnf(refute_0_160,plain,
( multiply(add(a,b),add(b,add(a,b))) != multiply(add(a,b),a)
| multiply(add(a,b),add(b,add(a,b))) != add(add(a,b),add(b,c))
| multiply(add(a,b),a) = add(add(a,b),add(b,c)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(a,b),add(b,add(a,b))),add(add(a,b),add(b,c))) ),[0],$fot(multiply(add(a,b),a))]]) ).
cnf(refute_0_161,plain,
( multiply(add(a,b),add(b,add(a,b))) != add(add(a,b),add(b,c))
| multiply(add(a,b),a) = add(add(a,b),add(b,c)) ),
inference(resolve,[$cnf( $equal(multiply(add(a,b),add(b,add(a,b))),multiply(add(a,b),a)) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
( X_15 != add(X_14,add(X_14,X_15))
| add(X_14,add(X_14,X_15)) = X_15 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(X_15)),bind(Y0,$fot(add(X_14,add(X_14,X_15))))]]) ).
cnf(refute_0_163,plain,
add(X_14,add(X_14,X_15)) = X_15,
inference(resolve,[$cnf( $equal(X_15,add(X_14,add(X_14,X_15))) )],[refute_0_126,refute_0_162]) ).
cnf(refute_0_164,plain,
add(b,add(b,c)) = c,
inference(subst,[],[refute_0_163:[bind(X_14,$fot(b)),bind(X_15,$fot(c))]]) ).
cnf(refute_0_165,plain,
add(a,add(b,add(b,c))) = add(a,add(b,add(b,c))),
introduced(tautology,[refl,[$fot(add(a,add(b,add(b,c))))]]) ).
cnf(refute_0_166,plain,
( add(a,add(b,add(b,c))) != add(a,add(b,add(b,c)))
| add(b,add(b,c)) != c
| add(a,add(b,add(b,c))) = add(a,c) ),
introduced(tautology,[equality,[$cnf( $equal(add(a,add(b,add(b,c))),add(a,add(b,add(b,c)))) ),[1,1],$fot(c)]]) ).
cnf(refute_0_167,plain,
( add(b,add(b,c)) != c
| add(a,add(b,add(b,c))) = add(a,c) ),
inference(resolve,[$cnf( $equal(add(a,add(b,add(b,c))),add(a,add(b,add(b,c)))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
add(a,add(b,add(b,c))) = add(a,c),
inference(resolve,[$cnf( $equal(add(b,add(b,c)),c) )],[refute_0_164,refute_0_167]) ).
cnf(refute_0_169,plain,
add(add(X,Y),add(Y,X_17)) = add(X,add(Y,add(Y,X_17))),
inference(subst,[],[associative_addition:[bind(Z,$fot(add(Y,X_17)))]]) ).
cnf(refute_0_170,plain,
X_17 = add(Y,add(Y,X_17)),
inference(subst,[],[refute_0_126:[bind(X_14,$fot(Y)),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_171,plain,
( X_17 != add(Y,add(Y,X_17))
| add(Y,add(Y,X_17)) = X_17 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(X_17)),bind(Y0,$fot(add(Y,add(Y,X_17))))]]) ).
cnf(refute_0_172,plain,
add(Y,add(Y,X_17)) = X_17,
inference(resolve,[$cnf( $equal(X_17,add(Y,add(Y,X_17))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
( add(Y,add(Y,X_17)) != X_17
| add(add(X,Y),add(Y,X_17)) != add(X,add(Y,add(Y,X_17)))
| add(add(X,Y),add(Y,X_17)) = add(X,X_17) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X,Y),add(Y,X_17)),add(X,add(Y,add(Y,X_17)))) ),[1,1],$fot(X_17)]]) ).
cnf(refute_0_174,plain,
( add(add(X,Y),add(Y,X_17)) != add(X,add(Y,add(Y,X_17)))
| add(add(X,Y),add(Y,X_17)) = add(X,X_17) ),
inference(resolve,[$cnf( $equal(add(Y,add(Y,X_17)),X_17) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
add(add(X,Y),add(Y,X_17)) = add(X,X_17),
inference(resolve,[$cnf( $equal(add(add(X,Y),add(Y,X_17)),add(X,add(Y,add(Y,X_17)))) )],[refute_0_169,refute_0_174]) ).
cnf(refute_0_176,plain,
add(add(X,Y),X_17) = add(X,add(Y,X_17)),
inference(subst,[],[associative_addition:[bind(Z,$fot(X_17))]]) ).
cnf(refute_0_177,plain,
add(Y,add(add(X,Y),X_17)) = add(Y,add(add(X,Y),X_17)),
introduced(tautology,[refl,[$fot(add(Y,add(add(X,Y),X_17)))]]) ).
cnf(refute_0_178,plain,
( add(Y,add(add(X,Y),X_17)) != add(Y,add(add(X,Y),X_17))
| add(add(X,Y),X_17) != add(X,add(Y,X_17))
| add(Y,add(add(X,Y),X_17)) = add(Y,add(X,add(Y,X_17))) ),
introduced(tautology,[equality,[$cnf( $equal(add(Y,add(add(X,Y),X_17)),add(Y,add(add(X,Y),X_17))) ),[1,1],$fot(add(X,add(Y,X_17)))]]) ).
cnf(refute_0_179,plain,
( add(add(X,Y),X_17) != add(X,add(Y,X_17))
| add(Y,add(add(X,Y),X_17)) = add(Y,add(X,add(Y,X_17))) ),
inference(resolve,[$cnf( $equal(add(Y,add(add(X,Y),X_17)),add(Y,add(add(X,Y),X_17))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
add(Y,add(add(X,Y),X_17)) = add(Y,add(X,add(Y,X_17))),
inference(resolve,[$cnf( $equal(add(add(X,Y),X_17),add(X,add(Y,X_17))) )],[refute_0_176,refute_0_179]) ).
cnf(refute_0_181,plain,
add(add(X_13,X_14),X_15) = add(X_13,add(X_14,X_15)),
inference(subst,[],[associative_addition:[bind(X,$fot(X_13)),bind(Y,$fot(X_14)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_182,plain,
add(X_14,X_13) = add(X_13,X_14),
inference(subst,[],[commutative_addition:[bind(X,$fot(X_14)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_183,plain,
( add(X_14,X_13) != add(X_13,X_14)
| add(X_13,X_14) = add(X_14,X_13) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(add(X_14,X_13))),bind(Y0,$fot(add(X_13,X_14)))]]) ).
cnf(refute_0_184,plain,
add(X_13,X_14) = add(X_14,X_13),
inference(resolve,[$cnf( $equal(add(X_14,X_13),add(X_13,X_14)) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
( add(X_13,X_14) != add(X_14,X_13)
| add(add(X_13,X_14),X_15) != add(X_13,add(X_14,X_15))
| add(add(X_14,X_13),X_15) = add(X_13,add(X_14,X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_13,X_14),X_15),add(X_13,add(X_14,X_15))) ),[0,0],$fot(add(X_14,X_13))]]) ).
cnf(refute_0_186,plain,
( add(add(X_13,X_14),X_15) != add(X_13,add(X_14,X_15))
| add(add(X_14,X_13),X_15) = add(X_13,add(X_14,X_15)) ),
inference(resolve,[$cnf( $equal(add(X_13,X_14),add(X_14,X_13)) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
add(add(X_14,X_13),X_15) = add(X_13,add(X_14,X_15)),
inference(resolve,[$cnf( $equal(add(add(X_13,X_14),X_15),add(X_13,add(X_14,X_15))) )],[refute_0_181,refute_0_186]) ).
cnf(refute_0_188,plain,
add(add(X_14,X_13),X_15) = add(X_14,add(X_13,X_15)),
inference(subst,[],[associative_addition:[bind(X,$fot(X_14)),bind(Y,$fot(X_13)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_189,plain,
( add(add(X_14,X_13),X_15) != add(X_13,add(X_14,X_15))
| add(add(X_14,X_13),X_15) != add(X_14,add(X_13,X_15))
| add(X_14,add(X_13,X_15)) = add(X_13,add(X_14,X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_14,X_13),X_15),add(X_13,add(X_14,X_15))) ),[0],$fot(add(X_14,add(X_13,X_15)))]]) ).
cnf(refute_0_190,plain,
( add(add(X_14,X_13),X_15) != add(X_13,add(X_14,X_15))
| add(X_14,add(X_13,X_15)) = add(X_13,add(X_14,X_15)) ),
inference(resolve,[$cnf( $equal(add(add(X_14,X_13),X_15),add(X_14,add(X_13,X_15))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
add(X_14,add(X_13,X_15)) = add(X_13,add(X_14,X_15)),
inference(resolve,[$cnf( $equal(add(add(X_14,X_13),X_15),add(X_13,add(X_14,X_15))) )],[refute_0_187,refute_0_190]) ).
cnf(refute_0_192,plain,
( add(X_14,add(X_13,X_15)) != add(X_13,add(X_14,X_15))
| add(X_13,add(X_14,X_15)) = add(X_14,add(X_13,X_15)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(add(X_14,add(X_13,X_15)))),bind(Y0,$fot(add(X_13,add(X_14,X_15))))]]) ).
cnf(refute_0_193,plain,
add(X_13,add(X_14,X_15)) = add(X_14,add(X_13,X_15)),
inference(resolve,[$cnf( $equal(add(X_14,add(X_13,X_15)),add(X_13,add(X_14,X_15))) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
add(add(X,Y),add(Y,X_17)) = add(Y,add(add(X,Y),X_17)),
inference(subst,[],[refute_0_193:[bind(X_13,$fot(add(X,Y))),bind(X_14,$fot(Y)),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_195,plain,
( add(Y,add(add(X,Y),X_17)) != add(Y,add(X,add(Y,X_17)))
| add(add(X,Y),add(Y,X_17)) != add(Y,add(add(X,Y),X_17))
| add(add(X,Y),add(Y,X_17)) = add(Y,add(X,add(Y,X_17))) ),
inference(subst,[],[refute_0_86:[bind(X0,$fot(add(add(X,Y),add(Y,X_17)))),bind(Y0,$fot(add(Y,add(add(X,Y),X_17)))),bind(Z0,$fot(add(Y,add(X,add(Y,X_17)))))]]) ).
cnf(refute_0_196,plain,
( add(Y,add(add(X,Y),X_17)) != add(Y,add(X,add(Y,X_17)))
| add(add(X,Y),add(Y,X_17)) = add(Y,add(X,add(Y,X_17))) ),
inference(resolve,[$cnf( $equal(add(add(X,Y),add(Y,X_17)),add(Y,add(add(X,Y),X_17))) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
add(add(X,Y),add(Y,X_17)) = add(Y,add(X,add(Y,X_17))),
inference(resolve,[$cnf( $equal(add(Y,add(add(X,Y),X_17)),add(Y,add(X,add(Y,X_17)))) )],[refute_0_180,refute_0_196]) ).
cnf(refute_0_198,plain,
( add(add(X,Y),add(Y,X_17)) != add(X,X_17)
| add(add(X,Y),add(Y,X_17)) != add(Y,add(X,add(Y,X_17)))
| add(Y,add(X,add(Y,X_17))) = add(X,X_17) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X,Y),add(Y,X_17)),add(X,X_17)) ),[0],$fot(add(Y,add(X,add(Y,X_17))))]]) ).
cnf(refute_0_199,plain,
( add(add(X,Y),add(Y,X_17)) != add(X,X_17)
| add(Y,add(X,add(Y,X_17))) = add(X,X_17) ),
inference(resolve,[$cnf( $equal(add(add(X,Y),add(Y,X_17)),add(Y,add(X,add(Y,X_17)))) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
add(Y,add(X,add(Y,X_17))) = add(X,X_17),
inference(resolve,[$cnf( $equal(add(add(X,Y),add(Y,X_17)),add(X,X_17)) )],[refute_0_175,refute_0_199]) ).
cnf(refute_0_201,plain,
add(Y,add(X,add(Y,add(X_23,add(X_24,Y))))) = add(X,add(X_23,add(X_24,Y))),
inference(subst,[],[refute_0_200:[bind(X_17,$fot(add(X_23,add(X_24,Y))))]]) ).
cnf(refute_0_202,plain,
add(Y,add(X_23,add(X_24,Y))) = add(X_23,X_24),
inference(subst,[],[refute_0_145:[bind(X,$fot(X_23)),bind(Y,$fot(X_24)),bind(X_19,$fot(Y))]]) ).
cnf(refute_0_203,plain,
( add(Y,add(X,add(Y,add(X_23,add(X_24,Y))))) != add(X,add(X_23,add(X_24,Y)))
| add(Y,add(X_23,add(X_24,Y))) != add(X_23,X_24)
| add(Y,add(X,add(X_23,X_24))) = add(X,add(X_23,add(X_24,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(add(Y,add(X,add(Y,add(X_23,add(X_24,Y))))),add(X,add(X_23,add(X_24,Y)))) ),[0,1,1],$fot(add(X_23,X_24))]]) ).
cnf(refute_0_204,plain,
( add(Y,add(X,add(Y,add(X_23,add(X_24,Y))))) != add(X,add(X_23,add(X_24,Y)))
| add(Y,add(X,add(X_23,X_24))) = add(X,add(X_23,add(X_24,Y))) ),
inference(resolve,[$cnf( $equal(add(Y,add(X_23,add(X_24,Y))),add(X_23,X_24)) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
add(Y,add(X,add(X_23,X_24))) = add(X,add(X_23,add(X_24,Y))),
inference(resolve,[$cnf( $equal(add(Y,add(X,add(Y,add(X_23,add(X_24,Y))))),add(X,add(X_23,add(X_24,Y)))) )],[refute_0_201,refute_0_204]) ).
cnf(refute_0_206,plain,
( add(Y,add(X,add(X_23,X_24))) != add(X,add(X_23,add(X_24,Y)))
| add(X,add(X_23,add(X_24,Y))) = add(Y,add(X,add(X_23,X_24))) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(add(Y,add(X,add(X_23,X_24))))),bind(Y0,$fot(add(X,add(X_23,add(X_24,Y)))))]]) ).
cnf(refute_0_207,plain,
add(X,add(X_23,add(X_24,Y))) = add(Y,add(X,add(X_23,X_24))),
inference(resolve,[$cnf( $equal(add(Y,add(X,add(X_23,X_24))),add(X,add(X_23,add(X_24,Y)))) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
add(b,add(b,add(c,a))) = add(a,add(b,add(b,c))),
inference(subst,[],[refute_0_207:[bind(X,$fot(b)),bind(Y,$fot(a)),bind(X_23,$fot(b)),bind(X_24,$fot(c))]]) ).
cnf(refute_0_209,plain,
add(b,add(c,add(a,b))) = add(b,add(b,add(c,a))),
inference(subst,[],[refute_0_207:[bind(X,$fot(b)),bind(Y,$fot(b)),bind(X_23,$fot(c)),bind(X_24,$fot(a))]]) ).
cnf(refute_0_210,plain,
( add(b,add(b,add(c,a))) != add(a,add(b,add(b,c)))
| add(b,add(c,add(a,b))) != add(b,add(b,add(c,a)))
| add(b,add(c,add(a,b))) = add(a,add(b,add(b,c))) ),
inference(subst,[],[refute_0_86:[bind(X0,$fot(add(b,add(c,add(a,b))))),bind(Y0,$fot(add(b,add(b,add(c,a))))),bind(Z0,$fot(add(a,add(b,add(b,c)))))]]) ).
cnf(refute_0_211,plain,
( add(b,add(b,add(c,a))) != add(a,add(b,add(b,c)))
| add(b,add(c,add(a,b))) = add(a,add(b,add(b,c))) ),
inference(resolve,[$cnf( $equal(add(b,add(c,add(a,b))),add(b,add(b,add(c,a)))) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
add(b,add(c,add(a,b))) = add(a,add(b,add(b,c))),
inference(resolve,[$cnf( $equal(add(b,add(b,add(c,a))),add(a,add(b,add(b,c)))) )],[refute_0_208,refute_0_211]) ).
cnf(refute_0_213,plain,
add(add(a,b),add(b,c)) = add(b,add(c,add(a,b))),
inference(subst,[],[refute_0_151:[bind(X_14,$fot(add(a,b))),bind(X_23,$fot(b)),bind(X_24,$fot(c))]]) ).
cnf(refute_0_214,plain,
( add(add(a,b),add(b,c)) != add(b,add(c,add(a,b)))
| add(b,add(c,add(a,b))) != add(a,add(b,add(b,c)))
| add(add(a,b),add(b,c)) = add(a,add(b,add(b,c))) ),
inference(subst,[],[refute_0_86:[bind(X0,$fot(add(add(a,b),add(b,c)))),bind(Y0,$fot(add(b,add(c,add(a,b))))),bind(Z0,$fot(add(a,add(b,add(b,c)))))]]) ).
cnf(refute_0_215,plain,
( add(b,add(c,add(a,b))) != add(a,add(b,add(b,c)))
| add(add(a,b),add(b,c)) = add(a,add(b,add(b,c))) ),
inference(resolve,[$cnf( $equal(add(add(a,b),add(b,c)),add(b,add(c,add(a,b)))) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
add(add(a,b),add(b,c)) = add(a,add(b,add(b,c))),
inference(resolve,[$cnf( $equal(add(b,add(c,add(a,b))),add(a,add(b,add(b,c)))) )],[refute_0_212,refute_0_215]) ).
cnf(refute_0_217,plain,
( add(add(a,b),add(b,c)) != add(a,add(b,add(b,c)))
| add(a,add(b,add(b,c))) != add(a,c)
| add(add(a,b),add(b,c)) = add(a,c) ),
inference(subst,[],[refute_0_86:[bind(X0,$fot(add(add(a,b),add(b,c)))),bind(Y0,$fot(add(a,add(b,add(b,c))))),bind(Z0,$fot(add(a,c)))]]) ).
cnf(refute_0_218,plain,
( add(a,add(b,add(b,c))) != add(a,c)
| add(add(a,b),add(b,c)) = add(a,c) ),
inference(resolve,[$cnf( $equal(add(add(a,b),add(b,c)),add(a,add(b,add(b,c)))) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
add(add(a,b),add(b,c)) = add(a,c),
inference(resolve,[$cnf( $equal(add(a,add(b,add(b,c))),add(a,c)) )],[refute_0_168,refute_0_218]) ).
cnf(refute_0_220,plain,
( multiply(add(a,b),a) != add(add(a,b),add(b,c))
| add(add(a,b),add(b,c)) != add(a,c)
| multiply(add(a,b),a) = add(a,c) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(add(a,b),a),add(a,c)) ),[0],$fot(add(add(a,b),add(b,c)))]]) ).
cnf(refute_0_221,plain,
( multiply(add(a,b),a) != add(add(a,b),add(b,c))
| multiply(add(a,b),a) = add(a,c) ),
inference(resolve,[$cnf( $equal(add(add(a,b),add(b,c)),add(a,c)) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
( multiply(add(a,b),add(b,add(a,b))) != add(add(a,b),add(b,c))
| multiply(add(a,b),a) = add(a,c) ),
inference(resolve,[$cnf( $equal(multiply(add(a,b),a),add(add(a,b),add(b,c))) )],[refute_0_161,refute_0_221]) ).
cnf(refute_0_223,plain,
multiply(add(a,b),a) = add(a,c),
inference(resolve,[$cnf( $equal(multiply(add(a,b),add(b,add(a,b))),add(add(a,b),add(b,c))) )],[refute_0_63,refute_0_222]) ).
cnf(refute_0_224,plain,
( multiply(add(add(a,b),a),a) != add(a,multiply(add(a,b),a))
| multiply(add(a,b),a) != add(a,c)
| multiply(add(add(a,b),a),a) = add(a,add(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(add(a,b),a),a),add(a,multiply(add(a,b),a))) ),[1,1],$fot(add(a,c))]]) ).
cnf(refute_0_225,plain,
( multiply(add(add(a,b),a),a) != add(a,multiply(add(a,b),a))
| multiply(add(add(a,b),a),a) = add(a,add(a,c)) ),
inference(resolve,[$cnf( $equal(multiply(add(a,b),a),add(a,c)) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
multiply(add(add(a,b),a),a) = add(a,add(a,c)),
inference(resolve,[$cnf( $equal(multiply(add(add(a,b),a),a),add(a,multiply(add(a,b),a))) )],[refute_0_14,refute_0_225]) ).
cnf(refute_0_227,plain,
add(a,add(a,b)) = b,
inference(subst,[],[refute_0_163:[bind(X_14,$fot(a)),bind(X_15,$fot(b))]]) ).
cnf(refute_0_228,plain,
multiply(add(a,add(a,b)),a) = multiply(add(a,add(a,b)),a),
introduced(tautology,[refl,[$fot(multiply(add(a,add(a,b)),a))]]) ).
cnf(refute_0_229,plain,
( multiply(add(a,add(a,b)),a) != multiply(add(a,add(a,b)),a)
| add(a,add(a,b)) != b
| multiply(add(a,add(a,b)),a) = multiply(b,a) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(a,add(a,b)),a),multiply(add(a,add(a,b)),a)) ),[1,0],$fot(b)]]) ).
cnf(refute_0_230,plain,
( add(a,add(a,b)) != b
| multiply(add(a,add(a,b)),a) = multiply(b,a) ),
inference(resolve,[$cnf( $equal(multiply(add(a,add(a,b)),a),multiply(add(a,add(a,b)),a)) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
multiply(add(a,add(a,b)),a) = multiply(b,a),
inference(resolve,[$cnf( $equal(add(a,add(a,b)),b) )],[refute_0_227,refute_0_230]) ).
cnf(refute_0_232,plain,
multiply(add(X_67,X_68),X_68) = add(X_68,multiply(X_67,X_68)),
inference(subst,[],[refute_0_13:[bind(X_57,$fot(X_67)),bind(X_59,$fot(X_68))]]) ).
cnf(refute_0_233,plain,
add(X_68,X_67) = add(X_67,X_68),
inference(subst,[],[commutative_addition:[bind(X,$fot(X_68)),bind(Y,$fot(X_67))]]) ).
cnf(refute_0_234,plain,
( add(X_68,X_67) != add(X_67,X_68)
| add(X_67,X_68) = add(X_68,X_67) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(add(X_68,X_67))),bind(Y0,$fot(add(X_67,X_68)))]]) ).
cnf(refute_0_235,plain,
add(X_67,X_68) = add(X_68,X_67),
inference(resolve,[$cnf( $equal(add(X_68,X_67),add(X_67,X_68)) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
( multiply(add(X_67,X_68),X_68) != add(X_68,multiply(X_67,X_68))
| add(X_67,X_68) != add(X_68,X_67)
| multiply(add(X_68,X_67),X_68) = add(X_68,multiply(X_67,X_68)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(X_67,X_68),X_68),add(X_68,multiply(X_67,X_68))) ),[0,0],$fot(add(X_68,X_67))]]) ).
cnf(refute_0_237,plain,
( multiply(add(X_67,X_68),X_68) != add(X_68,multiply(X_67,X_68))
| multiply(add(X_68,X_67),X_68) = add(X_68,multiply(X_67,X_68)) ),
inference(resolve,[$cnf( $equal(add(X_67,X_68),add(X_68,X_67)) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
multiply(add(X_68,X_67),X_68) = add(X_68,multiply(X_67,X_68)),
inference(resolve,[$cnf( $equal(multiply(add(X_67,X_68),X_68),add(X_68,multiply(X_67,X_68))) )],[refute_0_232,refute_0_237]) ).
cnf(refute_0_239,plain,
( multiply(add(X_57,X_59),X_59) != add(X_59,multiply(X_57,X_59))
| add(X_59,multiply(X_57,X_59)) = multiply(add(X_57,X_59),X_59) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(add(X_57,X_59),X_59))),bind(Y0,$fot(add(X_59,multiply(X_57,X_59))))]]) ).
cnf(refute_0_240,plain,
add(X_59,multiply(X_57,X_59)) = multiply(add(X_57,X_59),X_59),
inference(resolve,[$cnf( $equal(multiply(add(X_57,X_59),X_59),add(X_59,multiply(X_57,X_59))) )],[refute_0_13,refute_0_239]) ).
cnf(refute_0_241,plain,
add(X_68,multiply(X_67,X_68)) = multiply(add(X_67,X_68),X_68),
inference(subst,[],[refute_0_240:[bind(X_57,$fot(X_67)),bind(X_59,$fot(X_68))]]) ).
cnf(refute_0_242,plain,
( multiply(add(X_68,X_67),X_68) != add(X_68,multiply(X_67,X_68))
| add(X_68,multiply(X_67,X_68)) != multiply(add(X_67,X_68),X_68)
| multiply(add(X_68,X_67),X_68) = multiply(add(X_67,X_68),X_68) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(add(X_68,X_67),X_68),multiply(add(X_67,X_68),X_68)) ),[0],$fot(add(X_68,multiply(X_67,X_68)))]]) ).
cnf(refute_0_243,plain,
( multiply(add(X_68,X_67),X_68) != add(X_68,multiply(X_67,X_68))
| multiply(add(X_68,X_67),X_68) = multiply(add(X_67,X_68),X_68) ),
inference(resolve,[$cnf( $equal(add(X_68,multiply(X_67,X_68)),multiply(add(X_67,X_68),X_68)) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
multiply(add(X_68,X_67),X_68) = multiply(add(X_67,X_68),X_68),
inference(resolve,[$cnf( $equal(multiply(add(X_68,X_67),X_68),add(X_68,multiply(X_67,X_68))) )],[refute_0_238,refute_0_243]) ).
cnf(refute_0_245,plain,
( multiply(add(X_68,X_67),X_68) != multiply(add(X_67,X_68),X_68)
| multiply(add(X_67,X_68),X_68) = multiply(add(X_68,X_67),X_68) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(add(X_68,X_67),X_68))),bind(Y0,$fot(multiply(add(X_67,X_68),X_68)))]]) ).
cnf(refute_0_246,plain,
multiply(add(X_67,X_68),X_68) = multiply(add(X_68,X_67),X_68),
inference(resolve,[$cnf( $equal(multiply(add(X_68,X_67),X_68),multiply(add(X_67,X_68),X_68)) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
multiply(add(add(a,b),a),a) = multiply(add(a,add(a,b)),a),
inference(subst,[],[refute_0_246:[bind(X_67,$fot(add(a,b))),bind(X_68,$fot(a))]]) ).
cnf(refute_0_248,plain,
( multiply(add(add(a,b),a),a) != multiply(add(a,add(a,b)),a)
| multiply(add(a,add(a,b)),a) != multiply(b,a)
| multiply(add(add(a,b),a),a) = multiply(b,a) ),
inference(subst,[],[refute_0_86:[bind(X0,$fot(multiply(add(add(a,b),a),a))),bind(Y0,$fot(multiply(add(a,add(a,b)),a))),bind(Z0,$fot(multiply(b,a)))]]) ).
cnf(refute_0_249,plain,
( multiply(add(a,add(a,b)),a) != multiply(b,a)
| multiply(add(add(a,b),a),a) = multiply(b,a) ),
inference(resolve,[$cnf( $equal(multiply(add(add(a,b),a),a),multiply(add(a,add(a,b)),a)) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
multiply(add(add(a,b),a),a) = multiply(b,a),
inference(resolve,[$cnf( $equal(multiply(add(a,add(a,b)),a),multiply(b,a)) )],[refute_0_231,refute_0_249]) ).
cnf(refute_0_251,plain,
( multiply(add(add(a,b),a),a) != multiply(b,a)
| multiply(add(add(a,b),a),a) != add(a,add(a,c))
| multiply(b,a) = add(a,add(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(add(a,b),a),a),add(a,add(a,c))) ),[0],$fot(multiply(b,a))]]) ).
cnf(refute_0_252,plain,
( multiply(add(add(a,b),a),a) != add(a,add(a,c))
| multiply(b,a) = add(a,add(a,c)) ),
inference(resolve,[$cnf( $equal(multiply(add(add(a,b),a),a),multiply(b,a)) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
add(a,add(a,c)) = c,
inference(subst,[],[refute_0_163:[bind(X_14,$fot(a)),bind(X_15,$fot(c))]]) ).
cnf(refute_0_254,plain,
( multiply(b,a) != add(a,add(a,c))
| add(a,add(a,c)) != c
| multiply(b,a) = c ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(b,a),c) ),[0],$fot(add(a,add(a,c)))]]) ).
cnf(refute_0_255,plain,
( multiply(b,a) != add(a,add(a,c))
| multiply(b,a) = c ),
inference(resolve,[$cnf( $equal(add(a,add(a,c)),c) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
( multiply(add(add(a,b),a),a) != add(a,add(a,c))
| multiply(b,a) = c ),
inference(resolve,[$cnf( $equal(multiply(b,a),add(a,add(a,c))) )],[refute_0_252,refute_0_255]) ).
cnf(refute_0_257,plain,
multiply(b,a) = c,
inference(resolve,[$cnf( $equal(multiply(add(add(a,b),a),a),add(a,add(a,c))) )],[refute_0_226,refute_0_256]) ).
cnf(refute_0_258,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(b,a),c) )],[refute_0_257,prove_commutativity]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : RNG008-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n020.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 12:25:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.52/0.75 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.52/0.75
% 0.52/0.75 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.60/0.78
%------------------------------------------------------------------------------