TSTP Solution File: RNG008-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : RNG008-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 20:35:42 EDT 2022
% Result : Unsatisfiable 0.56s 0.75s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 57
% Syntax : Number of clauses : 217 ( 115 unt; 0 nHn; 137 RR)
% Number of literals : 364 ( 363 equ; 148 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 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 : 237 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
add(additive_identity,X) = X ).
cnf(distribute1,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ).
cnf(distribute2,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ).
cnf(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(right_identity,axiom,
add(X,additive_identity) = X ).
cnf(right_inverse,axiom,
add(X,additive_inverse(X)) = additive_identity ).
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,$fot(a))]]) ).
cnf(refute_0_15,plain,
multiply(X_39,add(X_38,X_39)) = add(multiply(X_39,X_38),multiply(X_39,X_39)),
inference(subst,[],[distribute1:[bind(X,$fot(X_39)),bind(Y,$fot(X_38)),bind(Z,$fot(X_39))]]) ).
cnf(refute_0_16,plain,
multiply(X_39,X_39) = X_39,
inference(subst,[],[boolean_ring:[bind(X,$fot(X_39))]]) ).
cnf(refute_0_17,plain,
( multiply(X_39,X_39) != X_39
| multiply(X_39,add(X_38,X_39)) != add(multiply(X_39,X_38),multiply(X_39,X_39))
| multiply(X_39,add(X_38,X_39)) = add(multiply(X_39,X_38),X_39) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(X_39,add(X_38,X_39)),add(multiply(X_39,X_38),multiply(X_39,X_39))) ),[1,1],$fot(X_39)]]) ).
cnf(refute_0_18,plain,
( multiply(X_39,add(X_38,X_39)) != add(multiply(X_39,X_38),multiply(X_39,X_39))
| multiply(X_39,add(X_38,X_39)) = add(multiply(X_39,X_38),X_39) ),
inference(resolve,[$cnf( $equal(multiply(X_39,X_39),X_39) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
multiply(X_39,add(X_38,X_39)) = add(multiply(X_39,X_38),X_39),
inference(resolve,[$cnf( $equal(multiply(X_39,add(X_38,X_39)),add(multiply(X_39,X_38),multiply(X_39,X_39))) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
add(multiply(X_39,X_38),X_39) = add(X_39,multiply(X_39,X_38)),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_39)),bind(Y,$fot(multiply(X_39,X_38)))]]) ).
cnf(refute_0_21,plain,
( multiply(X_39,add(X_38,X_39)) != add(multiply(X_39,X_38),X_39)
| add(multiply(X_39,X_38),X_39) != add(X_39,multiply(X_39,X_38))
| multiply(X_39,add(X_38,X_39)) = add(X_39,multiply(X_39,X_38)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_39,add(X_38,X_39)),add(X_39,multiply(X_39,X_38))) ),[0],$fot(add(multiply(X_39,X_38),X_39))]]) ).
cnf(refute_0_22,plain,
( multiply(X_39,add(X_38,X_39)) != add(multiply(X_39,X_38),X_39)
| multiply(X_39,add(X_38,X_39)) = add(X_39,multiply(X_39,X_38)) ),
inference(resolve,[$cnf( $equal(add(multiply(X_39,X_38),X_39),add(X_39,multiply(X_39,X_38))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
multiply(X_39,add(X_38,X_39)) = add(X_39,multiply(X_39,X_38)),
inference(resolve,[$cnf( $equal(multiply(X_39,add(X_38,X_39)),add(multiply(X_39,X_38),X_39)) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(add(a,b),add(b,add(a,b))) = add(add(a,b),multiply(add(a,b),b)),
inference(subst,[],[refute_0_23:[bind(X_38,$fot(b)),bind(X_39,$fot(add(a,b)))]]) ).
cnf(refute_0_25,plain,
multiply(add(X_57,a),b) = add(multiply(X_57,b),multiply(a,b)),
inference(subst,[],[distribute2:[bind(X,$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( $equal(multiply(add(a,b),add(b,add(a,b))),add(add(a,b),multiply(add(a,b),b))) )],[refute_0_24,refute_0_62]) ).
cnf(refute_0_64,plain,
add(a,additive_identity) = a,
inference(subst,[],[right_identity:[bind(X,$fot(a))]]) ).
cnf(refute_0_65,plain,
multiply(additive_inverse(X_12),additive_inverse(X_12)) = additive_inverse(X_12),
inference(subst,[],[boolean_ring:[bind(X,$fot(additive_inverse(X_12)))]]) ).
cnf(refute_0_66,plain,
multiply(additive_inverse(X_12),additive_inverse(X_12)) = additive_inverse(multiply(additive_inverse(X_12),X_12)),
inference(subst,[],[multiply_additive_inverse1:[bind(X,$fot(additive_inverse(X_12))),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_67,plain,
( multiply(additive_inverse(X_12),additive_inverse(X_12)) != additive_inverse(X_12)
| multiply(additive_inverse(X_12),additive_inverse(X_12)) != additive_inverse(multiply(additive_inverse(X_12),X_12))
| additive_inverse(multiply(additive_inverse(X_12),X_12)) = additive_inverse(X_12) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(additive_inverse(X_12),additive_inverse(X_12)),additive_inverse(X_12)) ),[0],$fot(additive_inverse(multiply(additive_inverse(X_12),X_12)))]]) ).
cnf(refute_0_68,plain,
( multiply(additive_inverse(X_12),additive_inverse(X_12)) != additive_inverse(X_12)
| additive_inverse(multiply(additive_inverse(X_12),X_12)) = additive_inverse(X_12) ),
inference(resolve,[$cnf( $equal(multiply(additive_inverse(X_12),additive_inverse(X_12)),additive_inverse(multiply(additive_inverse(X_12),X_12))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
additive_inverse(multiply(additive_inverse(X_12),X_12)) = additive_inverse(X_12),
inference(resolve,[$cnf( $equal(multiply(additive_inverse(X_12),additive_inverse(X_12)),additive_inverse(X_12)) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
additive_inverse(additive_inverse(X_12)) = X_12,
inference(subst,[],[additive_inverse_additive_inverse:[bind(X,$fot(X_12))]]) ).
cnf(refute_0_71,plain,
multiply(X_12,X_12) = X_12,
inference(subst,[],[boolean_ring:[bind(X,$fot(X_12))]]) ).
cnf(refute_0_72,plain,
additive_inverse(multiply(X_12,X_12)) = additive_inverse(multiply(X_12,X_12)),
introduced(tautology,[refl,[$fot(additive_inverse(multiply(X_12,X_12)))]]) ).
cnf(refute_0_73,plain,
( multiply(X_12,X_12) != X_12
| additive_inverse(multiply(X_12,X_12)) != additive_inverse(multiply(X_12,X_12))
| additive_inverse(multiply(X_12,X_12)) = additive_inverse(X_12) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(X_12,X_12)),additive_inverse(multiply(X_12,X_12))) ),[1,0],$fot(X_12)]]) ).
cnf(refute_0_74,plain,
( multiply(X_12,X_12) != X_12
| additive_inverse(multiply(X_12,X_12)) = additive_inverse(X_12) ),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X_12,X_12)),additive_inverse(multiply(X_12,X_12))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
additive_inverse(multiply(X_12,X_12)) = additive_inverse(X_12),
inference(resolve,[$cnf( $equal(multiply(X_12,X_12),X_12) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
multiply(additive_inverse(X_12),X_12) = additive_inverse(multiply(X_12,X_12)),
inference(subst,[],[multiply_additive_inverse2:[bind(X,$fot(X_12)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_77,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_78,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_7,refute_0_77]) ).
cnf(refute_0_79,plain,
( multiply(additive_inverse(X_12),X_12) != additive_inverse(multiply(X_12,X_12))
| additive_inverse(multiply(X_12,X_12)) != additive_inverse(X_12)
| multiply(additive_inverse(X_12),X_12) = additive_inverse(X_12) ),
inference(subst,[],[refute_0_78:[bind(X0,$fot(multiply(additive_inverse(X_12),X_12))),bind(Y0,$fot(additive_inverse(multiply(X_12,X_12)))),bind(Z0,$fot(additive_inverse(X_12)))]]) ).
cnf(refute_0_80,plain,
( additive_inverse(multiply(X_12,X_12)) != additive_inverse(X_12)
| multiply(additive_inverse(X_12),X_12) = additive_inverse(X_12) ),
inference(resolve,[$cnf( $equal(multiply(additive_inverse(X_12),X_12),additive_inverse(multiply(X_12,X_12))) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
multiply(additive_inverse(X_12),X_12) = additive_inverse(X_12),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(X_12,X_12)),additive_inverse(X_12)) )],[refute_0_75,refute_0_80]) ).
cnf(refute_0_82,plain,
additive_inverse(multiply(additive_inverse(X_12),X_12)) = additive_inverse(multiply(additive_inverse(X_12),X_12)),
introduced(tautology,[refl,[$fot(additive_inverse(multiply(additive_inverse(X_12),X_12)))]]) ).
cnf(refute_0_83,plain,
( multiply(additive_inverse(X_12),X_12) != additive_inverse(X_12)
| additive_inverse(multiply(additive_inverse(X_12),X_12)) != additive_inverse(multiply(additive_inverse(X_12),X_12))
| additive_inverse(multiply(additive_inverse(X_12),X_12)) = additive_inverse(additive_inverse(X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_12),X_12)),additive_inverse(multiply(additive_inverse(X_12),X_12))) ),[1,0],$fot(additive_inverse(X_12))]]) ).
cnf(refute_0_84,plain,
( multiply(additive_inverse(X_12),X_12) != additive_inverse(X_12)
| additive_inverse(multiply(additive_inverse(X_12),X_12)) = additive_inverse(additive_inverse(X_12)) ),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_12),X_12)),additive_inverse(multiply(additive_inverse(X_12),X_12))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
additive_inverse(multiply(additive_inverse(X_12),X_12)) = additive_inverse(additive_inverse(X_12)),
inference(resolve,[$cnf( $equal(multiply(additive_inverse(X_12),X_12),additive_inverse(X_12)) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
( additive_inverse(multiply(additive_inverse(X_12),X_12)) != additive_inverse(additive_inverse(X_12))
| additive_inverse(additive_inverse(X_12)) != X_12
| additive_inverse(multiply(additive_inverse(X_12),X_12)) = X_12 ),
inference(subst,[],[refute_0_78:[bind(X0,$fot(additive_inverse(multiply(additive_inverse(X_12),X_12)))),bind(Y0,$fot(additive_inverse(additive_inverse(X_12)))),bind(Z0,$fot(X_12))]]) ).
cnf(refute_0_87,plain,
( additive_inverse(additive_inverse(X_12)) != X_12
| additive_inverse(multiply(additive_inverse(X_12),X_12)) = X_12 ),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_12),X_12)),additive_inverse(additive_inverse(X_12))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
additive_inverse(multiply(additive_inverse(X_12),X_12)) = X_12,
inference(resolve,[$cnf( $equal(additive_inverse(additive_inverse(X_12)),X_12) )],[refute_0_70,refute_0_87]) ).
cnf(refute_0_89,plain,
( additive_inverse(multiply(additive_inverse(X_12),X_12)) != X_12
| additive_inverse(multiply(additive_inverse(X_12),X_12)) != additive_inverse(X_12)
| X_12 = additive_inverse(X_12) ),
introduced(tautology,[equality,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_12),X_12)),additive_inverse(X_12)) ),[0],$fot(X_12)]]) ).
cnf(refute_0_90,plain,
( additive_inverse(multiply(additive_inverse(X_12),X_12)) != additive_inverse(X_12)
| X_12 = additive_inverse(X_12) ),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_12),X_12)),X_12) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
X_12 = additive_inverse(X_12),
inference(resolve,[$cnf( $equal(additive_inverse(multiply(additive_inverse(X_12),X_12)),additive_inverse(X_12)) )],[refute_0_69,refute_0_90]) ).
cnf(refute_0_92,plain,
( X_12 != additive_inverse(X_12)
| additive_inverse(X_12) = X_12 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(X_12)),bind(Y0,$fot(additive_inverse(X_12)))]]) ).
cnf(refute_0_93,plain,
additive_inverse(X_12) = X_12,
inference(resolve,[$cnf( $equal(X_12,additive_inverse(X_12)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
additive_inverse(X) = X,
inference(subst,[],[refute_0_93:[bind(X_12,$fot(X))]]) ).
cnf(refute_0_95,plain,
add(X,additive_inverse(X)) = add(X,additive_inverse(X)),
introduced(tautology,[refl,[$fot(add(X,additive_inverse(X)))]]) ).
cnf(refute_0_96,plain,
( add(X,additive_inverse(X)) != add(X,additive_inverse(X))
| additive_inverse(X) != X
| add(X,additive_inverse(X)) = add(X,X) ),
introduced(tautology,[equality,[$cnf( $equal(add(X,additive_inverse(X)),add(X,additive_inverse(X))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_97,plain,
( additive_inverse(X) != X
| add(X,additive_inverse(X)) = add(X,X) ),
inference(resolve,[$cnf( $equal(add(X,additive_inverse(X)),add(X,additive_inverse(X))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
add(X,additive_inverse(X)) = add(X,X),
inference(resolve,[$cnf( $equal(additive_inverse(X),X) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
( add(X,additive_inverse(X)) != add(X,X)
| add(X,additive_inverse(X)) != additive_identity
| add(X,X) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(add(X,additive_inverse(X)),additive_identity) ),[0],$fot(add(X,X))]]) ).
cnf(refute_0_100,plain,
( add(X,additive_inverse(X)) != additive_identity
| add(X,X) = additive_identity ),
inference(resolve,[$cnf( $equal(add(X,additive_inverse(X)),add(X,X)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
add(X,X) = additive_identity,
inference(resolve,[$cnf( $equal(add(X,additive_inverse(X)),additive_identity) )],[right_inverse,refute_0_100]) ).
cnf(refute_0_102,plain,
add(b,b) = additive_identity,
inference(subst,[],[refute_0_101:[bind(X,$fot(b))]]) ).
cnf(refute_0_103,plain,
add(a,add(b,b)) = add(a,add(b,b)),
introduced(tautology,[refl,[$fot(add(a,add(b,b)))]]) ).
cnf(refute_0_104,plain,
( add(a,add(b,b)) != add(a,add(b,b))
| add(b,b) != additive_identity
| add(a,add(b,b)) = add(a,additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(a,add(b,b)),add(a,add(b,b))) ),[1,1],$fot(additive_identity)]]) ).
cnf(refute_0_105,plain,
( add(b,b) != additive_identity
| add(a,add(b,b)) = add(a,additive_identity) ),
inference(resolve,[$cnf( $equal(add(a,add(b,b)),add(a,add(b,b))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
add(a,add(b,b)) = add(a,additive_identity),
inference(resolve,[$cnf( $equal(add(b,b),additive_identity) )],[refute_0_102,refute_0_105]) ).
cnf(refute_0_107,plain,
( add(a,add(b,b)) != add(a,additive_identity)
| add(a,additive_identity) != a
| add(a,add(b,b)) = a ),
inference(subst,[],[refute_0_78:[bind(X0,$fot(add(a,add(b,b)))),bind(Y0,$fot(add(a,additive_identity))),bind(Z0,$fot(a))]]) ).
cnf(refute_0_108,plain,
( add(a,additive_identity) != a
| add(a,add(b,b)) = a ),
inference(resolve,[$cnf( $equal(add(a,add(b,b)),add(a,additive_identity)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
add(a,add(b,b)) = a,
inference(resolve,[$cnf( $equal(add(a,additive_identity),a) )],[refute_0_64,refute_0_108]) ).
cnf(refute_0_110,plain,
add(add(X_16,X_16),X_17) = add(X_16,add(X_16,X_17)),
inference(subst,[],[associative_addition:[bind(X,$fot(X_16)),bind(Y,$fot(X_16)),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_111,plain,
add(X_16,X_16) = additive_identity,
inference(subst,[],[refute_0_101:[bind(X,$fot(X_16))]]) ).
cnf(refute_0_112,plain,
( add(X_16,X_16) != additive_identity
| add(add(X_16,X_16),X_17) != add(X_16,add(X_16,X_17))
| add(additive_identity,X_17) = add(X_16,add(X_16,X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_16,X_16),X_17),add(X_16,add(X_16,X_17))) ),[0,0],$fot(additive_identity)]]) ).
cnf(refute_0_113,plain,
( add(add(X_16,X_16),X_17) != add(X_16,add(X_16,X_17))
| add(additive_identity,X_17) = add(X_16,add(X_16,X_17)) ),
inference(resolve,[$cnf( $equal(add(X_16,X_16),additive_identity) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
add(additive_identity,X_17) = add(X_16,add(X_16,X_17)),
inference(resolve,[$cnf( $equal(add(add(X_16,X_16),X_17),add(X_16,add(X_16,X_17))) )],[refute_0_110,refute_0_113]) ).
cnf(refute_0_115,plain,
add(additive_identity,X_17) = X_17,
inference(subst,[],[left_identity:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_116,plain,
( add(additive_identity,X_17) != X_17
| add(additive_identity,X_17) != add(X_16,add(X_16,X_17))
| X_17 = add(X_16,add(X_16,X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(add(additive_identity,X_17),add(X_16,add(X_16,X_17))) ),[0],$fot(X_17)]]) ).
cnf(refute_0_117,plain,
( add(additive_identity,X_17) != add(X_16,add(X_16,X_17))
| X_17 = add(X_16,add(X_16,X_17)) ),
inference(resolve,[$cnf( $equal(add(additive_identity,X_17),X_17) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
X_17 = add(X_16,add(X_16,X_17)),
inference(resolve,[$cnf( $equal(add(additive_identity,X_17),add(X_16,add(X_16,X_17))) )],[refute_0_114,refute_0_117]) ).
cnf(refute_0_119,plain,
add(X_22,add(X_23,X_16)) = add(X_16,add(X_16,add(X_22,add(X_23,X_16)))),
inference(subst,[],[refute_0_118:[bind(X_17,$fot(add(X_22,add(X_23,X_16))))]]) ).
cnf(refute_0_120,plain,
add(add(X_15,X_17),X_17) = add(X_15,add(X_17,X_17)),
inference(subst,[],[associative_addition:[bind(X,$fot(X_15)),bind(Y,$fot(X_17)),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_121,plain,
add(X_17,X_17) = additive_identity,
inference(subst,[],[refute_0_101:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_122,plain,
( add(X_17,X_17) != additive_identity
| add(add(X_15,X_17),X_17) != add(X_15,add(X_17,X_17))
| add(add(X_15,X_17),X_17) = add(X_15,additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_15,X_17),X_17),add(X_15,add(X_17,X_17))) ),[1,1],$fot(additive_identity)]]) ).
cnf(refute_0_123,plain,
( add(add(X_15,X_17),X_17) != add(X_15,add(X_17,X_17))
| add(add(X_15,X_17),X_17) = add(X_15,additive_identity) ),
inference(resolve,[$cnf( $equal(add(X_17,X_17),additive_identity) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
add(add(X_15,X_17),X_17) = add(X_15,additive_identity),
inference(resolve,[$cnf( $equal(add(add(X_15,X_17),X_17),add(X_15,add(X_17,X_17))) )],[refute_0_120,refute_0_123]) ).
cnf(refute_0_125,plain,
add(add(X_15,X_17),X_17) = add(X_17,add(X_15,X_17)),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_17)),bind(Y,$fot(add(X_15,X_17)))]]) ).
cnf(refute_0_126,plain,
( add(add(X_15,X_17),X_17) != add(X_15,additive_identity)
| add(add(X_15,X_17),X_17) != add(X_17,add(X_15,X_17))
| add(X_17,add(X_15,X_17)) = add(X_15,additive_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_15,X_17),X_17),add(X_15,additive_identity)) ),[0],$fot(add(X_17,add(X_15,X_17)))]]) ).
cnf(refute_0_127,plain,
( add(add(X_15,X_17),X_17) != add(X_15,additive_identity)
| add(X_17,add(X_15,X_17)) = add(X_15,additive_identity) ),
inference(resolve,[$cnf( $equal(add(add(X_15,X_17),X_17),add(X_17,add(X_15,X_17))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
add(X_15,additive_identity) = X_15,
inference(subst,[],[right_identity:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_129,plain,
( add(X_15,additive_identity) != X_15
| add(X_17,add(X_15,X_17)) != add(X_15,additive_identity)
| add(X_17,add(X_15,X_17)) = X_15 ),
introduced(tautology,[equality,[$cnf( $equal(add(X_17,add(X_15,X_17)),add(X_15,additive_identity)) ),[1],$fot(X_15)]]) ).
cnf(refute_0_130,plain,
( add(X_17,add(X_15,X_17)) != add(X_15,additive_identity)
| add(X_17,add(X_15,X_17)) = X_15 ),
inference(resolve,[$cnf( $equal(add(X_15,additive_identity),X_15) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
( add(add(X_15,X_17),X_17) != add(X_15,additive_identity)
| add(X_17,add(X_15,X_17)) = X_15 ),
inference(resolve,[$cnf( $equal(add(X_17,add(X_15,X_17)),add(X_15,additive_identity)) )],[refute_0_127,refute_0_130]) ).
cnf(refute_0_132,plain,
add(X_17,add(X_15,X_17)) = X_15,
inference(resolve,[$cnf( $equal(add(add(X_15,X_17),X_17),add(X_15,additive_identity)) )],[refute_0_124,refute_0_131]) ).
cnf(refute_0_133,plain,
add(X_21,add(add(X,Y),X_21)) = add(X,Y),
inference(subst,[],[refute_0_132:[bind(X_15,$fot(add(X,Y))),bind(X_17,$fot(X_21))]]) ).
cnf(refute_0_134,plain,
add(add(X,Y),X_21) = add(X,add(Y,X_21)),
inference(subst,[],[associative_addition:[bind(Z,$fot(X_21))]]) ).
cnf(refute_0_135,plain,
( add(X_21,add(add(X,Y),X_21)) != add(X,Y)
| add(add(X,Y),X_21) != add(X,add(Y,X_21))
| add(X_21,add(X,add(Y,X_21))) = add(X,Y) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_21,add(add(X,Y),X_21)),add(X,Y)) ),[0,1],$fot(add(X,add(Y,X_21)))]]) ).
cnf(refute_0_136,plain,
( add(X_21,add(add(X,Y),X_21)) != add(X,Y)
| add(X_21,add(X,add(Y,X_21))) = add(X,Y) ),
inference(resolve,[$cnf( $equal(add(add(X,Y),X_21),add(X,add(Y,X_21))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
add(X_21,add(X,add(Y,X_21))) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X_21,add(add(X,Y),X_21)),add(X,Y)) )],[refute_0_133,refute_0_136]) ).
cnf(refute_0_138,plain,
add(X_16,add(X_22,add(X_23,X_16))) = add(X_22,X_23),
inference(subst,[],[refute_0_137:[bind(X,$fot(X_22)),bind(Y,$fot(X_23)),bind(X_21,$fot(X_16))]]) ).
cnf(refute_0_139,plain,
( add(X_16,add(X_22,add(X_23,X_16))) != add(X_22,X_23)
| add(X_22,add(X_23,X_16)) != add(X_16,add(X_16,add(X_22,add(X_23,X_16))))
| add(X_22,add(X_23,X_16)) = add(X_16,add(X_22,X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_22,add(X_23,X_16)),add(X_16,add(X_16,add(X_22,add(X_23,X_16))))) ),[1,1],$fot(add(X_22,X_23))]]) ).
cnf(refute_0_140,plain,
( add(X_22,add(X_23,X_16)) != add(X_16,add(X_16,add(X_22,add(X_23,X_16))))
| add(X_22,add(X_23,X_16)) = add(X_16,add(X_22,X_23)) ),
inference(resolve,[$cnf( $equal(add(X_16,add(X_22,add(X_23,X_16))),add(X_22,X_23)) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
add(X_22,add(X_23,X_16)) = add(X_16,add(X_22,X_23)),
inference(resolve,[$cnf( $equal(add(X_22,add(X_23,X_16)),add(X_16,add(X_16,add(X_22,add(X_23,X_16))))) )],[refute_0_119,refute_0_140]) ).
cnf(refute_0_142,plain,
( add(X_22,add(X_23,X_16)) != add(X_16,add(X_22,X_23))
| add(X_16,add(X_22,X_23)) = add(X_22,add(X_23,X_16)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(add(X_22,add(X_23,X_16)))),bind(Y0,$fot(add(X_16,add(X_22,X_23))))]]) ).
cnf(refute_0_143,plain,
add(X_16,add(X_22,X_23)) = add(X_22,add(X_23,X_16)),
inference(resolve,[$cnf( $equal(add(X_22,add(X_23,X_16)),add(X_16,add(X_22,X_23))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
add(b,add(a,b)) = add(a,add(b,b)),
inference(subst,[],[refute_0_143:[bind(X_16,$fot(b)),bind(X_22,$fot(a)),bind(X_23,$fot(b))]]) ).
cnf(refute_0_145,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_78:[bind(X0,$fot(add(b,add(a,b)))),bind(Y0,$fot(add(a,add(b,b)))),bind(Z0,$fot(a))]]) ).
cnf(refute_0_146,plain,
( add(a,add(b,b)) != a
| add(b,add(a,b)) = a ),
inference(resolve,[$cnf( $equal(add(b,add(a,b)),add(a,add(b,b))) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
add(b,add(a,b)) = a,
inference(resolve,[$cnf( $equal(add(a,add(b,b)),a) )],[refute_0_109,refute_0_146]) ).
cnf(refute_0_148,plain,
multiply(add(a,b),add(b,add(a,b))) = multiply(add(a,b),add(b,add(a,b))),
introduced(tautology,[refl,[$fot(multiply(add(a,b),add(b,add(a,b))))]]) ).
cnf(refute_0_149,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_150,plain,
( add(b,add(a,b)) != a
| multiply(add(a,b),add(b,add(a,b))) = multiply(add(a,b),a) ),
inference(resolve,[$cnf( $equal(multiply(add(a,b),add(b,add(a,b))),multiply(add(a,b),add(b,add(a,b)))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
multiply(add(a,b),add(b,add(a,b))) = multiply(add(a,b),a),
inference(resolve,[$cnf( $equal(add(b,add(a,b)),a) )],[refute_0_147,refute_0_150]) ).
cnf(refute_0_152,plain,
( multiply(add(a,b),add(b,add(a,b))) != multiply(add(a,b),a)
| multiply(add(a,b),add(b,add(a,b))) != add(add(a,b),add(b,c))
| multiply(add(a,b),a) = add(add(a,b),add(b,c)) ),
introduced(tautology,[equality,[$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_153,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( $equal(multiply(add(a,b),add(b,add(a,b))),multiply(add(a,b),a)) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
add(c,a) = add(a,c),
inference(subst,[],[refute_0_9:[bind(X,$fot(a)),bind(Y,$fot(c))]]) ).
cnf(refute_0_155,plain,
add(b,add(c,add(a,b))) = add(c,a),
inference(subst,[],[refute_0_137:[bind(X,$fot(c)),bind(Y,$fot(a)),bind(X_21,$fot(b))]]) ).
cnf(refute_0_156,plain,
( add(b,add(c,add(a,b))) != add(c,a)
| add(c,a) != add(a,c)
| add(b,add(c,add(a,b))) = add(a,c) ),
inference(subst,[],[refute_0_78:[bind(X0,$fot(add(b,add(c,add(a,b))))),bind(Y0,$fot(add(c,a))),bind(Z0,$fot(add(a,c)))]]) ).
cnf(refute_0_157,plain,
( add(c,a) != add(a,c)
| add(b,add(c,add(a,b))) = add(a,c) ),
inference(resolve,[$cnf( $equal(add(b,add(c,add(a,b))),add(c,a)) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
add(b,add(c,add(a,b))) = add(a,c),
inference(resolve,[$cnf( $equal(add(c,a),add(a,c)) )],[refute_0_154,refute_0_157]) ).
cnf(refute_0_159,plain,
add(add(a,b),add(b,c)) = add(b,add(c,add(a,b))),
inference(subst,[],[refute_0_143:[bind(X_16,$fot(add(a,b))),bind(X_22,$fot(b)),bind(X_23,$fot(c))]]) ).
cnf(refute_0_160,plain,
( add(add(a,b),add(b,c)) != add(b,add(c,add(a,b)))
| add(b,add(c,add(a,b))) != add(a,c)
| add(add(a,b),add(b,c)) = add(a,c) ),
inference(subst,[],[refute_0_78:[bind(X0,$fot(add(add(a,b),add(b,c)))),bind(Y0,$fot(add(b,add(c,add(a,b))))),bind(Z0,$fot(add(a,c)))]]) ).
cnf(refute_0_161,plain,
( add(b,add(c,add(a,b))) != add(a,c)
| add(add(a,b),add(b,c)) = add(a,c) ),
inference(resolve,[$cnf( $equal(add(add(a,b),add(b,c)),add(b,add(c,add(a,b)))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
add(add(a,b),add(b,c)) = add(a,c),
inference(resolve,[$cnf( $equal(add(b,add(c,add(a,b))),add(a,c)) )],[refute_0_158,refute_0_161]) ).
cnf(refute_0_163,plain,
( multiply(add(a,b),a) != add(add(a,b),add(b,c))
| add(add(a,b),add(b,c)) != add(a,c)
| multiply(add(a,b),a) = add(a,c) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(add(a,b),a),add(a,c)) ),[0],$fot(add(add(a,b),add(b,c)))]]) ).
cnf(refute_0_164,plain,
( multiply(add(a,b),a) != add(add(a,b),add(b,c))
| multiply(add(a,b),a) = add(a,c) ),
inference(resolve,[$cnf( $equal(add(add(a,b),add(b,c)),add(a,c)) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
( multiply(add(a,b),add(b,add(a,b))) != add(add(a,b),add(b,c))
| multiply(add(a,b),a) = add(a,c) ),
inference(resolve,[$cnf( $equal(multiply(add(a,b),a),add(add(a,b),add(b,c))) )],[refute_0_153,refute_0_164]) ).
cnf(refute_0_166,plain,
multiply(add(a,b),a) = add(a,c),
inference(resolve,[$cnf( $equal(multiply(add(a,b),add(b,add(a,b))),add(add(a,b),add(b,c))) )],[refute_0_63,refute_0_165]) ).
cnf(refute_0_167,plain,
( multiply(add(add(a,b),a),a) != add(a,multiply(add(a,b),a))
| multiply(add(a,b),a) != add(a,c)
| multiply(add(add(a,b),a),a) = add(a,add(a,c)) ),
introduced(tautology,[equality,[$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_168,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( $equal(multiply(add(a,b),a),add(a,c)) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
multiply(add(add(a,b),a),a) = add(a,add(a,c)),
inference(resolve,[$cnf( $equal(multiply(add(add(a,b),a),a),add(a,multiply(add(a,b),a))) )],[refute_0_14,refute_0_168]) ).
cnf(refute_0_170,plain,
( X_17 != add(X_16,add(X_16,X_17))
| add(X_16,add(X_16,X_17)) = X_17 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(X_17)),bind(Y0,$fot(add(X_16,add(X_16,X_17))))]]) ).
cnf(refute_0_171,plain,
add(X_16,add(X_16,X_17)) = X_17,
inference(resolve,[$cnf( $equal(X_17,add(X_16,add(X_16,X_17))) )],[refute_0_118,refute_0_170]) ).
cnf(refute_0_172,plain,
add(a,add(a,b)) = b,
inference(subst,[],[refute_0_171:[bind(X_16,$fot(a)),bind(X_17,$fot(b))]]) ).
cnf(refute_0_173,plain,
multiply(add(a,add(a,b)),a) = multiply(add(a,add(a,b)),a),
introduced(tautology,[refl,[$fot(multiply(add(a,add(a,b)),a))]]) ).
cnf(refute_0_174,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_175,plain,
( add(a,add(a,b)) != b
| multiply(add(a,add(a,b)),a) = multiply(b,a) ),
inference(resolve,[$cnf( $equal(multiply(add(a,add(a,b)),a),multiply(add(a,add(a,b)),a)) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
multiply(add(a,add(a,b)),a) = multiply(b,a),
inference(resolve,[$cnf( $equal(add(a,add(a,b)),b) )],[refute_0_172,refute_0_175]) ).
cnf(refute_0_177,plain,
multiply(add(X_67,X_68),X_68) = add(X_68,multiply(X_67,X_68)),
inference(subst,[],[refute_0_13:[bind(X_57,$fot(X_67)),bind(X_59,$fot(X_68))]]) ).
cnf(refute_0_178,plain,
add(X_68,X_67) = add(X_67,X_68),
inference(subst,[],[commutative_addition:[bind(X,$fot(X_68)),bind(Y,$fot(X_67))]]) ).
cnf(refute_0_179,plain,
( add(X_68,X_67) != add(X_67,X_68)
| add(X_67,X_68) = add(X_68,X_67) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(add(X_68,X_67))),bind(Y0,$fot(add(X_67,X_68)))]]) ).
cnf(refute_0_180,plain,
add(X_67,X_68) = add(X_68,X_67),
inference(resolve,[$cnf( $equal(add(X_68,X_67),add(X_67,X_68)) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
( multiply(add(X_67,X_68),X_68) != add(X_68,multiply(X_67,X_68))
| add(X_67,X_68) != add(X_68,X_67)
| multiply(add(X_68,X_67),X_68) = add(X_68,multiply(X_67,X_68)) ),
introduced(tautology,[equality,[$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_182,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( $equal(add(X_67,X_68),add(X_68,X_67)) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
multiply(add(X_68,X_67),X_68) = add(X_68,multiply(X_67,X_68)),
inference(resolve,[$cnf( $equal(multiply(add(X_67,X_68),X_68),add(X_68,multiply(X_67,X_68))) )],[refute_0_177,refute_0_182]) ).
cnf(refute_0_184,plain,
( multiply(add(X_57,X_59),X_59) != add(X_59,multiply(X_57,X_59))
| add(X_59,multiply(X_57,X_59)) = multiply(add(X_57,X_59),X_59) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(add(X_57,X_59),X_59))),bind(Y0,$fot(add(X_59,multiply(X_57,X_59))))]]) ).
cnf(refute_0_185,plain,
add(X_59,multiply(X_57,X_59)) = multiply(add(X_57,X_59),X_59),
inference(resolve,[$cnf( $equal(multiply(add(X_57,X_59),X_59),add(X_59,multiply(X_57,X_59))) )],[refute_0_13,refute_0_184]) ).
cnf(refute_0_186,plain,
add(X_68,multiply(X_67,X_68)) = multiply(add(X_67,X_68),X_68),
inference(subst,[],[refute_0_185:[bind(X_57,$fot(X_67)),bind(X_59,$fot(X_68))]]) ).
cnf(refute_0_187,plain,
( multiply(add(X_68,X_67),X_68) != add(X_68,multiply(X_67,X_68))
| add(X_68,multiply(X_67,X_68)) != multiply(add(X_67,X_68),X_68)
| multiply(add(X_68,X_67),X_68) = multiply(add(X_67,X_68),X_68) ),
introduced(tautology,[equality,[$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_188,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( $equal(add(X_68,multiply(X_67,X_68)),multiply(add(X_67,X_68),X_68)) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
multiply(add(X_68,X_67),X_68) = multiply(add(X_67,X_68),X_68),
inference(resolve,[$cnf( $equal(multiply(add(X_68,X_67),X_68),add(X_68,multiply(X_67,X_68))) )],[refute_0_183,refute_0_188]) ).
cnf(refute_0_190,plain,
( multiply(add(X_68,X_67),X_68) != multiply(add(X_67,X_68),X_68)
| multiply(add(X_67,X_68),X_68) = multiply(add(X_68,X_67),X_68) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(add(X_68,X_67),X_68))),bind(Y0,$fot(multiply(add(X_67,X_68),X_68)))]]) ).
cnf(refute_0_191,plain,
multiply(add(X_67,X_68),X_68) = multiply(add(X_68,X_67),X_68),
inference(resolve,[$cnf( $equal(multiply(add(X_68,X_67),X_68),multiply(add(X_67,X_68),X_68)) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
multiply(add(add(a,b),a),a) = multiply(add(a,add(a,b)),a),
inference(subst,[],[refute_0_191:[bind(X_67,$fot(add(a,b))),bind(X_68,$fot(a))]]) ).
cnf(refute_0_193,plain,
( multiply(add(add(a,b),a),a) != multiply(add(a,add(a,b)),a)
| multiply(add(a,add(a,b)),a) != multiply(b,a)
| multiply(add(add(a,b),a),a) = multiply(b,a) ),
inference(subst,[],[refute_0_78:[bind(X0,$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_194,plain,
( multiply(add(a,add(a,b)),a) != multiply(b,a)
| multiply(add(add(a,b),a),a) = multiply(b,a) ),
inference(resolve,[$cnf( $equal(multiply(add(add(a,b),a),a),multiply(add(a,add(a,b)),a)) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
multiply(add(add(a,b),a),a) = multiply(b,a),
inference(resolve,[$cnf( $equal(multiply(add(a,add(a,b)),a),multiply(b,a)) )],[refute_0_176,refute_0_194]) ).
cnf(refute_0_196,plain,
( multiply(add(add(a,b),a),a) != multiply(b,a)
| multiply(add(add(a,b),a),a) != add(a,add(a,c))
| multiply(b,a) = add(a,add(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(add(add(a,b),a),a),add(a,add(a,c))) ),[0],$fot(multiply(b,a))]]) ).
cnf(refute_0_197,plain,
( multiply(add(add(a,b),a),a) != add(a,add(a,c))
| multiply(b,a) = add(a,add(a,c)) ),
inference(resolve,[$cnf( $equal(multiply(add(add(a,b),a),a),multiply(b,a)) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
add(a,add(a,c)) = c,
inference(subst,[],[refute_0_171:[bind(X_16,$fot(a)),bind(X_17,$fot(c))]]) ).
cnf(refute_0_199,plain,
( multiply(b,a) != add(a,add(a,c))
| add(a,add(a,c)) != c
| multiply(b,a) = c ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(b,a),c) ),[0],$fot(add(a,add(a,c)))]]) ).
cnf(refute_0_200,plain,
( multiply(b,a) != add(a,add(a,c))
| multiply(b,a) = c ),
inference(resolve,[$cnf( $equal(add(a,add(a,c)),c) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
( multiply(add(add(a,b),a),a) != add(a,add(a,c))
| multiply(b,a) = c ),
inference(resolve,[$cnf( $equal(multiply(b,a),add(a,add(a,c))) )],[refute_0_197,refute_0_200]) ).
cnf(refute_0_202,plain,
multiply(b,a) = c,
inference(resolve,[$cnf( $equal(multiply(add(add(a,b),a),a),add(a,add(a,c))) )],[refute_0_169,refute_0_201]) ).
cnf(refute_0_203,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(b,a),c) )],[refute_0_202,prove_commutativity]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG008-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon May 30 18:45:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.56/0.75 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.56/0.75
% 0.56/0.75 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.60/0.78
%------------------------------------------------------------------------------