TSTP Solution File: BOO013-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : BOO013-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 : Thu Jul 14 23:44:35 EDT 2022
% Result : Unsatisfiable 0.18s 0.50s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 49
% Syntax : Number of clauses : 170 ( 82 unt; 0 nHn; 135 RR)
% Number of literals : 296 ( 295 equ; 128 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 94 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_of_add,axiom,
add(X,Y) = add(Y,X) ).
cnf(distributivity1,axiom,
add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)) ).
cnf(distributivity2,axiom,
add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)) ).
cnf(additive_inverse1,axiom,
add(X,inverse(X)) = multiplicative_identity ).
cnf(multiplicative_inverse1,axiom,
multiply(X,inverse(X)) = additive_identity ).
cnf(multiplicative_id1,axiom,
multiply(X,multiplicative_identity) = X ).
cnf(multiplicative_id2,axiom,
multiply(multiplicative_identity,X) = X ).
cnf(additive_id1,axiom,
add(X,additive_identity) = X ).
cnf(b_and_multiplicative_identity,hypothesis,
add(a,b) = multiplicative_identity ).
cnf(c_and_multiplicative_identity,hypothesis,
add(a,c) = multiplicative_identity ).
cnf(b_a_additive_identity,hypothesis,
multiply(a,b) = additive_identity ).
cnf(c_a_additive_identity,hypothesis,
multiply(a,c) = additive_identity ).
cnf(prove_b_is_a,negated_conjecture,
b != c ).
cnf(refute_0_0,plain,
add(multiply(a,X_11),c) = multiply(add(a,c),add(X_11,c)),
inference(subst,[],[distributivity1:[bind(X,$fot(a)),bind(Y,$fot(X_11)),bind(Z,$fot(c))]]) ).
cnf(refute_0_1,plain,
( add(multiply(a,X_11),c) != multiply(add(a,c),add(X_11,c))
| add(a,c) != multiplicative_identity
| add(multiply(a,X_11),c) = multiply(multiplicative_identity,add(X_11,c)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(a,X_11),c),multiply(add(a,c),add(X_11,c))) ),[1,0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_2,plain,
( add(multiply(a,X_11),c) != multiply(add(a,c),add(X_11,c))
| add(multiply(a,X_11),c) = multiply(multiplicative_identity,add(X_11,c)) ),
inference(resolve,[$cnf( $equal(add(a,c),multiplicative_identity) )],[c_and_multiplicative_identity,refute_0_1]) ).
cnf(refute_0_3,plain,
add(multiply(a,X_11),c) = multiply(multiplicative_identity,add(X_11,c)),
inference(resolve,[$cnf( $equal(add(multiply(a,X_11),c),multiply(add(a,c),add(X_11,c))) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_5,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_6,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( add(X,Y) != add(Y,X)
| add(Y,X) = add(X,Y) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(add(X,Y))),bind(Y0,$fot(add(Y,X)))]]) ).
cnf(refute_0_8,plain,
add(Y,X) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X,Y),add(Y,X)) )],[commutativity_of_add,refute_0_7]) ).
cnf(refute_0_9,plain,
add(multiply(a,X_11),c) = add(c,multiply(a,X_11)),
inference(subst,[],[refute_0_8:[bind(X,$fot(c)),bind(Y,$fot(multiply(a,X_11)))]]) ).
cnf(refute_0_10,plain,
( add(multiply(a,X_11),c) != multiply(multiplicative_identity,add(X_11,c))
| add(multiply(a,X_11),c) != add(c,multiply(a,X_11))
| add(c,multiply(a,X_11)) = multiply(multiplicative_identity,add(X_11,c)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(a,X_11),c),multiply(multiplicative_identity,add(X_11,c))) ),[0],$fot(add(c,multiply(a,X_11)))]]) ).
cnf(refute_0_11,plain,
( add(multiply(a,X_11),c) != multiply(multiplicative_identity,add(X_11,c))
| add(c,multiply(a,X_11)) = multiply(multiplicative_identity,add(X_11,c)) ),
inference(resolve,[$cnf( $equal(add(multiply(a,X_11),c),add(c,multiply(a,X_11))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
multiply(multiplicative_identity,add(X_11,c)) = add(X_11,c),
inference(subst,[],[multiplicative_id2:[bind(X,$fot(add(X_11,c)))]]) ).
cnf(refute_0_13,plain,
( multiply(multiplicative_identity,add(X_11,c)) != add(X_11,c)
| add(c,multiply(a,X_11)) != multiply(multiplicative_identity,add(X_11,c))
| add(c,multiply(a,X_11)) = add(X_11,c) ),
introduced(tautology,[equality,[$cnf( $equal(add(c,multiply(a,X_11)),multiply(multiplicative_identity,add(X_11,c))) ),[1],$fot(add(X_11,c))]]) ).
cnf(refute_0_14,plain,
( add(c,multiply(a,X_11)) != multiply(multiplicative_identity,add(X_11,c))
| add(c,multiply(a,X_11)) = add(X_11,c) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,add(X_11,c)),add(X_11,c)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( add(multiply(a,X_11),c) != multiply(multiplicative_identity,add(X_11,c))
| add(c,multiply(a,X_11)) = add(X_11,c) ),
inference(resolve,[$cnf( $equal(add(c,multiply(a,X_11)),multiply(multiplicative_identity,add(X_11,c))) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
add(c,multiply(a,X_11)) = add(X_11,c),
inference(resolve,[$cnf( $equal(add(multiply(a,X_11),c),multiply(multiplicative_identity,add(X_11,c))) )],[refute_0_3,refute_0_15]) ).
cnf(refute_0_17,plain,
add(c,multiply(a,inverse(a))) = add(inverse(a),c),
inference(subst,[],[refute_0_16:[bind(X_11,$fot(inverse(a)))]]) ).
cnf(refute_0_18,plain,
multiply(a,inverse(a)) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(a))]]) ).
cnf(refute_0_19,plain,
( multiply(a,inverse(a)) != additive_identity
| add(c,multiply(a,inverse(a))) != add(inverse(a),c)
| add(c,additive_identity) = add(inverse(a),c) ),
introduced(tautology,[equality,[$cnf( $equal(add(c,multiply(a,inverse(a))),add(inverse(a),c)) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_20,plain,
( add(c,multiply(a,inverse(a))) != add(inverse(a),c)
| add(c,additive_identity) = add(inverse(a),c) ),
inference(resolve,[$cnf( $equal(multiply(a,inverse(a)),additive_identity) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
add(c,additive_identity) = add(inverse(a),c),
inference(resolve,[$cnf( $equal(add(c,multiply(a,inverse(a))),add(inverse(a),c)) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
add(c,additive_identity) = c,
inference(subst,[],[additive_id1:[bind(X,$fot(c))]]) ).
cnf(refute_0_23,plain,
( add(c,additive_identity) != add(inverse(a),c)
| add(c,additive_identity) != c
| c = add(inverse(a),c) ),
introduced(tautology,[equality,[$cnf( $equal(add(c,additive_identity),add(inverse(a),c)) ),[0],$fot(c)]]) ).
cnf(refute_0_24,plain,
( add(c,additive_identity) != add(inverse(a),c)
| c = add(inverse(a),c) ),
inference(resolve,[$cnf( $equal(add(c,additive_identity),c) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
add(multiply(a,X_11),b) = multiply(add(a,b),add(X_11,b)),
inference(subst,[],[distributivity1:[bind(X,$fot(a)),bind(Y,$fot(X_11)),bind(Z,$fot(b))]]) ).
cnf(refute_0_26,plain,
( add(multiply(a,X_11),b) != multiply(add(a,b),add(X_11,b))
| add(a,b) != multiplicative_identity
| add(multiply(a,X_11),b) = multiply(multiplicative_identity,add(X_11,b)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(a,X_11),b),multiply(add(a,b),add(X_11,b))) ),[1,0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_27,plain,
( add(multiply(a,X_11),b) != multiply(add(a,b),add(X_11,b))
| add(multiply(a,X_11),b) = multiply(multiplicative_identity,add(X_11,b)) ),
inference(resolve,[$cnf( $equal(add(a,b),multiplicative_identity) )],[b_and_multiplicative_identity,refute_0_26]) ).
cnf(refute_0_28,plain,
add(multiply(a,X_11),b) = multiply(multiplicative_identity,add(X_11,b)),
inference(resolve,[$cnf( $equal(add(multiply(a,X_11),b),multiply(add(a,b),add(X_11,b))) )],[refute_0_25,refute_0_27]) ).
cnf(refute_0_29,plain,
add(multiply(a,X_11),b) = add(b,multiply(a,X_11)),
inference(subst,[],[refute_0_8:[bind(X,$fot(b)),bind(Y,$fot(multiply(a,X_11)))]]) ).
cnf(refute_0_30,plain,
( add(multiply(a,X_11),b) != multiply(multiplicative_identity,add(X_11,b))
| add(multiply(a,X_11),b) != add(b,multiply(a,X_11))
| add(b,multiply(a,X_11)) = multiply(multiplicative_identity,add(X_11,b)) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(a,X_11),b),multiply(multiplicative_identity,add(X_11,b))) ),[0],$fot(add(b,multiply(a,X_11)))]]) ).
cnf(refute_0_31,plain,
( add(multiply(a,X_11),b) != multiply(multiplicative_identity,add(X_11,b))
| add(b,multiply(a,X_11)) = multiply(multiplicative_identity,add(X_11,b)) ),
inference(resolve,[$cnf( $equal(add(multiply(a,X_11),b),add(b,multiply(a,X_11))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
multiply(multiplicative_identity,add(X_11,b)) = add(X_11,b),
inference(subst,[],[multiplicative_id2:[bind(X,$fot(add(X_11,b)))]]) ).
cnf(refute_0_33,plain,
( multiply(multiplicative_identity,add(X_11,b)) != add(X_11,b)
| add(b,multiply(a,X_11)) != multiply(multiplicative_identity,add(X_11,b))
| add(b,multiply(a,X_11)) = add(X_11,b) ),
introduced(tautology,[equality,[$cnf( $equal(add(b,multiply(a,X_11)),multiply(multiplicative_identity,add(X_11,b))) ),[1],$fot(add(X_11,b))]]) ).
cnf(refute_0_34,plain,
( add(b,multiply(a,X_11)) != multiply(multiplicative_identity,add(X_11,b))
| add(b,multiply(a,X_11)) = add(X_11,b) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,add(X_11,b)),add(X_11,b)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( add(multiply(a,X_11),b) != multiply(multiplicative_identity,add(X_11,b))
| add(b,multiply(a,X_11)) = add(X_11,b) ),
inference(resolve,[$cnf( $equal(add(b,multiply(a,X_11)),multiply(multiplicative_identity,add(X_11,b))) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
add(b,multiply(a,X_11)) = add(X_11,b),
inference(resolve,[$cnf( $equal(add(multiply(a,X_11),b),multiply(multiplicative_identity,add(X_11,b))) )],[refute_0_28,refute_0_35]) ).
cnf(refute_0_37,plain,
add(b,multiply(a,c)) = add(c,b),
inference(subst,[],[refute_0_36:[bind(X_11,$fot(c))]]) ).
cnf(refute_0_38,plain,
( multiply(a,c) != additive_identity
| add(b,multiply(a,c)) != add(c,b)
| add(b,additive_identity) = add(c,b) ),
introduced(tautology,[equality,[$cnf( $equal(add(b,multiply(a,c)),add(c,b)) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_39,plain,
( add(b,multiply(a,c)) != add(c,b)
| add(b,additive_identity) = add(c,b) ),
inference(resolve,[$cnf( $equal(multiply(a,c),additive_identity) )],[c_a_additive_identity,refute_0_38]) ).
cnf(refute_0_40,plain,
add(b,additive_identity) = add(c,b),
inference(resolve,[$cnf( $equal(add(b,multiply(a,c)),add(c,b)) )],[refute_0_37,refute_0_39]) ).
cnf(refute_0_41,plain,
add(b,additive_identity) = b,
inference(subst,[],[additive_id1:[bind(X,$fot(b))]]) ).
cnf(refute_0_42,plain,
( add(b,additive_identity) != add(c,b)
| add(b,additive_identity) != b
| b = add(c,b) ),
introduced(tautology,[equality,[$cnf( $equal(add(b,additive_identity),add(c,b)) ),[0],$fot(b)]]) ).
cnf(refute_0_43,plain,
( add(b,additive_identity) != add(c,b)
| b = add(c,b) ),
inference(resolve,[$cnf( $equal(add(b,additive_identity),b) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
add(c,b) = add(b,c),
inference(subst,[],[refute_0_8:[bind(X,$fot(b)),bind(Y,$fot(c))]]) ).
cnf(refute_0_45,plain,
( add(c,b) != add(b,c)
| b != add(c,b)
| b = add(b,c) ),
introduced(tautology,[equality,[$cnf( $equal(b,add(c,b)) ),[1],$fot(add(b,c))]]) ).
cnf(refute_0_46,plain,
( b != add(c,b)
| b = add(b,c) ),
inference(resolve,[$cnf( $equal(add(c,b),add(b,c)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( add(b,additive_identity) != add(c,b)
| b = add(b,c) ),
inference(resolve,[$cnf( $equal(b,add(c,b)) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
b = add(b,c),
inference(resolve,[$cnf( $equal(add(b,additive_identity),add(c,b)) )],[refute_0_40,refute_0_47]) ).
cnf(refute_0_49,plain,
( b != add(b,c)
| add(b,c) = b ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(b)),bind(Y0,$fot(add(b,c)))]]) ).
cnf(refute_0_50,plain,
add(b,c) = b,
inference(resolve,[$cnf( $equal(b,add(b,c)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_52,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_6,refute_0_51]) ).
cnf(refute_0_53,plain,
( add(b,c) != b
| add(c,b) != add(b,c)
| add(c,b) = b ),
inference(subst,[],[refute_0_52:[bind(X0,$fot(add(c,b))),bind(Y0,$fot(add(b,c))),bind(Z0,$fot(b))]]) ).
cnf(refute_0_54,plain,
( add(b,c) != b
| add(c,b) = b ),
inference(resolve,[$cnf( $equal(add(c,b),add(b,c)) )],[refute_0_44,refute_0_53]) ).
cnf(refute_0_55,plain,
add(c,b) = b,
inference(resolve,[$cnf( $equal(add(b,c),b) )],[refute_0_50,refute_0_54]) ).
cnf(refute_0_56,plain,
add(b,multiply(a,inverse(a))) = add(inverse(a),b),
inference(subst,[],[refute_0_36:[bind(X_11,$fot(inverse(a)))]]) ).
cnf(refute_0_57,plain,
( multiply(a,inverse(a)) != additive_identity
| add(b,multiply(a,inverse(a))) != add(inverse(a),b)
| add(b,additive_identity) = add(inverse(a),b) ),
introduced(tautology,[equality,[$cnf( $equal(add(b,multiply(a,inverse(a))),add(inverse(a),b)) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_58,plain,
( add(b,multiply(a,inverse(a))) != add(inverse(a),b)
| add(b,additive_identity) = add(inverse(a),b) ),
inference(resolve,[$cnf( $equal(multiply(a,inverse(a)),additive_identity) )],[refute_0_18,refute_0_57]) ).
cnf(refute_0_59,plain,
add(b,additive_identity) = add(inverse(a),b),
inference(resolve,[$cnf( $equal(add(b,multiply(a,inverse(a))),add(inverse(a),b)) )],[refute_0_56,refute_0_58]) ).
cnf(refute_0_60,plain,
( add(b,additive_identity) != add(inverse(a),b)
| add(b,additive_identity) != b
| b = add(inverse(a),b) ),
introduced(tautology,[equality,[$cnf( $equal(add(b,additive_identity),add(inverse(a),b)) ),[0],$fot(b)]]) ).
cnf(refute_0_61,plain,
( add(b,additive_identity) != add(inverse(a),b)
| b = add(inverse(a),b) ),
inference(resolve,[$cnf( $equal(add(b,additive_identity),b) )],[refute_0_41,refute_0_60]) ).
cnf(refute_0_62,plain,
add(multiply(X_10,X_11),inverse(X_11)) = multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11))),
inference(subst,[],[distributivity1:[bind(X,$fot(X_10)),bind(Y,$fot(X_11)),bind(Z,$fot(inverse(X_11)))]]) ).
cnf(refute_0_63,plain,
add(X_11,inverse(X_11)) = multiplicative_identity,
inference(subst,[],[additive_inverse1:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_64,plain,
( add(X_11,inverse(X_11)) != multiplicative_identity
| add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11)))
| add(multiply(X_10,X_11),inverse(X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11)))) ),[1,1],$fot(multiplicative_identity)]]) ).
cnf(refute_0_65,plain,
( add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11)))
| add(multiply(X_10,X_11),inverse(X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(X_11,inverse(X_11)),multiplicative_identity) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
add(multiply(X_10,X_11),inverse(X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity),
inference(resolve,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),multiply(add(X_10,inverse(X_11)),add(X_11,inverse(X_11)))) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
add(multiply(X_10,X_11),inverse(X_11)) = add(inverse(X_11),multiply(X_10,X_11)),
inference(subst,[],[refute_0_8:[bind(X,$fot(inverse(X_11))),bind(Y,$fot(multiply(X_10,X_11)))]]) ).
cnf(refute_0_68,plain,
( add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(multiply(X_10,X_11),inverse(X_11)) != add(inverse(X_11),multiply(X_10,X_11))
| add(inverse(X_11),multiply(X_10,X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity) ),
introduced(tautology,[equality,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),multiply(add(X_10,inverse(X_11)),multiplicative_identity)) ),[0],$fot(add(inverse(X_11),multiply(X_10,X_11)))]]) ).
cnf(refute_0_69,plain,
( add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(inverse(X_11),multiply(X_10,X_11)) = multiply(add(X_10,inverse(X_11)),multiplicative_identity) ),
inference(resolve,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),add(inverse(X_11),multiply(X_10,X_11))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
multiply(add(X_10,inverse(X_11)),multiplicative_identity) = add(X_10,inverse(X_11)),
inference(subst,[],[multiplicative_id1:[bind(X,$fot(add(X_10,inverse(X_11))))]]) ).
cnf(refute_0_71,plain,
( multiply(add(X_10,inverse(X_11)),multiplicative_identity) != add(X_10,inverse(X_11))
| add(inverse(X_11),multiply(X_10,X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(inverse(X_11),multiply(X_10,X_11)) = add(X_10,inverse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(X_11),multiply(X_10,X_11)),multiply(add(X_10,inverse(X_11)),multiplicative_identity)) ),[1],$fot(add(X_10,inverse(X_11)))]]) ).
cnf(refute_0_72,plain,
( add(inverse(X_11),multiply(X_10,X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(inverse(X_11),multiply(X_10,X_11)) = add(X_10,inverse(X_11)) ),
inference(resolve,[$cnf( $equal(multiply(add(X_10,inverse(X_11)),multiplicative_identity),add(X_10,inverse(X_11))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
( add(multiply(X_10,X_11),inverse(X_11)) != multiply(add(X_10,inverse(X_11)),multiplicative_identity)
| add(inverse(X_11),multiply(X_10,X_11)) = add(X_10,inverse(X_11)) ),
inference(resolve,[$cnf( $equal(add(inverse(X_11),multiply(X_10,X_11)),multiply(add(X_10,inverse(X_11)),multiplicative_identity)) )],[refute_0_69,refute_0_72]) ).
cnf(refute_0_74,plain,
add(inverse(X_11),multiply(X_10,X_11)) = add(X_10,inverse(X_11)),
inference(resolve,[$cnf( $equal(add(multiply(X_10,X_11),inverse(X_11)),multiply(add(X_10,inverse(X_11)),multiplicative_identity)) )],[refute_0_66,refute_0_73]) ).
cnf(refute_0_75,plain,
add(inverse(inverse(X_18)),multiply(X_18,inverse(X_18))) = add(X_18,inverse(inverse(X_18))),
inference(subst,[],[refute_0_74:[bind(X_10,$fot(X_18)),bind(X_11,$fot(inverse(X_18)))]]) ).
cnf(refute_0_76,plain,
multiply(X_18,inverse(X_18)) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(X_18))]]) ).
cnf(refute_0_77,plain,
( multiply(X_18,inverse(X_18)) != additive_identity
| add(inverse(inverse(X_18)),multiply(X_18,inverse(X_18))) != add(X_18,inverse(inverse(X_18)))
| add(inverse(inverse(X_18)),additive_identity) = add(X_18,inverse(inverse(X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(inverse(X_18)),multiply(X_18,inverse(X_18))),add(X_18,inverse(inverse(X_18)))) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_78,plain,
( add(inverse(inverse(X_18)),multiply(X_18,inverse(X_18))) != add(X_18,inverse(inverse(X_18)))
| add(inverse(inverse(X_18)),additive_identity) = add(X_18,inverse(inverse(X_18))) ),
inference(resolve,[$cnf( $equal(multiply(X_18,inverse(X_18)),additive_identity) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
add(inverse(inverse(X_18)),additive_identity) = add(X_18,inverse(inverse(X_18))),
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_18)),multiply(X_18,inverse(X_18))),add(X_18,inverse(inverse(X_18)))) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
add(inverse(inverse(X_18)),additive_identity) = inverse(inverse(X_18)),
inference(subst,[],[additive_id1:[bind(X,$fot(inverse(inverse(X_18))))]]) ).
cnf(refute_0_81,plain,
( add(inverse(inverse(X_18)),additive_identity) != add(X_18,inverse(inverse(X_18)))
| add(inverse(inverse(X_18)),additive_identity) != inverse(inverse(X_18))
| inverse(inverse(X_18)) = add(X_18,inverse(inverse(X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(inverse(X_18)),additive_identity),add(X_18,inverse(inverse(X_18)))) ),[0],$fot(inverse(inverse(X_18)))]]) ).
cnf(refute_0_82,plain,
( add(inverse(inverse(X_18)),additive_identity) != add(X_18,inverse(inverse(X_18)))
| inverse(inverse(X_18)) = add(X_18,inverse(inverse(X_18))) ),
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_18)),additive_identity),inverse(inverse(X_18))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
inverse(inverse(X_18)) = add(X_18,inverse(inverse(X_18))),
inference(resolve,[$cnf( $equal(add(inverse(inverse(X_18)),additive_identity),add(X_18,inverse(inverse(X_18)))) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
inverse(inverse(b)) = add(b,inverse(inverse(b))),
inference(subst,[],[refute_0_83:[bind(X_18,$fot(b))]]) ).
cnf(refute_0_85,plain,
add(a,multiply(b,X_26)) = multiply(add(a,b),add(a,X_26)),
inference(subst,[],[distributivity2:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_86,plain,
( add(a,multiply(b,X_26)) != multiply(add(a,b),add(a,X_26))
| add(a,b) != multiplicative_identity
| add(a,multiply(b,X_26)) = multiply(multiplicative_identity,add(a,X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(add(a,multiply(b,X_26)),multiply(add(a,b),add(a,X_26))) ),[1,0],$fot(multiplicative_identity)]]) ).
cnf(refute_0_87,plain,
( add(a,multiply(b,X_26)) != multiply(add(a,b),add(a,X_26))
| add(a,multiply(b,X_26)) = multiply(multiplicative_identity,add(a,X_26)) ),
inference(resolve,[$cnf( $equal(add(a,b),multiplicative_identity) )],[b_and_multiplicative_identity,refute_0_86]) ).
cnf(refute_0_88,plain,
add(a,multiply(b,X_26)) = multiply(multiplicative_identity,add(a,X_26)),
inference(resolve,[$cnf( $equal(add(a,multiply(b,X_26)),multiply(add(a,b),add(a,X_26))) )],[refute_0_85,refute_0_87]) ).
cnf(refute_0_89,plain,
multiply(multiplicative_identity,add(a,X_26)) = add(a,X_26),
inference(subst,[],[multiplicative_id2:[bind(X,$fot(add(a,X_26)))]]) ).
cnf(refute_0_90,plain,
( multiply(multiplicative_identity,add(a,X_26)) != add(a,X_26)
| add(a,multiply(b,X_26)) != multiply(multiplicative_identity,add(a,X_26))
| add(a,multiply(b,X_26)) = add(a,X_26) ),
introduced(tautology,[equality,[$cnf( $equal(add(a,multiply(b,X_26)),multiply(multiplicative_identity,add(a,X_26))) ),[1],$fot(add(a,X_26))]]) ).
cnf(refute_0_91,plain,
( add(a,multiply(b,X_26)) != multiply(multiplicative_identity,add(a,X_26))
| add(a,multiply(b,X_26)) = add(a,X_26) ),
inference(resolve,[$cnf( $equal(multiply(multiplicative_identity,add(a,X_26)),add(a,X_26)) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
add(a,multiply(b,X_26)) = add(a,X_26),
inference(resolve,[$cnf( $equal(add(a,multiply(b,X_26)),multiply(multiplicative_identity,add(a,X_26))) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
add(a,multiply(b,inverse(b))) = add(a,inverse(b)),
inference(subst,[],[refute_0_92:[bind(X_26,$fot(inverse(b)))]]) ).
cnf(refute_0_94,plain,
multiply(b,inverse(b)) = additive_identity,
inference(subst,[],[multiplicative_inverse1:[bind(X,$fot(b))]]) ).
cnf(refute_0_95,plain,
( multiply(b,inverse(b)) != additive_identity
| add(a,multiply(b,inverse(b))) != add(a,inverse(b))
| add(a,additive_identity) = add(a,inverse(b)) ),
introduced(tautology,[equality,[$cnf( $equal(add(a,multiply(b,inverse(b))),add(a,inverse(b))) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_96,plain,
( add(a,multiply(b,inverse(b))) != add(a,inverse(b))
| add(a,additive_identity) = add(a,inverse(b)) ),
inference(resolve,[$cnf( $equal(multiply(b,inverse(b)),additive_identity) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
add(a,additive_identity) = add(a,inverse(b)),
inference(resolve,[$cnf( $equal(add(a,multiply(b,inverse(b))),add(a,inverse(b))) )],[refute_0_93,refute_0_96]) ).
cnf(refute_0_98,plain,
add(a,additive_identity) = a,
inference(subst,[],[additive_id1:[bind(X,$fot(a))]]) ).
cnf(refute_0_99,plain,
( add(a,additive_identity) != add(a,inverse(b))
| add(a,additive_identity) != a
| a = add(a,inverse(b)) ),
introduced(tautology,[equality,[$cnf( $equal(add(a,additive_identity),add(a,inverse(b))) ),[0],$fot(a)]]) ).
cnf(refute_0_100,plain,
( add(a,additive_identity) != add(a,inverse(b))
| a = add(a,inverse(b)) ),
inference(resolve,[$cnf( $equal(add(a,additive_identity),a) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
add(inverse(b),multiply(a,b)) = add(a,inverse(b)),
inference(subst,[],[refute_0_74:[bind(X_10,$fot(a)),bind(X_11,$fot(b))]]) ).
cnf(refute_0_102,plain,
( multiply(a,b) != additive_identity
| add(inverse(b),multiply(a,b)) != add(a,inverse(b))
| add(inverse(b),additive_identity) = add(a,inverse(b)) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(b),multiply(a,b)),add(a,inverse(b))) ),[0,1],$fot(additive_identity)]]) ).
cnf(refute_0_103,plain,
( add(inverse(b),multiply(a,b)) != add(a,inverse(b))
| add(inverse(b),additive_identity) = add(a,inverse(b)) ),
inference(resolve,[$cnf( $equal(multiply(a,b),additive_identity) )],[b_a_additive_identity,refute_0_102]) ).
cnf(refute_0_104,plain,
add(inverse(b),additive_identity) = add(a,inverse(b)),
inference(resolve,[$cnf( $equal(add(inverse(b),multiply(a,b)),add(a,inverse(b))) )],[refute_0_101,refute_0_103]) ).
cnf(refute_0_105,plain,
add(inverse(b),additive_identity) = inverse(b),
inference(subst,[],[additive_id1:[bind(X,$fot(inverse(b)))]]) ).
cnf(refute_0_106,plain,
( add(inverse(b),additive_identity) != add(a,inverse(b))
| add(inverse(b),additive_identity) != inverse(b)
| inverse(b) = add(a,inverse(b)) ),
introduced(tautology,[equality,[$cnf( $equal(add(inverse(b),additive_identity),add(a,inverse(b))) ),[0],$fot(inverse(b))]]) ).
cnf(refute_0_107,plain,
( add(inverse(b),additive_identity) != add(a,inverse(b))
| inverse(b) = add(a,inverse(b)) ),
inference(resolve,[$cnf( $equal(add(inverse(b),additive_identity),inverse(b)) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
inverse(b) = add(a,inverse(b)),
inference(resolve,[$cnf( $equal(add(inverse(b),additive_identity),add(a,inverse(b))) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
( inverse(b) != add(a,inverse(b))
| add(a,inverse(b)) = inverse(b) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(inverse(b))),bind(Y0,$fot(add(a,inverse(b))))]]) ).
cnf(refute_0_110,plain,
add(a,inverse(b)) = inverse(b),
inference(resolve,[$cnf( $equal(inverse(b),add(a,inverse(b))) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
( add(a,inverse(b)) != inverse(b)
| a != add(a,inverse(b))
| a = inverse(b) ),
introduced(tautology,[equality,[$cnf( $equal(a,add(a,inverse(b))) ),[1],$fot(inverse(b))]]) ).
cnf(refute_0_112,plain,
( a != add(a,inverse(b))
| a = inverse(b) ),
inference(resolve,[$cnf( $equal(add(a,inverse(b)),inverse(b)) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
( add(a,additive_identity) != add(a,inverse(b))
| a = inverse(b) ),
inference(resolve,[$cnf( $equal(a,add(a,inverse(b))) )],[refute_0_100,refute_0_112]) ).
cnf(refute_0_114,plain,
a = inverse(b),
inference(resolve,[$cnf( $equal(add(a,additive_identity),add(a,inverse(b))) )],[refute_0_97,refute_0_113]) ).
cnf(refute_0_115,plain,
( a != inverse(b)
| inverse(b) = a ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(a)),bind(Y0,$fot(inverse(b)))]]) ).
cnf(refute_0_116,plain,
inverse(b) = a,
inference(resolve,[$cnf( $equal(a,inverse(b)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
( inverse(b) != a
| inverse(inverse(b)) != add(b,inverse(inverse(b)))
| inverse(inverse(b)) = add(b,inverse(a)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(b)),add(b,inverse(inverse(b)))) ),[1,1,0],$fot(a)]]) ).
cnf(refute_0_118,plain,
( inverse(inverse(b)) != add(b,inverse(inverse(b)))
| inverse(inverse(b)) = add(b,inverse(a)) ),
inference(resolve,[$cnf( $equal(inverse(b),a) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
inverse(inverse(b)) = add(b,inverse(a)),
inference(resolve,[$cnf( $equal(inverse(inverse(b)),add(b,inverse(inverse(b)))) )],[refute_0_84,refute_0_118]) ).
cnf(refute_0_120,plain,
inverse(inverse(b)) = inverse(inverse(b)),
introduced(tautology,[refl,[$fot(inverse(inverse(b)))]]) ).
cnf(refute_0_121,plain,
( inverse(b) != a
| inverse(inverse(b)) != inverse(inverse(b))
| inverse(inverse(b)) = inverse(a) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(b)),inverse(inverse(b))) ),[1,0],$fot(a)]]) ).
cnf(refute_0_122,plain,
( inverse(b) != a
| inverse(inverse(b)) = inverse(a) ),
inference(resolve,[$cnf( $equal(inverse(inverse(b)),inverse(inverse(b))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
inverse(inverse(b)) = inverse(a),
inference(resolve,[$cnf( $equal(inverse(b),a) )],[refute_0_116,refute_0_122]) ).
cnf(refute_0_124,plain,
( inverse(inverse(b)) != add(b,inverse(a))
| inverse(inverse(b)) != inverse(a)
| inverse(a) = add(b,inverse(a)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(b)),add(b,inverse(a))) ),[0],$fot(inverse(a))]]) ).
cnf(refute_0_125,plain,
( inverse(inverse(b)) != add(b,inverse(a))
| inverse(a) = add(b,inverse(a)) ),
inference(resolve,[$cnf( $equal(inverse(inverse(b)),inverse(a)) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
inverse(a) = add(b,inverse(a)),
inference(resolve,[$cnf( $equal(inverse(inverse(b)),add(b,inverse(a))) )],[refute_0_119,refute_0_125]) ).
cnf(refute_0_127,plain,
( inverse(a) != add(b,inverse(a))
| add(b,inverse(a)) = inverse(a) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(inverse(a))),bind(Y0,$fot(add(b,inverse(a))))]]) ).
cnf(refute_0_128,plain,
add(b,inverse(a)) = inverse(a),
inference(resolve,[$cnf( $equal(inverse(a),add(b,inverse(a))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
add(inverse(a),b) = add(b,inverse(a)),
inference(subst,[],[refute_0_8:[bind(X,$fot(b)),bind(Y,$fot(inverse(a)))]]) ).
cnf(refute_0_130,plain,
( add(b,inverse(a)) != inverse(a)
| add(inverse(a),b) != add(b,inverse(a))
| add(inverse(a),b) = inverse(a) ),
inference(subst,[],[refute_0_52:[bind(X0,$fot(add(inverse(a),b))),bind(Y0,$fot(add(b,inverse(a)))),bind(Z0,$fot(inverse(a)))]]) ).
cnf(refute_0_131,plain,
( add(b,inverse(a)) != inverse(a)
| add(inverse(a),b) = inverse(a) ),
inference(resolve,[$cnf( $equal(add(inverse(a),b),add(b,inverse(a))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
add(inverse(a),b) = inverse(a),
inference(resolve,[$cnf( $equal(add(b,inverse(a)),inverse(a)) )],[refute_0_128,refute_0_131]) ).
cnf(refute_0_133,plain,
( add(inverse(a),b) != inverse(a)
| b != add(inverse(a),b)
| b = inverse(a) ),
introduced(tautology,[equality,[$cnf( $equal(b,add(inverse(a),b)) ),[1],$fot(inverse(a))]]) ).
cnf(refute_0_134,plain,
( b != add(inverse(a),b)
| b = inverse(a) ),
inference(resolve,[$cnf( $equal(add(inverse(a),b),inverse(a)) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
( add(b,additive_identity) != add(inverse(a),b)
| b = inverse(a) ),
inference(resolve,[$cnf( $equal(b,add(inverse(a),b)) )],[refute_0_61,refute_0_134]) ).
cnf(refute_0_136,plain,
b = inverse(a),
inference(resolve,[$cnf( $equal(add(b,additive_identity),add(inverse(a),b)) )],[refute_0_59,refute_0_135]) ).
cnf(refute_0_137,plain,
( b != inverse(a)
| inverse(a) = b ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(b)),bind(Y0,$fot(inverse(a)))]]) ).
cnf(refute_0_138,plain,
inverse(a) = b,
inference(resolve,[$cnf( $equal(b,inverse(a)) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
add(c,inverse(a)) = add(c,inverse(a)),
introduced(tautology,[refl,[$fot(add(c,inverse(a)))]]) ).
cnf(refute_0_140,plain,
( add(c,inverse(a)) != add(c,inverse(a))
| inverse(a) != b
| add(c,inverse(a)) = add(c,b) ),
introduced(tautology,[equality,[$cnf( $equal(add(c,inverse(a)),add(c,inverse(a))) ),[1,1],$fot(b)]]) ).
cnf(refute_0_141,plain,
( inverse(a) != b
| add(c,inverse(a)) = add(c,b) ),
inference(resolve,[$cnf( $equal(add(c,inverse(a)),add(c,inverse(a))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
add(c,inverse(a)) = add(c,b),
inference(resolve,[$cnf( $equal(inverse(a),b) )],[refute_0_138,refute_0_141]) ).
cnf(refute_0_143,plain,
( add(c,b) != b
| add(c,inverse(a)) != add(c,b)
| add(c,inverse(a)) = b ),
inference(subst,[],[refute_0_52:[bind(X0,$fot(add(c,inverse(a)))),bind(Y0,$fot(add(c,b))),bind(Z0,$fot(b))]]) ).
cnf(refute_0_144,plain,
( add(c,b) != b
| add(c,inverse(a)) = b ),
inference(resolve,[$cnf( $equal(add(c,inverse(a)),add(c,b)) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
add(c,inverse(a)) = b,
inference(resolve,[$cnf( $equal(add(c,b),b) )],[refute_0_55,refute_0_144]) ).
cnf(refute_0_146,plain,
add(inverse(a),c) = add(c,inverse(a)),
inference(subst,[],[refute_0_8:[bind(X,$fot(c)),bind(Y,$fot(inverse(a)))]]) ).
cnf(refute_0_147,plain,
( add(c,inverse(a)) != b
| add(inverse(a),c) != add(c,inverse(a))
| add(inverse(a),c) = b ),
inference(subst,[],[refute_0_52:[bind(X0,$fot(add(inverse(a),c))),bind(Y0,$fot(add(c,inverse(a)))),bind(Z0,$fot(b))]]) ).
cnf(refute_0_148,plain,
( add(c,inverse(a)) != b
| add(inverse(a),c) = b ),
inference(resolve,[$cnf( $equal(add(inverse(a),c),add(c,inverse(a))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
add(inverse(a),c) = b,
inference(resolve,[$cnf( $equal(add(c,inverse(a)),b) )],[refute_0_145,refute_0_148]) ).
cnf(refute_0_150,plain,
( add(inverse(a),c) != b
| c != add(inverse(a),c)
| c = b ),
introduced(tautology,[equality,[$cnf( $equal(c,add(inverse(a),c)) ),[1],$fot(b)]]) ).
cnf(refute_0_151,plain,
( c != add(inverse(a),c)
| c = b ),
inference(resolve,[$cnf( $equal(add(inverse(a),c),b) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
( add(c,additive_identity) != add(inverse(a),c)
| c = b ),
inference(resolve,[$cnf( $equal(c,add(inverse(a),c)) )],[refute_0_24,refute_0_151]) ).
cnf(refute_0_153,plain,
c = b,
inference(resolve,[$cnf( $equal(add(c,additive_identity),add(inverse(a),c)) )],[refute_0_21,refute_0_152]) ).
cnf(refute_0_154,plain,
( c != b
| b = c ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(c)),bind(Y0,$fot(b))]]) ).
cnf(refute_0_155,plain,
c != b,
inference(resolve,[$cnf( $equal(b,c) )],[refute_0_154,prove_b_is_a]) ).
cnf(refute_0_156,plain,
$false,
inference(resolve,[$cnf( $equal(c,b) )],[refute_0_153,refute_0_155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : BOO013-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.12 % 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 : Wed Jun 1 15:13:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.50 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.50
% 0.18/0.50 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.52
%------------------------------------------------------------------------------