TSTP Solution File: ROB011-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ROB011-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 20:54:33 EDT 2022
% Result : Unsatisfiable 0.77s 1.00s
% Output : CNFRefutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 41
% Syntax : Number of clauses : 106 ( 55 unt; 0 nHn; 92 RR)
% Number of literals : 182 ( 181 equ; 79 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_of_add,axiom,
add(X,Y) = add(Y,X) ).
cnf(associativity_of_add,axiom,
add(add(X,Y),Z) = add(X,add(Y,Z)) ).
cnf(robbins_axiom,axiom,
negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X ).
cnf(one_times_x,axiom,
multiply(one,X) = X ).
cnf(condition,hypothesis,
negate(add(a,negate(b))) = c ).
cnf(prove_base_step,negated_conjecture,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != c ).
cnf(refute_0_0,plain,
multiply(one,add(a,c)) = add(a,c),
inference(subst,[],[one_times_x:[bind(X,$fot(add(a,c)))]]) ).
cnf(refute_0_1,plain,
add(b,multiply(one,add(a,c))) = add(b,multiply(one,add(a,c))),
introduced(tautology,[refl,[$fot(add(b,multiply(one,add(a,c))))]]) ).
cnf(refute_0_2,plain,
( multiply(one,add(a,c)) != add(a,c)
| add(b,multiply(one,add(a,c))) != add(b,multiply(one,add(a,c)))
| add(b,multiply(one,add(a,c))) = add(b,add(a,c)) ),
introduced(tautology,[equality,[$cnf( $equal(add(b,multiply(one,add(a,c))),add(b,multiply(one,add(a,c)))) ),[1,1],$fot(add(a,c))]]) ).
cnf(refute_0_3,plain,
( multiply(one,add(a,c)) != add(a,c)
| add(b,multiply(one,add(a,c))) = add(b,add(a,c)) ),
inference(resolve,[$cnf( $equal(add(b,multiply(one,add(a,c))),add(b,multiply(one,add(a,c)))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
add(b,multiply(one,add(a,c))) = add(b,add(a,c)),
inference(resolve,[$cnf( $equal(multiply(one,add(a,c)),add(a,c)) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
negate(add(b,multiply(one,add(a,c)))) = negate(add(b,multiply(one,add(a,c)))),
introduced(tautology,[refl,[$fot(negate(add(b,multiply(one,add(a,c)))))]]) ).
cnf(refute_0_6,plain,
( add(b,multiply(one,add(a,c))) != add(b,add(a,c))
| negate(add(b,multiply(one,add(a,c)))) != negate(add(b,multiply(one,add(a,c))))
| negate(add(b,multiply(one,add(a,c)))) = negate(add(b,add(a,c))) ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(b,multiply(one,add(a,c)))),negate(add(b,multiply(one,add(a,c))))) ),[1,0],$fot(add(b,add(a,c)))]]) ).
cnf(refute_0_7,plain,
( add(b,multiply(one,add(a,c))) != add(b,add(a,c))
| negate(add(b,multiply(one,add(a,c)))) = negate(add(b,add(a,c))) ),
inference(resolve,[$cnf( $equal(negate(add(b,multiply(one,add(a,c)))),negate(add(b,multiply(one,add(a,c))))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
negate(add(b,multiply(one,add(a,c)))) = negate(add(b,add(a,c))),
inference(resolve,[$cnf( $equal(add(b,multiply(one,add(a,c))),add(b,add(a,c))) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
add(a,negate(add(b,multiply(one,add(a,c))))) = add(a,negate(add(b,multiply(one,add(a,c))))),
introduced(tautology,[refl,[$fot(add(a,negate(add(b,multiply(one,add(a,c))))))]]) ).
cnf(refute_0_10,plain,
( add(a,negate(add(b,multiply(one,add(a,c))))) != add(a,negate(add(b,multiply(one,add(a,c)))))
| negate(add(b,multiply(one,add(a,c)))) != negate(add(b,add(a,c)))
| add(a,negate(add(b,multiply(one,add(a,c))))) = add(a,negate(add(b,add(a,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(add(a,negate(add(b,multiply(one,add(a,c))))),add(a,negate(add(b,multiply(one,add(a,c)))))) ),[1,1],$fot(negate(add(b,add(a,c))))]]) ).
cnf(refute_0_11,plain,
( negate(add(b,multiply(one,add(a,c)))) != negate(add(b,add(a,c)))
| add(a,negate(add(b,multiply(one,add(a,c))))) = add(a,negate(add(b,add(a,c)))) ),
inference(resolve,[$cnf( $equal(add(a,negate(add(b,multiply(one,add(a,c))))),add(a,negate(add(b,multiply(one,add(a,c)))))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
add(a,negate(add(b,multiply(one,add(a,c))))) = add(a,negate(add(b,add(a,c)))),
inference(resolve,[$cnf( $equal(negate(add(b,multiply(one,add(a,c)))),negate(add(b,add(a,c)))) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) = negate(add(a,negate(add(b,multiply(one,add(a,c)))))),
introduced(tautology,[refl,[$fot(negate(add(a,negate(add(b,multiply(one,add(a,c)))))))]]) ).
cnf(refute_0_14,plain,
( add(a,negate(add(b,multiply(one,add(a,c))))) != add(a,negate(add(b,add(a,c))))
| negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != negate(add(a,negate(add(b,multiply(one,add(a,c))))))
| negate(add(a,negate(add(b,multiply(one,add(a,c)))))) = negate(add(a,negate(add(b,add(a,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(a,negate(add(b,multiply(one,add(a,c)))))),negate(add(a,negate(add(b,multiply(one,add(a,c))))))) ),[1,0],$fot(add(a,negate(add(b,add(a,c)))))]]) ).
cnf(refute_0_15,plain,
( add(a,negate(add(b,multiply(one,add(a,c))))) != add(a,negate(add(b,add(a,c))))
| negate(add(a,negate(add(b,multiply(one,add(a,c)))))) = negate(add(a,negate(add(b,add(a,c))))) ),
inference(resolve,[$cnf( $equal(negate(add(a,negate(add(b,multiply(one,add(a,c)))))),negate(add(a,negate(add(b,multiply(one,add(a,c))))))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
negate(add(a,negate(add(b,multiply(one,add(a,c)))))) = negate(add(a,negate(add(b,add(a,c))))),
inference(resolve,[$cnf( $equal(add(a,negate(add(b,multiply(one,add(a,c))))),add(a,negate(add(b,add(a,c))))) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
( negate(add(a,negate(add(b,multiply(one,add(a,c)))))) != negate(add(a,negate(add(b,add(a,c)))))
| negate(add(a,negate(add(b,add(a,c))))) != c
| negate(add(a,negate(add(b,multiply(one,add(a,c)))))) = c ),
introduced(tautology,[equality,[$cnf( ~ $equal(negate(add(a,negate(add(b,multiply(one,add(a,c)))))),c) ),[0],$fot(negate(add(a,negate(add(b,add(a,c))))))]]) ).
cnf(refute_0_18,plain,
( negate(add(a,negate(add(b,add(a,c))))) != c
| negate(add(a,negate(add(b,multiply(one,add(a,c)))))) = c ),
inference(resolve,[$cnf( $equal(negate(add(a,negate(add(b,multiply(one,add(a,c)))))),negate(add(a,negate(add(b,add(a,c)))))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
negate(add(a,negate(add(b,add(a,c))))) != c,
inference(resolve,[$cnf( $equal(negate(add(a,negate(add(b,multiply(one,add(a,c)))))),c) )],[refute_0_18,prove_base_step]) ).
cnf(refute_0_20,plain,
( add(X,Y) != add(Y,X)
| negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) != X
| negate(add(negate(add(Y,X)),negate(add(X,negate(Y))))) = X ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))),X) ),[0,0,0,0],$fot(add(Y,X))]]) ).
cnf(refute_0_21,plain,
( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) != X
| negate(add(negate(add(Y,X)),negate(add(X,negate(Y))))) = X ),
inference(resolve,[$cnf( $equal(add(X,Y),add(Y,X)) )],[commutativity_of_add,refute_0_20]) ).
cnf(refute_0_22,plain,
negate(add(negate(add(Y,X)),negate(add(X,negate(Y))))) = X,
inference(resolve,[$cnf( $equal(negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))),X) )],[robbins_axiom,refute_0_21]) ).
cnf(refute_0_23,plain,
negate(add(negate(add(add(a,b),c)),negate(add(c,negate(add(a,b)))))) = c,
inference(subst,[],[refute_0_22:[bind(X,$fot(c)),bind(Y,$fot(add(a,b)))]]) ).
cnf(refute_0_24,plain,
negate(add(negate(add(a,b)),negate(add(a,negate(b))))) = a,
inference(subst,[],[robbins_axiom:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_25,plain,
( negate(add(a,negate(b))) != c
| negate(add(negate(add(a,b)),negate(add(a,negate(b))))) != a
| negate(add(negate(add(a,b)),c)) = a ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(a,b)),negate(add(a,negate(b))))),a) ),[0,0,1],$fot(c)]]) ).
cnf(refute_0_26,plain,
( negate(add(negate(add(a,b)),negate(add(a,negate(b))))) != a
| negate(add(negate(add(a,b)),c)) = a ),
inference(resolve,[$cnf( $equal(negate(add(a,negate(b))),c) )],[condition,refute_0_25]) ).
cnf(refute_0_27,plain,
negate(add(negate(add(a,b)),c)) = a,
inference(resolve,[$cnf( $equal(negate(add(negate(add(a,b)),negate(add(a,negate(b))))),a) )],[refute_0_24,refute_0_26]) ).
cnf(refute_0_28,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_29,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_30,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( add(X,Y) != add(Y,X)
| add(Y,X) = add(X,Y) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(add(X,Y))),bind(Y0,$fot(add(Y,X)))]]) ).
cnf(refute_0_32,plain,
add(Y,X) = add(X,Y),
inference(resolve,[$cnf( $equal(add(X,Y),add(Y,X)) )],[commutativity_of_add,refute_0_31]) ).
cnf(refute_0_33,plain,
add(negate(add(a,b)),c) = add(c,negate(add(a,b))),
inference(subst,[],[refute_0_32:[bind(X,$fot(c)),bind(Y,$fot(negate(add(a,b))))]]) ).
cnf(refute_0_34,plain,
negate(add(negate(add(a,b)),c)) = negate(add(negate(add(a,b)),c)),
introduced(tautology,[refl,[$fot(negate(add(negate(add(a,b)),c)))]]) ).
cnf(refute_0_35,plain,
( add(negate(add(a,b)),c) != add(c,negate(add(a,b)))
| negate(add(negate(add(a,b)),c)) != negate(add(negate(add(a,b)),c))
| negate(add(negate(add(a,b)),c)) = negate(add(c,negate(add(a,b)))) ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(a,b)),c)),negate(add(negate(add(a,b)),c))) ),[1,0],$fot(add(c,negate(add(a,b))))]]) ).
cnf(refute_0_36,plain,
( add(negate(add(a,b)),c) != add(c,negate(add(a,b)))
| negate(add(negate(add(a,b)),c)) = negate(add(c,negate(add(a,b)))) ),
inference(resolve,[$cnf( $equal(negate(add(negate(add(a,b)),c)),negate(add(negate(add(a,b)),c))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
negate(add(negate(add(a,b)),c)) = negate(add(c,negate(add(a,b)))),
inference(resolve,[$cnf( $equal(add(negate(add(a,b)),c),add(c,negate(add(a,b)))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
( negate(add(negate(add(a,b)),c)) != a
| negate(add(negate(add(a,b)),c)) != negate(add(c,negate(add(a,b))))
| negate(add(c,negate(add(a,b)))) = a ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(a,b)),c)),a) ),[0],$fot(negate(add(c,negate(add(a,b)))))]]) ).
cnf(refute_0_39,plain,
( negate(add(negate(add(a,b)),c)) != a
| negate(add(c,negate(add(a,b)))) = a ),
inference(resolve,[$cnf( $equal(negate(add(negate(add(a,b)),c)),negate(add(c,negate(add(a,b))))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
negate(add(c,negate(add(a,b)))) = a,
inference(resolve,[$cnf( $equal(negate(add(negate(add(a,b)),c)),a) )],[refute_0_27,refute_0_39]) ).
cnf(refute_0_41,plain,
( negate(add(c,negate(add(a,b)))) != a
| negate(add(negate(add(add(a,b),c)),negate(add(c,negate(add(a,b)))))) != c
| negate(add(negate(add(add(a,b),c)),a)) = c ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(add(a,b),c)),negate(add(c,negate(add(a,b)))))),c) ),[0,0,1],$fot(a)]]) ).
cnf(refute_0_42,plain,
( negate(add(negate(add(add(a,b),c)),negate(add(c,negate(add(a,b)))))) != c
| negate(add(negate(add(add(a,b),c)),a)) = c ),
inference(resolve,[$cnf( $equal(negate(add(c,negate(add(a,b)))),a) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
negate(add(negate(add(add(a,b),c)),a)) = c,
inference(resolve,[$cnf( $equal(negate(add(negate(add(add(a,b),c)),negate(add(c,negate(add(a,b)))))),c) )],[refute_0_23,refute_0_42]) ).
cnf(refute_0_44,plain,
add(add(a,b),c) = add(a,add(b,c)),
inference(subst,[],[associativity_of_add:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(c))]]) ).
cnf(refute_0_45,plain,
negate(add(add(a,b),c)) = negate(add(add(a,b),c)),
introduced(tautology,[refl,[$fot(negate(add(add(a,b),c)))]]) ).
cnf(refute_0_46,plain,
( add(add(a,b),c) != add(a,add(b,c))
| negate(add(add(a,b),c)) != negate(add(add(a,b),c))
| negate(add(add(a,b),c)) = negate(add(a,add(b,c))) ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(add(a,b),c)),negate(add(add(a,b),c))) ),[1,0],$fot(add(a,add(b,c)))]]) ).
cnf(refute_0_47,plain,
( add(add(a,b),c) != add(a,add(b,c))
| negate(add(add(a,b),c)) = negate(add(a,add(b,c))) ),
inference(resolve,[$cnf( $equal(negate(add(add(a,b),c)),negate(add(add(a,b),c))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
negate(add(add(a,b),c)) = negate(add(a,add(b,c))),
inference(resolve,[$cnf( $equal(add(add(a,b),c),add(a,add(b,c))) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
add(a,negate(add(add(a,b),c))) = add(a,negate(add(add(a,b),c))),
introduced(tautology,[refl,[$fot(add(a,negate(add(add(a,b),c))))]]) ).
cnf(refute_0_50,plain,
( add(a,negate(add(add(a,b),c))) != add(a,negate(add(add(a,b),c)))
| negate(add(add(a,b),c)) != negate(add(a,add(b,c)))
| add(a,negate(add(add(a,b),c))) = add(a,negate(add(a,add(b,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(add(a,negate(add(add(a,b),c))),add(a,negate(add(add(a,b),c)))) ),[1,1],$fot(negate(add(a,add(b,c))))]]) ).
cnf(refute_0_51,plain,
( negate(add(add(a,b),c)) != negate(add(a,add(b,c)))
| add(a,negate(add(add(a,b),c))) = add(a,negate(add(a,add(b,c)))) ),
inference(resolve,[$cnf( $equal(add(a,negate(add(add(a,b),c))),add(a,negate(add(add(a,b),c)))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
add(a,negate(add(add(a,b),c))) = add(a,negate(add(a,add(b,c)))),
inference(resolve,[$cnf( $equal(negate(add(add(a,b),c)),negate(add(a,add(b,c)))) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
add(negate(add(add(a,b),c)),a) = add(a,negate(add(add(a,b),c))),
inference(subst,[],[refute_0_32:[bind(X,$fot(a)),bind(Y,$fot(negate(add(add(a,b),c))))]]) ).
cnf(refute_0_54,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_55,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_30,refute_0_54]) ).
cnf(refute_0_56,plain,
( add(a,negate(add(add(a,b),c))) != add(a,negate(add(a,add(b,c))))
| add(negate(add(add(a,b),c)),a) != add(a,negate(add(add(a,b),c)))
| add(negate(add(add(a,b),c)),a) = add(a,negate(add(a,add(b,c)))) ),
inference(subst,[],[refute_0_55:[bind(X0,$fot(add(negate(add(add(a,b),c)),a))),bind(Y0,$fot(add(a,negate(add(add(a,b),c))))),bind(Z0,$fot(add(a,negate(add(a,add(b,c))))))]]) ).
cnf(refute_0_57,plain,
( add(a,negate(add(add(a,b),c))) != add(a,negate(add(a,add(b,c))))
| add(negate(add(add(a,b),c)),a) = add(a,negate(add(a,add(b,c)))) ),
inference(resolve,[$cnf( $equal(add(negate(add(add(a,b),c)),a),add(a,negate(add(add(a,b),c)))) )],[refute_0_53,refute_0_56]) ).
cnf(refute_0_58,plain,
add(negate(add(add(a,b),c)),a) = add(a,negate(add(a,add(b,c)))),
inference(resolve,[$cnf( $equal(add(a,negate(add(add(a,b),c))),add(a,negate(add(a,add(b,c))))) )],[refute_0_52,refute_0_57]) ).
cnf(refute_0_59,plain,
negate(add(negate(add(add(a,b),c)),a)) = negate(add(negate(add(add(a,b),c)),a)),
introduced(tautology,[refl,[$fot(negate(add(negate(add(add(a,b),c)),a)))]]) ).
cnf(refute_0_60,plain,
( add(negate(add(add(a,b),c)),a) != add(a,negate(add(a,add(b,c))))
| negate(add(negate(add(add(a,b),c)),a)) != negate(add(negate(add(add(a,b),c)),a))
| negate(add(negate(add(add(a,b),c)),a)) = negate(add(a,negate(add(a,add(b,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(add(a,b),c)),a)),negate(add(negate(add(add(a,b),c)),a))) ),[1,0],$fot(add(a,negate(add(a,add(b,c)))))]]) ).
cnf(refute_0_61,plain,
( add(negate(add(add(a,b),c)),a) != add(a,negate(add(a,add(b,c))))
| negate(add(negate(add(add(a,b),c)),a)) = negate(add(a,negate(add(a,add(b,c))))) ),
inference(resolve,[$cnf( $equal(negate(add(negate(add(add(a,b),c)),a)),negate(add(negate(add(add(a,b),c)),a))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
negate(add(negate(add(add(a,b),c)),a)) = negate(add(a,negate(add(a,add(b,c))))),
inference(resolve,[$cnf( $equal(add(negate(add(add(a,b),c)),a),add(a,negate(add(a,add(b,c))))) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
( negate(add(negate(add(add(a,b),c)),a)) != c
| negate(add(negate(add(add(a,b),c)),a)) != negate(add(a,negate(add(a,add(b,c)))))
| negate(add(a,negate(add(a,add(b,c))))) = c ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(add(a,b),c)),a)),c) ),[0],$fot(negate(add(a,negate(add(a,add(b,c))))))]]) ).
cnf(refute_0_64,plain,
( negate(add(negate(add(add(a,b),c)),a)) != c
| negate(add(a,negate(add(a,add(b,c))))) = c ),
inference(resolve,[$cnf( $equal(negate(add(negate(add(add(a,b),c)),a)),negate(add(a,negate(add(a,add(b,c)))))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
negate(add(a,negate(add(a,add(b,c))))) = c,
inference(resolve,[$cnf( $equal(negate(add(negate(add(add(a,b),c)),a)),c) )],[refute_0_43,refute_0_64]) ).
cnf(refute_0_66,plain,
add(add(X_11,X_12),X_13) = add(X_11,add(X_12,X_13)),
inference(subst,[],[associativity_of_add:[bind(X,$fot(X_11)),bind(Y,$fot(X_12)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_67,plain,
add(X_12,X_11) = add(X_11,X_12),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(X_12)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_68,plain,
( add(X_12,X_11) != add(X_11,X_12)
| add(X_11,X_12) = add(X_12,X_11) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(add(X_12,X_11))),bind(Y0,$fot(add(X_11,X_12)))]]) ).
cnf(refute_0_69,plain,
add(X_11,X_12) = add(X_12,X_11),
inference(resolve,[$cnf( $equal(add(X_12,X_11),add(X_11,X_12)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( add(X_11,X_12) != add(X_12,X_11)
| add(add(X_11,X_12),X_13) != add(X_11,add(X_12,X_13))
| add(add(X_12,X_11),X_13) = add(X_11,add(X_12,X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_11,X_12),X_13),add(X_11,add(X_12,X_13))) ),[0,0],$fot(add(X_12,X_11))]]) ).
cnf(refute_0_71,plain,
( add(add(X_11,X_12),X_13) != add(X_11,add(X_12,X_13))
| add(add(X_12,X_11),X_13) = add(X_11,add(X_12,X_13)) ),
inference(resolve,[$cnf( $equal(add(X_11,X_12),add(X_12,X_11)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
add(add(X_12,X_11),X_13) = add(X_11,add(X_12,X_13)),
inference(resolve,[$cnf( $equal(add(add(X_11,X_12),X_13),add(X_11,add(X_12,X_13))) )],[refute_0_66,refute_0_71]) ).
cnf(refute_0_73,plain,
add(add(X_12,X_11),X_13) = add(X_12,add(X_11,X_13)),
inference(subst,[],[associativity_of_add:[bind(X,$fot(X_12)),bind(Y,$fot(X_11)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_74,plain,
( add(add(X_12,X_11),X_13) != add(X_11,add(X_12,X_13))
| add(add(X_12,X_11),X_13) != add(X_12,add(X_11,X_13))
| add(X_12,add(X_11,X_13)) = add(X_11,add(X_12,X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_12,X_11),X_13),add(X_11,add(X_12,X_13))) ),[0],$fot(add(X_12,add(X_11,X_13)))]]) ).
cnf(refute_0_75,plain,
( add(add(X_12,X_11),X_13) != add(X_11,add(X_12,X_13))
| add(X_12,add(X_11,X_13)) = add(X_11,add(X_12,X_13)) ),
inference(resolve,[$cnf( $equal(add(add(X_12,X_11),X_13),add(X_12,add(X_11,X_13))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
add(X_12,add(X_11,X_13)) = add(X_11,add(X_12,X_13)),
inference(resolve,[$cnf( $equal(add(add(X_12,X_11),X_13),add(X_11,add(X_12,X_13))) )],[refute_0_72,refute_0_75]) ).
cnf(refute_0_77,plain,
( add(X_12,add(X_11,X_13)) != add(X_11,add(X_12,X_13))
| add(X_11,add(X_12,X_13)) = add(X_12,add(X_11,X_13)) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(add(X_12,add(X_11,X_13)))),bind(Y0,$fot(add(X_11,add(X_12,X_13))))]]) ).
cnf(refute_0_78,plain,
add(X_11,add(X_12,X_13)) = add(X_12,add(X_11,X_13)),
inference(resolve,[$cnf( $equal(add(X_12,add(X_11,X_13)),add(X_11,add(X_12,X_13))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
add(b,add(a,c)) = add(a,add(b,c)),
inference(subst,[],[refute_0_78:[bind(X_11,$fot(b)),bind(X_12,$fot(a)),bind(X_13,$fot(c))]]) ).
cnf(refute_0_80,plain,
negate(add(b,add(a,c))) = negate(add(b,add(a,c))),
introduced(tautology,[refl,[$fot(negate(add(b,add(a,c))))]]) ).
cnf(refute_0_81,plain,
( add(b,add(a,c)) != add(a,add(b,c))
| negate(add(b,add(a,c))) != negate(add(b,add(a,c)))
| negate(add(b,add(a,c))) = negate(add(a,add(b,c))) ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(b,add(a,c))),negate(add(b,add(a,c)))) ),[1,0],$fot(add(a,add(b,c)))]]) ).
cnf(refute_0_82,plain,
( add(b,add(a,c)) != add(a,add(b,c))
| negate(add(b,add(a,c))) = negate(add(a,add(b,c))) ),
inference(resolve,[$cnf( $equal(negate(add(b,add(a,c))),negate(add(b,add(a,c)))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
negate(add(b,add(a,c))) = negate(add(a,add(b,c))),
inference(resolve,[$cnf( $equal(add(b,add(a,c)),add(a,add(b,c))) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
add(a,negate(add(b,add(a,c)))) = add(a,negate(add(b,add(a,c)))),
introduced(tautology,[refl,[$fot(add(a,negate(add(b,add(a,c)))))]]) ).
cnf(refute_0_85,plain,
( add(a,negate(add(b,add(a,c)))) != add(a,negate(add(b,add(a,c))))
| negate(add(b,add(a,c))) != negate(add(a,add(b,c)))
| add(a,negate(add(b,add(a,c)))) = add(a,negate(add(a,add(b,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(add(a,negate(add(b,add(a,c)))),add(a,negate(add(b,add(a,c))))) ),[1,1],$fot(negate(add(a,add(b,c))))]]) ).
cnf(refute_0_86,plain,
( negate(add(b,add(a,c))) != negate(add(a,add(b,c)))
| add(a,negate(add(b,add(a,c)))) = add(a,negate(add(a,add(b,c)))) ),
inference(resolve,[$cnf( $equal(add(a,negate(add(b,add(a,c)))),add(a,negate(add(b,add(a,c))))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
add(a,negate(add(b,add(a,c)))) = add(a,negate(add(a,add(b,c)))),
inference(resolve,[$cnf( $equal(negate(add(b,add(a,c))),negate(add(a,add(b,c)))) )],[refute_0_83,refute_0_86]) ).
cnf(refute_0_88,plain,
negate(add(a,negate(add(b,add(a,c))))) = negate(add(a,negate(add(b,add(a,c))))),
introduced(tautology,[refl,[$fot(negate(add(a,negate(add(b,add(a,c))))))]]) ).
cnf(refute_0_89,plain,
( add(a,negate(add(b,add(a,c)))) != add(a,negate(add(a,add(b,c))))
| negate(add(a,negate(add(b,add(a,c))))) != negate(add(a,negate(add(b,add(a,c)))))
| negate(add(a,negate(add(b,add(a,c))))) = negate(add(a,negate(add(a,add(b,c))))) ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(a,negate(add(b,add(a,c))))),negate(add(a,negate(add(b,add(a,c)))))) ),[1,0],$fot(add(a,negate(add(a,add(b,c)))))]]) ).
cnf(refute_0_90,plain,
( add(a,negate(add(b,add(a,c)))) != add(a,negate(add(a,add(b,c))))
| negate(add(a,negate(add(b,add(a,c))))) = negate(add(a,negate(add(a,add(b,c))))) ),
inference(resolve,[$cnf( $equal(negate(add(a,negate(add(b,add(a,c))))),negate(add(a,negate(add(b,add(a,c)))))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
negate(add(a,negate(add(b,add(a,c))))) = negate(add(a,negate(add(a,add(b,c))))),
inference(resolve,[$cnf( $equal(add(a,negate(add(b,add(a,c)))),add(a,negate(add(a,add(b,c))))) )],[refute_0_87,refute_0_90]) ).
cnf(refute_0_92,plain,
( negate(add(a,negate(add(a,add(b,c))))) != c
| negate(add(a,negate(add(b,add(a,c))))) != negate(add(a,negate(add(a,add(b,c)))))
| negate(add(a,negate(add(b,add(a,c))))) = c ),
inference(subst,[],[refute_0_55:[bind(X0,$fot(negate(add(a,negate(add(b,add(a,c))))))),bind(Y0,$fot(negate(add(a,negate(add(a,add(b,c))))))),bind(Z0,$fot(c))]]) ).
cnf(refute_0_93,plain,
( negate(add(a,negate(add(a,add(b,c))))) != c
| negate(add(a,negate(add(b,add(a,c))))) = c ),
inference(resolve,[$cnf( $equal(negate(add(a,negate(add(b,add(a,c))))),negate(add(a,negate(add(a,add(b,c)))))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
negate(add(a,negate(add(b,add(a,c))))) = c,
inference(resolve,[$cnf( $equal(negate(add(a,negate(add(a,add(b,c))))),c) )],[refute_0_65,refute_0_93]) ).
cnf(refute_0_95,plain,
( c != c
| negate(add(a,negate(add(b,add(a,c))))) != c
| negate(add(a,negate(add(b,add(a,c))))) = c ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(a,negate(add(b,add(a,c))))),c) ),[0,0,1,0,1,1],$fot(c)]]) ).
cnf(refute_0_96,plain,
( c != c
| negate(add(a,negate(add(b,add(a,c))))) = c ),
inference(resolve,[$cnf( $equal(negate(add(a,negate(add(b,add(a,c))))),c) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
c != c,
inference(resolve,[$cnf( $equal(negate(add(a,negate(add(b,add(a,c))))),c) )],[refute_0_96,refute_0_19]) ).
cnf(refute_0_98,plain,
c = c,
introduced(tautology,[refl,[$fot(c)]]) ).
cnf(refute_0_99,plain,
$false,
inference(resolve,[$cnf( $equal(c,c) )],[refute_0_98,refute_0_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ROB011-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 9 16:19:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.77/1.00 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.77/1.00
% 0.77/1.00 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.86/1.01
%------------------------------------------------------------------------------