TSTP Solution File: ROB003-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ROB003-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 20:54:31 EDT 2022
% Result : Unsatisfiable 0.19s 0.50s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 45
% Syntax : Number of clauses : 139 ( 73 unt; 0 nHn; 74 RR)
% Number of literals : 237 ( 236 equ; 100 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 156 ( 12 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(there_exists_a_constant,hypothesis,
add(X,c) = c ).
cnf(prove_huntingtons_axiom,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b ).
cnf(refute_0_0,plain,
add(X,negate(Y)) = add(negate(Y),X),
inference(subst,[],[commutativity_of_add:[bind(Y,$fot(negate(Y)))]]) ).
cnf(refute_0_1,plain,
( add(X,negate(Y)) != add(negate(Y),X)
| negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) != X
| negate(add(negate(add(X,Y)),negate(add(negate(Y),X)))) = X ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))),X) ),[0,0,1,0],$fot(add(negate(Y),X))]]) ).
cnf(refute_0_2,plain,
( negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) != X
| negate(add(negate(add(X,Y)),negate(add(negate(Y),X)))) = X ),
inference(resolve,[$cnf( $equal(add(X,negate(Y)),add(negate(Y),X)) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
negate(add(negate(add(X,Y)),negate(add(negate(Y),X)))) = X,
inference(resolve,[$cnf( $equal(negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))),X) )],[robbins_axiom,refute_0_2]) ).
cnf(refute_0_4,plain,
negate(add(negate(add(X_7,c)),negate(add(negate(c),X_7)))) = X_7,
inference(subst,[],[refute_0_3:[bind(X,$fot(X_7)),bind(Y,$fot(c))]]) ).
cnf(refute_0_5,plain,
add(X_7,c) = c,
inference(subst,[],[there_exists_a_constant:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_6,plain,
( add(X_7,c) != c
| negate(add(negate(add(X_7,c)),negate(add(negate(c),X_7)))) != X_7
| negate(add(negate(c),negate(add(negate(c),X_7)))) = X_7 ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(X_7,c)),negate(add(negate(c),X_7)))),X_7) ),[0,0,0,0],$fot(c)]]) ).
cnf(refute_0_7,plain,
( negate(add(negate(add(X_7,c)),negate(add(negate(c),X_7)))) != X_7
| negate(add(negate(c),negate(add(negate(c),X_7)))) = X_7 ),
inference(resolve,[$cnf( $equal(add(X_7,c),c) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
negate(add(negate(c),negate(add(negate(c),X_7)))) = X_7,
inference(resolve,[$cnf( $equal(negate(add(negate(add(X_7,c)),negate(add(negate(c),X_7)))),X_7) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,negate(add(negate(c),negate(c))))))) = X,
inference(subst,[],[robbins_axiom:[bind(Y,$fot(add(negate(c),negate(c))))]]) ).
cnf(refute_0_10,plain,
negate(add(negate(add(c,Y)),negate(add(c,negate(Y))))) = c,
inference(subst,[],[robbins_axiom:[bind(X,$fot(c))]]) ).
cnf(refute_0_11,plain,
add(X,c) = add(c,X),
inference(subst,[],[commutativity_of_add:[bind(Y,$fot(c))]]) ).
cnf(refute_0_12,plain,
( add(X,c) != add(c,X)
| add(X,c) != c
| add(c,X) = c ),
introduced(tautology,[equality,[$cnf( $equal(add(X,c),c) ),[0],$fot(add(c,X))]]) ).
cnf(refute_0_13,plain,
( add(X,c) != c
| add(c,X) = c ),
inference(resolve,[$cnf( $equal(add(X,c),add(c,X)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
add(c,X) = c,
inference(resolve,[$cnf( $equal(add(X,c),c) )],[there_exists_a_constant,refute_0_13]) ).
cnf(refute_0_15,plain,
add(c,negate(Y)) = c,
inference(subst,[],[refute_0_14:[bind(X,$fot(negate(Y)))]]) ).
cnf(refute_0_16,plain,
( add(c,negate(Y)) != c
| negate(add(negate(add(c,Y)),negate(add(c,negate(Y))))) != c
| negate(add(negate(add(c,Y)),negate(c))) = c ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(c,Y)),negate(add(c,negate(Y))))),c) ),[0,0,1,0],$fot(c)]]) ).
cnf(refute_0_17,plain,
( negate(add(negate(add(c,Y)),negate(add(c,negate(Y))))) != c
| negate(add(negate(add(c,Y)),negate(c))) = c ),
inference(resolve,[$cnf( $equal(add(c,negate(Y)),c) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
negate(add(negate(add(c,Y)),negate(c))) = c,
inference(resolve,[$cnf( $equal(negate(add(negate(add(c,Y)),negate(add(c,negate(Y))))),c) )],[refute_0_10,refute_0_17]) ).
cnf(refute_0_19,plain,
add(c,Y) = c,
inference(subst,[],[refute_0_14:[bind(X,$fot(Y))]]) ).
cnf(refute_0_20,plain,
negate(add(c,Y)) = negate(add(c,Y)),
introduced(tautology,[refl,[$fot(negate(add(c,Y)))]]) ).
cnf(refute_0_21,plain,
( add(c,Y) != c
| negate(add(c,Y)) != negate(add(c,Y))
| negate(add(c,Y)) = negate(c) ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(c,Y)),negate(add(c,Y))) ),[1,0],$fot(c)]]) ).
cnf(refute_0_22,plain,
( add(c,Y) != c
| negate(add(c,Y)) = negate(c) ),
inference(resolve,[$cnf( $equal(negate(add(c,Y)),negate(add(c,Y))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
negate(add(c,Y)) = negate(c),
inference(resolve,[$cnf( $equal(add(c,Y),c) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
add(negate(c),negate(add(c,Y))) = add(negate(c),negate(add(c,Y))),
introduced(tautology,[refl,[$fot(add(negate(c),negate(add(c,Y))))]]) ).
cnf(refute_0_25,plain,
( add(negate(c),negate(add(c,Y))) != add(negate(c),negate(add(c,Y)))
| negate(add(c,Y)) != negate(c)
| add(negate(c),negate(add(c,Y))) = add(negate(c),negate(c)) ),
introduced(tautology,[equality,[$cnf( $equal(add(negate(c),negate(add(c,Y))),add(negate(c),negate(add(c,Y)))) ),[1,1],$fot(negate(c))]]) ).
cnf(refute_0_26,plain,
( negate(add(c,Y)) != negate(c)
| add(negate(c),negate(add(c,Y))) = add(negate(c),negate(c)) ),
inference(resolve,[$cnf( $equal(add(negate(c),negate(add(c,Y))),add(negate(c),negate(add(c,Y)))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
add(negate(c),negate(add(c,Y))) = add(negate(c),negate(c)),
inference(resolve,[$cnf( $equal(negate(add(c,Y)),negate(c)) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
X0 = X0,
introduced(tautology,[refl,[$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( $equal(add(X,Y),add(Y,X)) )],[commutativity_of_add,refute_0_31]) ).
cnf(refute_0_33,plain,
add(negate(add(c,Y)),negate(c)) = add(negate(c),negate(add(c,Y))),
inference(subst,[],[refute_0_32:[bind(X,$fot(negate(c))),bind(Y,$fot(negate(add(c,Y))))]]) ).
cnf(refute_0_34,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_35,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_30,refute_0_34]) ).
cnf(refute_0_36,plain,
( add(negate(add(c,Y)),negate(c)) != add(negate(c),negate(add(c,Y)))
| add(negate(c),negate(add(c,Y))) != add(negate(c),negate(c))
| add(negate(add(c,Y)),negate(c)) = add(negate(c),negate(c)) ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(add(negate(add(c,Y)),negate(c)))),bind(Y0,$fot(add(negate(c),negate(add(c,Y))))),bind(Z0,$fot(add(negate(c),negate(c))))]]) ).
cnf(refute_0_37,plain,
( add(negate(c),negate(add(c,Y))) != add(negate(c),negate(c))
| add(negate(add(c,Y)),negate(c)) = add(negate(c),negate(c)) ),
inference(resolve,[$cnf( $equal(add(negate(add(c,Y)),negate(c)),add(negate(c),negate(add(c,Y)))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
add(negate(add(c,Y)),negate(c)) = add(negate(c),negate(c)),
inference(resolve,[$cnf( $equal(add(negate(c),negate(add(c,Y))),add(negate(c),negate(c))) )],[refute_0_27,refute_0_37]) ).
cnf(refute_0_39,plain,
negate(add(negate(add(c,Y)),negate(c))) = negate(add(negate(add(c,Y)),negate(c))),
introduced(tautology,[refl,[$fot(negate(add(negate(add(c,Y)),negate(c))))]]) ).
cnf(refute_0_40,plain,
( add(negate(add(c,Y)),negate(c)) != add(negate(c),negate(c))
| negate(add(negate(add(c,Y)),negate(c))) != negate(add(negate(add(c,Y)),negate(c)))
| negate(add(negate(add(c,Y)),negate(c))) = negate(add(negate(c),negate(c))) ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(c,Y)),negate(c))),negate(add(negate(add(c,Y)),negate(c)))) ),[1,0],$fot(add(negate(c),negate(c)))]]) ).
cnf(refute_0_41,plain,
( add(negate(add(c,Y)),negate(c)) != add(negate(c),negate(c))
| negate(add(negate(add(c,Y)),negate(c))) = negate(add(negate(c),negate(c))) ),
inference(resolve,[$cnf( $equal(negate(add(negate(add(c,Y)),negate(c))),negate(add(negate(add(c,Y)),negate(c)))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
negate(add(negate(add(c,Y)),negate(c))) = negate(add(negate(c),negate(c))),
inference(resolve,[$cnf( $equal(add(negate(add(c,Y)),negate(c)),add(negate(c),negate(c))) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
( negate(add(negate(add(c,Y)),negate(c))) != c
| negate(add(negate(add(c,Y)),negate(c))) != negate(add(negate(c),negate(c)))
| negate(add(negate(c),negate(c))) = c ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(c,Y)),negate(c))),c) ),[0],$fot(negate(add(negate(c),negate(c))))]]) ).
cnf(refute_0_44,plain,
( negate(add(negate(add(c,Y)),negate(c))) != c
| negate(add(negate(c),negate(c))) = c ),
inference(resolve,[$cnf( $equal(negate(add(negate(add(c,Y)),negate(c))),negate(add(negate(c),negate(c)))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
negate(add(negate(c),negate(c))) = c,
inference(resolve,[$cnf( $equal(negate(add(negate(add(c,Y)),negate(c))),c) )],[refute_0_18,refute_0_44]) ).
cnf(refute_0_46,plain,
( negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,negate(add(negate(c),negate(c))))))) != X
| negate(add(negate(c),negate(c))) != c
| negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c)))) = X ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,negate(add(negate(c),negate(c))))))),X) ),[0,0,1,0,1],$fot(c)]]) ).
cnf(refute_0_47,plain,
( negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,negate(add(negate(c),negate(c))))))) != X
| negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c)))) = X ),
inference(resolve,[$cnf( $equal(negate(add(negate(c),negate(c))),c) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c)))) = X,
inference(resolve,[$cnf( $equal(negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,negate(add(negate(c),negate(c))))))),X) )],[refute_0_9,refute_0_47]) ).
cnf(refute_0_49,plain,
negate(add(X,c)) = negate(add(X,c)),
introduced(tautology,[refl,[$fot(negate(add(X,c)))]]) ).
cnf(refute_0_50,plain,
( add(X,c) != c
| negate(add(X,c)) != negate(add(X,c))
| negate(add(X,c)) = negate(c) ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(X,c)),negate(add(X,c))) ),[1,0],$fot(c)]]) ).
cnf(refute_0_51,plain,
( add(X,c) != c
| negate(add(X,c)) = negate(c) ),
inference(resolve,[$cnf( $equal(negate(add(X,c)),negate(add(X,c))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
negate(add(X,c)) = negate(c),
inference(resolve,[$cnf( $equal(add(X,c),c) )],[there_exists_a_constant,refute_0_51]) ).
cnf(refute_0_53,plain,
add(negate(add(X,c)),negate(add(X,add(negate(c),negate(c))))) = add(negate(add(X,c)),negate(add(X,add(negate(c),negate(c))))),
introduced(tautology,[refl,[$fot(add(negate(add(X,c)),negate(add(X,add(negate(c),negate(c))))))]]) ).
cnf(refute_0_54,plain,
( add(negate(add(X,c)),negate(add(X,add(negate(c),negate(c))))) != add(negate(add(X,c)),negate(add(X,add(negate(c),negate(c)))))
| negate(add(X,c)) != negate(c)
| add(negate(add(X,c)),negate(add(X,add(negate(c),negate(c))))) = add(negate(c),negate(add(X,add(negate(c),negate(c))))) ),
introduced(tautology,[equality,[$cnf( $equal(add(negate(add(X,c)),negate(add(X,add(negate(c),negate(c))))),add(negate(add(X,c)),negate(add(X,add(negate(c),negate(c)))))) ),[1,0],$fot(negate(c))]]) ).
cnf(refute_0_55,plain,
( negate(add(X,c)) != negate(c)
| add(negate(add(X,c)),negate(add(X,add(negate(c),negate(c))))) = add(negate(c),negate(add(X,add(negate(c),negate(c))))) ),
inference(resolve,[$cnf( $equal(add(negate(add(X,c)),negate(add(X,add(negate(c),negate(c))))),add(negate(add(X,c)),negate(add(X,add(negate(c),negate(c)))))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
add(negate(add(X,c)),negate(add(X,add(negate(c),negate(c))))) = add(negate(c),negate(add(X,add(negate(c),negate(c))))),
inference(resolve,[$cnf( $equal(negate(add(X,c)),negate(c)) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c))) = add(negate(add(X,c)),negate(add(X,add(negate(c),negate(c))))),
inference(subst,[],[refute_0_32:[bind(X,$fot(negate(add(X,c)))),bind(Y,$fot(negate(add(X,add(negate(c),negate(c))))))]]) ).
cnf(refute_0_58,plain,
( add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c))) != add(negate(add(X,c)),negate(add(X,add(negate(c),negate(c)))))
| add(negate(add(X,c)),negate(add(X,add(negate(c),negate(c))))) != add(negate(c),negate(add(X,add(negate(c),negate(c)))))
| add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c))) = add(negate(c),negate(add(X,add(negate(c),negate(c))))) ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c))))),bind(Y0,$fot(add(negate(add(X,c)),negate(add(X,add(negate(c),negate(c))))))),bind(Z0,$fot(add(negate(c),negate(add(X,add(negate(c),negate(c)))))))]]) ).
cnf(refute_0_59,plain,
( add(negate(add(X,c)),negate(add(X,add(negate(c),negate(c))))) != add(negate(c),negate(add(X,add(negate(c),negate(c)))))
| add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c))) = add(negate(c),negate(add(X,add(negate(c),negate(c))))) ),
inference(resolve,[$cnf( $equal(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c))),add(negate(add(X,c)),negate(add(X,add(negate(c),negate(c)))))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c))) = add(negate(c),negate(add(X,add(negate(c),negate(c))))),
inference(resolve,[$cnf( $equal(add(negate(add(X,c)),negate(add(X,add(negate(c),negate(c))))),add(negate(c),negate(add(X,add(negate(c),negate(c)))))) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c)))) = negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c)))),
introduced(tautology,[refl,[$fot(negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c)))))]]) ).
cnf(refute_0_62,plain,
( add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c))) != add(negate(c),negate(add(X,add(negate(c),negate(c)))))
| negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c)))) != negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c))))
| negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c)))) = negate(add(negate(c),negate(add(X,add(negate(c),negate(c)))))) ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c)))),negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c))))) ),[1,0],$fot(add(negate(c),negate(add(X,add(negate(c),negate(c))))))]]) ).
cnf(refute_0_63,plain,
( add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c))) != add(negate(c),negate(add(X,add(negate(c),negate(c)))))
| negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c)))) = negate(add(negate(c),negate(add(X,add(negate(c),negate(c)))))) ),
inference(resolve,[$cnf( $equal(negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c)))),negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c))))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c)))) = negate(add(negate(c),negate(add(X,add(negate(c),negate(c)))))),
inference(resolve,[$cnf( $equal(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c))),add(negate(c),negate(add(X,add(negate(c),negate(c)))))) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
( negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c)))) != X
| negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c)))) != negate(add(negate(c),negate(add(X,add(negate(c),negate(c))))))
| negate(add(negate(c),negate(add(X,add(negate(c),negate(c)))))) = X ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c)))),X) ),[0],$fot(negate(add(negate(c),negate(add(X,add(negate(c),negate(c)))))))]]) ).
cnf(refute_0_66,plain,
( negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c)))) != X
| negate(add(negate(c),negate(add(X,add(negate(c),negate(c)))))) = X ),
inference(resolve,[$cnf( $equal(negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c)))),negate(add(negate(c),negate(add(X,add(negate(c),negate(c))))))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
negate(add(negate(c),negate(add(X,add(negate(c),negate(c)))))) = X,
inference(resolve,[$cnf( $equal(negate(add(negate(add(X,add(negate(c),negate(c)))),negate(add(X,c)))),X) )],[refute_0_48,refute_0_66]) ).
cnf(refute_0_68,plain,
negate(add(negate(c),negate(add(X_6,add(negate(c),negate(c)))))) = X_6,
inference(subst,[],[refute_0_67:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_69,plain,
add(add(negate(c),negate(c)),X_6) = add(X_6,add(negate(c),negate(c))),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(add(negate(c),negate(c)))),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_70,plain,
( add(add(negate(c),negate(c)),X_6) != add(X_6,add(negate(c),negate(c)))
| add(X_6,add(negate(c),negate(c))) = add(add(negate(c),negate(c)),X_6) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(add(add(negate(c),negate(c)),X_6))),bind(Y0,$fot(add(X_6,add(negate(c),negate(c)))))]]) ).
cnf(refute_0_71,plain,
add(X_6,add(negate(c),negate(c))) = add(add(negate(c),negate(c)),X_6),
inference(resolve,[$cnf( $equal(add(add(negate(c),negate(c)),X_6),add(X_6,add(negate(c),negate(c)))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( add(X_6,add(negate(c),negate(c))) != add(add(negate(c),negate(c)),X_6)
| negate(add(negate(c),negate(add(X_6,add(negate(c),negate(c)))))) != X_6
| negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))) = X_6 ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(c),negate(add(X_6,add(negate(c),negate(c)))))),X_6) ),[0,0,1,0],$fot(add(add(negate(c),negate(c)),X_6))]]) ).
cnf(refute_0_73,plain,
( negate(add(negate(c),negate(add(X_6,add(negate(c),negate(c)))))) != X_6
| negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))) = X_6 ),
inference(resolve,[$cnf( $equal(add(X_6,add(negate(c),negate(c))),add(add(negate(c),negate(c)),X_6)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))) = X_6,
inference(resolve,[$cnf( $equal(negate(add(negate(c),negate(add(X_6,add(negate(c),negate(c)))))),X_6) )],[refute_0_68,refute_0_73]) ).
cnf(refute_0_75,plain,
add(add(negate(c),negate(c)),X_6) = add(negate(c),add(negate(c),X_6)),
inference(subst,[],[associativity_of_add:[bind(X,$fot(negate(c))),bind(Y,$fot(negate(c))),bind(Z,$fot(X_6))]]) ).
cnf(refute_0_76,plain,
negate(add(add(negate(c),negate(c)),X_6)) = negate(add(add(negate(c),negate(c)),X_6)),
introduced(tautology,[refl,[$fot(negate(add(add(negate(c),negate(c)),X_6)))]]) ).
cnf(refute_0_77,plain,
( add(add(negate(c),negate(c)),X_6) != add(negate(c),add(negate(c),X_6))
| negate(add(add(negate(c),negate(c)),X_6)) != negate(add(add(negate(c),negate(c)),X_6))
| negate(add(add(negate(c),negate(c)),X_6)) = negate(add(negate(c),add(negate(c),X_6))) ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(add(negate(c),negate(c)),X_6)),negate(add(add(negate(c),negate(c)),X_6))) ),[1,0],$fot(add(negate(c),add(negate(c),X_6)))]]) ).
cnf(refute_0_78,plain,
( add(add(negate(c),negate(c)),X_6) != add(negate(c),add(negate(c),X_6))
| negate(add(add(negate(c),negate(c)),X_6)) = negate(add(negate(c),add(negate(c),X_6))) ),
inference(resolve,[$cnf( $equal(negate(add(add(negate(c),negate(c)),X_6)),negate(add(add(negate(c),negate(c)),X_6))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
negate(add(add(negate(c),negate(c)),X_6)) = negate(add(negate(c),add(negate(c),X_6))),
inference(resolve,[$cnf( $equal(add(add(negate(c),negate(c)),X_6),add(negate(c),add(negate(c),X_6))) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
add(negate(c),negate(add(add(negate(c),negate(c)),X_6))) = add(negate(c),negate(add(add(negate(c),negate(c)),X_6))),
introduced(tautology,[refl,[$fot(add(negate(c),negate(add(add(negate(c),negate(c)),X_6))))]]) ).
cnf(refute_0_81,plain,
( add(negate(c),negate(add(add(negate(c),negate(c)),X_6))) != add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))
| negate(add(add(negate(c),negate(c)),X_6)) != negate(add(negate(c),add(negate(c),X_6)))
| add(negate(c),negate(add(add(negate(c),negate(c)),X_6))) = add(negate(c),negate(add(negate(c),add(negate(c),X_6)))) ),
introduced(tautology,[equality,[$cnf( $equal(add(negate(c),negate(add(add(negate(c),negate(c)),X_6))),add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))) ),[1,1],$fot(negate(add(negate(c),add(negate(c),X_6))))]]) ).
cnf(refute_0_82,plain,
( negate(add(add(negate(c),negate(c)),X_6)) != negate(add(negate(c),add(negate(c),X_6)))
| add(negate(c),negate(add(add(negate(c),negate(c)),X_6))) = add(negate(c),negate(add(negate(c),add(negate(c),X_6)))) ),
inference(resolve,[$cnf( $equal(add(negate(c),negate(add(add(negate(c),negate(c)),X_6))),add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
add(negate(c),negate(add(add(negate(c),negate(c)),X_6))) = add(negate(c),negate(add(negate(c),add(negate(c),X_6)))),
inference(resolve,[$cnf( $equal(negate(add(add(negate(c),negate(c)),X_6)),negate(add(negate(c),add(negate(c),X_6)))) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))) = negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))),
introduced(tautology,[refl,[$fot(negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))))]]) ).
cnf(refute_0_85,plain,
( add(negate(c),negate(add(add(negate(c),negate(c)),X_6))) != add(negate(c),negate(add(negate(c),add(negate(c),X_6))))
| negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))) != negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6))))
| negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))) = negate(add(negate(c),negate(add(negate(c),add(negate(c),X_6))))) ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))),negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6))))) ),[1,0],$fot(add(negate(c),negate(add(negate(c),add(negate(c),X_6)))))]]) ).
cnf(refute_0_86,plain,
( add(negate(c),negate(add(add(negate(c),negate(c)),X_6))) != add(negate(c),negate(add(negate(c),add(negate(c),X_6))))
| negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))) = negate(add(negate(c),negate(add(negate(c),add(negate(c),X_6))))) ),
inference(resolve,[$cnf( $equal(negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))),negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6))))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))) = negate(add(negate(c),negate(add(negate(c),add(negate(c),X_6))))),
inference(resolve,[$cnf( $equal(add(negate(c),negate(add(add(negate(c),negate(c)),X_6))),add(negate(c),negate(add(negate(c),add(negate(c),X_6))))) )],[refute_0_83,refute_0_86]) ).
cnf(refute_0_88,plain,
( negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))) != X_6
| negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))) != negate(add(negate(c),negate(add(negate(c),add(negate(c),X_6)))))
| negate(add(negate(c),negate(add(negate(c),add(negate(c),X_6))))) = X_6 ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))),X_6) ),[0],$fot(negate(add(negate(c),negate(add(negate(c),add(negate(c),X_6))))))]]) ).
cnf(refute_0_89,plain,
( negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))) != X_6
| negate(add(negate(c),negate(add(negate(c),add(negate(c),X_6))))) = X_6 ),
inference(resolve,[$cnf( $equal(negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))),negate(add(negate(c),negate(add(negate(c),add(negate(c),X_6)))))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
negate(add(negate(c),negate(add(negate(c),add(negate(c),X_6))))) = X_6,
inference(resolve,[$cnf( $equal(negate(add(negate(c),negate(add(add(negate(c),negate(c)),X_6)))),X_6) )],[refute_0_74,refute_0_89]) ).
cnf(refute_0_91,plain,
negate(add(negate(c),negate(add(negate(c),add(negate(c),X_6))))) = add(negate(c),X_6),
inference(subst,[],[refute_0_8:[bind(X_7,$fot(add(negate(c),X_6)))]]) ).
cnf(refute_0_92,plain,
( negate(add(negate(c),negate(add(negate(c),add(negate(c),X_6))))) != X_6
| negate(add(negate(c),negate(add(negate(c),add(negate(c),X_6))))) != add(negate(c),X_6)
| add(negate(c),X_6) = X_6 ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(c),negate(add(negate(c),add(negate(c),X_6))))),X_6) ),[0],$fot(add(negate(c),X_6))]]) ).
cnf(refute_0_93,plain,
( negate(add(negate(c),negate(add(negate(c),add(negate(c),X_6))))) != X_6
| add(negate(c),X_6) = X_6 ),
inference(resolve,[$cnf( $equal(negate(add(negate(c),negate(add(negate(c),add(negate(c),X_6))))),add(negate(c),X_6)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
add(negate(c),X_6) = X_6,
inference(resolve,[$cnf( $equal(negate(add(negate(c),negate(add(negate(c),add(negate(c),X_6))))),X_6) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
add(negate(c),X_7) = X_7,
inference(subst,[],[refute_0_94:[bind(X_6,$fot(X_7))]]) ).
cnf(refute_0_96,plain,
negate(add(negate(c),X_7)) = negate(add(negate(c),X_7)),
introduced(tautology,[refl,[$fot(negate(add(negate(c),X_7)))]]) ).
cnf(refute_0_97,plain,
( add(negate(c),X_7) != X_7
| negate(add(negate(c),X_7)) != negate(add(negate(c),X_7))
| negate(add(negate(c),X_7)) = negate(X_7) ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(c),X_7)),negate(add(negate(c),X_7))) ),[1,0],$fot(X_7)]]) ).
cnf(refute_0_98,plain,
( add(negate(c),X_7) != X_7
| negate(add(negate(c),X_7)) = negate(X_7) ),
inference(resolve,[$cnf( $equal(negate(add(negate(c),X_7)),negate(add(negate(c),X_7))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
negate(add(negate(c),X_7)) = negate(X_7),
inference(resolve,[$cnf( $equal(add(negate(c),X_7),X_7) )],[refute_0_95,refute_0_98]) ).
cnf(refute_0_100,plain,
add(negate(c),negate(add(negate(c),X_7))) = negate(add(negate(c),X_7)),
inference(subst,[],[refute_0_94:[bind(X_6,$fot(negate(add(negate(c),X_7))))]]) ).
cnf(refute_0_101,plain,
( add(negate(c),negate(add(negate(c),X_7))) != negate(add(negate(c),X_7))
| negate(add(negate(c),X_7)) != negate(X_7)
| add(negate(c),negate(add(negate(c),X_7))) = negate(X_7) ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(add(negate(c),negate(add(negate(c),X_7))))),bind(Y0,$fot(negate(add(negate(c),X_7)))),bind(Z0,$fot(negate(X_7)))]]) ).
cnf(refute_0_102,plain,
( negate(add(negate(c),X_7)) != negate(X_7)
| add(negate(c),negate(add(negate(c),X_7))) = negate(X_7) ),
inference(resolve,[$cnf( $equal(add(negate(c),negate(add(negate(c),X_7))),negate(add(negate(c),X_7))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
add(negate(c),negate(add(negate(c),X_7))) = negate(X_7),
inference(resolve,[$cnf( $equal(negate(add(negate(c),X_7)),negate(X_7)) )],[refute_0_99,refute_0_102]) ).
cnf(refute_0_104,plain,
negate(add(negate(c),negate(add(negate(c),X_7)))) = negate(add(negate(c),negate(add(negate(c),X_7)))),
introduced(tautology,[refl,[$fot(negate(add(negate(c),negate(add(negate(c),X_7)))))]]) ).
cnf(refute_0_105,plain,
( add(negate(c),negate(add(negate(c),X_7))) != negate(X_7)
| negate(add(negate(c),negate(add(negate(c),X_7)))) != negate(add(negate(c),negate(add(negate(c),X_7))))
| negate(add(negate(c),negate(add(negate(c),X_7)))) = negate(negate(X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(c),negate(add(negate(c),X_7)))),negate(add(negate(c),negate(add(negate(c),X_7))))) ),[1,0],$fot(negate(X_7))]]) ).
cnf(refute_0_106,plain,
( add(negate(c),negate(add(negate(c),X_7))) != negate(X_7)
| negate(add(negate(c),negate(add(negate(c),X_7)))) = negate(negate(X_7)) ),
inference(resolve,[$cnf( $equal(negate(add(negate(c),negate(add(negate(c),X_7)))),negate(add(negate(c),negate(add(negate(c),X_7))))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
negate(add(negate(c),negate(add(negate(c),X_7)))) = negate(negate(X_7)),
inference(resolve,[$cnf( $equal(add(negate(c),negate(add(negate(c),X_7))),negate(X_7)) )],[refute_0_103,refute_0_106]) ).
cnf(refute_0_108,plain,
( negate(add(negate(c),negate(add(negate(c),X_7)))) != X_7
| negate(add(negate(c),negate(add(negate(c),X_7)))) != negate(negate(X_7))
| negate(negate(X_7)) = X_7 ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(c),negate(add(negate(c),X_7)))),X_7) ),[0],$fot(negate(negate(X_7)))]]) ).
cnf(refute_0_109,plain,
( negate(add(negate(c),negate(add(negate(c),X_7)))) != X_7
| negate(negate(X_7)) = X_7 ),
inference(resolve,[$cnf( $equal(negate(add(negate(c),negate(add(negate(c),X_7)))),negate(negate(X_7))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
negate(negate(X_7)) = X_7,
inference(resolve,[$cnf( $equal(negate(add(negate(c),negate(add(negate(c),X_7)))),X_7) )],[refute_0_8,refute_0_109]) ).
cnf(refute_0_111,plain,
negate(negate(b)) = b,
inference(subst,[],[refute_0_110:[bind(X_7,$fot(b))]]) ).
cnf(refute_0_112,plain,
negate(negate(add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7))))) = add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7))),
inference(subst,[],[refute_0_110:[bind(X_7,$fot(add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7)))))]]) ).
cnf(refute_0_113,plain,
negate(add(negate(add(X_7,X_8)),negate(add(negate(X_8),X_7)))) = X_7,
inference(subst,[],[refute_0_3:[bind(X,$fot(X_7)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_114,plain,
add(X_8,X_7) = add(X_7,X_8),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(X_8)),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_115,plain,
( add(X_8,X_7) != add(X_7,X_8)
| add(X_7,X_8) = add(X_8,X_7) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(add(X_8,X_7))),bind(Y0,$fot(add(X_7,X_8)))]]) ).
cnf(refute_0_116,plain,
add(X_7,X_8) = add(X_8,X_7),
inference(resolve,[$cnf( $equal(add(X_8,X_7),add(X_7,X_8)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
( add(X_7,X_8) != add(X_8,X_7)
| negate(add(negate(add(X_7,X_8)),negate(add(negate(X_8),X_7)))) != X_7
| negate(add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7)))) = X_7 ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(X_7,X_8)),negate(add(negate(X_8),X_7)))),X_7) ),[0,0,0,0],$fot(add(X_8,X_7))]]) ).
cnf(refute_0_118,plain,
( negate(add(negate(add(X_7,X_8)),negate(add(negate(X_8),X_7)))) != X_7
| negate(add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7)))) = X_7 ),
inference(resolve,[$cnf( $equal(add(X_7,X_8),add(X_8,X_7)) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
negate(add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7)))) = X_7,
inference(resolve,[$cnf( $equal(negate(add(negate(add(X_7,X_8)),negate(add(negate(X_8),X_7)))),X_7) )],[refute_0_113,refute_0_118]) ).
cnf(refute_0_120,plain,
( negate(add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7)))) != X_7
| negate(negate(add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7))))) != add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7)))
| negate(X_7) = add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7))) ),
introduced(tautology,[equality,[$cnf( $equal(negate(negate(add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7))))),add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7)))) ),[0,0],$fot(X_7)]]) ).
cnf(refute_0_121,plain,
( negate(negate(add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7))))) != add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7)))
| negate(X_7) = add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7))) ),
inference(resolve,[$cnf( $equal(negate(add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7)))),X_7) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
negate(X_7) = add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7))),
inference(resolve,[$cnf( $equal(negate(negate(add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7))))),add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7)))) )],[refute_0_112,refute_0_121]) ).
cnf(refute_0_123,plain,
( negate(X_7) != add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7)))
| add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7))) = negate(X_7) ),
inference(subst,[],[refute_0_30:[bind(X0,$fot(negate(X_7))),bind(Y0,$fot(add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7)))))]]) ).
cnf(refute_0_124,plain,
add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7))) = negate(X_7),
inference(resolve,[$cnf( $equal(negate(X_7),add(negate(add(X_8,X_7)),negate(add(negate(X_8),X_7)))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = negate(negate(b)),
inference(subst,[],[refute_0_124:[bind(X_7,$fot(negate(b))),bind(X_8,$fot(a))]]) ).
cnf(refute_0_126,plain,
( add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != negate(negate(b))
| negate(negate(b)) != b
| add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))))),bind(Y0,$fot(negate(negate(b)))),bind(Z0,$fot(b))]]) ).
cnf(refute_0_127,plain,
( negate(negate(b)) != b
| add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b ),
inference(resolve,[$cnf( $equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),negate(negate(b))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b,
inference(resolve,[$cnf( $equal(negate(negate(b)),b) )],[refute_0_111,refute_0_127]) ).
cnf(refute_0_129,plain,
( add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b
| b != b
| add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b) ),[0],$fot(b)]]) ).
cnf(refute_0_130,plain,
( b != b
| add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b ),
inference(resolve,[$cnf( $equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
b != b,
inference(resolve,[$cnf( $equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b) )],[refute_0_130,prove_huntingtons_axiom]) ).
cnf(refute_0_132,plain,
b = b,
introduced(tautology,[refl,[$fot(b)]]) ).
cnf(refute_0_133,plain,
$false,
inference(resolve,[$cnf( $equal(b,b) )],[refute_0_132,refute_0_131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ROB003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n019.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 : Thu Jun 9 13:17:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.50 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.50
% 0.19/0.50 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.52
%------------------------------------------------------------------------------