TSTP Solution File: ROB002-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ROB002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 20:54:30 EDT 2022
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 40 ( 23 unt; 0 nHn; 24 RR)
% Number of literals : 65 ( 64 equ; 27 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_of_add,axiom,
add(X,Y) = add(Y,X) ).
cnf(robbins_axiom,axiom,
negate(add(negate(add(X,Y)),negate(add(X,negate(Y))))) = X ).
cnf(double_negation,hypothesis,
negate(negate(X)) = X ).
cnf(prove_huntingtons_axiom,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b ).
cnf(refute_0_0,plain,
negate(negate(b)) = b,
inference(subst,[],[double_negation:[bind(X,$fot(b))]]) ).
cnf(refute_0_1,plain,
negate(negate(add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2)))))) = add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2)))),
inference(subst,[],[double_negation:[bind(X,$fot(add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2))))))]]) ).
cnf(refute_0_2,plain,
negate(add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2))))) = X_1,
inference(subst,[],[robbins_axiom:[bind(X,$fot(X_1)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_3,plain,
( negate(add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2))))) != X_1
| negate(negate(add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2)))))) != add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2))))
| negate(X_1) = add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2)))) ),
introduced(tautology,[equality,[$cnf( $equal(negate(negate(add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2)))))),add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2))))) ),[0,0],$fot(X_1)]]) ).
cnf(refute_0_4,plain,
( negate(negate(add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2)))))) != add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2))))
| negate(X_1) = add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2)))) ),
inference(resolve,[$cnf( $equal(negate(add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2))))),X_1) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
negate(X_1) = add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2)))),
inference(resolve,[$cnf( $equal(negate(negate(add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2)))))),add(negate(add(X_1,X_2)),negate(add(X_1,negate(X_2))))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
negate(X_5) = add(negate(add(X_5,X_6)),negate(add(X_5,negate(X_6)))),
inference(subst,[],[refute_0_5:[bind(X_1,$fot(X_5)),bind(X_2,$fot(X_6))]]) ).
cnf(refute_0_7,plain,
add(negate(X_6),X_5) = add(X_5,negate(X_6)),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(negate(X_6))),bind(Y,$fot(X_5))]]) ).
cnf(refute_0_8,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_9,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_10,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( add(negate(X_6),X_5) != add(X_5,negate(X_6))
| add(X_5,negate(X_6)) = add(negate(X_6),X_5) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(add(negate(X_6),X_5))),bind(Y0,$fot(add(X_5,negate(X_6))))]]) ).
cnf(refute_0_12,plain,
add(X_5,negate(X_6)) = add(negate(X_6),X_5),
inference(resolve,[$cnf( $equal(add(negate(X_6),X_5),add(X_5,negate(X_6))) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
( add(X_5,negate(X_6)) != add(negate(X_6),X_5)
| negate(X_5) != add(negate(add(X_5,X_6)),negate(add(X_5,negate(X_6))))
| negate(X_5) = add(negate(add(X_5,X_6)),negate(add(negate(X_6),X_5))) ),
introduced(tautology,[equality,[$cnf( $equal(negate(X_5),add(negate(add(X_5,X_6)),negate(add(X_5,negate(X_6))))) ),[1,1,0],$fot(add(negate(X_6),X_5))]]) ).
cnf(refute_0_14,plain,
( negate(X_5) != add(negate(add(X_5,X_6)),negate(add(X_5,negate(X_6))))
| negate(X_5) = add(negate(add(X_5,X_6)),negate(add(negate(X_6),X_5))) ),
inference(resolve,[$cnf( $equal(add(X_5,negate(X_6)),add(negate(X_6),X_5)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
negate(X_5) = add(negate(add(X_5,X_6)),negate(add(negate(X_6),X_5))),
inference(resolve,[$cnf( $equal(negate(X_5),add(negate(add(X_5,X_6)),negate(add(X_5,negate(X_6))))) )],[refute_0_6,refute_0_14]) ).
cnf(refute_0_16,plain,
negate(X_10) = add(negate(add(X_10,X_11)),negate(add(negate(X_11),X_10))),
inference(subst,[],[refute_0_15:[bind(X_5,$fot(X_10)),bind(X_6,$fot(X_11))]]) ).
cnf(refute_0_17,plain,
add(X_11,X_10) = add(X_10,X_11),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_18,plain,
( add(X_11,X_10) != add(X_10,X_11)
| add(X_10,X_11) = add(X_11,X_10) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(add(X_11,X_10))),bind(Y0,$fot(add(X_10,X_11)))]]) ).
cnf(refute_0_19,plain,
add(X_10,X_11) = add(X_11,X_10),
inference(resolve,[$cnf( $equal(add(X_11,X_10),add(X_10,X_11)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( add(X_10,X_11) != add(X_11,X_10)
| negate(X_10) != add(negate(add(X_10,X_11)),negate(add(negate(X_11),X_10)))
| negate(X_10) = add(negate(add(X_11,X_10)),negate(add(negate(X_11),X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(negate(X_10),add(negate(add(X_10,X_11)),negate(add(negate(X_11),X_10)))) ),[1,0,0],$fot(add(X_11,X_10))]]) ).
cnf(refute_0_21,plain,
( negate(X_10) != add(negate(add(X_10,X_11)),negate(add(negate(X_11),X_10)))
| negate(X_10) = add(negate(add(X_11,X_10)),negate(add(negate(X_11),X_10))) ),
inference(resolve,[$cnf( $equal(add(X_10,X_11),add(X_11,X_10)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
negate(X_10) = add(negate(add(X_11,X_10)),negate(add(negate(X_11),X_10))),
inference(resolve,[$cnf( $equal(negate(X_10),add(negate(add(X_10,X_11)),negate(add(negate(X_11),X_10)))) )],[refute_0_16,refute_0_21]) ).
cnf(refute_0_23,plain,
( negate(X_10) != add(negate(add(X_11,X_10)),negate(add(negate(X_11),X_10)))
| add(negate(add(X_11,X_10)),negate(add(negate(X_11),X_10))) = negate(X_10) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(negate(X_10))),bind(Y0,$fot(add(negate(add(X_11,X_10)),negate(add(negate(X_11),X_10)))))]]) ).
cnf(refute_0_24,plain,
add(negate(add(X_11,X_10)),negate(add(negate(X_11),X_10))) = negate(X_10),
inference(resolve,[$cnf( $equal(negate(X_10),add(negate(add(X_11,X_10)),negate(add(negate(X_11),X_10)))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = negate(negate(b)),
inference(subst,[],[refute_0_24:[bind(X_10,$fot(negate(b))),bind(X_11,$fot(a))]]) ).
cnf(refute_0_26,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_27,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_10,refute_0_26]) ).
cnf(refute_0_28,plain,
( add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != negate(negate(b))
| negate(negate(b)) != b
| add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b ),
inference(subst,[],[refute_0_27:[bind(X0,$fot(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))))),bind(Y0,$fot(negate(negate(b)))),bind(Z,$fot(b))]]) ).
cnf(refute_0_29,plain,
( negate(negate(b)) != b
| add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b ),
inference(resolve,[$cnf( $equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),negate(negate(b))) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b,
inference(resolve,[$cnf( $equal(negate(negate(b)),b) )],[refute_0_0,refute_0_29]) ).
cnf(refute_0_31,plain,
( add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b
| b != b
| add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b) ),[0],$fot(b)]]) ).
cnf(refute_0_32,plain,
( b != b
| add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b ),
inference(resolve,[$cnf( $equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
b != b,
inference(resolve,[$cnf( $equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b) )],[refute_0_32,prove_huntingtons_axiom]) ).
cnf(refute_0_34,plain,
b = b,
introduced(tautology,[refl,[$fot(b)]]) ).
cnf(refute_0_35,plain,
$false,
inference(resolve,[$cnf( $equal(b,b) )],[refute_0_34,refute_0_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ROB002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 9 16:06:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.39
%------------------------------------------------------------------------------