TSTP Solution File: ROB021-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ROB021-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 20:54:36 EDT 2022
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of clauses : 34 ( 18 unt; 0 nHn; 18 RR)
% Number of literals : 55 ( 54 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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 : 56 ( 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(negative_equality_implies_positive_equality,hypothesis,
( negate(X) != negate(Y)
| X = Y ) ).
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(add(negate(add(X_3,X_2)),negate(add(X_2,negate(X_3))))) != negate(X_10)
| add(negate(add(X_3,X_2)),negate(add(X_2,negate(X_3)))) = X_10 ),
inference(subst,[],[negative_equality_implies_positive_equality:[bind(X,$fot(add(negate(add(X_3,X_2)),negate(add(X_2,negate(X_3)))))),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_1,plain,
negate(add(negate(add(X_2,X_3)),negate(add(X_2,negate(X_3))))) = X_2,
inference(subst,[],[robbins_axiom:[bind(X,$fot(X_2)),bind(Y,$fot(X_3))]]) ).
cnf(refute_0_2,plain,
add(X_3,X_2) = add(X_2,X_3),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(X_3)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_3,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_4,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_5,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( add(X_3,X_2) != add(X_2,X_3)
| add(X_2,X_3) = add(X_3,X_2) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(add(X_3,X_2))),bind(Y0,$fot(add(X_2,X_3)))]]) ).
cnf(refute_0_7,plain,
add(X_2,X_3) = add(X_3,X_2),
inference(resolve,[$cnf( $equal(add(X_3,X_2),add(X_2,X_3)) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( add(X_2,X_3) != add(X_3,X_2)
| negate(add(negate(add(X_2,X_3)),negate(add(X_2,negate(X_3))))) != X_2
| negate(add(negate(add(X_3,X_2)),negate(add(X_2,negate(X_3))))) = X_2 ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(X_2,X_3)),negate(add(X_2,negate(X_3))))),X_2) ),[0,0,0,0],$fot(add(X_3,X_2))]]) ).
cnf(refute_0_9,plain,
( negate(add(negate(add(X_2,X_3)),negate(add(X_2,negate(X_3))))) != X_2
| negate(add(negate(add(X_3,X_2)),negate(add(X_2,negate(X_3))))) = X_2 ),
inference(resolve,[$cnf( $equal(add(X_2,X_3),add(X_3,X_2)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
negate(add(negate(add(X_3,X_2)),negate(add(X_2,negate(X_3))))) = X_2,
inference(resolve,[$cnf( $equal(negate(add(negate(add(X_2,X_3)),negate(add(X_2,negate(X_3))))),X_2) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
( X_2 != negate(X_10)
| negate(add(negate(add(X_3,X_2)),negate(add(X_2,negate(X_3))))) != X_2
| negate(add(negate(add(X_3,X_2)),negate(add(X_2,negate(X_3))))) = negate(X_10) ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(X_3,X_2)),negate(add(X_2,negate(X_3))))),X_2) ),[1],$fot(negate(X_10))]]) ).
cnf(refute_0_12,plain,
( X_2 != negate(X_10)
| negate(add(negate(add(X_3,X_2)),negate(add(X_2,negate(X_3))))) = negate(X_10) ),
inference(resolve,[$cnf( $equal(negate(add(negate(add(X_3,X_2)),negate(add(X_2,negate(X_3))))),X_2) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( X_2 != negate(X_10)
| add(negate(add(X_3,X_2)),negate(add(X_2,negate(X_3)))) = X_10 ),
inference(resolve,[$cnf( $equal(negate(add(negate(add(X_3,X_2)),negate(add(X_2,negate(X_3))))),negate(X_10)) )],[refute_0_12,refute_0_0]) ).
cnf(refute_0_14,plain,
( negate(X_10) != negate(X_10)
| add(negate(add(X_3,negate(X_10))),negate(add(negate(X_10),negate(X_3)))) = X_10 ),
inference(subst,[],[refute_0_13:[bind(X_2,$fot(negate(X_10)))]]) ).
cnf(refute_0_15,plain,
negate(X_10) = negate(X_10),
introduced(tautology,[refl,[$fot(negate(X_10))]]) ).
cnf(refute_0_16,plain,
add(negate(add(X_3,negate(X_10))),negate(add(negate(X_10),negate(X_3)))) = X_10,
inference(resolve,[$cnf( $equal(negate(X_10),negate(X_10)) )],[refute_0_15,refute_0_14]) ).
cnf(refute_0_17,plain,
add(negate(add(X_12,negate(X_11))),negate(add(negate(X_11),negate(X_12)))) = X_11,
inference(subst,[],[refute_0_16:[bind(X_10,$fot(X_11)),bind(X_3,$fot(X_12))]]) ).
cnf(refute_0_18,plain,
add(negate(X_12),negate(X_11)) = add(negate(X_11),negate(X_12)),
inference(subst,[],[commutativity_of_add:[bind(X,$fot(negate(X_12))),bind(Y,$fot(negate(X_11)))]]) ).
cnf(refute_0_19,plain,
( add(negate(X_12),negate(X_11)) != add(negate(X_11),negate(X_12))
| add(negate(X_11),negate(X_12)) = add(negate(X_12),negate(X_11)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(add(negate(X_12),negate(X_11)))),bind(Y0,$fot(add(negate(X_11),negate(X_12))))]]) ).
cnf(refute_0_20,plain,
add(negate(X_11),negate(X_12)) = add(negate(X_12),negate(X_11)),
inference(resolve,[$cnf( $equal(add(negate(X_12),negate(X_11)),add(negate(X_11),negate(X_12))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( add(negate(X_11),negate(X_12)) != add(negate(X_12),negate(X_11))
| add(negate(add(X_12,negate(X_11))),negate(add(negate(X_11),negate(X_12)))) != X_11
| add(negate(add(X_12,negate(X_11))),negate(add(negate(X_12),negate(X_11)))) = X_11 ),
introduced(tautology,[equality,[$cnf( $equal(add(negate(add(X_12,negate(X_11))),negate(add(negate(X_11),negate(X_12)))),X_11) ),[0,1,0],$fot(add(negate(X_12),negate(X_11)))]]) ).
cnf(refute_0_22,plain,
( add(negate(add(X_12,negate(X_11))),negate(add(negate(X_11),negate(X_12)))) != X_11
| add(negate(add(X_12,negate(X_11))),negate(add(negate(X_12),negate(X_11)))) = X_11 ),
inference(resolve,[$cnf( $equal(add(negate(X_11),negate(X_12)),add(negate(X_12),negate(X_11))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
add(negate(add(X_12,negate(X_11))),negate(add(negate(X_12),negate(X_11)))) = X_11,
inference(resolve,[$cnf( $equal(add(negate(add(X_12,negate(X_11))),negate(add(negate(X_11),negate(X_12)))),X_11) )],[refute_0_17,refute_0_22]) ).
cnf(refute_0_24,plain,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b,
inference(subst,[],[refute_0_23:[bind(X_11,$fot(b)),bind(X_12,$fot(a))]]) ).
cnf(refute_0_25,plain,
( add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b
| b != b
| add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b) ),[0],$fot(b)]]) ).
cnf(refute_0_26,plain,
( b != b
| add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) = b ),
inference(resolve,[$cnf( $equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
b != b,
inference(resolve,[$cnf( $equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b) )],[refute_0_26,prove_huntingtons_axiom]) ).
cnf(refute_0_28,plain,
b = b,
introduced(tautology,[refl,[$fot(b)]]) ).
cnf(refute_0_29,plain,
$false,
inference(resolve,[$cnf( $equal(b,b) )],[refute_0_28,refute_0_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ROB021-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n028.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 15:01:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.39
%------------------------------------------------------------------------------