TSTP Solution File: ROB010-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ROB010-1 : 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 20:54:33 EDT 2022
% Result : Unsatisfiable 0.12s 0.33s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of clauses : 38 ( 21 unt; 0 nHn; 34 RR)
% Number of literals : 63 ( 62 equ; 27 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 13 ( 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(condition,hypothesis,
negate(add(a,negate(b))) = c ).
cnf(prove_result,negated_conjecture,
negate(add(c,negate(add(b,a)))) != a ).
cnf(refute_0_0,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_1,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_2,plain,
( negate(add(negate(add(a,b)),negate(add(a,negate(b))))) != a
| negate(add(negate(add(a,b)),c)) = a ),
inference(resolve,[$cnf( $equal(negate(add(a,negate(b))),c) )],[condition,refute_0_1]) ).
cnf(refute_0_3,plain,
negate(add(negate(add(a,b)),c)) = a,
inference(resolve,[$cnf( $equal(negate(add(negate(add(a,b)),negate(add(a,negate(b))))),a) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
X0 = X0,
introduced(tautology,[refl,[$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( $equal(add(X,Y),add(Y,X)) )],[commutativity_of_add,refute_0_7]) ).
cnf(refute_0_9,plain,
add(negate(add(a,b)),c) = add(c,negate(add(a,b))),
inference(subst,[],[refute_0_8:[bind(X,$fot(c)),bind(Y,$fot(negate(add(a,b))))]]) ).
cnf(refute_0_10,plain,
negate(add(negate(add(a,b)),c)) = negate(add(negate(add(a,b)),c)),
introduced(tautology,[refl,[$fot(negate(add(negate(add(a,b)),c)))]]) ).
cnf(refute_0_11,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_12,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( $equal(negate(add(negate(add(a,b)),c)),negate(add(negate(add(a,b)),c))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
negate(add(negate(add(a,b)),c)) = negate(add(c,negate(add(a,b)))),
inference(resolve,[$cnf( $equal(add(negate(add(a,b)),c),add(c,negate(add(a,b)))) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
( negate(add(negate(add(a,b)),c)) != a
| negate(add(negate(add(a,b)),c)) != negate(add(c,negate(add(a,b))))
| negate(add(c,negate(add(a,b)))) = a ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(negate(add(a,b)),c)),a) ),[0],$fot(negate(add(c,negate(add(a,b)))))]]) ).
cnf(refute_0_15,plain,
( negate(add(negate(add(a,b)),c)) != a
| negate(add(c,negate(add(a,b)))) = a ),
inference(resolve,[$cnf( $equal(negate(add(negate(add(a,b)),c)),negate(add(c,negate(add(a,b))))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
negate(add(c,negate(add(a,b)))) = a,
inference(resolve,[$cnf( $equal(negate(add(negate(add(a,b)),c)),a) )],[refute_0_3,refute_0_15]) ).
cnf(refute_0_17,plain,
add(b,a) = add(a,b),
inference(subst,[],[refute_0_8:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_18,plain,
negate(add(b,a)) = negate(add(b,a)),
introduced(tautology,[refl,[$fot(negate(add(b,a)))]]) ).
cnf(refute_0_19,plain,
( add(b,a) != add(a,b)
| negate(add(b,a)) != negate(add(b,a))
| negate(add(b,a)) = negate(add(a,b)) ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(b,a)),negate(add(b,a))) ),[1,0],$fot(add(a,b))]]) ).
cnf(refute_0_20,plain,
( add(b,a) != add(a,b)
| negate(add(b,a)) = negate(add(a,b)) ),
inference(resolve,[$cnf( $equal(negate(add(b,a)),negate(add(b,a))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
negate(add(b,a)) = negate(add(a,b)),
inference(resolve,[$cnf( $equal(add(b,a),add(a,b)) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
add(c,negate(add(b,a))) = add(c,negate(add(b,a))),
introduced(tautology,[refl,[$fot(add(c,negate(add(b,a))))]]) ).
cnf(refute_0_23,plain,
( add(c,negate(add(b,a))) != add(c,negate(add(b,a)))
| negate(add(b,a)) != negate(add(a,b))
| add(c,negate(add(b,a))) = add(c,negate(add(a,b))) ),
introduced(tautology,[equality,[$cnf( $equal(add(c,negate(add(b,a))),add(c,negate(add(b,a)))) ),[1,1],$fot(negate(add(a,b)))]]) ).
cnf(refute_0_24,plain,
( negate(add(b,a)) != negate(add(a,b))
| add(c,negate(add(b,a))) = add(c,negate(add(a,b))) ),
inference(resolve,[$cnf( $equal(add(c,negate(add(b,a))),add(c,negate(add(b,a)))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
add(c,negate(add(b,a))) = add(c,negate(add(a,b))),
inference(resolve,[$cnf( $equal(negate(add(b,a)),negate(add(a,b))) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
negate(add(c,negate(add(b,a)))) = negate(add(c,negate(add(b,a)))),
introduced(tautology,[refl,[$fot(negate(add(c,negate(add(b,a)))))]]) ).
cnf(refute_0_27,plain,
( add(c,negate(add(b,a))) != add(c,negate(add(a,b)))
| negate(add(c,negate(add(b,a)))) != negate(add(c,negate(add(b,a))))
| negate(add(c,negate(add(b,a)))) = negate(add(c,negate(add(a,b)))) ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(c,negate(add(b,a)))),negate(add(c,negate(add(b,a))))) ),[1,0],$fot(add(c,negate(add(a,b))))]]) ).
cnf(refute_0_28,plain,
( add(c,negate(add(b,a))) != add(c,negate(add(a,b)))
| negate(add(c,negate(add(b,a)))) = negate(add(c,negate(add(a,b)))) ),
inference(resolve,[$cnf( $equal(negate(add(c,negate(add(b,a)))),negate(add(c,negate(add(b,a))))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
negate(add(c,negate(add(b,a)))) = negate(add(c,negate(add(a,b)))),
inference(resolve,[$cnf( $equal(add(c,negate(add(b,a))),add(c,negate(add(a,b)))) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
( negate(add(c,negate(add(a,b)))) != a
| negate(add(c,negate(add(b,a)))) != negate(add(c,negate(add(a,b))))
| negate(add(c,negate(add(b,a)))) = a ),
introduced(tautology,[equality,[$cnf( $equal(negate(add(c,negate(add(b,a)))),negate(add(c,negate(add(a,b))))) ),[1],$fot(a)]]) ).
cnf(refute_0_31,plain,
( negate(add(c,negate(add(a,b)))) != a
| negate(add(c,negate(add(b,a)))) = a ),
inference(resolve,[$cnf( $equal(negate(add(c,negate(add(b,a)))),negate(add(c,negate(add(a,b))))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
negate(add(c,negate(add(a,b)))) != a,
inference(resolve,[$cnf( $equal(negate(add(c,negate(add(b,a)))),a) )],[refute_0_31,prove_result]) ).
cnf(refute_0_33,plain,
$false,
inference(resolve,[$cnf( $equal(negate(add(c,negate(add(a,b)))),a) )],[refute_0_16,refute_0_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ROB010-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.11 % Command : metis --show proof --show saturation %s
% 0.12/0.32 % Computer : n028.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Thu Jun 9 15:23:32 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33
% 0.12/0.33 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.33
%------------------------------------------------------------------------------