TSTP Solution File: COL054-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL054-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 : Fri Jul 15 00:36:19 EDT 2022
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 29 ( 18 unt; 0 nHn; 19 RR)
% Number of literals : 44 ( 43 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 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 : 41 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(mocking_bird_exists,axiom,
response(mocking_bird,Y) = response(Y,Y) ).
cnf(composer_exists,hypothesis,
response(compose(X,Y),W) = response(X,response(Y,W)) ).
cnf(prove_birds_are_compatible,negated_conjecture,
( response(a,X) != Y
| response(b,Y) != X ) ).
cnf(refute_0_0,plain,
( response(a,X) != response(a,X)
| response(b,response(a,X)) != X ),
inference(subst,[],[prove_birds_are_compatible:[bind(Y,$fot(response(a,X)))]]) ).
cnf(refute_0_1,plain,
response(a,X) = response(a,X),
introduced(tautology,[refl,[$fot(response(a,X))]]) ).
cnf(refute_0_2,plain,
response(b,response(a,X)) != X,
inference(resolve,[$cnf( $equal(response(a,X),response(a,X)) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
response(b,response(a,response(X_6,compose(a,X_6)))) != response(X_6,compose(a,X_6)),
inference(subst,[],[refute_0_2:[bind(X,$fot(response(X_6,compose(a,X_6))))]]) ).
cnf(refute_0_4,plain,
response(mocking_bird,compose(X_3,X_4)) = response(compose(X_3,X_4),compose(X_3,X_4)),
inference(subst,[],[mocking_bird_exists:[bind(Y,$fot(compose(X_3,X_4)))]]) ).
cnf(refute_0_5,plain,
response(compose(X_3,X_4),compose(X_3,X_4)) = response(X_3,response(X_4,compose(X_3,X_4))),
inference(subst,[],[composer_exists:[bind(W,$fot(compose(X_3,X_4))),bind(X,$fot(X_3)),bind(Y,$fot(X_4))]]) ).
cnf(refute_0_6,plain,
( response(compose(X_3,X_4),compose(X_3,X_4)) != response(X_3,response(X_4,compose(X_3,X_4)))
| response(mocking_bird,compose(X_3,X_4)) != response(compose(X_3,X_4),compose(X_3,X_4))
| response(mocking_bird,compose(X_3,X_4)) = response(X_3,response(X_4,compose(X_3,X_4))) ),
introduced(tautology,[equality,[$cnf( $equal(response(mocking_bird,compose(X_3,X_4)),response(compose(X_3,X_4),compose(X_3,X_4))) ),[1],$fot(response(X_3,response(X_4,compose(X_3,X_4))))]]) ).
cnf(refute_0_7,plain,
( response(mocking_bird,compose(X_3,X_4)) != response(compose(X_3,X_4),compose(X_3,X_4))
| response(mocking_bird,compose(X_3,X_4)) = response(X_3,response(X_4,compose(X_3,X_4))) ),
inference(resolve,[$cnf( $equal(response(compose(X_3,X_4),compose(X_3,X_4)),response(X_3,response(X_4,compose(X_3,X_4)))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
response(mocking_bird,compose(X_3,X_4)) = response(X_3,response(X_4,compose(X_3,X_4))),
inference(resolve,[$cnf( $equal(response(mocking_bird,compose(X_3,X_4)),response(compose(X_3,X_4),compose(X_3,X_4))) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
response(mocking_bird,compose(a,X_6)) = response(a,response(X_6,compose(a,X_6))),
inference(subst,[],[refute_0_8:[bind(X_3,$fot(a)),bind(X_4,$fot(X_6))]]) ).
cnf(refute_0_10,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_11,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_12,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( response(mocking_bird,compose(a,X_6)) != response(a,response(X_6,compose(a,X_6)))
| response(a,response(X_6,compose(a,X_6))) = response(mocking_bird,compose(a,X_6)) ),
inference(subst,[],[refute_0_12:[bind(X0,$fot(response(mocking_bird,compose(a,X_6)))),bind(Y0,$fot(response(a,response(X_6,compose(a,X_6)))))]]) ).
cnf(refute_0_14,plain,
response(a,response(X_6,compose(a,X_6))) = response(mocking_bird,compose(a,X_6)),
inference(resolve,[$cnf( $equal(response(mocking_bird,compose(a,X_6)),response(a,response(X_6,compose(a,X_6)))) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
( response(a,response(X_6,compose(a,X_6))) != response(mocking_bird,compose(a,X_6))
| response(b,response(mocking_bird,compose(a,X_6))) != response(X_6,compose(a,X_6))
| response(b,response(a,response(X_6,compose(a,X_6)))) = response(X_6,compose(a,X_6)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(response(b,response(a,response(X_6,compose(a,X_6)))),response(X_6,compose(a,X_6))) ),[0,1],$fot(response(mocking_bird,compose(a,X_6)))]]) ).
cnf(refute_0_16,plain,
( response(b,response(mocking_bird,compose(a,X_6))) != response(X_6,compose(a,X_6))
| response(b,response(a,response(X_6,compose(a,X_6)))) = response(X_6,compose(a,X_6)) ),
inference(resolve,[$cnf( $equal(response(a,response(X_6,compose(a,X_6))),response(mocking_bird,compose(a,X_6))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
response(b,response(mocking_bird,compose(a,X_6))) != response(X_6,compose(a,X_6)),
inference(resolve,[$cnf( $equal(response(b,response(a,response(X_6,compose(a,X_6)))),response(X_6,compose(a,X_6))) )],[refute_0_16,refute_0_3]) ).
cnf(refute_0_18,plain,
response(b,response(mocking_bird,compose(a,compose(X,Y)))) != response(compose(X,Y),compose(a,compose(X,Y))),
inference(subst,[],[refute_0_17:[bind(X_6,$fot(compose(X,Y)))]]) ).
cnf(refute_0_19,plain,
response(compose(X,Y),compose(a,compose(X,Y))) = response(X,response(Y,compose(a,compose(X,Y)))),
inference(subst,[],[composer_exists:[bind(W,$fot(compose(a,compose(X,Y))))]]) ).
cnf(refute_0_20,plain,
( response(b,response(mocking_bird,compose(a,compose(X,Y)))) != response(X,response(Y,compose(a,compose(X,Y))))
| response(compose(X,Y),compose(a,compose(X,Y))) != response(X,response(Y,compose(a,compose(X,Y))))
| response(b,response(mocking_bird,compose(a,compose(X,Y)))) = response(compose(X,Y),compose(a,compose(X,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(response(b,response(mocking_bird,compose(a,compose(X,Y)))),response(compose(X,Y),compose(a,compose(X,Y)))) ),[1],$fot(response(X,response(Y,compose(a,compose(X,Y)))))]]) ).
cnf(refute_0_21,plain,
( response(b,response(mocking_bird,compose(a,compose(X,Y)))) != response(X,response(Y,compose(a,compose(X,Y))))
| response(b,response(mocking_bird,compose(a,compose(X,Y)))) = response(compose(X,Y),compose(a,compose(X,Y))) ),
inference(resolve,[$cnf( $equal(response(compose(X,Y),compose(a,compose(X,Y))),response(X,response(Y,compose(a,compose(X,Y))))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
response(b,response(mocking_bird,compose(a,compose(X,Y)))) != response(X,response(Y,compose(a,compose(X,Y)))),
inference(resolve,[$cnf( $equal(response(b,response(mocking_bird,compose(a,compose(X,Y)))),response(compose(X,Y),compose(a,compose(X,Y)))) )],[refute_0_21,refute_0_18]) ).
cnf(refute_0_23,plain,
response(b,response(mocking_bird,compose(a,compose(b,mocking_bird)))) != response(b,response(mocking_bird,compose(a,compose(b,mocking_bird)))),
inference(subst,[],[refute_0_22:[bind(X,$fot(b)),bind(Y,$fot(mocking_bird))]]) ).
cnf(refute_0_24,plain,
response(b,response(mocking_bird,compose(a,compose(b,mocking_bird)))) = response(b,response(mocking_bird,compose(a,compose(b,mocking_bird)))),
introduced(tautology,[refl,[$fot(response(b,response(mocking_bird,compose(a,compose(b,mocking_bird)))))]]) ).
cnf(refute_0_25,plain,
$false,
inference(resolve,[$cnf( $equal(response(b,response(mocking_bird,compose(a,compose(b,mocking_bird)))),response(b,response(mocking_bird,compose(a,compose(b,mocking_bird))))) )],[refute_0_24,refute_0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL054-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n020.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 : Tue May 31 11:43:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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
%------------------------------------------------------------------------------