%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL053-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of clauses : 15 ( 11 unt; 0 nHn; 12 RR)
% Number of literals : 21 ( 20 equ; 12 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(composer_exists,axiom,
response(compose(X,Y),W) = response(X,response(Y,W)) ).
cnf(prove_bird_exists,negated_conjecture,
response(U,f(U)) != response(a,response(b,response(c,f(U)))) ).
cnf(refute_0_0,plain,
response(compose(X_2,X_3),f(compose(X_2,X_3))) != response(a,response(b,response(c,f(compose(X_2,X_3))))),
inference(subst,[],[prove_bird_exists:[bind(U,$fot(compose(X_2,X_3)))]]) ).
cnf(refute_0_1,plain,
response(compose(X_2,X_3),f(compose(X_2,X_3))) = response(X_2,response(X_3,f(compose(X_2,X_3)))),
inference(subst,[],[composer_exists:[bind(W,$fot(f(compose(X_2,X_3)))),bind(X,$fot(X_2)),bind(Y,$fot(X_3))]]) ).
cnf(refute_0_2,plain,
( response(X_2,response(X_3,f(compose(X_2,X_3)))) != response(a,response(b,response(c,f(compose(X_2,X_3)))))
| response(compose(X_2,X_3),f(compose(X_2,X_3))) != response(X_2,response(X_3,f(compose(X_2,X_3))))
| response(compose(X_2,X_3),f(compose(X_2,X_3))) = response(a,response(b,response(c,f(compose(X_2,X_3))))) ),
introduced(tautology,[equality,[$cnf( $equal(response(compose(X_2,X_3),f(compose(X_2,X_3))),response(X_2,response(X_3,f(compose(X_2,X_3))))) ),[1],$fot(response(a,response(b,response(c,f(compose(X_2,X_3))))))]]) ).
cnf(refute_0_3,plain,
( response(X_2,response(X_3,f(compose(X_2,X_3)))) != response(a,response(b,response(c,f(compose(X_2,X_3)))))
| response(compose(X_2,X_3),f(compose(X_2,X_3))) = response(a,response(b,response(c,f(compose(X_2,X_3))))) ),
inference(resolve,[$cnf( $equal(response(compose(X_2,X_3),f(compose(X_2,X_3))),response(X_2,response(X_3,f(compose(X_2,X_3))))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
response(X_2,response(X_3,f(compose(X_2,X_3)))) != response(a,response(b,response(c,f(compose(X_2,X_3))))),
inference(resolve,[$cnf( $equal(response(compose(X_2,X_3),f(compose(X_2,X_3))),response(a,response(b,response(c,f(compose(X_2,X_3)))))) )],[refute_0_3,refute_0_0]) ).
cnf(refute_0_5,plain,
response(X_4,response(compose(X,Y),f(compose(X_4,compose(X,Y))))) != response(a,response(b,response(c,f(compose(X_4,compose(X,Y)))))),
inference(subst,[],[refute_0_4:[bind(X_2,$fot(X_4)),bind(X_3,$fot(compose(X,Y)))]]) ).
cnf(refute_0_6,plain,
response(compose(X,Y),f(compose(X_4,compose(X,Y)))) = response(X,response(Y,f(compose(X_4,compose(X,Y))))),
inference(subst,[],[composer_exists:[bind(W,$fot(f(compose(X_4,compose(X,Y)))))]]) ).
cnf(refute_0_7,plain,
( response(X_4,response(X,response(Y,f(compose(X_4,compose(X,Y)))))) != response(a,response(b,response(c,f(compose(X_4,compose(X,Y))))))
| response(compose(X,Y),f(compose(X_4,compose(X,Y)))) != response(X,response(Y,f(compose(X_4,compose(X,Y)))))
| response(X_4,response(compose(X,Y),f(compose(X_4,compose(X,Y))))) = response(a,response(b,response(c,f(compose(X_4,compose(X,Y)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(response(X_4,response(compose(X,Y),f(compose(X_4,compose(X,Y))))),response(a,response(b,response(c,f(compose(X_4,compose(X,Y))))))) ),[0,1],$fot(response(X,response(Y,f(compose(X_4,compose(X,Y))))))]]) ).
cnf(refute_0_8,plain,
( response(X_4,response(X,response(Y,f(compose(X_4,compose(X,Y)))))) != response(a,response(b,response(c,f(compose(X_4,compose(X,Y))))))
| response(X_4,response(compose(X,Y),f(compose(X_4,compose(X,Y))))) = response(a,response(b,response(c,f(compose(X_4,compose(X,Y)))))) ),
inference(resolve,[$cnf( $equal(response(compose(X,Y),f(compose(X_4,compose(X,Y)))),response(X,response(Y,f(compose(X_4,compose(X,Y)))))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
response(X_4,response(X,response(Y,f(compose(X_4,compose(X,Y)))))) != response(a,response(b,response(c,f(compose(X_4,compose(X,Y)))))),
inference(resolve,[$cnf( $equal(response(X_4,response(compose(X,Y),f(compose(X_4,compose(X,Y))))),response(a,response(b,response(c,f(compose(X_4,compose(X,Y))))))) )],[refute_0_8,refute_0_5]) ).
cnf(refute_0_10,plain,
response(a,response(b,response(c,f(compose(a,compose(b,c)))))) != response(a,response(b,response(c,f(compose(a,compose(b,c)))))),
inference(subst,[],[refute_0_9:[bind(X,$fot(b)),bind(Y,$fot(c)),bind(X_4,$fot(a))]]) ).
cnf(refute_0_11,plain,
response(a,response(b,response(c,f(compose(a,compose(b,c)))))) = response(a,response(b,response(c,f(compose(a,compose(b,c)))))),
introduced(tautology,[refl,[$fot(response(a,response(b,response(c,f(compose(a,compose(b,c)))))))]]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( $equal(response(a,response(b,response(c,f(compose(a,compose(b,c)))))),response(a,response(b,response(c,f(compose(a,compose(b,c))))))) )],[refute_0_11,refute_0_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : COL053-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n021.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 04:30:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.34
%------------------------------------------------------------------------------