%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL031-1 : 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 : Fri Jul 15 00:36:15 EDT 2022
% Result : Unsatisfiable 0.14s 0.36s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 22 ( 14 unt; 0 nHn; 15 RR)
% Number of literals : 33 ( 32 equ; 16 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(l_definition,axiom,
apply(apply(l,X),Y) = apply(X,apply(Y,Y)) ).
cnf(o_definition,axiom,
apply(apply(o,X),Y) = apply(Y,apply(X,Y)) ).
cnf(prove_fixed_point,negated_conjecture,
apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))) ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( apply(apply(o,X),Y) != apply(Y,apply(X,Y))
| apply(Y,apply(X,Y)) = apply(apply(o,X),Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(apply(apply(o,X),Y))),bind(Y0,$fot(apply(Y,apply(X,Y))))]]) ).
cnf(refute_0_4,plain,
apply(Y,apply(X,Y)) = apply(apply(o,X),Y),
inference(resolve,[$cnf( $equal(apply(apply(o,X),Y),apply(Y,apply(X,Y))) )],[o_definition,refute_0_3]) ).
cnf(refute_0_5,plain,
apply(f(Y),apply(Y,f(Y))) = apply(apply(o,Y),f(Y)),
inference(subst,[],[refute_0_4:[bind(X,$fot(Y)),bind(Y,$fot(f(Y)))]]) ).
cnf(refute_0_6,plain,
( apply(Y,f(Y)) != apply(apply(o,Y),f(Y))
| apply(f(Y),apply(Y,f(Y))) != apply(apply(o,Y),f(Y))
| apply(Y,f(Y)) = apply(f(Y),apply(Y,f(Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(Y,f(Y)),apply(f(Y),apply(Y,f(Y)))) ),[1],$fot(apply(apply(o,Y),f(Y)))]]) ).
cnf(refute_0_7,plain,
( apply(Y,f(Y)) != apply(apply(o,Y),f(Y))
| apply(Y,f(Y)) = apply(f(Y),apply(Y,f(Y))) ),
inference(resolve,[$cnf( $equal(apply(f(Y),apply(Y,f(Y))),apply(apply(o,Y),f(Y))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
apply(Y,f(Y)) != apply(apply(o,Y),f(Y)),
inference(resolve,[$cnf( $equal(apply(Y,f(Y)),apply(f(Y),apply(Y,f(Y)))) )],[refute_0_7,prove_fixed_point]) ).
cnf(refute_0_9,plain,
apply(apply(X_2,X_2),f(apply(X_2,X_2))) != apply(apply(o,apply(X_2,X_2)),f(apply(X_2,X_2))),
inference(subst,[],[refute_0_8:[bind(Y,$fot(apply(X_2,X_2)))]]) ).
cnf(refute_0_10,plain,
apply(apply(l,o),X_2) = apply(o,apply(X_2,X_2)),
inference(subst,[],[l_definition:[bind(X,$fot(o)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_11,plain,
( apply(apply(l,o),X_2) != apply(o,apply(X_2,X_2))
| apply(o,apply(X_2,X_2)) = apply(apply(l,o),X_2) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(apply(apply(l,o),X_2))),bind(Y0,$fot(apply(o,apply(X_2,X_2))))]]) ).
cnf(refute_0_12,plain,
apply(o,apply(X_2,X_2)) = apply(apply(l,o),X_2),
inference(resolve,[$cnf( $equal(apply(apply(l,o),X_2),apply(o,apply(X_2,X_2))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( apply(apply(X_2,X_2),f(apply(X_2,X_2))) != apply(apply(apply(l,o),X_2),f(apply(X_2,X_2)))
| apply(o,apply(X_2,X_2)) != apply(apply(l,o),X_2)
| apply(apply(X_2,X_2),f(apply(X_2,X_2))) = apply(apply(o,apply(X_2,X_2)),f(apply(X_2,X_2))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(X_2,X_2),f(apply(X_2,X_2))),apply(apply(o,apply(X_2,X_2)),f(apply(X_2,X_2)))) ),[1,0],$fot(apply(apply(l,o),X_2))]]) ).
cnf(refute_0_14,plain,
( apply(apply(X_2,X_2),f(apply(X_2,X_2))) != apply(apply(apply(l,o),X_2),f(apply(X_2,X_2)))
| apply(apply(X_2,X_2),f(apply(X_2,X_2))) = apply(apply(o,apply(X_2,X_2)),f(apply(X_2,X_2))) ),
inference(resolve,[$cnf( $equal(apply(o,apply(X_2,X_2)),apply(apply(l,o),X_2)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
apply(apply(X_2,X_2),f(apply(X_2,X_2))) != apply(apply(apply(l,o),X_2),f(apply(X_2,X_2))),
inference(resolve,[$cnf( $equal(apply(apply(X_2,X_2),f(apply(X_2,X_2))),apply(apply(o,apply(X_2,X_2)),f(apply(X_2,X_2)))) )],[refute_0_14,refute_0_9]) ).
cnf(refute_0_16,plain,
apply(apply(apply(l,o),apply(l,o)),f(apply(apply(l,o),apply(l,o)))) != apply(apply(apply(l,o),apply(l,o)),f(apply(apply(l,o),apply(l,o)))),
inference(subst,[],[refute_0_15:[bind(X_2,$fot(apply(l,o)))]]) ).
cnf(refute_0_17,plain,
apply(apply(apply(l,o),apply(l,o)),f(apply(apply(l,o),apply(l,o)))) = apply(apply(apply(l,o),apply(l,o)),f(apply(apply(l,o),apply(l,o)))),
introduced(tautology,[refl,[$fot(apply(apply(apply(l,o),apply(l,o)),f(apply(apply(l,o),apply(l,o)))))]]) ).
cnf(refute_0_18,plain,
$false,
inference(resolve,[$cnf( $equal(apply(apply(apply(l,o),apply(l,o)),f(apply(apply(l,o),apply(l,o)))),apply(apply(apply(l,o),apply(l,o)),f(apply(apply(l,o),apply(l,o))))) )],[refute_0_17,refute_0_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COL031-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue May 31 11:16:07 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36
% 0.14/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.36
%------------------------------------------------------------------------------