%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL015-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 00:36:13 EDT 2022
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 21 ( 14 unt; 0 nHn; 13 RR)
% Number of literals : 31 ( 30 equ; 14 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; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(m_definition,axiom,
apply(m,X) = apply(X,X) ).
cnf(q_definition,axiom,
apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) ).
cnf(prove_fixed_point,negated_conjecture,
Y != apply(combinator,Y) ).
cnf(refute_0_0,plain,
apply(X_11,apply(apply(q,X_11),combinator)) != apply(combinator,apply(X_11,apply(apply(q,X_11),combinator))),
inference(subst,[],[prove_fixed_point:[bind(Y,$fot(apply(X_11,apply(apply(q,X_11),combinator))))]]) ).
cnf(refute_0_1,plain,
apply(m,apply(apply(q,X_2),X_3)) = apply(apply(apply(q,X_2),X_3),apply(apply(q,X_2),X_3)),
inference(subst,[],[m_definition:[bind(X,$fot(apply(apply(q,X_2),X_3)))]]) ).
cnf(refute_0_2,plain,
apply(apply(apply(q,X_2),X_3),apply(apply(q,X_2),X_3)) = apply(X_3,apply(X_2,apply(apply(q,X_2),X_3))),
inference(subst,[],[q_definition:[bind(X,$fot(X_2)),bind(Y,$fot(X_3)),bind(Z,$fot(apply(apply(q,X_2),X_3)))]]) ).
cnf(refute_0_3,plain,
( apply(apply(apply(q,X_2),X_3),apply(apply(q,X_2),X_3)) != apply(X_3,apply(X_2,apply(apply(q,X_2),X_3)))
| apply(m,apply(apply(q,X_2),X_3)) != apply(apply(apply(q,X_2),X_3),apply(apply(q,X_2),X_3))
| apply(m,apply(apply(q,X_2),X_3)) = apply(X_3,apply(X_2,apply(apply(q,X_2),X_3))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(m,apply(apply(q,X_2),X_3)),apply(apply(apply(q,X_2),X_3),apply(apply(q,X_2),X_3))) ),[1],$fot(apply(X_3,apply(X_2,apply(apply(q,X_2),X_3))))]]) ).
cnf(refute_0_4,plain,
( apply(m,apply(apply(q,X_2),X_3)) != apply(apply(apply(q,X_2),X_3),apply(apply(q,X_2),X_3))
| apply(m,apply(apply(q,X_2),X_3)) = apply(X_3,apply(X_2,apply(apply(q,X_2),X_3))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(q,X_2),X_3),apply(apply(q,X_2),X_3)),apply(X_3,apply(X_2,apply(apply(q,X_2),X_3)))) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
apply(m,apply(apply(q,X_2),X_3)) = apply(X_3,apply(X_2,apply(apply(q,X_2),X_3))),
inference(resolve,[$cnf( $equal(apply(m,apply(apply(q,X_2),X_3)),apply(apply(apply(q,X_2),X_3),apply(apply(q,X_2),X_3))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
apply(m,apply(apply(q,X_11),combinator)) = apply(combinator,apply(X_11,apply(apply(q,X_11),combinator))),
inference(subst,[],[refute_0_5:[bind(X_2,$fot(X_11)),bind(X_3,$fot(combinator))]]) ).
cnf(refute_0_7,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_8,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_9,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( apply(m,apply(apply(q,X_11),combinator)) != apply(combinator,apply(X_11,apply(apply(q,X_11),combinator)))
| apply(combinator,apply(X_11,apply(apply(q,X_11),combinator))) = apply(m,apply(apply(q,X_11),combinator)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(apply(m,apply(apply(q,X_11),combinator)))),bind(Y0,$fot(apply(combinator,apply(X_11,apply(apply(q,X_11),combinator)))))]]) ).
cnf(refute_0_11,plain,
apply(combinator,apply(X_11,apply(apply(q,X_11),combinator))) = apply(m,apply(apply(q,X_11),combinator)),
inference(resolve,[$cnf( $equal(apply(m,apply(apply(q,X_11),combinator)),apply(combinator,apply(X_11,apply(apply(q,X_11),combinator)))) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
( apply(X_11,apply(apply(q,X_11),combinator)) != apply(m,apply(apply(q,X_11),combinator))
| apply(combinator,apply(X_11,apply(apply(q,X_11),combinator))) != apply(m,apply(apply(q,X_11),combinator))
| apply(X_11,apply(apply(q,X_11),combinator)) = apply(combinator,apply(X_11,apply(apply(q,X_11),combinator))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(X_11,apply(apply(q,X_11),combinator)),apply(combinator,apply(X_11,apply(apply(q,X_11),combinator)))) ),[1],$fot(apply(m,apply(apply(q,X_11),combinator)))]]) ).
cnf(refute_0_13,plain,
( apply(X_11,apply(apply(q,X_11),combinator)) != apply(m,apply(apply(q,X_11),combinator))
| apply(X_11,apply(apply(q,X_11),combinator)) = apply(combinator,apply(X_11,apply(apply(q,X_11),combinator))) ),
inference(resolve,[$cnf( $equal(apply(combinator,apply(X_11,apply(apply(q,X_11),combinator))),apply(m,apply(apply(q,X_11),combinator))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
apply(X_11,apply(apply(q,X_11),combinator)) != apply(m,apply(apply(q,X_11),combinator)),
inference(resolve,[$cnf( $equal(apply(X_11,apply(apply(q,X_11),combinator)),apply(combinator,apply(X_11,apply(apply(q,X_11),combinator)))) )],[refute_0_13,refute_0_0]) ).
cnf(refute_0_15,plain,
apply(m,apply(apply(q,m),combinator)) != apply(m,apply(apply(q,m),combinator)),
inference(subst,[],[refute_0_14:[bind(X_11,$fot(m))]]) ).
cnf(refute_0_16,plain,
apply(m,apply(apply(q,m),combinator)) = apply(m,apply(apply(q,m),combinator)),
introduced(tautology,[refl,[$fot(apply(m,apply(apply(q,m),combinator)))]]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( $equal(apply(m,apply(apply(q,m),combinator)),apply(m,apply(apply(q,m),combinator))) )],[refute_0_16,refute_0_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL015-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue May 31 04:12:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.40 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.40
%------------------------------------------------------------------------------