TSTP Solution File: COL075-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL075-2 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 00:36:26 EDT 2022
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 33 ( 20 unt; 0 nHn; 19 RR)
% Number of literals : 52 ( 51 equ; 22 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; 2 con; 0-2 aty)
% Number of variables : 52 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(k_definition,axiom,
apply(apply(k,X),Y) = X ).
cnf(abstraction,axiom,
apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,apply(k,Z)),apply(Y,Z)) ).
cnf(prove_diagonal_combinator,negated_conjecture,
apply(apply(Y,b(Y)),c(Y)) != apply(b(Y),b(Y)) ).
cnf(refute_0_0,plain,
apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(abstraction,abstraction),k))),c(apply(apply(abstraction,abstraction),k))) != apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))),
inference(subst,[],[prove_diagonal_combinator:[bind(Y,$fot(apply(apply(abstraction,abstraction),k)))]]) ).
cnf(refute_0_1,plain,
apply(apply(apply(abstraction,X_5),apply(k,X)),X_7) = apply(apply(X_5,apply(k,X_7)),apply(apply(k,X),X_7)),
inference(subst,[],[abstraction:[bind(X,$fot(X_5)),bind(Y,$fot(apply(k,X))),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_2,plain,
apply(apply(k,X),X_7) = X,
inference(subst,[],[k_definition:[bind(Y,$fot(X_7))]]) ).
cnf(refute_0_3,plain,
( apply(apply(apply(abstraction,X_5),apply(k,X)),X_7) != apply(apply(X_5,apply(k,X_7)),apply(apply(k,X),X_7))
| apply(apply(k,X),X_7) != X
| apply(apply(apply(abstraction,X_5),apply(k,X)),X_7) = apply(apply(X_5,apply(k,X_7)),X) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(abstraction,X_5),apply(k,X)),X_7),apply(apply(X_5,apply(k,X_7)),apply(apply(k,X),X_7))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_4,plain,
( apply(apply(apply(abstraction,X_5),apply(k,X)),X_7) != apply(apply(X_5,apply(k,X_7)),apply(apply(k,X),X_7))
| apply(apply(apply(abstraction,X_5),apply(k,X)),X_7) = apply(apply(X_5,apply(k,X_7)),X) ),
inference(resolve,[$cnf( $equal(apply(apply(k,X),X_7),X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
apply(apply(apply(abstraction,X_5),apply(k,X)),X_7) = apply(apply(X_5,apply(k,X_7)),X),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,X_5),apply(k,X)),X_7),apply(apply(X_5,apply(k,X_7)),apply(apply(k,X),X_7))) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
apply(apply(apply(abstraction,apply(k,X_10)),apply(k,X_10)),X_12) = apply(apply(apply(k,X_10),apply(k,X_12)),X_10),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_10)),bind(X_5,$fot(apply(k,X_10))),bind(X_7,$fot(X_12))]]) ).
cnf(refute_0_7,plain,
apply(apply(apply(abstraction,abstraction),k),X_10) = apply(apply(abstraction,apply(k,X_10)),apply(k,X_10)),
inference(subst,[],[abstraction:[bind(X,$fot(abstraction)),bind(Y,$fot(k)),bind(Z,$fot(X_10))]]) ).
cnf(refute_0_8,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_9,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_10,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( apply(apply(apply(abstraction,abstraction),k),X_10) != apply(apply(abstraction,apply(k,X_10)),apply(k,X_10))
| apply(apply(abstraction,apply(k,X_10)),apply(k,X_10)) = apply(apply(apply(abstraction,abstraction),k),X_10) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(apply(apply(apply(abstraction,abstraction),k),X_10))),bind(Y0,$fot(apply(apply(abstraction,apply(k,X_10)),apply(k,X_10))))]]) ).
cnf(refute_0_12,plain,
apply(apply(abstraction,apply(k,X_10)),apply(k,X_10)) = apply(apply(apply(abstraction,abstraction),k),X_10),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,abstraction),k),X_10),apply(apply(abstraction,apply(k,X_10)),apply(k,X_10))) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
( apply(apply(apply(abstraction,apply(k,X_10)),apply(k,X_10)),X_12) != apply(apply(apply(k,X_10),apply(k,X_12)),X_10)
| apply(apply(abstraction,apply(k,X_10)),apply(k,X_10)) != apply(apply(apply(abstraction,abstraction),k),X_10)
| apply(apply(apply(apply(abstraction,abstraction),k),X_10),X_12) = apply(apply(apply(k,X_10),apply(k,X_12)),X_10) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(abstraction,apply(k,X_10)),apply(k,X_10)),X_12),apply(apply(apply(k,X_10),apply(k,X_12)),X_10)) ),[0,0],$fot(apply(apply(apply(abstraction,abstraction),k),X_10))]]) ).
cnf(refute_0_14,plain,
( apply(apply(apply(abstraction,apply(k,X_10)),apply(k,X_10)),X_12) != apply(apply(apply(k,X_10),apply(k,X_12)),X_10)
| apply(apply(apply(apply(abstraction,abstraction),k),X_10),X_12) = apply(apply(apply(k,X_10),apply(k,X_12)),X_10) ),
inference(resolve,[$cnf( $equal(apply(apply(abstraction,apply(k,X_10)),apply(k,X_10)),apply(apply(apply(abstraction,abstraction),k),X_10)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
apply(apply(apply(apply(abstraction,abstraction),k),X_10),X_12) = apply(apply(apply(k,X_10),apply(k,X_12)),X_10),
inference(resolve,[$cnf( $equal(apply(apply(apply(abstraction,apply(k,X_10)),apply(k,X_10)),X_12),apply(apply(apply(k,X_10),apply(k,X_12)),X_10)) )],[refute_0_6,refute_0_14]) ).
cnf(refute_0_16,plain,
apply(apply(k,X_10),apply(k,X_12)) = X_10,
inference(subst,[],[k_definition:[bind(X,$fot(X_10)),bind(Y,$fot(apply(k,X_12)))]]) ).
cnf(refute_0_17,plain,
apply(apply(apply(k,X_10),apply(k,X_12)),X_10) = apply(apply(apply(k,X_10),apply(k,X_12)),X_10),
introduced(tautology,[refl,[$fot(apply(apply(apply(k,X_10),apply(k,X_12)),X_10))]]) ).
cnf(refute_0_18,plain,
( apply(apply(apply(k,X_10),apply(k,X_12)),X_10) != apply(apply(apply(k,X_10),apply(k,X_12)),X_10)
| apply(apply(k,X_10),apply(k,X_12)) != X_10
| apply(apply(apply(k,X_10),apply(k,X_12)),X_10) = apply(X_10,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(k,X_10),apply(k,X_12)),X_10),apply(apply(apply(k,X_10),apply(k,X_12)),X_10)) ),[1,0],$fot(X_10)]]) ).
cnf(refute_0_19,plain,
( apply(apply(k,X_10),apply(k,X_12)) != X_10
| apply(apply(apply(k,X_10),apply(k,X_12)),X_10) = apply(X_10,X_10) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(k,X_10),apply(k,X_12)),X_10),apply(apply(apply(k,X_10),apply(k,X_12)),X_10)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
apply(apply(apply(k,X_10),apply(k,X_12)),X_10) = apply(X_10,X_10),
inference(resolve,[$cnf( $equal(apply(apply(k,X_10),apply(k,X_12)),X_10) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
( apply(apply(apply(apply(abstraction,abstraction),k),X_10),X_12) != apply(apply(apply(k,X_10),apply(k,X_12)),X_10)
| apply(apply(apply(k,X_10),apply(k,X_12)),X_10) != apply(X_10,X_10)
| apply(apply(apply(apply(abstraction,abstraction),k),X_10),X_12) = apply(X_10,X_10) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(abstraction,abstraction),k),X_10),X_12),apply(X_10,X_10)) ),[0],$fot(apply(apply(apply(k,X_10),apply(k,X_12)),X_10))]]) ).
cnf(refute_0_22,plain,
( apply(apply(apply(apply(abstraction,abstraction),k),X_10),X_12) != apply(apply(apply(k,X_10),apply(k,X_12)),X_10)
| apply(apply(apply(apply(abstraction,abstraction),k),X_10),X_12) = apply(X_10,X_10) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(k,X_10),apply(k,X_12)),X_10),apply(X_10,X_10)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
apply(apply(apply(apply(abstraction,abstraction),k),X_10),X_12) = apply(X_10,X_10),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(abstraction,abstraction),k),X_10),X_12),apply(apply(apply(k,X_10),apply(k,X_12)),X_10)) )],[refute_0_15,refute_0_22]) ).
cnf(refute_0_24,plain,
apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(abstraction,abstraction),k))),c(apply(apply(abstraction,abstraction),k))) = apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))),
inference(subst,[],[refute_0_23:[bind(X_10,$fot(b(apply(apply(abstraction,abstraction),k)))),bind(X_12,$fot(c(apply(apply(abstraction,abstraction),k))))]]) ).
cnf(refute_0_25,plain,
( apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(abstraction,abstraction),k))),c(apply(apply(abstraction,abstraction),k))) != apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k)))
| apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))) != apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k)))
| apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(abstraction,abstraction),k))),c(apply(apply(abstraction,abstraction),k))) = apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(abstraction,abstraction),k))),c(apply(apply(abstraction,abstraction),k))),apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k)))) ),[0],$fot(apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))))]]) ).
cnf(refute_0_26,plain,
( apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))) != apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k)))
| apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(abstraction,abstraction),k))),c(apply(apply(abstraction,abstraction),k))) = apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(abstraction,abstraction),k))),c(apply(apply(abstraction,abstraction),k))),apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k)))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))) != apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(abstraction,abstraction),k))),c(apply(apply(abstraction,abstraction),k))),apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k)))) )],[refute_0_26,refute_0_0]) ).
cnf(refute_0_28,plain,
apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))) = apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))),
introduced(tautology,[refl,[$fot(apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))))]]) ).
cnf(refute_0_29,plain,
$false,
inference(resolve,[$cnf( $equal(apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))),apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k)))) )],[refute_0_28,refute_0_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL075-2 : TPTP v8.1.0. Released v1.2.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n027.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 12:33:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.37
%------------------------------------------------------------------------------