TSTP Solution File: COL020-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL020-1 : 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 00:36:14 EDT 2022
% Result : Unsatisfiable 13.02s 13.21s
% Output : CNFRefutation 13.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of clauses : 31 ( 20 unt; 0 nHn; 17 RR)
% Number of literals : 46 ( 45 equ; 19 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; 4 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(s_definition,axiom,
apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)) ).
cnf(b_definition,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
cnf(c_definition,axiom,
apply(apply(apply(c,X),Y),Z) = apply(apply(X,Z),Y) ).
cnf(prove_fixed_point,negated_conjecture,
Y != apply(combinator,Y) ).
cnf(refute_0_0,plain,
apply(apply(X_82,X_81),X_81) != apply(combinator,apply(apply(X_82,X_81),X_81)),
inference(subst,[],[prove_fixed_point:[bind(Y,$fot(apply(apply(X_82,X_81),X_81)))]]) ).
cnf(refute_0_1,plain,
apply(apply(apply(b,X),apply(X_21,Z)),Z) = apply(X,apply(apply(X_21,Z),Z)),
inference(subst,[],[b_definition:[bind(Y,$fot(apply(X_21,Z)))]]) ).
cnf(refute_0_2,plain,
apply(apply(apply(c,X),Y),apply(X_8,Y)) = apply(apply(X,apply(X_8,Y)),Y),
inference(subst,[],[c_definition:[bind(Z,$fot(apply(X_8,Y)))]]) ).
cnf(refute_0_3,plain,
apply(apply(apply(s,apply(c,X)),X_8),Y) = apply(apply(apply(c,X),Y),apply(X_8,Y)),
inference(subst,[],[s_definition:[bind(X,$fot(apply(c,X))),bind(Y,$fot(X_8)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_4,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_5,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_6,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( apply(apply(apply(s,apply(c,X)),X_8),Y) != apply(apply(apply(c,X),Y),apply(X_8,Y))
| apply(apply(apply(c,X),Y),apply(X_8,Y)) = apply(apply(apply(s,apply(c,X)),X_8),Y) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(apply(apply(apply(s,apply(c,X)),X_8),Y))),bind(Y0,$fot(apply(apply(apply(c,X),Y),apply(X_8,Y))))]]) ).
cnf(refute_0_8,plain,
apply(apply(apply(c,X),Y),apply(X_8,Y)) = apply(apply(apply(s,apply(c,X)),X_8),Y),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,apply(c,X)),X_8),Y),apply(apply(apply(c,X),Y),apply(X_8,Y))) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( apply(apply(apply(c,X),Y),apply(X_8,Y)) != apply(apply(X,apply(X_8,Y)),Y)
| apply(apply(apply(c,X),Y),apply(X_8,Y)) != apply(apply(apply(s,apply(c,X)),X_8),Y)
| apply(apply(apply(s,apply(c,X)),X_8),Y) = apply(apply(X,apply(X_8,Y)),Y) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(c,X),Y),apply(X_8,Y)),apply(apply(X,apply(X_8,Y)),Y)) ),[0],$fot(apply(apply(apply(s,apply(c,X)),X_8),Y))]]) ).
cnf(refute_0_10,plain,
( apply(apply(apply(c,X),Y),apply(X_8,Y)) != apply(apply(X,apply(X_8,Y)),Y)
| apply(apply(apply(s,apply(c,X)),X_8),Y) = apply(apply(X,apply(X_8,Y)),Y) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(c,X),Y),apply(X_8,Y)),apply(apply(apply(s,apply(c,X)),X_8),Y)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
apply(apply(apply(s,apply(c,X)),X_8),Y) = apply(apply(X,apply(X_8,Y)),Y),
inference(resolve,[$cnf( $equal(apply(apply(apply(c,X),Y),apply(X_8,Y)),apply(apply(X,apply(X_8,Y)),Y)) )],[refute_0_2,refute_0_10]) ).
cnf(refute_0_12,plain,
apply(apply(apply(s,apply(c,apply(b,X))),X_21),Z) = apply(apply(apply(b,X),apply(X_21,Z)),Z),
inference(subst,[],[refute_0_11:[bind(X,$fot(apply(b,X))),bind(Y,$fot(Z)),bind(X_8,$fot(X_21))]]) ).
cnf(refute_0_13,plain,
( apply(apply(apply(s,apply(c,apply(b,X))),X_21),Z) != apply(apply(apply(b,X),apply(X_21,Z)),Z)
| apply(apply(apply(b,X),apply(X_21,Z)),Z) = apply(apply(apply(s,apply(c,apply(b,X))),X_21),Z) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(apply(apply(apply(s,apply(c,apply(b,X))),X_21),Z))),bind(Y0,$fot(apply(apply(apply(b,X),apply(X_21,Z)),Z)))]]) ).
cnf(refute_0_14,plain,
apply(apply(apply(b,X),apply(X_21,Z)),Z) = apply(apply(apply(s,apply(c,apply(b,X))),X_21),Z),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,apply(c,apply(b,X))),X_21),Z),apply(apply(apply(b,X),apply(X_21,Z)),Z)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( apply(apply(apply(b,X),apply(X_21,Z)),Z) != apply(X,apply(apply(X_21,Z),Z))
| apply(apply(apply(b,X),apply(X_21,Z)),Z) != apply(apply(apply(s,apply(c,apply(b,X))),X_21),Z)
| apply(apply(apply(s,apply(c,apply(b,X))),X_21),Z) = apply(X,apply(apply(X_21,Z),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(b,X),apply(X_21,Z)),Z),apply(X,apply(apply(X_21,Z),Z))) ),[0],$fot(apply(apply(apply(s,apply(c,apply(b,X))),X_21),Z))]]) ).
cnf(refute_0_16,plain,
( apply(apply(apply(b,X),apply(X_21,Z)),Z) != apply(X,apply(apply(X_21,Z),Z))
| apply(apply(apply(s,apply(c,apply(b,X))),X_21),Z) = apply(X,apply(apply(X_21,Z),Z)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),apply(X_21,Z)),Z),apply(apply(apply(s,apply(c,apply(b,X))),X_21),Z)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
apply(apply(apply(s,apply(c,apply(b,X))),X_21),Z) = apply(X,apply(apply(X_21,Z),Z)),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),apply(X_21,Z)),Z),apply(X,apply(apply(X_21,Z),Z))) )],[refute_0_1,refute_0_16]) ).
cnf(refute_0_18,plain,
apply(apply(apply(s,apply(c,apply(b,combinator))),X_82),X_81) = apply(combinator,apply(apply(X_82,X_81),X_81)),
inference(subst,[],[refute_0_17:[bind(X,$fot(combinator)),bind(Z,$fot(X_81)),bind(X_21,$fot(X_82))]]) ).
cnf(refute_0_19,plain,
( apply(apply(apply(s,apply(c,apply(b,combinator))),X_82),X_81) != apply(combinator,apply(apply(X_82,X_81),X_81))
| apply(combinator,apply(apply(X_82,X_81),X_81)) = apply(apply(apply(s,apply(c,apply(b,combinator))),X_82),X_81) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(apply(apply(apply(s,apply(c,apply(b,combinator))),X_82),X_81))),bind(Y0,$fot(apply(combinator,apply(apply(X_82,X_81),X_81))))]]) ).
cnf(refute_0_20,plain,
apply(combinator,apply(apply(X_82,X_81),X_81)) = apply(apply(apply(s,apply(c,apply(b,combinator))),X_82),X_81),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,apply(c,apply(b,combinator))),X_82),X_81),apply(combinator,apply(apply(X_82,X_81),X_81))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( apply(apply(X_82,X_81),X_81) != apply(apply(apply(s,apply(c,apply(b,combinator))),X_82),X_81)
| apply(combinator,apply(apply(X_82,X_81),X_81)) != apply(apply(apply(s,apply(c,apply(b,combinator))),X_82),X_81)
| apply(apply(X_82,X_81),X_81) = apply(combinator,apply(apply(X_82,X_81),X_81)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(X_82,X_81),X_81),apply(combinator,apply(apply(X_82,X_81),X_81))) ),[1],$fot(apply(apply(apply(s,apply(c,apply(b,combinator))),X_82),X_81))]]) ).
cnf(refute_0_22,plain,
( apply(apply(X_82,X_81),X_81) != apply(apply(apply(s,apply(c,apply(b,combinator))),X_82),X_81)
| apply(apply(X_82,X_81),X_81) = apply(combinator,apply(apply(X_82,X_81),X_81)) ),
inference(resolve,[$cnf( $equal(apply(combinator,apply(apply(X_82,X_81),X_81)),apply(apply(apply(s,apply(c,apply(b,combinator))),X_82),X_81)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
apply(apply(X_82,X_81),X_81) != apply(apply(apply(s,apply(c,apply(b,combinator))),X_82),X_81),
inference(resolve,[$cnf( $equal(apply(apply(X_82,X_81),X_81),apply(combinator,apply(apply(X_82,X_81),X_81))) )],[refute_0_22,refute_0_0]) ).
cnf(refute_0_24,plain,
apply(apply(apply(s,apply(c,apply(b,combinator))),apply(s,apply(c,apply(b,combinator)))),apply(s,apply(c,apply(b,combinator)))) != apply(apply(apply(s,apply(c,apply(b,combinator))),apply(s,apply(c,apply(b,combinator)))),apply(s,apply(c,apply(b,combinator)))),
inference(subst,[],[refute_0_23:[bind(X_81,$fot(apply(s,apply(c,apply(b,combinator))))),bind(X_82,$fot(apply(s,apply(c,apply(b,combinator)))))]]) ).
cnf(refute_0_25,plain,
apply(apply(apply(s,apply(c,apply(b,combinator))),apply(s,apply(c,apply(b,combinator)))),apply(s,apply(c,apply(b,combinator)))) = apply(apply(apply(s,apply(c,apply(b,combinator))),apply(s,apply(c,apply(b,combinator)))),apply(s,apply(c,apply(b,combinator)))),
introduced(tautology,[refl,[$fot(apply(apply(apply(s,apply(c,apply(b,combinator))),apply(s,apply(c,apply(b,combinator)))),apply(s,apply(c,apply(b,combinator)))))]]) ).
cnf(refute_0_26,plain,
$false,
inference(resolve,[$cnf( $equal(apply(apply(apply(s,apply(c,apply(b,combinator))),apply(s,apply(c,apply(b,combinator)))),apply(s,apply(c,apply(b,combinator)))),apply(apply(apply(s,apply(c,apply(b,combinator))),apply(s,apply(c,apply(b,combinator)))),apply(s,apply(c,apply(b,combinator))))) )],[refute_0_25,refute_0_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : COL020-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue May 31 04:47:36 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 13.02/13.21 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.02/13.21
% 13.02/13.21 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.02/13.21
%------------------------------------------------------------------------------