TSTP Solution File: COL061-2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL061-2 : TPTP v8.1.0. Bugfixed v1.2.0.
% 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 00:36:21 EDT 2022
% Result : Unsatisfiable 0.12s 0.34s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of clauses : 50 ( 26 unt; 0 nHn; 47 RR)
% Number of literals : 87 ( 86 equ; 39 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; 5 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_definition,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ).
cnf(t_definition,axiom,
apply(apply(t,X),Y) = apply(Y,X) ).
cnf(prove_q1_combinator,negated_conjecture,
apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z) != apply(x,apply(z,y)) ).
cnf(refute_0_0,plain,
apply(apply(t,y),z) = apply(z,y),
inference(subst,[],[t_definition:[bind(X,$fot(y)),bind(Y,$fot(z))]]) ).
cnf(refute_0_1,plain,
apply(x,apply(apply(t,y),z)) = apply(x,apply(apply(t,y),z)),
introduced(tautology,[refl,[$fot(apply(x,apply(apply(t,y),z)))]]) ).
cnf(refute_0_2,plain,
( apply(apply(t,y),z) != apply(z,y)
| apply(x,apply(apply(t,y),z)) != apply(x,apply(apply(t,y),z))
| apply(x,apply(apply(t,y),z)) = apply(x,apply(z,y)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(x,apply(apply(t,y),z)),apply(x,apply(apply(t,y),z))) ),[1,1],$fot(apply(z,y))]]) ).
cnf(refute_0_3,plain,
( apply(apply(t,y),z) != apply(z,y)
| apply(x,apply(apply(t,y),z)) = apply(x,apply(z,y)) ),
inference(resolve,[$cnf( $equal(apply(x,apply(apply(t,y),z)),apply(x,apply(apply(t,y),z))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
apply(x,apply(apply(t,y),z)) = apply(x,apply(z,y)),
inference(resolve,[$cnf( $equal(apply(apply(t,y),z),apply(z,y)) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
apply(apply(apply(b,x),apply(t,y)),z) = apply(x,apply(apply(t,y),z)),
inference(subst,[],[b_definition:[bind(X,$fot(x)),bind(Y,$fot(apply(t,y))),bind(Z,$fot(z))]]) ).
cnf(refute_0_6,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_7,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_8,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_10,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( apply(apply(apply(b,x),apply(t,y)),z) != apply(x,apply(apply(t,y),z))
| apply(x,apply(apply(t,y),z)) != apply(x,apply(z,y))
| apply(apply(apply(b,x),apply(t,y)),z) = apply(x,apply(z,y)) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(apply(apply(apply(b,x),apply(t,y)),z))),bind(Y0,$fot(apply(x,apply(apply(t,y),z)))),bind(Z0,$fot(apply(x,apply(z,y))))]]) ).
cnf(refute_0_12,plain,
( apply(x,apply(apply(t,y),z)) != apply(x,apply(z,y))
| apply(apply(apply(b,x),apply(t,y)),z) = apply(x,apply(z,y)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,x),apply(t,y)),z),apply(x,apply(apply(t,y),z))) )],[refute_0_5,refute_0_11]) ).
cnf(refute_0_13,plain,
apply(apply(apply(b,x),apply(t,y)),z) = apply(x,apply(z,y)),
inference(resolve,[$cnf( $equal(apply(x,apply(apply(t,y),z)),apply(x,apply(z,y))) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
apply(apply(apply(b,apply(b,x)),t),y) = apply(apply(b,x),apply(t,y)),
inference(subst,[],[b_definition:[bind(X,$fot(apply(b,x))),bind(Y,$fot(t)),bind(Z,$fot(y))]]) ).
cnf(refute_0_15,plain,
apply(apply(apply(b,b),b),x) = apply(b,apply(b,x)),
inference(subst,[],[b_definition:[bind(X,$fot(b)),bind(Y,$fot(b)),bind(Z,$fot(x))]]) ).
cnf(refute_0_16,plain,
apply(apply(apply(apply(b,b),b),x),t) = apply(apply(apply(apply(b,b),b),x),t),
introduced(tautology,[refl,[$fot(apply(apply(apply(apply(b,b),b),x),t))]]) ).
cnf(refute_0_17,plain,
( apply(apply(apply(apply(b,b),b),x),t) != apply(apply(apply(apply(b,b),b),x),t)
| apply(apply(apply(b,b),b),x) != apply(b,apply(b,x))
| apply(apply(apply(apply(b,b),b),x),t) = apply(apply(b,apply(b,x)),t) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(apply(b,b),b),x),t),apply(apply(apply(apply(b,b),b),x),t)) ),[1,0],$fot(apply(b,apply(b,x)))]]) ).
cnf(refute_0_18,plain,
( apply(apply(apply(b,b),b),x) != apply(b,apply(b,x))
| apply(apply(apply(apply(b,b),b),x),t) = apply(apply(b,apply(b,x)),t) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(b,b),b),x),t),apply(apply(apply(apply(b,b),b),x),t)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
apply(apply(apply(apply(b,b),b),x),t) = apply(apply(b,apply(b,x)),t),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,b),b),x),apply(b,apply(b,x))) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
apply(apply(t,t),apply(apply(apply(b,b),b),x)) = apply(apply(apply(apply(b,b),b),x),t),
inference(subst,[],[t_definition:[bind(X,$fot(t)),bind(Y,$fot(apply(apply(apply(b,b),b),x)))]]) ).
cnf(refute_0_21,plain,
apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x) = apply(apply(t,t),apply(apply(apply(b,b),b),x)),
inference(subst,[],[b_definition:[bind(X,$fot(apply(t,t))),bind(Y,$fot(apply(apply(b,b),b))),bind(Z,$fot(x))]]) ).
cnf(refute_0_22,plain,
( apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x) != apply(apply(t,t),apply(apply(apply(b,b),b),x))
| apply(apply(t,t),apply(apply(apply(b,b),b),x)) != apply(apply(apply(apply(b,b),b),x),t)
| apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x) = apply(apply(apply(apply(b,b),b),x),t) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x))),bind(Y0,$fot(apply(apply(t,t),apply(apply(apply(b,b),b),x)))),bind(Z0,$fot(apply(apply(apply(apply(b,b),b),x),t)))]]) ).
cnf(refute_0_23,plain,
( apply(apply(t,t),apply(apply(apply(b,b),b),x)) != apply(apply(apply(apply(b,b),b),x),t)
| apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x) = apply(apply(apply(apply(b,b),b),x),t) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),apply(apply(t,t),apply(apply(apply(b,b),b),x))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x) = apply(apply(apply(apply(b,b),b),x),t),
inference(resolve,[$cnf( $equal(apply(apply(t,t),apply(apply(apply(b,b),b),x)),apply(apply(apply(apply(b,b),b),x),t)) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
( apply(apply(apply(apply(b,b),b),x),t) != apply(apply(b,apply(b,x)),t)
| apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x) != apply(apply(apply(apply(b,b),b),x),t)
| apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x) = apply(apply(b,apply(b,x)),t) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x))),bind(Y0,$fot(apply(apply(apply(apply(b,b),b),x),t))),bind(Z0,$fot(apply(apply(b,apply(b,x)),t)))]]) ).
cnf(refute_0_26,plain,
( apply(apply(apply(apply(b,b),b),x),t) != apply(apply(b,apply(b,x)),t)
| apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x) = apply(apply(b,apply(b,x)),t) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),apply(apply(apply(apply(b,b),b),x),t)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x) = apply(apply(b,apply(b,x)),t),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(b,b),b),x),t),apply(apply(b,apply(b,x)),t)) )],[refute_0_19,refute_0_26]) ).
cnf(refute_0_28,plain,
apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y) = apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),
introduced(tautology,[refl,[$fot(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y))]]) ).
cnf(refute_0_29,plain,
( apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y) != apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y)
| apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x) != apply(apply(b,apply(b,x)),t)
| apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y) = apply(apply(apply(b,apply(b,x)),t),y) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y)) ),[1,0],$fot(apply(apply(b,apply(b,x)),t))]]) ).
cnf(refute_0_30,plain,
( apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x) != apply(apply(b,apply(b,x)),t)
| apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y) = apply(apply(apply(b,apply(b,x)),t),y) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y) = apply(apply(apply(b,apply(b,x)),t),y),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),apply(apply(b,apply(b,x)),t)) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
( apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y) != apply(apply(apply(b,apply(b,x)),t),y)
| apply(apply(apply(b,apply(b,x)),t),y) != apply(apply(b,x),apply(t,y))
| apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y) = apply(apply(b,x),apply(t,y)) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y))),bind(Y0,$fot(apply(apply(apply(b,apply(b,x)),t),y))),bind(Z0,$fot(apply(apply(b,x),apply(t,y))))]]) ).
cnf(refute_0_33,plain,
( apply(apply(apply(b,apply(b,x)),t),y) != apply(apply(b,x),apply(t,y))
| apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y) = apply(apply(b,x),apply(t,y)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),apply(apply(apply(b,apply(b,x)),t),y)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y) = apply(apply(b,x),apply(t,y)),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(b,x)),t),y),apply(apply(b,x),apply(t,y))) )],[refute_0_14,refute_0_33]) ).
cnf(refute_0_35,plain,
apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z) = apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z),
introduced(tautology,[refl,[$fot(apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z))]]) ).
cnf(refute_0_36,plain,
( apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z) != apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z)
| apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y) != apply(apply(b,x),apply(t,y))
| apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z) = apply(apply(apply(b,x),apply(t,y)),z) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z),apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z)) ),[1,0],$fot(apply(apply(b,x),apply(t,y)))]]) ).
cnf(refute_0_37,plain,
( apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y) != apply(apply(b,x),apply(t,y))
| apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z) = apply(apply(apply(b,x),apply(t,y)),z) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z),apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z) = apply(apply(apply(b,x),apply(t,y)),z),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),apply(apply(b,x),apply(t,y))) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
( apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z) != apply(apply(apply(b,x),apply(t,y)),z)
| apply(apply(apply(b,x),apply(t,y)),z) != apply(x,apply(z,y))
| apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z) = apply(x,apply(z,y)) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z))),bind(Y0,$fot(apply(apply(apply(b,x),apply(t,y)),z))),bind(Z0,$fot(apply(x,apply(z,y))))]]) ).
cnf(refute_0_40,plain,
( apply(apply(apply(b,x),apply(t,y)),z) != apply(x,apply(z,y))
| apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z) = apply(x,apply(z,y)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z),apply(apply(apply(b,x),apply(t,y)),z)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z) = apply(x,apply(z,y)),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,x),apply(t,y)),z),apply(x,apply(z,y))) )],[refute_0_13,refute_0_40]) ).
cnf(refute_0_42,plain,
( apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z) != apply(x,apply(z,y))
| apply(x,apply(z,y)) != apply(x,apply(z,y))
| apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z) = apply(x,apply(z,y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z),apply(x,apply(z,y))) ),[0],$fot(apply(x,apply(z,y)))]]) ).
cnf(refute_0_43,plain,
( apply(x,apply(z,y)) != apply(x,apply(z,y))
| apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z) = apply(x,apply(z,y)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z),apply(x,apply(z,y))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
apply(x,apply(z,y)) != apply(x,apply(z,y)),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z),apply(x,apply(z,y))) )],[refute_0_43,prove_q1_combinator]) ).
cnf(refute_0_45,plain,
apply(x,apply(z,y)) = apply(x,apply(z,y)),
introduced(tautology,[refl,[$fot(apply(x,apply(z,y)))]]) ).
cnf(refute_0_46,plain,
$false,
inference(resolve,[$cnf( $equal(apply(x,apply(z,y)),apply(x,apply(z,y))) )],[refute_0_45,refute_0_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL061-2 : TPTP v8.1.0. Bugfixed v1.2.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n022.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 16:10:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.35
%------------------------------------------------------------------------------