TSTP Solution File: COL060-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL060-3 : TPTP v8.1.0. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 00:36:20 EDT 2022
% Result : Unsatisfiable 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of clauses : 42 ( 22 unt; 0 nHn; 39 RR)
% Number of literals : 73 ( 72 equ; 33 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 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_q_combinator,negated_conjecture,
apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z) != apply(y,apply(x,z)) ).
cnf(refute_0_0,plain,
apply(apply(apply(b,y),x),z) = apply(y,apply(x,z)),
inference(subst,[],[b_definition:[bind(X,$fot(y)),bind(Y,$fot(x)),bind(Z,$fot(z))]]) ).
cnf(refute_0_1,plain,
apply(apply(t,x),apply(b,y)) = apply(apply(b,y),x),
inference(subst,[],[t_definition:[bind(X,$fot(x)),bind(Y,$fot(apply(b,y)))]]) ).
cnf(refute_0_2,plain,
apply(apply(apply(b,apply(t,x)),b),y) = apply(apply(t,x),apply(b,y)),
inference(subst,[],[b_definition:[bind(X,$fot(apply(t,x))),bind(Y,$fot(b)),bind(Z,$fot(y))]]) ).
cnf(refute_0_3,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_4,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_5,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( apply(apply(apply(b,apply(t,x)),b),y) != apply(apply(t,x),apply(b,y))
| apply(apply(t,x),apply(b,y)) != apply(apply(b,y),x)
| apply(apply(apply(b,apply(t,x)),b),y) = apply(apply(b,y),x) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(apply(apply(apply(b,apply(t,x)),b),y))),bind(Y0,$fot(apply(apply(t,x),apply(b,y)))),bind(Z0,$fot(apply(apply(b,y),x)))]]) ).
cnf(refute_0_9,plain,
( apply(apply(t,x),apply(b,y)) != apply(apply(b,y),x)
| apply(apply(apply(b,apply(t,x)),b),y) = apply(apply(b,y),x) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(t,x)),b),y),apply(apply(t,x),apply(b,y))) )],[refute_0_2,refute_0_8]) ).
cnf(refute_0_10,plain,
apply(apply(apply(b,apply(t,x)),b),y) = apply(apply(b,y),x),
inference(resolve,[$cnf( $equal(apply(apply(t,x),apply(b,y)),apply(apply(b,y),x)) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
apply(apply(t,b),apply(b,apply(t,x))) = apply(apply(b,apply(t,x)),b),
inference(subst,[],[t_definition:[bind(X,$fot(b)),bind(Y,$fot(apply(b,apply(t,x))))]]) ).
cnf(refute_0_12,plain,
apply(apply(apply(b,apply(t,b)),b),apply(t,x)) = apply(apply(t,b),apply(b,apply(t,x))),
inference(subst,[],[b_definition:[bind(X,$fot(apply(t,b))),bind(Y,$fot(b)),bind(Z,$fot(apply(t,x)))]]) ).
cnf(refute_0_13,plain,
( apply(apply(apply(b,apply(t,b)),b),apply(t,x)) != apply(apply(t,b),apply(b,apply(t,x)))
| apply(apply(t,b),apply(b,apply(t,x))) != apply(apply(b,apply(t,x)),b)
| apply(apply(apply(b,apply(t,b)),b),apply(t,x)) = apply(apply(b,apply(t,x)),b) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(apply(apply(apply(b,apply(t,b)),b),apply(t,x)))),bind(Y0,$fot(apply(apply(t,b),apply(b,apply(t,x))))),bind(Z0,$fot(apply(apply(b,apply(t,x)),b)))]]) ).
cnf(refute_0_14,plain,
( apply(apply(t,b),apply(b,apply(t,x))) != apply(apply(b,apply(t,x)),b)
| apply(apply(apply(b,apply(t,b)),b),apply(t,x)) = apply(apply(b,apply(t,x)),b) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(t,b)),b),apply(t,x)),apply(apply(t,b),apply(b,apply(t,x)))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
apply(apply(apply(b,apply(t,b)),b),apply(t,x)) = apply(apply(b,apply(t,x)),b),
inference(resolve,[$cnf( $equal(apply(apply(t,b),apply(b,apply(t,x))),apply(apply(b,apply(t,x)),b)) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x) = apply(apply(apply(b,apply(t,b)),b),apply(t,x)),
inference(subst,[],[b_definition:[bind(X,$fot(apply(apply(b,apply(t,b)),b))),bind(Y,$fot(t)),bind(Z,$fot(x))]]) ).
cnf(refute_0_17,plain,
( apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x) != apply(apply(apply(b,apply(t,b)),b),apply(t,x))
| apply(apply(apply(b,apply(t,b)),b),apply(t,x)) != apply(apply(b,apply(t,x)),b)
| apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x) = apply(apply(b,apply(t,x)),b) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x))),bind(Y0,$fot(apply(apply(apply(b,apply(t,b)),b),apply(t,x)))),bind(Z0,$fot(apply(apply(b,apply(t,x)),b)))]]) ).
cnf(refute_0_18,plain,
( apply(apply(apply(b,apply(t,b)),b),apply(t,x)) != apply(apply(b,apply(t,x)),b)
| apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x) = apply(apply(b,apply(t,x)),b) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),apply(apply(apply(b,apply(t,b)),b),apply(t,x))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x) = apply(apply(b,apply(t,x)),b),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(t,b)),b),apply(t,x)),apply(apply(b,apply(t,x)),b)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y) = apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),
introduced(tautology,[refl,[$fot(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y))]]) ).
cnf(refute_0_21,plain,
( apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y) != apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y)
| apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x) != apply(apply(b,apply(t,x)),b)
| apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y) = apply(apply(apply(b,apply(t,x)),b),y) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y)) ),[1,0],$fot(apply(apply(b,apply(t,x)),b))]]) ).
cnf(refute_0_22,plain,
( apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x) != apply(apply(b,apply(t,x)),b)
| apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y) = apply(apply(apply(b,apply(t,x)),b),y) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y) = apply(apply(apply(b,apply(t,x)),b),y),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),apply(apply(b,apply(t,x)),b)) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
( apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y) != apply(apply(apply(b,apply(t,x)),b),y)
| apply(apply(apply(b,apply(t,x)),b),y) != apply(apply(b,y),x)
| apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y) = apply(apply(b,y),x) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y))),bind(Y0,$fot(apply(apply(apply(b,apply(t,x)),b),y))),bind(Z0,$fot(apply(apply(b,y),x)))]]) ).
cnf(refute_0_25,plain,
( apply(apply(apply(b,apply(t,x)),b),y) != apply(apply(b,y),x)
| apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y) = apply(apply(b,y),x) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),apply(apply(apply(b,apply(t,x)),b),y)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y) = apply(apply(b,y),x),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,apply(t,x)),b),y),apply(apply(b,y),x)) )],[refute_0_10,refute_0_25]) ).
cnf(refute_0_27,plain,
apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z) = apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z),
introduced(tautology,[refl,[$fot(apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z))]]) ).
cnf(refute_0_28,plain,
( apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z) != apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z)
| apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y) != apply(apply(b,y),x)
| apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z) = apply(apply(apply(b,y),x),z) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z),apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z)) ),[1,0],$fot(apply(apply(b,y),x))]]) ).
cnf(refute_0_29,plain,
( apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y) != apply(apply(b,y),x)
| apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z) = apply(apply(apply(b,y),x),z) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z),apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z) = apply(apply(apply(b,y),x),z),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),apply(apply(b,y),x)) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
( apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z) != apply(apply(apply(b,y),x),z)
| apply(apply(apply(b,y),x),z) != apply(y,apply(x,z))
| apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z) = apply(y,apply(x,z)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z))),bind(Y0,$fot(apply(apply(apply(b,y),x),z))),bind(Z0,$fot(apply(y,apply(x,z))))]]) ).
cnf(refute_0_32,plain,
( apply(apply(apply(b,y),x),z) != apply(y,apply(x,z))
| apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z) = apply(y,apply(x,z)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z),apply(apply(apply(b,y),x),z)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z) = apply(y,apply(x,z)),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,y),x),z),apply(y,apply(x,z))) )],[refute_0_0,refute_0_32]) ).
cnf(refute_0_34,plain,
( apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z) != apply(y,apply(x,z))
| apply(y,apply(x,z)) != apply(y,apply(x,z))
| apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z) = apply(y,apply(x,z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z),apply(y,apply(x,z))) ),[0],$fot(apply(y,apply(x,z)))]]) ).
cnf(refute_0_35,plain,
( apply(y,apply(x,z)) != apply(y,apply(x,z))
| apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z) = apply(y,apply(x,z)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z),apply(y,apply(x,z))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
apply(y,apply(x,z)) != apply(y,apply(x,z)),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,b)),b)),t),x),y),z),apply(y,apply(x,z))) )],[refute_0_35,prove_q_combinator]) ).
cnf(refute_0_37,plain,
apply(y,apply(x,z)) = apply(y,apply(x,z)),
introduced(tautology,[refl,[$fot(apply(y,apply(x,z)))]]) ).
cnf(refute_0_38,plain,
$false,
inference(resolve,[$cnf( $equal(apply(y,apply(x,z)),apply(y,apply(x,z))) )],[refute_0_37,refute_0_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL060-3 : TPTP v8.1.0. Bugfixed v1.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue May 31 16:16:56 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------