%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL037-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 00:36:16 EDT 2022
% Result : Unsatisfiable 9.13s 9.34s
% Output : CNFRefutation 9.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of clauses : 67 ( 39 unt; 0 nHn; 41 RR)
% Number of literals : 107 ( 106 equ; 51 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 151 ( 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,
apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))) ).
cnf(refute_0_0,plain,
apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5))) != apply(f(apply(apply(c,X_4),X_5)),apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5)))),
inference(subst,[],[prove_fixed_point:[bind(Y,$fot(apply(apply(c,X_4),X_5)))]]) ).
cnf(refute_0_1,plain,
apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5))) = apply(apply(X_4,f(apply(apply(c,X_4),X_5))),X_5),
inference(subst,[],[c_definition:[bind(X,$fot(X_4)),bind(Y,$fot(X_5)),bind(Z,$fot(f(apply(apply(c,X_4),X_5))))]]) ).
cnf(refute_0_2,plain,
( apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5))) != apply(apply(X_4,f(apply(apply(c,X_4),X_5))),X_5)
| apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5))) != apply(f(apply(apply(c,X_4),X_5)),apply(apply(X_4,f(apply(apply(c,X_4),X_5))),X_5))
| apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5))) = apply(f(apply(apply(c,X_4),X_5)),apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5))),apply(f(apply(apply(c,X_4),X_5)),apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5))))) ),[1,1],$fot(apply(apply(X_4,f(apply(apply(c,X_4),X_5))),X_5))]]) ).
cnf(refute_0_3,plain,
( apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5))) != apply(f(apply(apply(c,X_4),X_5)),apply(apply(X_4,f(apply(apply(c,X_4),X_5))),X_5))
| apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5))) = apply(f(apply(apply(c,X_4),X_5)),apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5)))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5))),apply(apply(X_4,f(apply(apply(c,X_4),X_5))),X_5)) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5))) != apply(f(apply(apply(c,X_4),X_5)),apply(apply(X_4,f(apply(apply(c,X_4),X_5))),X_5)),
inference(resolve,[$cnf( $equal(apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5))),apply(f(apply(apply(c,X_4),X_5)),apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5))))) )],[refute_0_3,refute_0_0]) ).
cnf(refute_0_5,plain,
( apply(apply(X_4,f(apply(apply(c,X_4),X_5))),X_5) != apply(f(apply(apply(c,X_4),X_5)),apply(apply(X_4,f(apply(apply(c,X_4),X_5))),X_5))
| apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5))) != apply(apply(X_4,f(apply(apply(c,X_4),X_5))),X_5)
| apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5))) = apply(f(apply(apply(c,X_4),X_5)),apply(apply(X_4,f(apply(apply(c,X_4),X_5))),X_5)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5))),apply(apply(X_4,f(apply(apply(c,X_4),X_5))),X_5)) ),[1],$fot(apply(f(apply(apply(c,X_4),X_5)),apply(apply(X_4,f(apply(apply(c,X_4),X_5))),X_5)))]]) ).
cnf(refute_0_6,plain,
( apply(apply(X_4,f(apply(apply(c,X_4),X_5))),X_5) != apply(f(apply(apply(c,X_4),X_5)),apply(apply(X_4,f(apply(apply(c,X_4),X_5))),X_5))
| apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5))) = apply(f(apply(apply(c,X_4),X_5)),apply(apply(X_4,f(apply(apply(c,X_4),X_5))),X_5)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5))),apply(apply(X_4,f(apply(apply(c,X_4),X_5))),X_5)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
apply(apply(X_4,f(apply(apply(c,X_4),X_5))),X_5) != apply(f(apply(apply(c,X_4),X_5)),apply(apply(X_4,f(apply(apply(c,X_4),X_5))),X_5)),
inference(resolve,[$cnf( $equal(apply(apply(apply(c,X_4),X_5),f(apply(apply(c,X_4),X_5))),apply(f(apply(apply(c,X_4),X_5)),apply(apply(X_4,f(apply(apply(c,X_4),X_5))),X_5))) )],[refute_0_6,refute_0_4]) ).
cnf(refute_0_8,plain,
apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8) != apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8)),
inference(subst,[],[refute_0_7:[bind(X_4,$fot(apply(c,X))),bind(X_5,$fot(X_8))]]) ).
cnf(refute_0_9,plain,
apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8) = apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))),
inference(subst,[],[c_definition:[bind(Y,$fot(f(apply(apply(c,apply(c,X)),X_8)))),bind(Z,$fot(X_8))]]) ).
cnf(refute_0_10,plain,
( apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))) != apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8))
| apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8) != apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8)))
| apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8) = apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8),apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8)))) ),[1],$fot(apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8)))]]) ).
cnf(refute_0_11,plain,
( apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))) != apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8))
| apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8) = apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8),apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8)))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))) != apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8)),
inference(resolve,[$cnf( $equal(apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8),apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8))) )],[refute_0_11,refute_0_8]) ).
cnf(refute_0_13,plain,
apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8)) = apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8)),
introduced(tautology,[refl,[$fot(apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8)))]]) ).
cnf(refute_0_14,plain,
( apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8) != apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8)))
| apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8)) != apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8))
| apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8)) = apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8)))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8)),apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8))) ),[1,1],$fot(apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))))]]) ).
cnf(refute_0_15,plain,
( apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8) != apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8)))
| apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8)) = apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8)))) ),
inference(resolve,[$cnf( $equal(apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8)),apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8)) = apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8)))),
inference(resolve,[$cnf( $equal(apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8),apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8)))) )],[refute_0_9,refute_0_15]) ).
cnf(refute_0_17,plain,
( apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))) != apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))))
| apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8)) != apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))))
| apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))) = apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))),apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8))) ),[1],$fot(apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8)))))]]) ).
cnf(refute_0_18,plain,
( apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))) != apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))))
| apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))) = apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8)) ),
inference(resolve,[$cnf( $equal(apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8)),apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))) != apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8)))),
inference(resolve,[$cnf( $equal(apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))),apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(apply(c,X),f(apply(apply(c,apply(c,X)),X_8))),X_8))) )],[refute_0_18,refute_0_12]) ).
cnf(refute_0_20,plain,
apply(apply(apply(b,X),apply(X_10,X)),Z) = apply(X,apply(apply(X_10,X),Z)),
inference(subst,[],[b_definition:[bind(Y,$fot(apply(X_10,X)))]]) ).
cnf(refute_0_21,plain,
apply(apply(apply(s,b),X_10),X) = apply(apply(b,X),apply(X_10,X)),
inference(subst,[],[s_definition:[bind(X,$fot(b)),bind(Y,$fot(X_10)),bind(Z,$fot(X))]]) ).
cnf(refute_0_22,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_23,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_24,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( apply(apply(apply(s,b),X_10),X) != apply(apply(b,X),apply(X_10,X))
| apply(apply(b,X),apply(X_10,X)) = apply(apply(apply(s,b),X_10),X) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(apply(apply(apply(s,b),X_10),X))),bind(Y0,$fot(apply(apply(b,X),apply(X_10,X))))]]) ).
cnf(refute_0_26,plain,
apply(apply(b,X),apply(X_10,X)) = apply(apply(apply(s,b),X_10),X),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,b),X_10),X),apply(apply(b,X),apply(X_10,X))) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
( apply(apply(apply(b,X),apply(X_10,X)),Z) != apply(X,apply(apply(X_10,X),Z))
| apply(apply(b,X),apply(X_10,X)) != apply(apply(apply(s,b),X_10),X)
| apply(apply(apply(apply(s,b),X_10),X),Z) = apply(X,apply(apply(X_10,X),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(b,X),apply(X_10,X)),Z),apply(X,apply(apply(X_10,X),Z))) ),[0,0],$fot(apply(apply(apply(s,b),X_10),X))]]) ).
cnf(refute_0_28,plain,
( apply(apply(apply(b,X),apply(X_10,X)),Z) != apply(X,apply(apply(X_10,X),Z))
| apply(apply(apply(apply(s,b),X_10),X),Z) = apply(X,apply(apply(X_10,X),Z)) ),
inference(resolve,[$cnf( $equal(apply(apply(b,X),apply(X_10,X)),apply(apply(apply(s,b),X_10),X)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
apply(apply(apply(apply(s,b),X_10),X),Z) = apply(X,apply(apply(X_10,X),Z)),
inference(resolve,[$cnf( $equal(apply(apply(apply(b,X),apply(X_10,X)),Z),apply(X,apply(apply(X_10,X),Z))) )],[refute_0_20,refute_0_28]) ).
cnf(refute_0_30,plain,
apply(apply(apply(apply(s,b),apply(c,X)),X_20),X_21) = apply(X_20,apply(apply(apply(c,X),X_20),X_21)),
inference(subst,[],[refute_0_29:[bind(X,$fot(X_20)),bind(Z,$fot(X_21)),bind(X_10,$fot(apply(c,X)))]]) ).
cnf(refute_0_31,plain,
apply(apply(apply(c,X),X_20),X_21) = apply(apply(X,X_21),X_20),
inference(subst,[],[c_definition:[bind(Y,$fot(X_20)),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_32,plain,
( apply(apply(apply(apply(s,b),apply(c,X)),X_20),X_21) != apply(X_20,apply(apply(apply(c,X),X_20),X_21))
| apply(apply(apply(c,X),X_20),X_21) != apply(apply(X,X_21),X_20)
| apply(apply(apply(apply(s,b),apply(c,X)),X_20),X_21) = apply(X_20,apply(apply(X,X_21),X_20)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(apply(s,b),apply(c,X)),X_20),X_21),apply(X_20,apply(apply(apply(c,X),X_20),X_21))) ),[1,1],$fot(apply(apply(X,X_21),X_20))]]) ).
cnf(refute_0_33,plain,
( apply(apply(apply(apply(s,b),apply(c,X)),X_20),X_21) != apply(X_20,apply(apply(apply(c,X),X_20),X_21))
| apply(apply(apply(apply(s,b),apply(c,X)),X_20),X_21) = apply(X_20,apply(apply(X,X_21),X_20)) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(c,X),X_20),X_21),apply(apply(X,X_21),X_20)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
apply(apply(apply(apply(s,b),apply(c,X)),X_20),X_21) = apply(X_20,apply(apply(X,X_21),X_20)),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(s,b),apply(c,X)),X_20),X_21),apply(X_20,apply(apply(apply(c,X),X_20),X_21))) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
( apply(apply(apply(apply(s,b),apply(c,X)),X_20),X_21) != apply(X_20,apply(apply(X,X_21),X_20))
| apply(X_20,apply(apply(X,X_21),X_20)) = apply(apply(apply(apply(s,b),apply(c,X)),X_20),X_21) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(apply(apply(apply(apply(s,b),apply(c,X)),X_20),X_21))),bind(Y0,$fot(apply(X_20,apply(apply(X,X_21),X_20))))]]) ).
cnf(refute_0_36,plain,
apply(X_20,apply(apply(X,X_21),X_20)) = apply(apply(apply(apply(s,b),apply(c,X)),X_20),X_21),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(s,b),apply(c,X)),X_20),X_21),apply(X_20,apply(apply(X,X_21),X_20))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8)))) = apply(apply(apply(apply(s,b),apply(c,X)),f(apply(apply(c,apply(c,X)),X_8))),X_8),
inference(subst,[],[refute_0_36:[bind(X_20,$fot(f(apply(apply(c,apply(c,X)),X_8)))),bind(X_21,$fot(X_8))]]) ).
cnf(refute_0_38,plain,
( apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))) != apply(apply(apply(apply(s,b),apply(c,X)),f(apply(apply(c,apply(c,X)),X_8))),X_8)
| apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8)))) != apply(apply(apply(apply(s,b),apply(c,X)),f(apply(apply(c,apply(c,X)),X_8))),X_8)
| apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))) = apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))),apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))))) ),[1],$fot(apply(apply(apply(apply(s,b),apply(c,X)),f(apply(apply(c,apply(c,X)),X_8))),X_8))]]) ).
cnf(refute_0_39,plain,
( apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))) != apply(apply(apply(apply(s,b),apply(c,X)),f(apply(apply(c,apply(c,X)),X_8))),X_8)
| apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))) = apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8)))) ),
inference(resolve,[$cnf( $equal(apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8)))),apply(apply(apply(apply(s,b),apply(c,X)),f(apply(apply(c,apply(c,X)),X_8))),X_8)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))) != apply(apply(apply(apply(s,b),apply(c,X)),f(apply(apply(c,apply(c,X)),X_8))),X_8),
inference(resolve,[$cnf( $equal(apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))),apply(f(apply(apply(c,apply(c,X)),X_8)),apply(apply(X,X_8),f(apply(apply(c,apply(c,X)),X_8))))) )],[refute_0_39,refute_0_19]) ).
cnf(refute_0_41,plain,
apply(apply(apply(apply(s,apply(c,c)),X_81),X_8),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))) != apply(apply(apply(apply(s,b),apply(c,apply(apply(s,apply(c,c)),X_81))),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))),X_8),
inference(subst,[],[refute_0_40:[bind(X,$fot(apply(apply(s,apply(c,c)),X_81)))]]) ).
cnf(refute_0_42,plain,
apply(apply(apply(c,apply(X_16,Y)),Y),Z) = apply(apply(apply(X_16,Y),Z),Y),
inference(subst,[],[c_definition:[bind(X,$fot(apply(X_16,Y)))]]) ).
cnf(refute_0_43,plain,
apply(apply(apply(c,X),Y),apply(X_10,Y)) = apply(apply(X,apply(X_10,Y)),Y),
inference(subst,[],[c_definition:[bind(Z,$fot(apply(X_10,Y)))]]) ).
cnf(refute_0_44,plain,
apply(apply(apply(s,apply(c,X)),X_10),Y) = apply(apply(apply(c,X),Y),apply(X_10,Y)),
inference(subst,[],[s_definition:[bind(X,$fot(apply(c,X))),bind(Y,$fot(X_10)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_45,plain,
( apply(apply(apply(s,apply(c,X)),X_10),Y) != apply(apply(apply(c,X),Y),apply(X_10,Y))
| apply(apply(apply(c,X),Y),apply(X_10,Y)) = apply(apply(apply(s,apply(c,X)),X_10),Y) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(apply(apply(apply(s,apply(c,X)),X_10),Y))),bind(Y0,$fot(apply(apply(apply(c,X),Y),apply(X_10,Y))))]]) ).
cnf(refute_0_46,plain,
apply(apply(apply(c,X),Y),apply(X_10,Y)) = apply(apply(apply(s,apply(c,X)),X_10),Y),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,apply(c,X)),X_10),Y),apply(apply(apply(c,X),Y),apply(X_10,Y))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( apply(apply(apply(c,X),Y),apply(X_10,Y)) != apply(apply(X,apply(X_10,Y)),Y)
| apply(apply(apply(c,X),Y),apply(X_10,Y)) != apply(apply(apply(s,apply(c,X)),X_10),Y)
| apply(apply(apply(s,apply(c,X)),X_10),Y) = apply(apply(X,apply(X_10,Y)),Y) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(c,X),Y),apply(X_10,Y)),apply(apply(X,apply(X_10,Y)),Y)) ),[0],$fot(apply(apply(apply(s,apply(c,X)),X_10),Y))]]) ).
cnf(refute_0_48,plain,
( apply(apply(apply(c,X),Y),apply(X_10,Y)) != apply(apply(X,apply(X_10,Y)),Y)
| apply(apply(apply(s,apply(c,X)),X_10),Y) = apply(apply(X,apply(X_10,Y)),Y) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(c,X),Y),apply(X_10,Y)),apply(apply(apply(s,apply(c,X)),X_10),Y)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
apply(apply(apply(s,apply(c,X)),X_10),Y) = apply(apply(X,apply(X_10,Y)),Y),
inference(resolve,[$cnf( $equal(apply(apply(apply(c,X),Y),apply(X_10,Y)),apply(apply(X,apply(X_10,Y)),Y)) )],[refute_0_43,refute_0_48]) ).
cnf(refute_0_50,plain,
apply(apply(apply(s,apply(c,c)),X_16),Y) = apply(apply(c,apply(X_16,Y)),Y),
inference(subst,[],[refute_0_49:[bind(X,$fot(c)),bind(X_10,$fot(X_16))]]) ).
cnf(refute_0_51,plain,
( apply(apply(apply(s,apply(c,c)),X_16),Y) != apply(apply(c,apply(X_16,Y)),Y)
| apply(apply(c,apply(X_16,Y)),Y) = apply(apply(apply(s,apply(c,c)),X_16),Y) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(apply(apply(apply(s,apply(c,c)),X_16),Y))),bind(Y0,$fot(apply(apply(c,apply(X_16,Y)),Y)))]]) ).
cnf(refute_0_52,plain,
apply(apply(c,apply(X_16,Y)),Y) = apply(apply(apply(s,apply(c,c)),X_16),Y),
inference(resolve,[$cnf( $equal(apply(apply(apply(s,apply(c,c)),X_16),Y),apply(apply(c,apply(X_16,Y)),Y)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( apply(apply(apply(c,apply(X_16,Y)),Y),Z) != apply(apply(apply(X_16,Y),Z),Y)
| apply(apply(c,apply(X_16,Y)),Y) != apply(apply(apply(s,apply(c,c)),X_16),Y)
| apply(apply(apply(apply(s,apply(c,c)),X_16),Y),Z) = apply(apply(apply(X_16,Y),Z),Y) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(c,apply(X_16,Y)),Y),Z),apply(apply(apply(X_16,Y),Z),Y)) ),[0,0],$fot(apply(apply(apply(s,apply(c,c)),X_16),Y))]]) ).
cnf(refute_0_54,plain,
( apply(apply(apply(c,apply(X_16,Y)),Y),Z) != apply(apply(apply(X_16,Y),Z),Y)
| apply(apply(apply(apply(s,apply(c,c)),X_16),Y),Z) = apply(apply(apply(X_16,Y),Z),Y) ),
inference(resolve,[$cnf( $equal(apply(apply(c,apply(X_16,Y)),Y),apply(apply(apply(s,apply(c,c)),X_16),Y)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
apply(apply(apply(apply(s,apply(c,c)),X_16),Y),Z) = apply(apply(apply(X_16,Y),Z),Y),
inference(resolve,[$cnf( $equal(apply(apply(apply(c,apply(X_16,Y)),Y),Z),apply(apply(apply(X_16,Y),Z),Y)) )],[refute_0_42,refute_0_54]) ).
cnf(refute_0_56,plain,
apply(apply(apply(apply(s,apply(c,c)),X_81),X_8),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))) = apply(apply(apply(X_81,X_8),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))),X_8),
inference(subst,[],[refute_0_55:[bind(Y,$fot(X_8)),bind(Z,$fot(f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8)))),bind(X_16,$fot(X_81))]]) ).
cnf(refute_0_57,plain,
( apply(apply(apply(X_81,X_8),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))),X_8) != apply(apply(apply(apply(s,b),apply(c,apply(apply(s,apply(c,c)),X_81))),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))),X_8)
| apply(apply(apply(apply(s,apply(c,c)),X_81),X_8),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))) != apply(apply(apply(X_81,X_8),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))),X_8)
| apply(apply(apply(apply(s,apply(c,c)),X_81),X_8),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))) = apply(apply(apply(apply(s,b),apply(c,apply(apply(s,apply(c,c)),X_81))),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(apply(s,apply(c,c)),X_81),X_8),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))),apply(apply(apply(X_81,X_8),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))),X_8)) ),[1],$fot(apply(apply(apply(apply(s,b),apply(c,apply(apply(s,apply(c,c)),X_81))),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))),X_8))]]) ).
cnf(refute_0_58,plain,
( apply(apply(apply(X_81,X_8),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))),X_8) != apply(apply(apply(apply(s,b),apply(c,apply(apply(s,apply(c,c)),X_81))),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))),X_8)
| apply(apply(apply(apply(s,apply(c,c)),X_81),X_8),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))) = apply(apply(apply(apply(s,b),apply(c,apply(apply(s,apply(c,c)),X_81))),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))),X_8) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(s,apply(c,c)),X_81),X_8),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))),apply(apply(apply(X_81,X_8),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))),X_8)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
apply(apply(apply(X_81,X_8),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))),X_8) != apply(apply(apply(apply(s,b),apply(c,apply(apply(s,apply(c,c)),X_81))),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))),X_8),
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(s,apply(c,c)),X_81),X_8),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))),apply(apply(apply(apply(s,b),apply(c,apply(apply(s,apply(c,c)),X_81))),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),X_81))),X_8))),X_8)) )],[refute_0_58,refute_0_41]) ).
cnf(refute_0_60,plain,
apply(apply(apply(apply(s,b),apply(c,apply(apply(s,apply(c,c)),apply(s,b)))),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),apply(s,b)))),apply(c,apply(apply(s,apply(c,c)),apply(s,b)))))),apply(c,apply(apply(s,apply(c,c)),apply(s,b)))) != apply(apply(apply(apply(s,b),apply(c,apply(apply(s,apply(c,c)),apply(s,b)))),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),apply(s,b)))),apply(c,apply(apply(s,apply(c,c)),apply(s,b)))))),apply(c,apply(apply(s,apply(c,c)),apply(s,b)))),
inference(subst,[],[refute_0_59:[bind(X_8,$fot(apply(c,apply(apply(s,apply(c,c)),apply(s,b))))),bind(X_81,$fot(apply(s,b)))]]) ).
cnf(refute_0_61,plain,
apply(apply(apply(apply(s,b),apply(c,apply(apply(s,apply(c,c)),apply(s,b)))),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),apply(s,b)))),apply(c,apply(apply(s,apply(c,c)),apply(s,b)))))),apply(c,apply(apply(s,apply(c,c)),apply(s,b)))) = apply(apply(apply(apply(s,b),apply(c,apply(apply(s,apply(c,c)),apply(s,b)))),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),apply(s,b)))),apply(c,apply(apply(s,apply(c,c)),apply(s,b)))))),apply(c,apply(apply(s,apply(c,c)),apply(s,b)))),
introduced(tautology,[refl,[$fot(apply(apply(apply(apply(s,b),apply(c,apply(apply(s,apply(c,c)),apply(s,b)))),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),apply(s,b)))),apply(c,apply(apply(s,apply(c,c)),apply(s,b)))))),apply(c,apply(apply(s,apply(c,c)),apply(s,b)))))]]) ).
cnf(refute_0_62,plain,
$false,
inference(resolve,[$cnf( $equal(apply(apply(apply(apply(s,b),apply(c,apply(apply(s,apply(c,c)),apply(s,b)))),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),apply(s,b)))),apply(c,apply(apply(s,apply(c,c)),apply(s,b)))))),apply(c,apply(apply(s,apply(c,c)),apply(s,b)))),apply(apply(apply(apply(s,b),apply(c,apply(apply(s,apply(c,c)),apply(s,b)))),f(apply(apply(c,apply(c,apply(apply(s,apply(c,c)),apply(s,b)))),apply(c,apply(apply(s,apply(c,c)),apply(s,b)))))),apply(c,apply(apply(s,apply(c,c)),apply(s,b))))) )],[refute_0_61,refute_0_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COL037-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n018.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 07:36:58 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 9.13/9.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.13/9.34
% 9.13/9.34 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.13/9.35
%------------------------------------------------------------------------------