%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : COL066-2 : TPTP v9.0.0. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n011.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 : 300s
% DateTime : Tue Jul 15 06:17:23 AM UTC 2025
% Result : Unsatisfiable 60.43s 60.57s
% Output : CNFRefutation 60.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 3 RR)
% Number of literals : 11 ( 10 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
file('theBenchmark.p',prove_p_combinator) ).
cnf(c1,axiom,
apply(apply(w,X),Y) = apply(apply(X,Y),Y),
file('theBenchmark.p',w_definition) ).
cnf(c3,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('theBenchmark.p',b_definition) ).
cnf(c4,axiom,
apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)),
file('theBenchmark.p',q_definition) ).
cnf(c5,plain,
apply(X,apply(Y,X)) = apply(apply(w,apply(q,Y)),X),
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c6,plain,
apply(apply(apply(w,q),X),Y) = apply(X,apply(X,Y)),
inference(equational,[status(thm)],[c1,c4]) ).
cnf(c7,plain,
apply(apply(apply(w,b),X),Y) = apply(X,apply(X,Y)),
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c15,plain,
apply(apply(apply(w,q),X),Y) = apply(apply(apply(w,b),X),Y),
inference(equational,[status(thm)],[c6,c7]) ).
cnf(c19,plain,
apply(apply(X,apply(Y,Z)),Z) = apply(apply(w,apply(apply(q,Y),X)),Z),
inference(equational,[status(thm)],[c1,c4]) ).
cnf(g1,plain,
apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) = apply(apply(x,y),apply(apply(x,y),z)),
inference(equational,[status(thm)],[c1,c4,c5,c7,c15,c19]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL066-2 : TPTP v9.0.0. Bugfixed v1.2.0.
% 0.11/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n011.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 : 300
% 0.12/0.33 % DateTime : Mon Jul 14 04:56:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 60.43/60.57 % SZS status Unsatisfiable
% 60.43/60.57 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------