%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : COL063-3 : TPTP v9.0.0. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n016.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 06:17:21 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.51s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of clauses : 6 ( 6 unt; 0 nHn; 3 RR)
% Number of literals : 6 ( 5 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,t)),b)),apply(apply(b,b),t)),x),y),z) != apply(apply(z,y),x),
file('theBenchmark.p',prove_f_combinator) ).
cnf(c1,axiom,
apply(apply(t,X),Y) = apply(Y,X),
file('theBenchmark.p',t_definition) ).
cnf(c2,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('theBenchmark.p',b_definition) ).
cnf(c5,plain,
apply(apply(apply(t,X),apply(b,Y)),Z) = apply(Y,apply(X,Z)),
inference(equational,[status(thm)],[c1,c2]) ).
cnf(g1,plain,
apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,t)),b)),apply(apply(b,b),t)),x),y),z) = apply(apply(z,y),x),
inference(equational,[status(thm)],[c1,c2,c5]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : COL063-3 : TPTP v9.0.0. Bugfixed v1.2.0.
% 0.08/0.13 % Command : run_Leo-III %s %d THM
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Jul 14 04:55:34 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.51 % SZS status Unsatisfiable
% 0.20/0.51 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------