%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : COL063-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n015.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 61.89s 62.12s
% Output : CNFRefutation 61.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 16 unt; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 0 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
apply(apply(apply(X,f(X)),g(X)),h(X)) != apply(apply(h(X),g(X)),f(X)),
file('theBenchmark.p',prove_f_combinator) ).
fof(e,plain,
! [X] :
( true != false
& eq(X,X) = true
& eq(apply(apply(apply(X,f(X)),g(X)),h(X)),apply(apply(h(X),g(X)),f(X))) = false ),
inference(encode_existential,[status(esa)],[g0]) ).
cnf(g1,plain,
true != false,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c1,plain,
eq(X,X) = true,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c2,axiom,
apply(apply(t,X),Y) = apply(Y,X),
file('theBenchmark.p',t_definition) ).
cnf(c3,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('theBenchmark.p',b_definition) ).
cnf(c4,plain,
eq(apply(apply(apply(X,f(X)),g(X)),h(X)),apply(apply(h(X),g(X)),f(X))) = false,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c12,plain,
eq(apply(apply(apply(X,apply(Y,f(apply(apply(b,X),Y)))),g(apply(apply(b,X),Y))),h(apply(apply(b,X),Y))),apply(apply(h(apply(apply(b,X),Y)),g(apply(apply(b,X),Y))),f(apply(apply(b,X),Y)))) = false,
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c67,plain,
eq(apply(apply(apply(X,apply(Y,apply(Z,f(apply(apply(b,X),apply(apply(b,Y),Z)))))),g(apply(apply(b,X),apply(apply(b,Y),Z)))),h(apply(apply(b,X),apply(apply(b,Y),Z)))),apply(apply(h(apply(apply(b,X),apply(apply(b,Y),Z))),g(apply(apply(b,X),apply(apply(b,Y),Z)))),f(apply(apply(b,X),apply(apply(b,Y),Z))))) = false,
inference(equational,[status(thm)],[c3,c12]) ).
cnf(c158,plain,
eq(apply(apply(apply(apply(X,apply(Y,f(apply(apply(b,apply(t,Z)),apply(apply(b,X),Y))))),Z),g(apply(apply(b,apply(t,Z)),apply(apply(b,X),Y)))),h(apply(apply(b,apply(t,Z)),apply(apply(b,X),Y)))),apply(apply(h(apply(apply(b,apply(t,Z)),apply(apply(b,X),Y))),g(apply(apply(b,apply(t,Z)),apply(apply(b,X),Y)))),f(apply(apply(b,apply(t,Z)),apply(apply(b,X),Y))))) = false,
inference(equational,[status(thm)],[c2,c67]) ).
cnf(c159,plain,
eq(apply(apply(apply(X,f(apply(apply(b,apply(t,Y)),apply(apply(b,b),X)))),apply(Y,g(apply(apply(b,apply(t,Y)),apply(apply(b,b),X))))),h(apply(apply(b,apply(t,Y)),apply(apply(b,b),X)))),apply(apply(h(apply(apply(b,apply(t,Y)),apply(apply(b,b),X))),g(apply(apply(b,apply(t,Y)),apply(apply(b,b),X)))),f(apply(apply(b,apply(t,Y)),apply(apply(b,b),X))))) = false,
inference(equational,[status(thm)],[c3,c158]) ).
cnf(c899,plain,
eq(apply(apply(apply(X,apply(Y,f(apply(apply(b,apply(t,Z)),apply(apply(b,b),apply(apply(b,X),Y)))))),apply(Z,g(apply(apply(b,apply(t,Z)),apply(apply(b,b),apply(apply(b,X),Y)))))),h(apply(apply(b,apply(t,Z)),apply(apply(b,b),apply(apply(b,X),Y))))),apply(apply(h(apply(apply(b,apply(t,Z)),apply(apply(b,b),apply(apply(b,X),Y)))),g(apply(apply(b,apply(t,Z)),apply(apply(b,b),apply(apply(b,X),Y))))),f(apply(apply(b,apply(t,Z)),apply(apply(b,b),apply(apply(b,X),Y)))))) = false,
inference(equational,[status(thm)],[c3,c159]) ).
cnf(c900,plain,
eq(apply(apply(X,f(apply(apply(b,apply(t,Y)),apply(apply(b,b),apply(apply(b,b),X))))),apply(apply(Y,g(apply(apply(b,apply(t,Y)),apply(apply(b,b),apply(apply(b,b),X))))),h(apply(apply(b,apply(t,Y)),apply(apply(b,b),apply(apply(b,b),X)))))),apply(apply(h(apply(apply(b,apply(t,Y)),apply(apply(b,b),apply(apply(b,b),X)))),g(apply(apply(b,apply(t,Y)),apply(apply(b,b),apply(apply(b,b),X))))),f(apply(apply(b,apply(t,Y)),apply(apply(b,b),apply(apply(b,b),X)))))) = false,
inference(equational,[status(thm)],[c3,c899]) ).
cnf(c901,plain,
eq(apply(apply(apply(X,g(apply(apply(b,apply(t,X)),apply(apply(b,b),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,X)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X)),apply(apply(b,b),apply(apply(b,b),t))))),apply(apply(h(apply(apply(b,apply(t,X)),apply(apply(b,b),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,X)),apply(apply(b,b),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,X)),apply(apply(b,b),apply(apply(b,b),t)))))) = false,
inference(equational,[status(thm)],[c2,c900]) ).
cnf(c902,plain,
true = false,
inference(equational,[status(thm)],[c1,c2,c901]) ).
cnf(g2,plain,
true = false,
inference(equational,[status(thm)],[c902]) ).
cnf(g3,plain,
$false,
inference(resolution,[status(thm)],[g1,g2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL063-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n015.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 04:55:34 EDT 2025
% 0.12/0.34 % CPUTime :
% 61.89/62.12 % SZS status Unsatisfiable
% 61.89/62.12 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------