%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : COL064-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n001.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 06:17:22 AM UTC 2025
% Result : Unsatisfiable 109.16s 109.21s
% Output : CNFRefutation 109.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 18 unt; 0 def)
% Number of atoms : 21 ( 20 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 : 16 ( 4 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 : 31 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
apply(apply(apply(X,f(X)),g(X)),h(X)) != apply(apply(h(X),f(X)),g(X)),
file('theBenchmark.p',prove_v_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),f(X)),g(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),f(X)),g(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)),f(apply(apply(b,X),Y))),g(apply(apply(b,X),Y)))) = false,
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c63,plain,
eq(apply(apply(apply(X,apply(Y,apply(Z,f(apply(apply(b,apply(apply(b,X),Y)),Z))))),g(apply(apply(b,apply(apply(b,X),Y)),Z))),h(apply(apply(b,apply(apply(b,X),Y)),Z))),apply(apply(h(apply(apply(b,apply(apply(b,X),Y)),Z)),f(apply(apply(b,apply(apply(b,X),Y)),Z))),g(apply(apply(b,apply(apply(b,X),Y)),Z)))) = false,
inference(equational,[status(thm)],[c3,c12]) ).
cnf(c459,plain,
eq(apply(apply(apply(X,apply(Y,apply(Z,apply(W,f(apply(apply(b,apply(apply(b,apply(apply(b,X),Y)),Z)),W)))))),g(apply(apply(b,apply(apply(b,apply(apply(b,X),Y)),Z)),W))),h(apply(apply(b,apply(apply(b,apply(apply(b,X),Y)),Z)),W))),apply(apply(h(apply(apply(b,apply(apply(b,apply(apply(b,X),Y)),Z)),W)),f(apply(apply(b,apply(apply(b,apply(apply(b,X),Y)),Z)),W))),g(apply(apply(b,apply(apply(b,apply(apply(b,X),Y)),Z)),W)))) = false,
inference(equational,[status(thm)],[c3,c63]) ).
cnf(c1284,plain,
eq(apply(apply(apply(apply(X,apply(Y,apply(Z,f(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,W)),X)),Y)),Z))))),W),g(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,W)),X)),Y)),Z))),h(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,W)),X)),Y)),Z))),apply(apply(h(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,W)),X)),Y)),Z)),f(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,W)),X)),Y)),Z))),g(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,W)),X)),Y)),Z)))) = false,
inference(equational,[status(thm)],[c2,c459]) ).
cnf(c1285,plain,
eq(apply(apply(apply(X,apply(Y,f(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,Z)),b)),X)),Y)))),apply(Z,g(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,Z)),b)),X)),Y)))),h(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,Z)),b)),X)),Y))),apply(apply(h(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,Z)),b)),X)),Y)),f(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,Z)),b)),X)),Y))),g(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,Z)),b)),X)),Y)))) = false,
inference(equational,[status(thm)],[c3,c1284]) ).
cnf(c1286,plain,
eq(apply(apply(X,f(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,Y)),b)),b)),X))),apply(apply(Y,g(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,Y)),b)),b)),X))),h(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,Y)),b)),b)),X)))),apply(apply(h(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,Y)),b)),b)),X)),f(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,Y)),b)),b)),X))),g(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,Y)),b)),b)),X)))) = false,
inference(equational,[status(thm)],[c3,c1285]) ).
cnf(c1287,plain,
eq(apply(apply(apply(X,g(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,X)),b)),b)),t))),h(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,X)),b)),b)),t))),f(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,X)),b)),b)),t))),apply(apply(h(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,X)),b)),b)),t)),f(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,X)),b)),b)),t))),g(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,X)),b)),b)),t)))) = false,
inference(equational,[status(thm)],[c2,c1286]) ).
cnf(c5057,plain,
eq(apply(apply(apply(X,apply(Y,g(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),b)),t)))),h(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),b)),t))),f(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),b)),t))),apply(apply(h(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),b)),t)),f(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),b)),t))),g(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X),Y))),b)),b)),t)))) = false,
inference(equational,[status(thm)],[c3,c1287]) ).
cnf(c5058,plain,
eq(apply(apply(X,g(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X))),b)),b)),t))),apply(h(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X))),b)),b)),t)),f(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X))),b)),b)),t)))),apply(apply(h(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X))),b)),b)),t)),f(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X))),b)),b)),t))),g(apply(apply(b,apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X))),b)),b)),t)))) = false,
inference(equational,[status(thm)],[c3,c5057]) ).
cnf(c5059,plain,
true = false,
inference(equational,[status(thm)],[c1,c2,c5058]) ).
cnf(g2,plain,
true = false,
inference(equational,[status(thm)],[c5059]) ).
cnf(g3,plain,
$false,
inference(resolution,[status(thm)],[g1,g2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL064-1 : TPTP v9.0.0. Released v1.0.0.
% 0.00/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n001.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 04:55:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 109.16/109.21 % SZS status Unsatisfiable
% 109.16/109.21 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------