%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : COL009-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n008.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 06:17:13 AM UTC 2025
% Result : Unsatisfiable 22.03s 22.17s
% Output : CNFRefutation 22.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 13 unt; 0 def)
% Number of atoms : 16 ( 15 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 : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
Y != apply(combinator,Y),
file('theBenchmark.p',prove_fixed_point) ).
fof(e,plain,
! [Y] :
( true != false
& eq(Y,Y) = true
& eq(Y,apply(combinator,Y)) = 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,plain,
eq(X,apply(combinator,X)) = false,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c3,axiom,
apply(apply(l2,X),Y) = apply(Y,apply(X,X)),
file('theBenchmark.p',l2_definition) ).
cnf(c4,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('theBenchmark.p',b_definition) ).
cnf(c12,plain,
apply(X,apply(Y,apply(Z,Z))) = apply(apply(l2,Z),apply(apply(b,X),Y)),
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c34,plain,
apply(X,apply(Y,apply(Z,apply(apply(b,Y),Z)))) = apply(apply(l2,apply(apply(b,Y),Z)),X),
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c158,plain,
eq(apply(X,apply(Y,Y)),apply(apply(l2,Y),apply(apply(b,combinator),X))) = false,
inference(equational,[status(thm)],[c2,c12]) ).
cnf(c159,plain,
eq(apply(apply(X,X),apply(Y,apply(Z,apply(apply(b,Y),Z)))),apply(apply(l2,X),apply(apply(b,combinator),apply(l2,apply(apply(b,Y),Z))))) = false,
inference(equational,[status(thm)],[c34,c158]) ).
cnf(c160,plain,
true = false,
inference(equational,[status(thm)],[c1,c159]) ).
cnf(g2,plain,
true = false,
inference(equational,[status(thm)],[c160]) ).
cnf(g3,plain,
$false,
inference(resolution,[status(thm)],[g1,g2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : COL009-1 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.13 % Command : run_Leo-III %s %d THM
% 0.13/0.34 % Computer : n008.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 04:48:04 EDT 2025
% 0.13/0.34 % CPUTime :
% 22.03/22.17 % SZS status Unsatisfiable
% 22.03/22.17 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------