%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : COL001-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n007.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 06:17:10 AM UTC 2025
% Result : Unsatisfiable 1.44s 1.61s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 16 ( 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,axiom,
apply(i,X) = X,
file('theBenchmark.p',i_definition) ).
cnf(c4,plain,
eq(X,apply(combinator,X)) = false,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c5,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('theBenchmark.p',b_definition) ).
cnf(c6,axiom,
apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)),
file('theBenchmark.p',s_definition) ).
cnf(c9,plain,
apply(apply(X,Y),Y) = apply(apply(apply(s,X),i),Y),
inference(equational,[status(thm)],[c2,c6]) ).
cnf(c23,plain,
apply(apply(apply(s,apply(b,X)),i),Y) = apply(X,apply(Y,Y)),
inference(equational,[status(thm)],[c5,c9]) ).
cnf(c24,plain,
eq(apply(X,X),apply(apply(apply(s,apply(b,combinator)),i),X)) = false,
inference(equational,[status(thm)],[c4,c23]) ).
cnf(c25,plain,
true = false,
inference(equational,[status(thm)],[c1,c24]) ).
cnf(g2,plain,
true = false,
inference(equational,[status(thm)],[c25]) ).
cnf(g3,plain,
$false,
inference(resolution,[status(thm)],[g1,g2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : COL001-2 : TPTP v9.0.0. Released v1.0.0.
% 0.00/0.09 % Command : run_Leo-III %s %d THM
% 0.08/0.29 % Computer : n007.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Mon Jul 14 04:45:04 EDT 2025
% 0.08/0.29 % CPUTime :
% 1.44/1.61 % SZS status Unsatisfiable
% 1.44/1.61 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------