%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : COL075-2 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n004.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 06:17:24 AM UTC 2025
% Result : Unsatisfiable 60.23s 60.41s
% Output : CNFRefutation 60.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 12 unt; 0 def)
% Number of atoms : 15 ( 14 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 : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 2 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
apply(apply(Y,b(Y)),c(Y)) != apply(b(Y),b(Y)),
file('theBenchmark.p',prove_diagonal_combinator) ).
fof(e,plain,
! [Y] :
( true != false
& eq(Y,Y) = true
& eq(apply(apply(Y,b(Y)),c(Y)),apply(b(Y),b(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(apply(k,X),Y) = X,
file('theBenchmark.p',k_definition) ).
cnf(c3,axiom,
apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,apply(k,Z)),apply(Y,Z)),
file('theBenchmark.p',abstraction) ).
cnf(c4,plain,
apply(apply(X,apply(k,Y)),apply(Z,Y)) = apply(apply(apply(abstraction,X),Z),Y),
inference(equational,[status(thm)],[c3]) ).
cnf(c7,plain,
apply(apply(apply(abstraction,X),apply(k,Y)),Z) = apply(apply(X,apply(k,Z)),Y),
inference(equational,[status(thm)],[c2,c4]) ).
cnf(c8,plain,
apply(apply(apply(apply(abstraction,abstraction),k),X),Y) = apply(X,X),
inference(equational,[status(thm)],[c2,c4,c7]) ).
cnf(c16,plain,
eq(apply(apply(X,b(X)),c(X)),apply(b(X),b(X))) = false,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c17,plain,
true = false,
inference(equational,[status(thm)],[c1,c8,c16]) ).
cnf(g2,plain,
true = false,
inference(equational,[status(thm)],[c17]) ).
cnf(g3,plain,
$false,
inference(resolution,[status(thm)],[g1,g2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL075-2 : TPTP v9.0.0. Released v1.2.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.32 % Computer : n004.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Mon Jul 14 04:57:34 EDT 2025
% 0.12/0.32 % CPUTime :
% 60.23/60.41 % SZS status Unsatisfiable
% 60.23/60.41 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------