%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : COL057-1 : TPTP v9.0.0. Released v1.0.0.
% 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 06:17:19 AM UTC 2025
% Result : Unsatisfiable 65.43s 65.50s
% Output : CNFRefutation 65.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% 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 : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))),
file('theBenchmark.p',prove_strong_fixed_point) ).
fof(e,plain,
! [Y] :
( true != false
& eq(Y,Y) = true
& eq(apply(Y,f(Y)),apply(f(Y),apply(Y,f(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(c3,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('theBenchmark.p',b_definition) ).
cnf(c4,axiom,
apply(apply(apply(c,X),Y),Z) = apply(apply(X,Z),Y),
file('theBenchmark.p',c_definition) ).
cnf(c5,axiom,
apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)),
file('theBenchmark.p',s_definition) ).
cnf(c6,plain,
apply(X,apply(Y,X)) = apply(apply(apply(s,i),Y),X),
inference(equational,[status(thm)],[c2,c5]) ).
cnf(c11,plain,
apply(apply(apply(s,apply(c,X)),Y),Z) = apply(apply(X,apply(Y,Z)),Z),
inference(equational,[status(thm)],[c4,c5]) ).
cnf(c26,plain,
eq(apply(X,f(X)),apply(f(X),apply(X,f(X)))) = false,
inference(split_conjunct,[status(thm)],[e]) ).
cnf(c63,plain,
apply(apply(apply(s,apply(c,apply(b,X))),Y),Z) = apply(X,apply(apply(Y,Z),Z)),
inference(equational,[status(thm)],[c3,c11]) ).
cnf(c154,plain,
eq(apply(X,f(X)),apply(apply(apply(s,i),X),f(X))) = false,
inference(equational,[status(thm)],[c6,c26]) ).
cnf(c155,plain,
eq(apply(apply(apply(X,Y),Y),f(apply(apply(X,Y),Y))),apply(apply(apply(apply(s,apply(c,apply(b,apply(s,i)))),X),Y),f(apply(apply(X,Y),Y)))) = false,
inference(equational,[status(thm)],[c63,c154]) ).
cnf(c156,plain,
true = false,
inference(equational,[status(thm)],[c1,c155]) ).
cnf(g2,plain,
true = false,
inference(equational,[status(thm)],[c156]) ).
cnf(g3,plain,
$false,
inference(resolution,[status(thm)],[g1,g2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL057-1 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Jul 14 04:54:04 EDT 2025
% 0.11/0.33 % CPUTime :
% 65.43/65.50 % SZS status Unsatisfiable
% 65.43/65.50 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------