%------------------------------------------------------------------------------
% File : Toma---0.7
% Problem : COL003-13 : TPTP v9.0.0. Released v2.1.0.
% 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 250.21s 250.29s
% Output : CNFRefutation 250.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 5 RR)
% Number of literals : 15 ( 14 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(g0,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('theBenchmark.p',prove_strong_fixed_point) ).
cnf(c1,axiom,
apply(apply(w,X),Y) = apply(apply(X,Y),Y),
file('theBenchmark.p',w_definition) ).
cnf(c2,plain,
apply(apply(w,w),X) = apply(apply(X,X),X),
inference(equational,[status(thm)],[c1]) ).
cnf(c3,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('theBenchmark.p',b_definition) ).
cnf(c4,plain,
apply(X,apply(Y,Y)) = apply(apply(w,apply(b,X)),Y),
inference(equational,[status(thm)],[c1,c3]) ).
cnf(c50,plain,
apply(apply(apply(apply(w,apply(b,b)),X),Y),Z) = apply(apply(X,X),apply(Y,Z)),
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c51,plain,
apply(apply(apply(w,apply(b,apply(b,X))),Y),Z) = apply(X,apply(apply(Y,Y),Z)),
inference(equational,[status(thm)],[c3,c4]) ).
cnf(c162,axiom,
strong_fixed_point = apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)),
file('theBenchmark.p',strong_fixed_point) ).
cnf(c163,plain,
apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)) = strong_fixed_point,
inference(equational,[status(thm)],[c162]) ).
cnf(c165,plain,
apply(apply(w,w),apply(w,apply(b,apply(b,X)))) = apply(strong_fixed_point,X),
inference(equational,[status(thm)],[c3,c163]) ).
cnf(c250,plain,
apply(apply(apply(apply(w,apply(b,b)),apply(X,Y)),X),Y) = apply(apply(w,w),apply(X,Y)),
inference(equational,[status(thm)],[c2,c50]) ).
cnf(c646,plain,
apply(apply(apply(w,apply(b,apply(b,X))),Y),apply(Z,W)) = apply(X,apply(apply(apply(apply(w,apply(b,b)),Y),Z),W)),
inference(equational,[status(thm)],[c50,c51]) ).
cnf(c647,plain,
apply(X,apply(strong_fixed_point,X)) = apply(strong_fixed_point,X),
inference(equational,[status(thm)],[c2,c165,c250,c646]) ).
cnf(g1,plain,
apply(strong_fixed_point,fixed_pt) = apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(equational,[status(thm)],[c647]) ).
cnf(g2,plain,
$false,
inference(resolution,[status(thm)],[g0,g1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : COL003-13 : TPTP v9.0.0. Released v2.1.0.
% 0.12/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n007.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 04:45:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 250.21/250.29 % SZS status Unsatisfiable
% 250.21/250.29 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------