%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL033-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:37:13 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.26s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 10 RR)
% Number of literals : 22 ( 21 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; 3 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_fixed_point) ).
cnf(c2,axiom,
apply(apply(apply(b,X),Y2),Z) = apply(X,apply(Y2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
cnf(c3,plain,
apply(apply(apply(b,m),l),f(apply(apply(b,m),l))) = apply(m,apply(l,f(apply(apply(b,m),l)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
apply(apply(l,X2),Y2) = apply(X2,apply(Y2,Y2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l_definition) ).
cnf(c5,plain,
apply(apply(l,X3),X2) = apply(X3,apply(X2,X2)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,axiom,
apply(m,X2) = apply(X2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c7,plain,
apply(X2,X2) = apply(m,X2),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
apply(X3,apply(X2,X2)) = apply(X3,apply(m,X2)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
apply(apply(l,X3),X2) = apply(X3,apply(m,X2)),
inference(transitivity,[status(thm)],[c5,c8]) ).
cnf(c10,plain,
apply(apply(l,X2),apply(l,X2)) = apply(X2,apply(m,apply(l,X2))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
apply(X2,apply(m,apply(l,X2))) = apply(apply(l,X2),apply(l,X2)),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
apply(m,apply(l,X2)) = apply(apply(l,X2),apply(l,X2)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c13,plain,
apply(apply(l,X2),apply(l,X2)) = apply(m,apply(l,X2)),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
apply(X2,apply(m,apply(l,X2))) = apply(m,apply(l,X2)),
inference(transitivity,[status(thm)],[c11,c13]) ).
cnf(c15,plain,
apply(f(apply(apply(b,m),l)),apply(m,apply(l,f(apply(apply(b,m),l))))) = apply(m,apply(l,f(apply(apply(b,m),l)))),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
apply(m,apply(l,f(apply(apply(b,m),l)))) = apply(f(apply(apply(b,m),l)),apply(m,apply(l,f(apply(apply(b,m),l))))),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
apply(apply(apply(b,m),l),f(apply(apply(b,m),l))) = apply(m,apply(l,f(apply(apply(b,m),l)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c18,plain,
apply(m,apply(l,f(apply(apply(b,m),l)))) = apply(apply(apply(b,m),l),f(apply(apply(b,m),l))),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
apply(f(apply(apply(b,m),l)),apply(m,apply(l,f(apply(apply(b,m),l))))) = apply(f(apply(apply(b,m),l)),apply(apply(apply(b,m),l),f(apply(apply(b,m),l)))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
apply(m,apply(l,f(apply(apply(b,m),l)))) = apply(f(apply(apply(b,m),l)),apply(apply(apply(b,m),l),f(apply(apply(b,m),l)))),
inference(transitivity,[status(thm)],[c16,c19]) ).
cnf(c21,plain,
apply(apply(apply(b,m),l),f(apply(apply(b,m),l))) = apply(f(apply(apply(b,m),l)),apply(apply(apply(b,m),l),f(apply(apply(b,m),l)))),
inference(transitivity,[status(thm)],[c3,c20]) ).
cnf(c22,plain,
$false,
inference(resolution,[status(thm)],[c1,c21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL033-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n020.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Mon Sep 28 21:31:04 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.26 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.19/0.26
% 0.19/0.26 % SZS status Unsatisfiable
% 0.19/0.26
% 0.19/0.26 % SZS output start CNFRefutation
% See solution above
% 0.19/0.28
% 0.19/0.28 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------