%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL024-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 09:37:12 AM UTC 2026
% Result : Unsatisfiable 0.06s 0.23s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 4 RR)
% Number of literals : 11 ( 10 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
Y != apply(combinator,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
cnf(c2,axiom,
apply(apply(apply(b,X),Y2),Z) = apply(X,apply(Y2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
cnf(c3,plain,
apply(apply(apply(b,X3),X2),apply(apply(b,X3),X2)) = apply(X3,apply(X2,apply(apply(b,X3),X2))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
apply(X3,apply(X2,apply(apply(b,X3),X2))) = apply(apply(apply(b,X3),X2),apply(apply(b,X3),X2)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
apply(m,X2) = apply(X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_definition) ).
cnf(c6,plain,
apply(m,apply(apply(b,X3),X2)) = apply(apply(apply(b,X3),X2),apply(apply(b,X3),X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
apply(apply(apply(b,X3),X2),apply(apply(b,X3),X2)) = apply(m,apply(apply(b,X3),X2)),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
apply(X3,apply(X2,apply(apply(b,X3),X2))) = apply(m,apply(apply(b,X3),X2)),
inference(transitivity,[status(thm)],[c4,c7]) ).
cnf(c9,plain,
apply(combinator,apply(m,apply(apply(b,combinator),m))) = apply(m,apply(apply(b,combinator),m)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
apply(m,apply(apply(b,combinator),m)) = apply(combinator,apply(m,apply(apply(b,combinator),m))),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
$false,
inference(resolution,[status(thm)],[c1,c10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL024-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.16 % Computer : n009.cluster.edu
% 0.06/0.16 % Model : x86_64 x86_64
% 0.06/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.16 % Memory : 8046.5625MB
% 0.06/0.16 % OS : Linux 6.8.0-71-generic
% 0.06/0.16 % CPULimit : 300
% 0.06/0.16 % WCLimit : 300
% 0.06/0.16 % DateTime : Mon Sep 28 21:30:00 UTC 2026
% 0.06/0.16 % CPUTime :
% 0.06/0.16 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.23 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 0.06/0.23
% 0.06/0.23 % SZS status Unsatisfiable
% 0.06/0.23
% 0.06/0.23 % SZS output start CNFRefutation
% See solution above
% 0.06/0.24
% 0.06/0.24 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------