%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL011-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 09:37:10 AM UTC 2026
% Result : Unsatisfiable 103.07s 13.36s
% Output : CNFRefutation 103.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 3 RR)
% Number of literals : 21 ( 20 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 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 : 46 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
Y != apply(combinator,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_fixed_point) ).
cnf(c2,axiom,
apply(apply(apply(q1,X),Y2),Z) = apply(X,apply(Z,Y2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',q1_definition) ).
cnf(c3,plain,
apply(apply(apply(q1,q1),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1)))),apply(o,apply(q1,q1))) = apply(q1,apply(apply(o,apply(q1,q1)),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
apply(apply(apply(q1,apply(apply(o,apply(q1,q1)),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1))))),X2),apply(apply(apply(q1,q1),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1)))),apply(o,apply(q1,q1)))) = apply(apply(apply(q1,apply(apply(o,apply(q1,q1)),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1))))),X2),apply(q1,apply(apply(o,apply(q1,q1)),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1)))))),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
apply(apply(apply(q1,apply(apply(o,apply(q1,q1)),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1))))),X2),apply(q1,apply(apply(o,apply(q1,q1)),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1)))))) = apply(apply(apply(o,apply(q1,q1)),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1)))),apply(apply(q1,apply(apply(o,apply(q1,q1)),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1))))),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
apply(apply(apply(q1,X2),apply(apply(X4,apply(apply(q1,apply(q1,X2)),X3)),X3)),X5) = apply(X2,apply(X5,apply(apply(X4,apply(apply(q1,apply(q1,X2)),X3)),X3))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c7,plain,
apply(X5,apply(X4,apply(apply(X3,apply(apply(q1,apply(q1,X5)),X2)),X2))) = apply(apply(apply(q1,X5),apply(apply(X3,apply(apply(q1,apply(q1,X5)),X2)),X2)),X4),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
apply(apply(apply(q1,X4),X2),apply(X3,apply(apply(q1,X4),X2))) = apply(X4,apply(apply(X3,apply(apply(q1,X4),X2)),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c9,plain,
apply(X4,apply(apply(X3,apply(apply(q1,X4),X2)),X2)) = apply(apply(apply(q1,X4),X2),apply(X3,apply(apply(q1,X4),X2))),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,axiom,
apply(apply(o,X2),Y2) = apply(Y2,apply(X2,Y2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',o_definition) ).
cnf(c11,plain,
apply(apply(o,X3),apply(apply(q1,X4),X2)) = apply(apply(apply(q1,X4),X2),apply(X3,apply(apply(q1,X4),X2))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
apply(apply(apply(q1,X4),X2),apply(X3,apply(apply(q1,X4),X2))) = apply(apply(o,X3),apply(apply(q1,X4),X2)),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
apply(X4,apply(apply(X3,apply(apply(q1,X4),X2)),X2)) = apply(apply(o,X3),apply(apply(q1,X4),X2)),
inference(transitivity,[status(thm)],[c9,c12]) ).
cnf(c14,plain,
apply(apply(q1,X4),apply(apply(X3,apply(apply(q1,apply(q1,X4)),X2)),X2)) = apply(apply(o,X3),apply(apply(q1,apply(q1,X4)),X2)),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
apply(apply(apply(q1,X5),apply(apply(X3,apply(apply(q1,apply(q1,X5)),X2)),X2)),X4) = apply(apply(apply(o,X3),apply(apply(q1,apply(q1,X5)),X2)),X4),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
apply(X5,apply(X4,apply(apply(X3,apply(apply(q1,apply(q1,X5)),X2)),X2))) = apply(apply(apply(o,X3),apply(apply(q1,apply(q1,X5)),X2)),X4),
inference(transitivity,[status(thm)],[c7,c15]) ).
cnf(c17,plain,
apply(combinator,apply(apply(apply(q1,apply(apply(o,apply(q1,q1)),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1))))),X2),apply(apply(apply(q1,q1),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1)))),apply(o,apply(q1,q1))))) = apply(apply(apply(o,apply(q1,q1)),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1)))),apply(apply(q1,apply(apply(o,apply(q1,q1)),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1))))),X2)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
apply(apply(apply(o,apply(q1,q1)),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1)))),apply(apply(q1,apply(apply(o,apply(q1,q1)),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1))))),X2)) = apply(combinator,apply(apply(apply(q1,apply(apply(o,apply(q1,q1)),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1))))),X2),apply(apply(apply(q1,q1),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1)))),apply(o,apply(q1,q1))))),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
apply(apply(apply(q1,apply(apply(o,apply(q1,q1)),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1))))),X2),apply(q1,apply(apply(o,apply(q1,q1)),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1)))))) = apply(combinator,apply(apply(apply(q1,apply(apply(o,apply(q1,q1)),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1))))),X2),apply(apply(apply(q1,q1),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1)))),apply(o,apply(q1,q1))))),
inference(transitivity,[status(thm)],[c5,c18]) ).
cnf(c20,plain,
apply(apply(apply(q1,apply(apply(o,apply(q1,q1)),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1))))),X2),apply(apply(apply(q1,q1),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1)))),apply(o,apply(q1,q1)))) = apply(combinator,apply(apply(apply(q1,apply(apply(o,apply(q1,q1)),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1))))),X2),apply(apply(apply(q1,q1),apply(apply(q1,apply(q1,combinator)),apply(o,apply(q1,q1)))),apply(o,apply(q1,q1))))),
inference(transitivity,[status(thm)],[c4,c19]) ).
cnf(c21,plain,
$false,
inference(resolution,[status(thm)],[c1,c20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.23 % Computer : n004.cluster.edu
% 0.07/0.23 % Model : x86_64 x86_64
% 0.07/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.23 % Memory : 8046.5625MB
% 0.07/0.23 % OS : Linux 6.8.0-71-generic
% 0.07/0.23 % CPULimit : 300
% 0.07/0.23 % WCLimit : 300
% 0.07/0.23 % DateTime : Mon Sep 28 21:29:37 UTC 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.24 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 103.07/13.36 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
% 103.07/13.36
% 103.07/13.36 % SZS status Unsatisfiable
% 103.07/13.36
% 103.07/13.36 % SZS output start CNFRefutation
% See solution above
% 103.07/13.38
% 103.07/13.38 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------