%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 09:37:08 AM UTC 2026
% Result : Unsatisfiable 12.40s 1.90s
% Output : CNFRefutation 13.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 2 RR)
% Number of literals : 24 ( 23 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 57 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
cnf(c2,axiom,
apply(apply(apply(s,X),Y2),Z) = apply(apply(X,Z),apply(Y2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).
cnf(c3,plain,
apply(apply(apply(s,X4),apply(apply(s,k),X3)),X2) = apply(apply(X4,X2),apply(apply(apply(s,k),X3),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
apply(apply(apply(s,k),X3),X2) = apply(apply(k,X2),apply(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c5,axiom,
apply(apply(k,X2),Y2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
cnf(c6,plain,
apply(apply(k,X2),apply(X3,X2)) = X2,
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
apply(apply(apply(s,k),X3),X2) = X2,
inference(transitivity,[status(thm)],[c4,c6]) ).
cnf(c8,plain,
apply(apply(X4,X2),apply(apply(apply(s,k),X3),X2)) = apply(apply(X4,X2),X2),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
apply(apply(apply(s,X4),apply(apply(s,k),X3)),X2) = apply(apply(X4,X2),X2),
inference(transitivity,[status(thm)],[c3,c8]) ).
cnf(c10,plain,
apply(apply(apply(s,apply(s,apply(k,X4))),apply(apply(s,k),X2)),X3) = apply(apply(apply(s,apply(k,X4)),X3),X3),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
apply(apply(apply(s,apply(k,X4)),X3),X2) = apply(apply(apply(k,X4),X2),apply(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
apply(apply(k,X3),X2) = X3,
inference(substitution,[status(thm)],[c5]) ).
cnf(c13,plain,
apply(apply(apply(k,X4),X2),apply(X3,X2)) = apply(X4,apply(X3,X2)),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
apply(apply(apply(s,apply(k,X4)),X3),X2) = apply(X4,apply(X3,X2)),
inference(transitivity,[status(thm)],[c11,c13]) ).
cnf(c15,plain,
apply(apply(apply(s,apply(k,X3)),X2),X2) = apply(X3,apply(X2,X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
apply(apply(apply(s,apply(s,apply(k,X4))),apply(apply(s,k),X2)),X3) = apply(X4,apply(X3,X3)),
inference(transitivity,[status(thm)],[c10,c15]) ).
cnf(c17,plain,
apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2))) = apply(apply(s,apply(apply(s,k),X3)),apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)))),
inference(substitution,[status(thm)],[c16]) ).
cnf(c18,plain,
apply(apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2))),f(apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2))))) = apply(apply(apply(s,apply(apply(s,k),X3)),apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)))),f(apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2))))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
apply(apply(apply(s,apply(apply(s,k),X4)),X3),X2) = apply(apply(apply(apply(s,k),X4),X2),apply(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c20,plain,
apply(apply(apply(apply(s,k),X4),X2),apply(X3,X2)) = apply(X2,apply(X3,X2)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c21,plain,
apply(apply(apply(s,apply(apply(s,k),X4)),X3),X2) = apply(X2,apply(X3,X2)),
inference(transitivity,[status(thm)],[c19,c20]) ).
cnf(c22,plain,
apply(apply(apply(s,apply(apply(s,k),X3)),apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)))),f(apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2))))) = apply(f(apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)))),apply(apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2))),f(apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)))))),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
apply(apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2))),f(apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2))))) = apply(f(apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)))),apply(apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2))),f(apply(apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)),apply(apply(s,apply(s,apply(k,apply(s,apply(apply(s,k),X3))))),apply(apply(s,k),X2)))))),
inference(transitivity,[status(thm)],[c18,c22]) ).
cnf(c24,plain,
$false,
inference(resolution,[status(thm)],[c1,c23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.16 % Computer : n017.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Mon Sep 28 21:24:51 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.40/1.90 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
% 12.40/1.90
% 12.40/1.90 % SZS status Unsatisfiable
% 12.40/1.90
% 12.40/1.90 % SZS output start CNFRefutation
% See solution above
% 13.16/1.92
% 13.16/1.92 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------