%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL064-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 09:37:21 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.23s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of clauses : 37 ( 37 unt; 0 nHn; 35 RR)
% Number of literals : 37 ( 36 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 5 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t))),x),y),z) != apply(apply(z,x),y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_combinator) ).
cnf(c2,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
cnf(c3,plain,
apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t))),x) = apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),apply(apply(b,b),t)),x)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t))),x),y) = apply(apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),apply(apply(b,b),t)),x)),y),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t))),x),y),z) = apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),apply(apply(b,b),t)),x)),y),z),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
apply(apply(apply(b,b),apply(apply(b,b),t)),x) = apply(b,apply(apply(apply(b,b),t),x)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c7,plain,
apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),apply(apply(b,b),t)),x)) = apply(apply(t,apply(apply(b,b),t)),apply(b,apply(apply(apply(b,b),t),x))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
apply(apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),apply(apply(b,b),t)),x)),y) = apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(apply(apply(b,b),t),x))),y),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),apply(apply(b,b),t)),x)),y),z) = apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(apply(apply(b,b),t),x))),y),z),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
apply(apply(apply(b,b),t),x) = apply(b,apply(t,x)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c11,plain,
apply(b,apply(apply(apply(b,b),t),x)) = apply(b,apply(b,apply(t,x))),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
apply(apply(t,apply(apply(b,b),t)),apply(b,apply(apply(apply(b,b),t),x))) = apply(apply(t,apply(apply(b,b),t)),apply(b,apply(b,apply(t,x)))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(apply(apply(b,b),t),x))),y) = apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(b,apply(t,x)))),y),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(apply(apply(b,b),t),x))),y),z) = apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(b,apply(t,x)))),y),z),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,axiom,
apply(apply(t,X2),Y2) = apply(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_definition) ).
cnf(c16,plain,
apply(apply(t,apply(apply(b,b),t)),apply(b,apply(b,apply(t,x)))) = apply(apply(b,apply(b,apply(t,x))),apply(apply(b,b),t)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(b,apply(t,x)))),y) = apply(apply(apply(b,apply(b,apply(t,x))),apply(apply(b,b),t)),y),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(b,apply(t,x)))),y),z) = apply(apply(apply(apply(b,apply(b,apply(t,x))),apply(apply(b,b),t)),y),z),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
apply(apply(apply(b,apply(b,apply(t,x))),apply(apply(b,b),t)),y) = apply(apply(b,apply(t,x)),apply(apply(apply(b,b),t),y)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c20,plain,
apply(apply(apply(apply(b,apply(b,apply(t,x))),apply(apply(b,b),t)),y),z) = apply(apply(apply(b,apply(t,x)),apply(apply(apply(b,b),t),y)),z),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
apply(apply(apply(b,apply(t,x)),apply(apply(apply(b,b),t),y)),z) = apply(apply(t,x),apply(apply(apply(apply(b,b),t),y),z)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
apply(apply(apply(b,b),t),y) = apply(b,apply(t,y)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c23,plain,
apply(apply(apply(apply(b,b),t),y),z) = apply(apply(b,apply(t,y)),z),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
apply(apply(t,x),apply(apply(apply(apply(b,b),t),y),z)) = apply(apply(t,x),apply(apply(b,apply(t,y)),z)),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
apply(apply(t,x),apply(apply(b,apply(t,y)),z)) = apply(apply(apply(b,apply(t,y)),z),x),
inference(substitution,[status(thm)],[c15]) ).
cnf(c26,plain,
apply(apply(apply(b,apply(t,y)),z),x) = apply(apply(t,y),apply(z,x)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c27,plain,
apply(apply(t,y),apply(z,x)) = apply(apply(z,x),y),
inference(substitution,[status(thm)],[c15]) ).
cnf(c28,plain,
apply(apply(apply(b,apply(t,y)),z),x) = apply(apply(z,x),y),
inference(transitivity,[status(thm)],[c26,c27]) ).
cnf(c29,plain,
apply(apply(t,x),apply(apply(b,apply(t,y)),z)) = apply(apply(z,x),y),
inference(transitivity,[status(thm)],[c25,c28]) ).
cnf(c30,plain,
apply(apply(t,x),apply(apply(apply(apply(b,b),t),y),z)) = apply(apply(z,x),y),
inference(transitivity,[status(thm)],[c24,c29]) ).
cnf(c31,plain,
apply(apply(apply(b,apply(t,x)),apply(apply(apply(b,b),t),y)),z) = apply(apply(z,x),y),
inference(transitivity,[status(thm)],[c21,c30]) ).
cnf(c32,plain,
apply(apply(apply(apply(b,apply(b,apply(t,x))),apply(apply(b,b),t)),y),z) = apply(apply(z,x),y),
inference(transitivity,[status(thm)],[c20,c31]) ).
cnf(c33,plain,
apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(b,apply(t,x)))),y),z) = apply(apply(z,x),y),
inference(transitivity,[status(thm)],[c18,c32]) ).
cnf(c34,plain,
apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(b,apply(apply(apply(b,b),t),x))),y),z) = apply(apply(z,x),y),
inference(transitivity,[status(thm)],[c14,c33]) ).
cnf(c35,plain,
apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),apply(apply(b,b),t)),x)),y),z) = apply(apply(z,x),y),
inference(transitivity,[status(thm)],[c9,c34]) ).
cnf(c36,plain,
apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),apply(apply(b,b),t))),x),y),z) = apply(apply(z,x),y),
inference(transitivity,[status(thm)],[c5,c35]) ).
cnf(c37,plain,
$false,
inference(resolution,[status(thm)],[c1,c36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL064-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.16 % Computer : n006.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Mon Sep 28 21:32:10 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.23 Command-line arguments: --no-flatten-goal
% 0.09/0.23
% 0.09/0.23 % SZS status Unsatisfiable
% 0.09/0.23
% 0.09/0.24 % SZS output start CNFRefutation
% See solution above
% 0.09/0.26
% 0.09/0.26 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------