%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL062-1 : 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 09:37:19 AM UTC 2026
% Result : Unsatisfiable 6.39s 1.08s
% Output : CNFRefutation 6.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 28 RR)
% Number of literals : 30 ( 29 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
apply(apply(apply(X,f(X)),g(X)),h(X)) != apply(apply(f(X),h(X)),g(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_combinator) ).
cnf(c2,axiom,
apply(apply(apply(b,X2),Y),Z) = apply(X2,apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
cnf(c3,plain,
apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),t),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),t),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
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),t)),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),t),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
apply(apply(t,X2),Y2) = apply(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_definition) ).
cnf(c7,plain,
apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),t),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))) = apply(apply(apply(apply(b,b),t),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(apply(b,b),t)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
apply(apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),t),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(apply(apply(apply(b,b),t),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(apply(b,b),t)),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),t),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(apply(apply(apply(apply(b,b),t),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(apply(b,b),t)),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
apply(apply(apply(b,b),t),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(b,apply(t,f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c11,plain,
apply(apply(apply(apply(b,b),t),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(apply(b,b),t)) = apply(apply(b,apply(t,f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(apply(b,b),t)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
apply(apply(apply(apply(apply(b,b),t),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(apply(b,b),t)),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(apply(b,apply(t,f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(apply(b,b),t)),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
apply(apply(apply(apply(apply(apply(b,b),t),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(apply(b,b),t)),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(apply(apply(b,apply(t,f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(apply(b,b),t)),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
apply(apply(apply(b,apply(t,f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(apply(b,b),t)),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(t,f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(apply(apply(b,b),t),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c15,plain,
apply(apply(apply(apply(b,apply(t,f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(apply(b,b),t)),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(apply(t,f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(apply(apply(b,b),t),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
apply(apply(t,f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(apply(apply(b,b),t),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))) = apply(apply(apply(apply(b,b),t),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c17,plain,
apply(apply(apply(t,f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(apply(apply(b,b),t),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(apply(apply(apply(b,b),t),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
apply(apply(apply(b,b),t),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(b,apply(t,g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c19,plain,
apply(apply(apply(apply(b,b),t),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(b,apply(t,g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
apply(apply(apply(apply(apply(b,b),t),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(apply(b,apply(t,g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
apply(apply(apply(b,apply(t,g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(t,g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
apply(apply(t,g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))) = apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c23,plain,
apply(apply(apply(b,apply(t,g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(transitivity,[status(thm)],[c21,c22]) ).
cnf(c24,plain,
apply(apply(apply(apply(apply(b,b),t),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(transitivity,[status(thm)],[c20,c23]) ).
cnf(c25,plain,
apply(apply(apply(t,f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(apply(apply(b,b),t),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(transitivity,[status(thm)],[c17,c24]) ).
cnf(c26,plain,
apply(apply(apply(apply(b,apply(t,f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),apply(apply(b,b),t)),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(transitivity,[status(thm)],[c15,c25]) ).
cnf(c27,plain,
apply(apply(apply(apply(apply(apply(b,b),t),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),apply(apply(b,b),t)),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(transitivity,[status(thm)],[c13,c26]) ).
cnf(c28,plain,
apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),t),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(transitivity,[status(thm)],[c9,c27]) ).
cnf(c29,plain,
apply(apply(apply(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)),f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))) = apply(apply(f(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t))),h(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),g(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)))),
inference(transitivity,[status(thm)],[c5,c28]) ).
cnf(c30,plain,
$false,
inference(resolution,[status(thm)],[c1,c29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL062-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n017.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 21:27:47 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.39/1.08 Command-line arguments: --flatten-regeneralise
% 6.39/1.08
% 6.39/1.08 % SZS status Unsatisfiable
% 6.39/1.08
% 6.39/1.08 % SZS output start CNFRefutation
% See solution above
% 6.39/1.10
% 6.39/1.10 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------