%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL004-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 0.10s 0.23s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of clauses : 42 ( 42 unt; 0 nHn; 40 RR)
% Number of literals : 42 ( 41 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 5 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_u_combinator) ).
cnf(c2,axiom,
apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).
cnf(c3,plain,
apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x) = apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) = apply(apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
apply(apply(k,X2),Y2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
cnf(c6,plain,
apply(apply(k,apply(s,apply(apply(s,k),k))),x) = apply(s,apply(apply(s,k),k)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)) = apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
apply(apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y) = apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y) = apply(apply(apply(apply(s,k),k),y),apply(apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x),y)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
apply(apply(apply(s,k),k),y) = apply(apply(k,y),apply(k,y)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c11,plain,
apply(apply(apply(apply(s,k),k),y),apply(apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x),y)) = apply(apply(apply(k,y),apply(k,y)),apply(apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x),y)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
apply(apply(k,y),apply(k,y)) = y,
inference(substitution,[status(thm)],[c5]) ).
cnf(c13,plain,
apply(apply(apply(k,y),apply(k,y)),apply(apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x),y)) = apply(y,apply(apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x),y)),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x) = apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c15,plain,
apply(apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x),y) = apply(apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x)),y),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
apply(y,apply(apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x),y)) = apply(y,apply(apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x)),y)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
apply(apply(apply(s,k),k),x) = apply(apply(k,x),apply(k,x)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c18,plain,
apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x)) = apply(apply(apply(k,x),apply(k,x)),apply(apply(apply(s,k),k),x)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
apply(apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x)),y) = apply(apply(apply(apply(k,x),apply(k,x)),apply(apply(apply(s,k),k),x)),y),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
apply(y,apply(apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x)),y)) = apply(y,apply(apply(apply(apply(k,x),apply(k,x)),apply(apply(apply(s,k),k),x)),y)),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
apply(apply(apply(s,k),k),x) = apply(apply(k,x),apply(k,x)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c22,plain,
apply(apply(apply(k,x),apply(k,x)),apply(apply(apply(s,k),k),x)) = apply(apply(apply(k,x),apply(k,x)),apply(apply(k,x),apply(k,x))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
apply(apply(apply(apply(k,x),apply(k,x)),apply(apply(apply(s,k),k),x)),y) = apply(apply(apply(apply(k,x),apply(k,x)),apply(apply(k,x),apply(k,x))),y),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
apply(y,apply(apply(apply(apply(k,x),apply(k,x)),apply(apply(apply(s,k),k),x)),y)) = apply(y,apply(apply(apply(apply(k,x),apply(k,x)),apply(apply(k,x),apply(k,x))),y)),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
apply(apply(k,x),apply(k,x)) = x,
inference(substitution,[status(thm)],[c5]) ).
cnf(c26,plain,
apply(apply(apply(k,x),apply(k,x)),apply(apply(k,x),apply(k,x))) = apply(x,apply(apply(k,x),apply(k,x))),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
apply(apply(apply(apply(k,x),apply(k,x)),apply(apply(k,x),apply(k,x))),y) = apply(apply(x,apply(apply(k,x),apply(k,x))),y),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
apply(y,apply(apply(apply(apply(k,x),apply(k,x)),apply(apply(k,x),apply(k,x))),y)) = apply(y,apply(apply(x,apply(apply(k,x),apply(k,x))),y)),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
apply(apply(k,x),apply(k,x)) = x,
inference(substitution,[status(thm)],[c5]) ).
cnf(c30,plain,
apply(x,apply(apply(k,x),apply(k,x))) = apply(x,x),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
apply(apply(x,apply(apply(k,x),apply(k,x))),y) = apply(apply(x,x),y),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
apply(y,apply(apply(x,apply(apply(k,x),apply(k,x))),y)) = apply(y,apply(apply(x,x),y)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
apply(y,apply(apply(apply(apply(k,x),apply(k,x)),apply(apply(k,x),apply(k,x))),y)) = apply(y,apply(apply(x,x),y)),
inference(transitivity,[status(thm)],[c28,c32]) ).
cnf(c34,plain,
apply(y,apply(apply(apply(apply(k,x),apply(k,x)),apply(apply(apply(s,k),k),x)),y)) = apply(y,apply(apply(x,x),y)),
inference(transitivity,[status(thm)],[c24,c33]) ).
cnf(c35,plain,
apply(y,apply(apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x)),y)) = apply(y,apply(apply(x,x),y)),
inference(transitivity,[status(thm)],[c20,c34]) ).
cnf(c36,plain,
apply(y,apply(apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x),y)) = apply(y,apply(apply(x,x),y)),
inference(transitivity,[status(thm)],[c16,c35]) ).
cnf(c37,plain,
apply(apply(apply(k,y),apply(k,y)),apply(apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x),y)) = apply(y,apply(apply(x,x),y)),
inference(transitivity,[status(thm)],[c13,c36]) ).
cnf(c38,plain,
apply(apply(apply(apply(s,k),k),y),apply(apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x),y)) = apply(y,apply(apply(x,x),y)),
inference(transitivity,[status(thm)],[c11,c37]) ).
cnf(c39,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y) = apply(y,apply(apply(x,x),y)),
inference(transitivity,[status(thm)],[c9,c38]) ).
cnf(c40,plain,
apply(apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y) = apply(y,apply(apply(x,x),y)),
inference(transitivity,[status(thm)],[c8,c39]) ).
cnf(c41,plain,
apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) = apply(y,apply(apply(x,x),y)),
inference(transitivity,[status(thm)],[c4,c40]) ).
cnf(c42,plain,
$false,
inference(resolution,[status(thm)],[c1,c41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL004-3 : 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 : n007.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 21:27:10 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.23 Command-line arguments: --no-flatten-goal
% 0.10/0.23
% 0.10/0.23 % SZS status Unsatisfiable
% 0.10/0.23
% 0.10/0.23 % SZS output start CNFRefutation
% See solution above
% 0.10/0.25
% 0.10/0.25 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------