%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL066-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 09:37:22 AM UTC 2026
% Result : Unsatisfiable 0.22s 0.31s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 27 RR)
% Number of literals : 36 ( 35 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 : 23 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p_combinator) ).
cnf(c2,axiom,
apply(apply(w,X),Y) = apply(apply(X,Y),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_definition) ).
cnf(c3,plain,
apply(apply(w,apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x)),y) = apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y) = apply(apply(w,apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x)),y),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) = apply(apply(apply(w,apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x)),y),z),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,axiom,
apply(apply(apply(q,X2),Y2),Z) = apply(Y2,apply(X2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',q_definition) ).
cnf(c7,plain,
apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x) = apply(apply(w,apply(q,apply(q,q))),apply(q,x)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
apply(w,apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x)) = apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
apply(apply(w,apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x)),y) = apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
apply(apply(apply(w,apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x)),y),z) = apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
apply(apply(w,apply(q,X2)),X3) = apply(apply(apply(q,X2),X3),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
apply(apply(apply(q,X2),X3),X3) = apply(X3,apply(X2,X3)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c13,plain,
apply(apply(w,apply(q,X2)),X3) = apply(X3,apply(X2,X3)),
inference(transitivity,[status(thm)],[c11,c12]) ).
cnf(c14,plain,
apply(apply(w,apply(q,apply(q,q))),apply(q,x)) = apply(apply(q,x),apply(apply(q,q),apply(q,x))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))) = apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y) = apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) = apply(apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y),z),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
apply(apply(w,apply(apply(q,X3),X2)),X4) = apply(apply(apply(apply(q,X3),X2),X4),X4),
inference(substitution,[status(thm)],[c2]) ).
cnf(c19,plain,
apply(apply(apply(q,X4),X3),X2) = apply(X3,apply(X4,X2)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c20,plain,
apply(apply(apply(apply(q,X4),X3),X2),X2) = apply(apply(X3,apply(X4,X2)),X2),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,plain,
apply(apply(w,apply(apply(q,X4),X3)),X2) = apply(apply(X3,apply(X4,X2)),X2),
inference(transitivity,[status(thm)],[c18,c20]) ).
cnf(c22,plain,
apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y) = apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
apply(apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y),z) = apply(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),z),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
apply(apply(apply(q,q),apply(q,x)),apply(x,y)) = apply(apply(q,x),apply(q,apply(x,y))),
inference(substitution,[status(thm)],[c6]) ).
cnf(c25,plain,
apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y) = apply(apply(apply(q,x),apply(q,apply(x,y))),y),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
apply(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),z) = apply(apply(apply(apply(q,x),apply(q,apply(x,y))),y),z),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
apply(apply(apply(q,x),apply(q,apply(x,y))),y) = apply(apply(q,apply(x,y)),apply(x,y)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c28,plain,
apply(apply(apply(apply(q,x),apply(q,apply(x,y))),y),z) = apply(apply(apply(q,apply(x,y)),apply(x,y)),z),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
apply(apply(apply(q,apply(x,y)),apply(x,y)),z) = apply(apply(x,y),apply(apply(x,y),z)),
inference(substitution,[status(thm)],[c6]) ).
cnf(c30,plain,
apply(apply(apply(apply(q,x),apply(q,apply(x,y))),y),z) = apply(apply(x,y),apply(apply(x,y),z)),
inference(transitivity,[status(thm)],[c28,c29]) ).
cnf(c31,plain,
apply(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),z) = apply(apply(x,y),apply(apply(x,y),z)),
inference(transitivity,[status(thm)],[c26,c30]) ).
cnf(c32,plain,
apply(apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y),z) = apply(apply(x,y),apply(apply(x,y),z)),
inference(transitivity,[status(thm)],[c23,c31]) ).
cnf(c33,plain,
apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) = apply(apply(x,y),apply(apply(x,y),z)),
inference(transitivity,[status(thm)],[c17,c32]) ).
cnf(c34,plain,
apply(apply(apply(w,apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x)),y),z) = apply(apply(x,y),apply(apply(x,y),z)),
inference(transitivity,[status(thm)],[c10,c33]) ).
cnf(c35,plain,
apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) = apply(apply(x,y),apply(apply(x,y),z)),
inference(transitivity,[status(thm)],[c5,c34]) ).
cnf(c36,plain,
$false,
inference(resolution,[status(thm)],[c1,c35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL066-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n013.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 21:33:17 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.31 Command-line arguments: --no-flatten-goal
% 0.22/0.31
% 0.22/0.31 % SZS status Unsatisfiable
% 0.22/0.31
% 0.22/0.31 % SZS output start CNFRefutation
% See solution above
% 0.22/0.33
% 0.22/0.33 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------