%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL061-3 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 0.07s 0.24s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 21 RR)
% Number of literals : 23 ( 22 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(apply(b,apply(t,t)),b)),b),x),y),z) != apply(x,apply(z,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_q1_combinator) ).
cnf(c2,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
cnf(c3,plain,
apply(apply(apply(b,apply(apply(b,apply(t,t)),b)),b),x) = apply(apply(apply(b,apply(t,t)),b),apply(b,x)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
apply(apply(apply(apply(b,apply(apply(b,apply(t,t)),b)),b),x),y) = apply(apply(apply(apply(b,apply(t,t)),b),apply(b,x)),y),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,t)),b)),b),x),y),z) = apply(apply(apply(apply(apply(b,apply(t,t)),b),apply(b,x)),y),z),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
apply(apply(apply(b,apply(t,t)),b),apply(b,x)) = apply(apply(t,t),apply(b,apply(b,x))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c7,plain,
apply(apply(apply(apply(b,apply(t,t)),b),apply(b,x)),y) = apply(apply(apply(t,t),apply(b,apply(b,x))),y),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,plain,
apply(apply(apply(apply(apply(b,apply(t,t)),b),apply(b,x)),y),z) = apply(apply(apply(apply(t,t),apply(b,apply(b,x))),y),z),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,axiom,
apply(apply(t,X2),Y2) = apply(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_definition) ).
cnf(c10,plain,
apply(apply(t,t),apply(b,apply(b,x))) = apply(apply(b,apply(b,x)),t),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
apply(apply(apply(t,t),apply(b,apply(b,x))),y) = apply(apply(apply(b,apply(b,x)),t),y),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
apply(apply(apply(apply(t,t),apply(b,apply(b,x))),y),z) = apply(apply(apply(apply(b,apply(b,x)),t),y),z),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
apply(apply(apply(b,apply(b,x)),t),y) = apply(apply(b,x),apply(t,y)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
apply(apply(apply(apply(b,apply(b,x)),t),y),z) = apply(apply(apply(b,x),apply(t,y)),z),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
apply(apply(apply(b,x),apply(t,y)),z) = apply(x,apply(apply(t,y),z)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c16,plain,
apply(apply(t,y),z) = apply(z,y),
inference(substitution,[status(thm)],[c9]) ).
cnf(c17,plain,
apply(x,apply(apply(t,y),z)) = apply(x,apply(z,y)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
apply(apply(apply(b,x),apply(t,y)),z) = apply(x,apply(z,y)),
inference(transitivity,[status(thm)],[c15,c17]) ).
cnf(c19,plain,
apply(apply(apply(apply(b,apply(b,x)),t),y),z) = apply(x,apply(z,y)),
inference(transitivity,[status(thm)],[c14,c18]) ).
cnf(c20,plain,
apply(apply(apply(apply(t,t),apply(b,apply(b,x))),y),z) = apply(x,apply(z,y)),
inference(transitivity,[status(thm)],[c12,c19]) ).
cnf(c21,plain,
apply(apply(apply(apply(apply(b,apply(t,t)),b),apply(b,x)),y),z) = apply(x,apply(z,y)),
inference(transitivity,[status(thm)],[c8,c20]) ).
cnf(c22,plain,
apply(apply(apply(apply(apply(b,apply(apply(b,apply(t,t)),b)),b),x),y),z) = apply(x,apply(z,y)),
inference(transitivity,[status(thm)],[c5,c21]) ).
cnf(c23,plain,
$false,
inference(resolution,[status(thm)],[c1,c22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL061-3 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n020.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 21:33:15 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.24 Command-line arguments: --no-flatten-goal
% 0.07/0.24
% 0.07/0.24 % SZS status Unsatisfiable
% 0.07/0.24
% 0.07/0.24 % SZS output start CNFRefutation
% See solution above
% 0.07/0.25
% 0.07/0.25 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------