%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : COL075-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 09:37:23 AM UTC 2026
% Result : Unsatisfiable 0.23s 0.34s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 3 RR)
% Number of literals : 16 ( 15 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
apply(apply(Y,b(Y)),c(Y)) != apply(b(Y),b(Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_diagonal_combinator) ).
cnf(c2,axiom,
apply(apply(apply(abstraction,X),Y2),Z) = apply(apply(X,apply(k,Z)),apply(Y2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstraction) ).
cnf(c3,plain,
apply(apply(apply(abstraction,abstraction),k),X2) = apply(apply(abstraction,apply(k,X2)),apply(k,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
apply(apply(apply(apply(abstraction,abstraction),k),X2),X3) = apply(apply(apply(abstraction,apply(k,X2)),apply(k,X2)),X3),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
apply(apply(apply(abstraction,X3),apply(k,X2)),X4) = apply(apply(X3,apply(k,X4)),apply(apply(k,X2),X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,axiom,
apply(apply(k,X2),Y2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
cnf(c7,plain,
apply(apply(k,X3),X2) = X3,
inference(substitution,[status(thm)],[c6]) ).
cnf(c8,plain,
apply(apply(X4,apply(k,X2)),apply(apply(k,X3),X2)) = apply(apply(X4,apply(k,X2)),X3),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
apply(apply(apply(abstraction,X4),apply(k,X3)),X2) = apply(apply(X4,apply(k,X2)),X3),
inference(transitivity,[status(thm)],[c5,c8]) ).
cnf(c10,plain,
apply(apply(apply(abstraction,apply(k,X3)),apply(k,X3)),X2) = apply(apply(apply(k,X3),apply(k,X2)),X3),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
apply(apply(k,X3),apply(k,X2)) = X3,
inference(substitution,[status(thm)],[c6]) ).
cnf(c12,plain,
apply(apply(apply(k,X3),apply(k,X2)),X3) = apply(X3,X3),
inference(congruence,[status(thm)],[c11]) ).
cnf(c13,plain,
apply(apply(apply(abstraction,apply(k,X3)),apply(k,X3)),X2) = apply(X3,X3),
inference(transitivity,[status(thm)],[c10,c12]) ).
cnf(c14,plain,
apply(apply(apply(apply(abstraction,abstraction),k),X3),X2) = apply(X3,X3),
inference(transitivity,[status(thm)],[c4,c13]) ).
cnf(c15,plain,
apply(apply(apply(apply(abstraction,abstraction),k),b(apply(apply(abstraction,abstraction),k))),c(apply(apply(abstraction,abstraction),k))) = apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
$false,
inference(resolution,[status(thm)],[c1,c15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL075-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.22 % Computer : n011.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Mon Sep 28 21:34:00 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.34 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.23/0.34
% 0.23/0.34 % SZS status Unsatisfiable
% 0.23/0.34
% 0.23/0.34 % SZS output start CNFRefutation
% See solution above
% 0.23/0.35
% 0.23/0.35 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------