%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : COL079-2 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Jul 24 10:52:20 AM UTC 2025
% Result : Unsatisfiable 82.05s 10.66s
% Output : CNFRefutation 82.05s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named prove_TRC2a)
% Comments :
%------------------------------------------------------------------------------
cnf(3,plain,
apply(abstraction,apply(abstraction,apply(abstraction,b))) != apply(abstraction,b),
inference(cnf,[status(esa)],[prove_TRC2a]) ).
cnf(l0,plain,
apply(abstraction,apply(abstraction,apply(abstraction,b))) != apply(abstraction,b),
inference(instantiation,[status(thm)],[3]) ).
cnf(2,plain,
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
inference(cnf,[status(esa)],[extensionality2]) ).
cnf(l1,plain,
( apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))) != apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)))
| apply(abstraction,apply(abstraction,apply(abstraction,b))) = apply(abstraction,b) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l2,plain,
( apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))) != apply(apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)))))
| apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))) = apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l7,plain,
( apply(apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))),n(apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))),apply(apply(apply(abstraction,b),k(apply(n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))))),apply(k(n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))),apply(n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))))))) != apply(apply(apply(apply(abstraction,b),k(apply(n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))))),apply(k(n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))),apply(n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))))),n(apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))),apply(apply(apply(abstraction,b),k(apply(n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))))),apply(k(n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))),apply(n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)))))))))
| apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))) = apply(apply(apply(abstraction,b),k(apply(n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))))),apply(k(n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))),apply(n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))))) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(1,plain,
apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,k(X2)),apply(X1,X2)),
inference(cnf,[status(esa)],[abstraction]) ).
cnf(l19,plain,
apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))) = apply(apply(apply(abstraction,apply(abstraction,b)),k(n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)))))),apply(n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)))))),
inference(instantiation,[status(thm)],[1]) ).
cnf(l37,plain,
apply(apply(apply(abstraction,apply(abstraction,b)),k(n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)))))),apply(n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)))))) = apply(apply(apply(abstraction,b),k(apply(n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))))),apply(k(n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))),apply(n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))))),
inference(instantiation,[status(thm)],[1]) ).
cnf(l64,plain,
apply(apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))) = apply(apply(b,k(n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)))))),apply(n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)))))),
inference(instantiation,[status(thm)],[1]) ).
cnf(0,plain,
apply(k(X0),X1) = X0,
inference(cnf,[status(esa)],[k_definition]) ).
cnf(l54,plain,
apply(k(apply(n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)))))),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))) = apply(n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))),
inference(instantiation,[status(thm)],[0]) ).
cnf(l58,plain,
apply(k(n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))),apply(n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)))))) = n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)))),
inference(instantiation,[status(thm)],[0]) ).
cnf(l59,plain,
apply(apply(apply(abstraction,b),k(apply(n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))))),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))) = apply(apply(b,k(n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)))))),apply(k(apply(n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)))))),n(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b)))))),
inference(instantiation,[status(thm)],[1]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l7,l19,l37,l64,l54,l58,l59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COL079-2 : TPTP v9.0.0. Released v1.2.0.
% 0.06/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Jul 20 05:54:19 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.34 % launching worker at depth: 10
% 0.12/0.34 % launching worker at depth: 11
% 0.19/0.53 % launching worker at depth: 12
% 82.05/10.66 % SZS status Theorem for theBenchmark
% 82.05/10.66 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------