%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : LCL066-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n031.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 : Mon Sep 7 12:13:06 PM UTC 2026
% Result : Unsatisfiable 67.11s 8.82s
% Output : CNFRefutation 67.11s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named prove_cn_3ERROR: Could not build tree for root finalERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(4,plain,
~ is_a_theorem(implies(a,implies(not(a),b))),
inference(cnf,[status(esa)],[prove_cn_3]) ).
cnf(l0,plain,
~ is_a_theorem(implies(a,implies(not(a),b))),
inference(instantiation,[status(thm)],[4]) ).
cnf(0,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1) ),
inference(cnf,[status(esa)],[condensed_detachment]) ).
cnf(l1,plain,
( ~ is_a_theorem(implies(a,implies(implies(not(a),a),implies(not(a),b))))
| ~ is_a_theorem(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),b))))
| is_a_theorem(implies(a,implies(not(a),b))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l3,plain,
( ~ is_a_theorem(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(implies(a,implies(not(a),a)),implies(a,implies(not(a),b)))))
| ~ is_a_theorem(implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(implies(a,implies(not(a),a)),implies(a,implies(not(a),b)))),implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),b)))))
| is_a_theorem(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),b)))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l5,plain,
( ~ is_a_theorem(implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(implies(a,implies(not(a),a)),implies(a,implies(not(a),b)))),implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),a)))))
| ~ is_a_theorem(implies(implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(implies(a,implies(not(a),a)),implies(a,implies(not(a),b)))),implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),a)))),implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(implies(a,implies(not(a),a)),implies(a,implies(not(a),b)))),implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),b))))))
| is_a_theorem(implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(implies(a,implies(not(a),a)),implies(a,implies(not(a),b)))),implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),b))))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l21,plain,
( ~ is_a_theorem(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),a))))
| ~ is_a_theorem(implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),a))),implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(implies(a,implies(not(a),a)),implies(a,implies(not(a),b)))),implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),a))))))
| is_a_theorem(implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(implies(a,implies(not(a),a)),implies(a,implies(not(a),b)))),implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),a))))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l2,plain,
( ~ is_a_theorem(implies(not(a),implies(a,b)))
| ~ is_a_theorem(implies(implies(not(a),implies(a,b)),implies(a,implies(implies(not(a),a),implies(not(a),b)))))
| is_a_theorem(implies(a,implies(implies(not(a),a),implies(not(a),b)))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(2,plain,
is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))),
inference(cnf,[status(esa)],[cn_35]) ).
cnf(l4,plain,
is_a_theorem(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(implies(a,implies(not(a),a)),implies(a,implies(not(a),b))))),
inference(instantiation,[status(thm)],[2]) ).
cnf(l35,plain,
( ~ is_a_theorem(implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))))
| ~ is_a_theorem(implies(implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))),implies(implies(not(a),implies(a,b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))))
| is_a_theorem(implies(implies(not(a),implies(a,b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l37,plain,
( ~ is_a_theorem(implies(implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))),implies(implies(not(a),implies(a,b)),implies(implies(not(a),a),implies(not(a),b)))))
| ~ is_a_theorem(implies(implies(implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))),implies(implies(not(a),implies(a,b)),implies(implies(not(a),a),implies(not(a),b)))),implies(implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))),implies(implies(not(a),implies(a,b)),implies(a,implies(implies(not(a),a),implies(not(a),b)))))))
| is_a_theorem(implies(implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))),implies(implies(not(a),implies(a,b)),implies(a,implies(implies(not(a),a),implies(not(a),b)))))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l34,plain,
( ~ is_a_theorem(implies(not(a),implies(not(b),not(a))))
| ~ is_a_theorem(implies(implies(not(a),implies(not(b),not(a))),implies(not(a),implies(a,b))))
| is_a_theorem(implies(not(a),implies(a,b))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l38,plain,
( ~ is_a_theorem(implies(implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))),implies(implies(implies(not(a),implies(a,b)),implies(implies(not(a),a),implies(not(a),b))),implies(implies(not(a),implies(a,b)),implies(a,implies(implies(not(a),a),implies(not(a),b)))))))
| ~ is_a_theorem(implies(implies(implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))),implies(implies(implies(not(a),implies(a,b)),implies(implies(not(a),a),implies(not(a),b))),implies(implies(not(a),implies(a,b)),implies(a,implies(implies(not(a),a),implies(not(a),b)))))),implies(implies(implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))),implies(implies(not(a),implies(a,b)),implies(implies(not(a),a),implies(not(a),b)))),implies(implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))),implies(implies(not(a),implies(a,b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))))))
| is_a_theorem(implies(implies(implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))),implies(implies(not(a),implies(a,b)),implies(implies(not(a),a),implies(not(a),b)))),implies(implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))),implies(implies(not(a),implies(a,b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l39,plain,
is_a_theorem(implies(implies(implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))),implies(implies(implies(not(a),implies(a,b)),implies(implies(not(a),a),implies(not(a),b))),implies(implies(not(a),implies(a,b)),implies(a,implies(implies(not(a),a),implies(not(a),b)))))),implies(implies(implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))),implies(implies(not(a),implies(a,b)),implies(implies(not(a),a),implies(not(a),b)))),implies(implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))),implies(implies(not(a),implies(a,b)),implies(a,implies(implies(not(a),a),implies(not(a),b)))))))),
inference(instantiation,[status(thm)],[2]) ).
cnf(1,plain,
is_a_theorem(implies(X0,implies(X1,X0))),
inference(cnf,[status(esa)],[cn_18]) ).
cnf(l29,plain,
is_a_theorem(implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),a))),implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(implies(a,implies(not(a),a)),implies(a,implies(not(a),b)))),implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),a)))))),
inference(instantiation,[status(thm)],[1]) ).
cnf(l41,plain,
is_a_theorem(implies(implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))),implies(implies(implies(not(a),implies(a,b)),implies(implies(not(a),a),implies(not(a),b))),implies(implies(not(a),implies(a,b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))))),
inference(instantiation,[status(thm)],[2]) ).
cnf(l20,plain,
( ~ is_a_theorem(implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(implies(a,implies(not(a),a)),implies(a,implies(not(a),b)))),implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),a))),implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),b))))))
| ~ is_a_theorem(implies(implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(implies(a,implies(not(a),a)),implies(a,implies(not(a),b)))),implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),a))),implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),b))))),implies(implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(implies(a,implies(not(a),a)),implies(a,implies(not(a),b)))),implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),a)))),implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(implies(a,implies(not(a),a)),implies(a,implies(not(a),b)))),implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),b)))))))
| is_a_theorem(implies(implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(implies(a,implies(not(a),a)),implies(a,implies(not(a),b)))),implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),a)))),implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(implies(a,implies(not(a),a)),implies(a,implies(not(a),b)))),implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),b)))))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l40,plain,
( ~ is_a_theorem(implies(implies(not(a),implies(a,b)),implies(implies(not(a),a),implies(not(a),b))))
| ~ is_a_theorem(implies(implies(implies(not(a),implies(a,b)),implies(implies(not(a),a),implies(not(a),b))),implies(implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))),implies(implies(not(a),implies(a,b)),implies(implies(not(a),a),implies(not(a),b))))))
| is_a_theorem(implies(implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))),implies(implies(not(a),implies(a,b)),implies(implies(not(a),a),implies(not(a),b))))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l28,plain,
( ~ is_a_theorem(implies(a,implies(not(a),a)))
| ~ is_a_theorem(implies(implies(a,implies(not(a),a)),implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),a)))))
| is_a_theorem(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),a)))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l33,plain,
is_a_theorem(implies(implies(a,implies(not(a),a)),implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),a))))),
inference(instantiation,[status(thm)],[1]) ).
cnf(l52,plain,
( ~ is_a_theorem(implies(not(a),implies(implies(not(b),not(a)),implies(a,b))))
| ~ is_a_theorem(implies(implies(not(a),implies(implies(not(b),not(a)),implies(a,b))),implies(implies(not(a),implies(not(b),not(a))),implies(not(a),implies(a,b)))))
| is_a_theorem(implies(implies(not(a),implies(not(b),not(a))),implies(not(a),implies(a,b)))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l32,plain,
is_a_theorem(implies(a,implies(not(a),a))),
inference(instantiation,[status(thm)],[1]) ).
cnf(l36,plain,
( ~ is_a_theorem(implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b)))))
| ~ is_a_theorem(implies(implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b)))),implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b)))))))
| is_a_theorem(implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b)))))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l46,plain,
is_a_theorem(implies(implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b)))),implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))))),
inference(instantiation,[status(thm)],[1]) ).
cnf(l42,plain,
is_a_theorem(implies(implies(implies(not(a),implies(a,b)),implies(implies(not(a),a),implies(not(a),b))),implies(implies(implies(not(a),implies(a,b)),implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))),implies(implies(not(a),implies(a,b)),implies(implies(not(a),a),implies(not(a),b)))))),
inference(instantiation,[status(thm)],[1]) ).
cnf(l24,plain,
is_a_theorem(implies(implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(implies(a,implies(not(a),a)),implies(a,implies(not(a),b)))),implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),a))),implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),b))))),implies(implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(implies(a,implies(not(a),a)),implies(a,implies(not(a),b)))),implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),a)))),implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(implies(a,implies(not(a),a)),implies(a,implies(not(a),b)))),implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),b))))))),
inference(instantiation,[status(thm)],[2]) ).
cnf(l50,plain,
is_a_theorem(implies(not(a),implies(not(b),not(a)))),
inference(instantiation,[status(thm)],[1]) ).
cnf(l22,plain,
is_a_theorem(implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(implies(a,implies(not(a),a)),implies(a,implies(not(a),b)))),implies(implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),a))),implies(implies(a,implies(implies(not(a),a),implies(not(a),b))),implies(a,implies(not(a),b)))))),
inference(instantiation,[status(thm)],[2]) ).
cnf(l43,plain,
is_a_theorem(implies(implies(not(a),implies(a,b)),implies(implies(not(a),a),implies(not(a),b)))),
inference(instantiation,[status(thm)],[2]) ).
cnf(l53,plain,
is_a_theorem(implies(implies(not(a),implies(implies(not(b),not(a)),implies(a,b))),implies(implies(not(a),implies(not(b),not(a))),implies(not(a),implies(a,b))))),
inference(instantiation,[status(thm)],[2]) ).
cnf(l44,plain,
is_a_theorem(implies(implies(implies(not(a),a),implies(not(a),b)),implies(a,implies(implies(not(a),a),implies(not(a),b))))),
inference(instantiation,[status(thm)],[1]) ).
cnf(l54,plain,
( ~ is_a_theorem(implies(implies(not(b),not(a)),implies(a,b)))
| ~ is_a_theorem(implies(implies(implies(not(b),not(a)),implies(a,b)),implies(not(a),implies(implies(not(b),not(a)),implies(a,b)))))
| is_a_theorem(implies(not(a),implies(implies(not(b),not(a)),implies(a,b)))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l61,plain,
is_a_theorem(implies(implies(implies(not(b),not(a)),implies(a,b)),implies(not(a),implies(implies(not(b),not(a)),implies(a,b))))),
inference(instantiation,[status(thm)],[1]) ).
cnf(3,plain,
is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
inference(cnf,[status(esa)],[cn_49]) ).
cnf(l60,plain,
is_a_theorem(implies(implies(not(b),not(a)),implies(a,b))),
inference(instantiation,[status(thm)],[3]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l5,l21,l2,l4,l35,l37,l34,l38,l39,l29,l41,l20,l40,l28,l33,l52,l32,l36,l46,l42,l24,l50,l22,l43,l53,l44,l54,l61,l60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL066-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n031.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 4 21:05:24 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % launching worker at depth: 1
% 0.14/0.36 % launching worker at depth: 7
% 0.14/0.36 % launching worker at depth: 5
% 0.14/0.36 % launching worker at depth: 8
% 0.14/0.36 % launching worker at depth: 3
% 0.14/0.36 % launching worker at depth: 6
% 0.14/0.36 % launching worker at depth: 2
% 0.14/0.36 % launching worker at depth: 4
% 0.14/0.36 % launching worker at depth: 9
% 0.14/0.36 % launching worker at depth: 10
% 0.14/0.36 % launching worker at depth: 11
% 0.14/0.42 % launching worker at depth: 12
% 34.47/4.77 % launching worker at depth: 13
% 67.11/8.82 % SZS status Theorem for theBenchmark
% 67.11/8.83 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------