%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : COL037-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 10:52:12 AM UTC 2025
% Result : Unsatisfiable 93.80s 12.11s
% Output : CNFRefutation 93.80s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named prove_fixed_point)
% Comments :
%------------------------------------------------------------------------------
cnf(3,plain,
apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))),
inference(cnf,[status(esa)],[prove_fixed_point]) ).
cnf(l0,plain,
apply(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))),f(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))))) != apply(f(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))))),apply(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))),f(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))))))),
inference(instantiation,[status(thm)],[3]) ).
cnf(2,plain,
apply(apply(apply(c,X0),X1),X2) = apply(apply(X0,X2),X1),
inference(cnf,[status(esa)],[c_definition]) ).
cnf(l2,plain,
apply(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))),f(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))))) = apply(apply(apply(apply(s,apply(c,c)),b),f(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))))),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))),
inference(instantiation,[status(thm)],[2]) ).
cnf(l31,plain,
apply(apply(apply(c,apply(b,f(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))))))),f(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))))),apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))))) = apply(apply(apply(b,f(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))))),apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))))),f(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))))),
inference(instantiation,[status(thm)],[2]) ).
cnf(1,plain,
apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(cnf,[status(esa)],[b_definition]) ).
cnf(l30,plain,
apply(apply(apply(b,f(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))))),apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))))),f(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))))) = apply(f(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))))),apply(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))),f(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))))))),
inference(instantiation,[status(thm)],[1]) ).
cnf(l27,plain,
apply(apply(apply(c,c),f(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))))),apply(b,f(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))))))) = apply(apply(c,apply(b,f(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))))))),f(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))))),
inference(instantiation,[status(thm)],[2]) ).
cnf(l29,plain,
apply(apply(apply(b,apply(c,apply(apply(s,apply(c,c)),b))),apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))) = apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))),
inference(instantiation,[status(thm)],[1]) ).
cnf(0,plain,
apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
inference(cnf,[status(esa)],[s_definition]) ).
cnf(l20,plain,
apply(apply(apply(s,apply(c,c)),b),f(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))))) = apply(apply(apply(c,c),f(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))))),apply(b,f(apply(apply(c,apply(apply(s,apply(c,c)),b)),apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))))))),
inference(instantiation,[status(thm)],[0]) ).
cnf(l24,plain,
apply(apply(apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))) = apply(apply(apply(b,apply(c,apply(apply(s,apply(c,c)),b))),apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),
inference(instantiation,[status(thm)],[2]) ).
cnf(l21,plain,
apply(apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))) = apply(apply(apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b)))))),apply(apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))),apply(s,apply(c,apply(b,apply(c,apply(apply(s,apply(c,c)),b))))))),
inference(instantiation,[status(thm)],[0]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l2,l31,l30,l27,l29,l20,l24,l21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : COL037-1 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.11 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.32 % Computer : n026.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun Jul 20 05:42:04 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % launching worker at depth: 3
% 0.11/0.33 % launching worker at depth: 5
% 0.11/0.33 % launching worker at depth: 1
% 0.11/0.33 % launching worker at depth: 6
% 0.11/0.33 % launching worker at depth: 2
% 0.11/0.33 % launching worker at depth: 4
% 0.11/0.33 % launching worker at depth: 7
% 0.11/0.33 % launching worker at depth: 8
% 0.11/0.33 % launching worker at depth: 9
% 0.11/0.33 % launching worker at depth: 10
% 0.11/0.34 % launching worker at depth: 11
% 46.40/6.20 % launching worker at depth: 12
% 93.80/12.11 % SZS status Theorem for theBenchmark
% 93.80/12.11 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------