%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : COL057-1 : TPTP v9.0.0. 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 : 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 10:52:16 AM UTC 2025
% Result : Unsatisfiable 72.09s 9.46s
% Output : CNFRefutation 72.09s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named prove_strong_fixed_point)
% Comments :
%------------------------------------------------------------------------------
cnf(4,plain,
apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))),
inference(cnf,[status(esa)],[prove_strong_fixed_point]) ).
cnf(l0,plain,
apply(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))))) != apply(f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))),apply(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))))),
inference(instantiation,[status(thm)],[4]) ).
cnf(1,plain,
apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(cnf,[status(esa)],[b_definition]) ).
cnf(l3,plain,
apply(apply(apply(b,f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))))),apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))),f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))))) = apply(f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))),apply(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))))),
inference(instantiation,[status(thm)],[1]) ).
cnf(l52,plain,
apply(apply(apply(b,f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))))),apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))),f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))))) = apply(f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))),apply(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))))),
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(l23,plain,
apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))) = apply(apply(apply(c,apply(b,apply(s,apply(b,i)))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))),
inference(instantiation,[status(thm)],[0]) ).
cnf(3,plain,
apply(i,X0) = X0,
inference(cnf,[status(esa)],[i_definition]) ).
cnf(l56,plain,
apply(i,apply(f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))),apply(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))))))) = apply(f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))),apply(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))))),
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(l38,plain,
apply(apply(apply(c,apply(b,apply(s,apply(b,i)))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))) = apply(apply(apply(b,apply(s,apply(b,i))),apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),
inference(instantiation,[status(thm)],[2]) ).
cnf(l16,plain,
apply(i,f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))))) = f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))),
inference(instantiation,[status(thm)],[3]) ).
cnf(l50,plain,
apply(apply(apply(b,i),f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))))),apply(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))))) = apply(i,apply(f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))),apply(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))))))),
inference(instantiation,[status(thm)],[1]) ).
cnf(l49,plain,
apply(apply(apply(s,apply(b,i)),apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))),f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))))) = apply(apply(apply(b,i),f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))))),apply(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))))),
inference(instantiation,[status(thm)],[0]) ).
cnf(l47,plain,
apply(apply(apply(b,apply(s,apply(b,i))),apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))) = apply(apply(s,apply(b,i)),apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))),
inference(instantiation,[status(thm)],[1]) ).
cnf(l46,plain,
apply(i,f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))))) = f(apply(apply(apply(s,apply(c,apply(b,apply(s,apply(b,i))))),apply(s,apply(c,apply(b,apply(s,apply(b,i)))))),apply(s,apply(c,apply(b,apply(s,apply(b,i))))))),
inference(instantiation,[status(thm)],[3]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l3,l52,l23,l56,l38,l16,l50,l49,l47,l46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : COL057-1 : TPTP v9.0.0. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/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 05:47:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % launching worker at depth: 2
% 0.12/0.33 % launching worker at depth: 5
% 0.12/0.33 % launching worker at depth: 4
% 0.12/0.33 % launching worker at depth: 6
% 0.12/0.33 % launching worker at depth: 3
% 0.12/0.33 % launching worker at depth: 7
% 0.12/0.33 % launching worker at depth: 1
% 0.12/0.33 % launching worker at depth: 8
% 0.12/0.33 % launching worker at depth: 9
% 0.12/0.33 % launching worker at depth: 10
% 0.18/0.38 % launching worker at depth: 11
% 72.09/9.46 % SZS status Theorem for theBenchmark
% 72.09/9.46 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------