%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : COL001-1 : 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 : n020.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 10:52:05 AM UTC 2025
% Result : Unsatisfiable 0.10s 0.35s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named prove_fixed_point)
% Comments :
%------------------------------------------------------------------------------
cnf(2,plain,
X0 != apply(combinator,X0),
inference(cnf,[status(esa)],[prove_fixed_point]) ).
cnf(l0,plain,
apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,combinator))),apply(apply(apply(s,k),apply(s,apply(k,combinator))),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,combinator))))) != apply(combinator,apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,combinator))),apply(apply(apply(s,k),apply(s,apply(k,combinator))),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,combinator)))))),
inference(instantiation,[status(thm)],[2]) ).
cnf(0,plain,
apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
inference(cnf,[status(esa)],[s_definition]) ).
cnf(l3,plain,
apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,combinator))) = apply(apply(s,apply(s,apply(k,combinator))),apply(apply(s,k),apply(s,apply(k,combinator)))),
inference(instantiation,[status(thm)],[0]) ).
cnf(l6,plain,
apply(apply(apply(s,k),apply(s,apply(k,combinator))),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,combinator)))) = apply(apply(k,apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,combinator)))),apply(apply(s,apply(k,combinator)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,combinator))))),
inference(instantiation,[status(thm)],[0]) ).
cnf(l12,plain,
apply(apply(apply(s,apply(k,combinator)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,combinator)))),apply(apply(apply(s,k),apply(s,apply(k,combinator))),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,combinator))))) = apply(apply(apply(k,combinator),apply(apply(apply(s,k),apply(s,apply(k,combinator))),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,combinator))))),apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,combinator))),apply(apply(apply(s,k),apply(s,apply(k,combinator))),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,combinator)))))),
inference(instantiation,[status(thm)],[0]) ).
cnf(l11,plain,
apply(apply(apply(s,apply(s,apply(k,combinator))),apply(apply(s,k),apply(s,apply(k,combinator)))),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,combinator)))) = apply(apply(apply(s,apply(k,combinator)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,combinator)))),apply(apply(apply(s,k),apply(s,apply(k,combinator))),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,combinator))))),
inference(instantiation,[status(thm)],[0]) ).
cnf(1,plain,
apply(apply(k,X0),X1) = X0,
inference(cnf,[status(esa)],[k_definition]) ).
cnf(l8,plain,
apply(apply(k,apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,combinator)))),apply(apply(s,apply(k,combinator)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,combinator))))) = apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,combinator))),
inference(instantiation,[status(thm)],[1]) ).
cnf(l14,plain,
apply(apply(k,combinator),apply(apply(apply(s,k),apply(s,apply(k,combinator))),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,combinator))))) = combinator,
inference(instantiation,[status(thm)],[1]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l3,l6,l12,l11,l8,l14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.06 % Problem : COL001-1 : TPTP v9.0.0. Released v1.0.0.
% 0.02/0.07 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.25 % Computer : n020.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Sun Jul 20 05:35:34 EDT 2025
% 0.06/0.25 % CPUTime :
% 0.06/0.25 % launching worker at depth: 1
% 0.06/0.25 % launching worker at depth: 8
% 0.06/0.25 % launching worker at depth: 2
% 0.06/0.25 % launching worker at depth: 3
% 0.06/0.25 % launching worker at depth: 4
% 0.06/0.25 % launching worker at depth: 6
% 0.06/0.25 % launching worker at depth: 7
% 0.06/0.25 % launching worker at depth: 5
% 0.06/0.25 % launching worker at depth: 9
% 0.10/0.25 % launching worker at depth: 10
% 0.10/0.26 % launching worker at depth: 11
% 0.10/0.35 % SZS status Theorem for theBenchmark
% 0.10/0.35 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------