%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : COL044-1 : 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 : n031.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 10:52:14 AM UTC 2025
% Result : Unsatisfiable 30.41s 4.21s
% Output : CNFRefutation 30.41s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named prove_fixed_point)
% Comments :
%------------------------------------------------------------------------------
cnf(2,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(apply(n,apply(b,apply(b,apply(n,b)))),X1_21),apply(n,apply(b,apply(b,apply(n,b))))),f(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21),apply(n,apply(b,apply(b,apply(n,b))))))) != apply(f(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21),apply(n,apply(b,apply(b,apply(n,b)))))),apply(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21),apply(n,apply(b,apply(b,apply(n,b))))),f(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21),apply(n,apply(b,apply(b,apply(n,b)))))))),
inference(instantiation,[status(thm)],[2]) ).
cnf(0,plain,
apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(cnf,[status(esa)],[b_definition]) ).
cnf(l15,plain,
apply(apply(apply(b,apply(n,b)),apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21)),apply(n,apply(b,apply(b,apply(n,b))))) = apply(apply(n,b),apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21),apply(n,apply(b,apply(b,apply(n,b)))))),
inference(instantiation,[status(thm)],[0]) ).
cnf(l17,plain,
apply(apply(apply(b,f(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21),apply(n,apply(b,apply(b,apply(n,b))))))),apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21),apply(n,apply(b,apply(b,apply(n,b)))))),f(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21),apply(n,apply(b,apply(b,apply(n,b))))))) = apply(f(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21),apply(n,apply(b,apply(b,apply(n,b)))))),apply(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21),apply(n,apply(b,apply(b,apply(n,b))))),f(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21),apply(n,apply(b,apply(b,apply(n,b)))))))),
inference(instantiation,[status(thm)],[0]) ).
cnf(1,plain,
apply(apply(apply(n,X0),X1),X2) = apply(apply(apply(X0,X2),X1),X2),
inference(cnf,[status(esa)],[n_definition]) ).
cnf(l13,plain,
apply(apply(apply(n,b),apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21),apply(n,apply(b,apply(b,apply(n,b)))))),f(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21),apply(n,apply(b,apply(b,apply(n,b))))))) = apply(apply(apply(b,f(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21),apply(n,apply(b,apply(b,apply(n,b))))))),apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21),apply(n,apply(b,apply(b,apply(n,b)))))),f(apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21),apply(n,apply(b,apply(b,apply(n,b))))))),
inference(instantiation,[status(thm)],[1]) ).
cnf(l7,plain,
apply(apply(apply(b,apply(b,apply(n,b))),apply(n,apply(b,apply(b,apply(n,b))))),X1_21) = apply(apply(b,apply(n,b)),apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21)),
inference(instantiation,[status(thm)],[0]) ).
cnf(l21,plain,
apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21),apply(n,apply(b,apply(b,apply(n,b))))) = apply(apply(apply(apply(b,apply(b,apply(n,b))),apply(n,apply(b,apply(b,apply(n,b))))),X1_21),apply(n,apply(b,apply(b,apply(n,b))))),
inference(instantiation,[status(thm)],[1]) ).
cnf(l27,plain,
apply(apply(apply(b,apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21)),n),apply(b,apply(b,apply(n,b)))) = apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21),apply(n,apply(b,apply(b,apply(n,b))))),
inference(instantiation,[status(thm)],[0]) ).
cnf(l8,plain,
apply(apply(apply(b,apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21)),n),apply(b,apply(b,apply(n,b)))) = apply(apply(apply(n,apply(b,apply(b,apply(n,b)))),X1_21),apply(n,apply(b,apply(b,apply(n,b))))),
inference(instantiation,[status(thm)],[0]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l15,l17,l13,l7,l21,l27,l8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COL044-1 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n031.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Jul 20 05:43:49 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % launching worker at depth: 1
% 0.13/0.34 % launching worker at depth: 4
% 0.13/0.34 % launching worker at depth: 7
% 0.13/0.34 % launching worker at depth: 6
% 0.13/0.34 % launching worker at depth: 2
% 0.13/0.34 % launching worker at depth: 5
% 0.13/0.34 % launching worker at depth: 3
% 0.13/0.34 % launching worker at depth: 8
% 0.13/0.34 % launching worker at depth: 9
% 0.13/0.34 % launching worker at depth: 10
% 0.13/0.35 % launching worker at depth: 11
% 2.41/0.65 % launching worker at depth: 12
% 30.41/4.21 % SZS status Theorem for theBenchmark
% 30.41/4.21 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------