%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : ANA004-4 : 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 : n019.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 09:50:28 AM UTC 2025
% Result : Unsatisfiable 6.21s 1.17s
% Output : CNFRefutation 6.21s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named clause_7_1)
% Comments :
%------------------------------------------------------------------------------
cnf(12,plain,
( ~ less_or_equal(absolute(add(add(f(xs(X0)),negate(f(a_real_number))),add(g(xs(X0)),negate(g(a_real_number))))),epsilon_0)
| less_or_equal(X0,n0) ),
inference(cnf,[status(esa)],[clause_7_1]) ).
cnf(l0,plain,
( ~ less_or_equal(absolute(add(add(f(xs(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))))),negate(f(a_real_number))),add(g(xs(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))))),negate(g(a_real_number))))),epsilon_0)
| less_or_equal(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))),n0) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(0,plain,
( ~ less_or_equal(add(absolute(X0),absolute(X1)),X2)
| less_or_equal(absolute(add(X0,X1)),X2) ),
inference(cnf,[status(esa)],[absolute_sum_less_or_equal_sum_of_absolutes2]) ).
cnf(l1,plain,
( ~ less_or_equal(add(absolute(add(f(xs(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))))),negate(f(a_real_number)))),absolute(add(g(xs(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))))),negate(g(a_real_number))))),epsilon_0)
| less_or_equal(absolute(add(add(f(xs(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))))),negate(f(a_real_number))),add(g(xs(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))))),negate(g(a_real_number))))),epsilon_0) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(4,plain,
( ~ less_or_equal(X0,half(X1))
| ~ less_or_equal(X2,half(X1))
| less_or_equal(add(X0,X2),X1) ),
inference(cnf,[status(esa)],[less_or_equal_sum_of_halves]) ).
cnf(l2,plain,
( ~ less_or_equal(absolute(add(f(xs(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))))),negate(f(a_real_number)))),half(epsilon_0))
| ~ less_or_equal(absolute(add(g(xs(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))))),negate(g(a_real_number)))),half(epsilon_0))
| less_or_equal(add(absolute(add(f(xs(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))))),negate(f(a_real_number)))),absolute(add(g(xs(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))))),negate(g(a_real_number))))),epsilon_0) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(8,plain,
( ~ less_or_equal(absolute(add(X0,negate(a_real_number))),delta_1(X1))
| less_or_equal(X1,n0)
| less_or_equal(absolute(add(f(X0),negate(f(a_real_number)))),X1) ),
inference(cnf,[status(esa)],[clause_3]) ).
cnf(l4,plain,
( ~ less_or_equal(absolute(add(xs(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0)))),negate(a_real_number))),delta_1(half(epsilon_0)))
| less_or_equal(half(epsilon_0),n0)
| less_or_equal(absolute(add(f(xs(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))))),negate(f(a_real_number)))),half(epsilon_0)) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(3,plain,
( ~ less_or_equal(minimum(X0,X1),n0)
| less_or_equal(X0,n0)
| less_or_equal(X1,n0) ),
inference(cnf,[status(esa)],[minimum9]) ).
cnf(l3,plain,
( ~ less_or_equal(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))),n0)
| less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(delta_1(half(epsilon_0)),n0) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(7,plain,
( ~ less_or_equal(delta_2(X0),n0)
| less_or_equal(X0,n0) ),
inference(cnf,[status(esa)],[clause_2]) ).
cnf(l7,plain,
( ~ less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(half(epsilon_0),n0) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(9,plain,
( ~ less_or_equal(absolute(add(X0,negate(a_real_number))),delta_2(X1))
| less_or_equal(X1,n0)
| less_or_equal(absolute(add(g(X0),negate(g(a_real_number)))),X1) ),
inference(cnf,[status(esa)],[clause_4]) ).
cnf(l254,plain,
( ~ less_or_equal(absolute(add(xs(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0)))),negate(a_real_number))),delta_2(half(epsilon_0)))
| less_or_equal(half(epsilon_0),n0)
| less_or_equal(absolute(add(g(xs(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))))),negate(g(a_real_number)))),half(epsilon_0)) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(1,plain,
( ~ less_or_equal(X0,minimum(X1,X2))
| less_or_equal(X0,X1) ),
inference(cnf,[status(esa)],[minimum3]) ).
cnf(l255,plain,
( ~ less_or_equal(absolute(add(xs(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0)))),negate(a_real_number))),minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))))
| less_or_equal(absolute(add(xs(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0)))),negate(a_real_number))),delta_2(half(epsilon_0))) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(5,plain,
( ~ less_or_equal(half(X0),n0)
| less_or_equal(X0,n0) ),
inference(cnf,[status(esa)],[zero_and_half]) ).
cnf(l87,plain,
( ~ less_or_equal(half(epsilon_0),n0)
| less_or_equal(epsilon_0,n0) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l291,plain,
( ~ less_or_equal(half(epsilon_0),n0)
| less_or_equal(epsilon_0,n0) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(11,plain,
( less_or_equal(X0,n0)
| less_or_equal(absolute(add(xs(X0),negate(a_real_number))),X0) ),
inference(cnf,[status(esa)],[clause_6]) ).
cnf(l259,plain,
( less_or_equal(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))),n0)
| less_or_equal(absolute(add(xs(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0)))),negate(a_real_number))),minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0)))) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l173,plain,
( ~ less_or_equal(half(epsilon_0),n0)
| less_or_equal(epsilon_0,n0) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(10,plain,
~ less_or_equal(epsilon_0,n0),
inference(cnf,[status(esa)],[clause_5]) ).
cnf(l174,plain,
~ less_or_equal(epsilon_0,n0),
inference(instantiation,[status(thm)],[10]) ).
cnf(l260,plain,
( ~ less_or_equal(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))),n0)
| less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(delta_1(half(epsilon_0)),n0) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(6,plain,
( ~ less_or_equal(delta_1(X0),n0)
| less_or_equal(X0,n0) ),
inference(cnf,[status(esa)],[clause_1]) ).
cnf(l5,plain,
( ~ less_or_equal(delta_1(half(epsilon_0)),n0)
| less_or_equal(half(epsilon_0),n0) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l400,plain,
( ~ less_or_equal(delta_1(half(epsilon_0)),n0)
| less_or_equal(half(epsilon_0),n0) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l292,plain,
~ less_or_equal(epsilon_0,n0),
inference(instantiation,[status(thm)],[10]) ).
cnf(l293,plain,
( ~ less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(half(epsilon_0),n0) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(2,plain,
( ~ less_or_equal(X0,minimum(X1,X2))
| less_or_equal(X0,X2) ),
inference(cnf,[status(esa)],[minimum7]) ).
cnf(l6,plain,
( ~ less_or_equal(absolute(add(xs(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0)))),negate(a_real_number))),minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))))
| less_or_equal(absolute(add(xs(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0)))),negate(a_real_number))),delta_1(half(epsilon_0))) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l9,plain,
( less_or_equal(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))),n0)
| less_or_equal(absolute(add(xs(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0)))),negate(a_real_number))),minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0)))) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l298,plain,
( ~ less_or_equal(half(epsilon_0),n0)
| less_or_equal(epsilon_0,n0) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l8,plain,
( ~ less_or_equal(half(epsilon_0),n0)
| less_or_equal(epsilon_0,n0) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l401,plain,
( ~ less_or_equal(half(epsilon_0),n0)
| less_or_equal(epsilon_0,n0) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l299,plain,
~ less_or_equal(epsilon_0,n0),
inference(instantiation,[status(thm)],[10]) ).
cnf(l88,plain,
~ less_or_equal(epsilon_0,n0),
inference(instantiation,[status(thm)],[10]) ).
cnf(l15,plain,
~ less_or_equal(epsilon_0,n0),
inference(instantiation,[status(thm)],[10]) ).
cnf(l10,plain,
( ~ less_or_equal(minimum(delta_2(half(epsilon_0)),delta_1(half(epsilon_0))),n0)
| less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(delta_1(half(epsilon_0)),n0) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l30,plain,
( ~ less_or_equal(delta_2(half(epsilon_0)),n0)
| less_or_equal(half(epsilon_0),n0) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l402,plain,
~ less_or_equal(epsilon_0,n0),
inference(instantiation,[status(thm)],[10]) ).
cnf(l33,plain,
( ~ less_or_equal(half(epsilon_0),n0)
| less_or_equal(epsilon_0,n0) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l34,plain,
~ less_or_equal(epsilon_0,n0),
inference(instantiation,[status(thm)],[10]) ).
cnf(l408,plain,
( ~ less_or_equal(delta_1(half(epsilon_0)),n0)
| less_or_equal(half(epsilon_0),n0) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l409,plain,
( ~ less_or_equal(half(epsilon_0),n0)
| less_or_equal(epsilon_0,n0) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l410,plain,
~ less_or_equal(epsilon_0,n0),
inference(instantiation,[status(thm)],[10]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l4,l3,l7,l254,l255,l87,l291,l259,l173,l174,l260,l5,l400,l292,l293,l6,l9,l298,l8,l401,l299,l88,l15,l10,l30,l402,l33,l34,l408,l409,l410]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ANA004-4 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Jul 20 03:45:19 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % launching worker at depth: 1
% 0.13/0.34 % launching worker at depth: 3
% 0.13/0.34 % launching worker at depth: 4
% 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: 7
% 0.13/0.34 % launching worker at depth: 5
% 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
% 0.13/0.34 % launching worker at depth: 11
% 0.13/0.35 % launching worker at depth: 12
% 0.13/0.40 % launching worker at depth: 13
% 0.19/0.44 % launching worker at depth: 14
% 0.19/0.52 % launching worker at depth: 15
% 3.76/0.87 % launching worker at depth: 16
% 6.21/1.17 % SZS status Theorem for theBenchmark
% 6.21/1.17 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------