%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM386+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n021.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 : Fri Jul 25 12:28:03 PM UTC 2025
% Result : Theorem 4.83s 0.96s
% Output : CNFRefutation 4.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 10 unt; 0 def)
% Number of atoms : 82 ( 36 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 86 ( 39 ~; 41 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 3 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t13_ordinal1,plain,
! [A,B] :
( in(A,succ(B))
<=> ( in(A,B)
| A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_ordinal1) ).
fof(t13_ordinal1_negated,plain,
~ ! [A,B] :
( in(A,succ(B))
<=> ( in(A,B)
| A = B ) ),
inference(negate_conjecture,[status(cth)],[t13_ordinal1]) ).
cnf(54,plain,
( in(sK14,succ(sK15))
| in(sK14,sK15)
| sK14 = sK15 ),
inference(cnf,[status(esa)],[t13_ordinal1_negated]) ).
cnf(l0,plain,
( in(sK14,succ(sK15))
| in(sK14,sK15)
| sK14 = sK15 ),
inference(instantiation,[status(thm)],[54]) ).
fof(d2_xboole_0,plain,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
cnf(13,plain,
( ~ in(X0,X1)
| X2 != set_union2(X1,X3)
| in(X0,X2) ),
inference(cnf,[status(esa)],[d2_xboole_0]) ).
cnf(l1,plain,
( ~ in(sK14,sK15)
| succ(sK15) != set_union2(sK15,singleton(sK15))
| in(sK14,succ(sK15)) ),
inference(instantiation,[status(thm)],[13]) ).
fof(d1_tarski,plain,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
cnf(7,plain,
( X0 != singleton(X1)
| X2 != X1
| in(X2,X0) ),
inference(cnf,[status(esa)],[d1_tarski]) ).
cnf(l7,plain,
( set_union2(singleton(sK15),singleton(sK15)) != singleton(sK15)
| sK14 != sK15
| in(sK14,set_union2(singleton(sK15),singleton(sK15))) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(55,plain,
( ~ in(sK14,succ(sK15))
| ~ in(sK14,sK15) ),
inference(cnf,[status(esa)],[t13_ordinal1_negated]) ).
cnf(l2,plain,
( ~ in(sK14,succ(sK15))
| ~ in(sK14,sK15) ),
inference(instantiation,[status(thm)],[55]) ).
fof(idempotence_k2_xboole_0,plain,
! [A,B] : set_union2(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
cnf(31,plain,
set_union2(X0,X0) = X0,
inference(cnf,[status(esa)],[idempotence_k2_xboole_0]) ).
cnf(l8,plain,
set_union2(singleton(sK15),singleton(sK15)) = singleton(sK15),
inference(instantiation,[status(thm)],[31]) ).
cnf(56,plain,
( ~ in(sK14,succ(sK15))
| sK14 != sK15 ),
inference(cnf,[status(esa)],[t13_ordinal1_negated]) ).
cnf(l3,plain,
( ~ in(sK14,succ(sK15))
| sK14 != sK15 ),
inference(instantiation,[status(thm)],[56]) ).
cnf(12,plain,
( ~ in(X0,X1)
| X1 != set_union2(X2,X3)
| in(X0,X2)
| in(X0,X3) ),
inference(cnf,[status(esa)],[d2_xboole_0]) ).
cnf(l13,plain,
( ~ in(sK14,set_union2(singleton(sK15),singleton(sK15)))
| set_union2(singleton(sK15),singleton(sK15)) != set_union2(singleton(sK15),singleton(sK15))
| in(sK14,singleton(sK15))
| in(sK14,singleton(sK15)) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(14,plain,
( ~ in(X0,X1)
| X2 != set_union2(X3,X1)
| in(X0,X2) ),
inference(cnf,[status(esa)],[d2_xboole_0]) ).
cnf(l29,plain,
( ~ in(sK14,singleton(sK15))
| succ(sK15) != set_union2(sK15,singleton(sK15))
| in(sK14,succ(sK15)) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(l90,plain,
( ~ in(sK14,singleton(sK15))
| succ(sK15) != set_union2(sK15,singleton(sK15))
| in(sK14,succ(sK15)) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(6,plain,
( ~ in(X0,X1)
| X1 != singleton(X2)
| X0 = X2 ),
inference(cnf,[status(esa)],[d1_tarski]) ).
cnf(l55,plain,
( ~ in(sK14,singleton(sK15))
| singleton(sK15) != singleton(sK15)
| sK14 = sK15 ),
inference(instantiation,[status(thm)],[6]) ).
fof(d1_ordinal1,plain,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
cnf(5,plain,
succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf,[status(esa)],[d1_ordinal1]) ).
cnf(l56,plain,
succ(sK15) = set_union2(sK15,singleton(sK15)),
inference(instantiation,[status(thm)],[5]) ).
cnf(l92,plain,
( ~ in(sK14,succ(sK15))
| sK14 != sK15 ),
inference(instantiation,[status(thm)],[56]) ).
cnf(l61,plain,
( ~ in(sK14,succ(sK15))
| succ(sK15) != set_union2(sK15,singleton(sK15))
| in(sK14,sK15)
| in(sK14,singleton(sK15)) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l67,plain,
succ(sK15) = set_union2(sK15,singleton(sK15)),
inference(instantiation,[status(thm)],[5]) ).
cnf(l91,plain,
succ(sK15) = set_union2(sK15,singleton(sK15)),
inference(instantiation,[status(thm)],[5]) ).
cnf(l102,plain,
( ~ in(sK14,succ(sK15))
| ~ in(sK14,sK15) ),
inference(instantiation,[status(thm)],[55]) ).
cnf(l5,plain,
succ(sK15) = set_union2(sK15,singleton(sK15)),
inference(instantiation,[status(thm)],[5]) ).
cnf(l97,plain,
( ~ in(sK14,succ(sK15))
| sK14 != sK15 ),
inference(instantiation,[status(thm)],[56]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l7,l2,l8,l3,l13,l29,l90,l55,l56,l92,l61,l67,l91,l102,l5,l97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM386+1 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n021.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 : Mon Jul 21 11:54:04 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % launching worker at depth: 1
% 0.13/0.34 % launching worker at depth: 2
% 0.13/0.34 % launching worker at depth: 8
% 0.13/0.34 % launching worker at depth: 5
% 0.13/0.34 % launching worker at depth: 4
% 0.13/0.34 % launching worker at depth: 3
% 0.13/0.34 % launching worker at depth: 6
% 0.13/0.34 % launching worker at depth: 7
% 0.13/0.35 % launching worker at depth: 9
% 0.13/0.37 % launching worker at depth: 10
% 4.83/0.96 % SZS status Theorem for theBenchmark
% 4.83/0.96 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------