%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET889+1 : TPTP v9.0.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n027.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 03:32:55 PM UTC 2025
% Result : Theorem 114.40s 14.74s
% Output : CNFRefutation 114.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 8 unt; 0 def)
% Number of atoms : 77 ( 35 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 77 ( 33 ~; 39 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 39 ( 2 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t30_zfmisc_1,plain,
! [A] : powerset(singleton(A)) = unordered_pair(empty_set,singleton(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_zfmisc_1) ).
fof(t30_zfmisc_1_negated,plain,
~ ! [A] : powerset(singleton(A)) = unordered_pair(empty_set,singleton(A)),
inference(negate_conjecture,[status(cth)],[t30_zfmisc_1]) ).
cnf(25,plain,
powerset(singleton(sK6)) != unordered_pair(empty_set,singleton(sK6)),
inference(cnf,[status(esa)],[t30_zfmisc_1_negated]) ).
cnf(l0,plain,
powerset(singleton(sK6)) != unordered_pair(empty_set,singleton(sK6)),
inference(instantiation,[status(thm)],[25]) ).
fof(d2_tarski,plain,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = A
| D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
cnf(11,plain,
( X0 = unordered_pair(X1,X2)
| in(sK2(X1,X2,X0),X0)
| sP1(X2,X1,X0) ),
inference(cnf,[status(esa)],[d2_tarski]) ).
cnf(l1,plain,
( powerset(singleton(sK6)) = unordered_pair(empty_set,singleton(sK6))
| in(sK2(empty_set,singleton(sK6),powerset(singleton(sK6))),powerset(singleton(sK6)))
| sP1(singleton(sK6),empty_set,powerset(singleton(sK6))) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(15,plain,
( sK2(X0,X1,X2) = X0
| sK2(X0,X1,X2) = X1
| ~ sP1(X1,X0,X2) ),
inference(cnf,[status(esa)],[d2_tarski]) ).
cnf(l3,plain,
( sK2(empty_set,singleton(sK6),powerset(singleton(sK6))) = empty_set
| sK2(empty_set,singleton(sK6),powerset(singleton(sK6))) = singleton(sK6)
| ~ sP1(singleton(sK6),empty_set,powerset(singleton(sK6))) ),
inference(instantiation,[status(thm)],[15]) ).
fof(d1_zfmisc_1,plain,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
cnf(2,plain,
( X0 != powerset(X1)
| ~ in(X2,X0)
| subset(X2,X1) ),
inference(cnf,[status(esa)],[d1_zfmisc_1]) ).
cnf(l59,plain,
( powerset(singleton(sK6)) != powerset(singleton(sK6))
| ~ in(sK2(empty_set,singleton(sK6),powerset(singleton(sK6))),powerset(singleton(sK6)))
| subset(sK2(empty_set,singleton(sK6),powerset(singleton(sK6))),singleton(sK6)) ),
inference(instantiation,[status(thm)],[2]) ).
fof(l4_zfmisc_1,plain,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = empty_set
| A = singleton(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
cnf(17,plain,
( ~ subset(X0,singleton(X1))
| X0 = singleton(X1)
| X0 = empty_set ),
inference(cnf,[status(esa)],[l4_zfmisc_1]) ).
cnf(l87,plain,
( ~ subset(sK2(empty_set,singleton(sK6),powerset(singleton(sK6))),singleton(sK6))
| sK2(empty_set,singleton(sK6),powerset(singleton(sK6))) = singleton(sK6)
| sK2(empty_set,singleton(sK6),powerset(singleton(sK6))) = empty_set ),
inference(instantiation,[status(thm)],[17]) ).
cnf(12,plain,
( sK2(X0,X1,X2) != X0
| X2 = unordered_pair(X0,X1)
| sP1(X1,X0,X2) ),
inference(cnf,[status(esa)],[d2_tarski]) ).
cnf(l105,plain,
( sK2(empty_set,singleton(sK6),powerset(singleton(sK6))) != empty_set
| powerset(singleton(sK6)) = unordered_pair(empty_set,singleton(sK6))
| sP1(singleton(sK6),empty_set,powerset(singleton(sK6))) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(14,plain,
( ~ in(sK2(X0,X1,X2),X2)
| ~ sP1(X1,X0,X2) ),
inference(cnf,[status(esa)],[d2_tarski]) ).
cnf(l116,plain,
( ~ in(sK2(empty_set,singleton(sK6),powerset(singleton(sK6))),powerset(singleton(sK6)))
| ~ sP1(singleton(sK6),empty_set,powerset(singleton(sK6))) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(3,plain,
( X0 != powerset(X1)
| ~ subset(X2,X1)
| in(X2,X0) ),
inference(cnf,[status(esa)],[d1_zfmisc_1]) ).
cnf(l58,plain,
( powerset(singleton(sK6)) != powerset(singleton(sK6))
| ~ subset(sK2(empty_set,singleton(sK6),powerset(singleton(sK6))),singleton(sK6))
| in(sK2(empty_set,singleton(sK6),powerset(singleton(sK6))),powerset(singleton(sK6))) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(18,plain,
( X0 != empty_set
| subset(X0,singleton(X1)) ),
inference(cnf,[status(esa)],[l4_zfmisc_1]) ).
cnf(l9,plain,
( sK2(empty_set,singleton(sK6),powerset(singleton(sK6))) != empty_set
| subset(sK2(empty_set,singleton(sK6),powerset(singleton(sK6))),singleton(sK6)) ),
inference(instantiation,[status(thm)],[18]) ).
cnf(l218,plain,
( ~ in(sK2(empty_set,singleton(sK6),powerset(singleton(sK6))),powerset(singleton(sK6)))
| ~ sP1(singleton(sK6),empty_set,powerset(singleton(sK6))) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(l36,plain,
( powerset(singleton(sK6)) != powerset(singleton(sK6))
| ~ subset(sK2(empty_set,singleton(sK6),powerset(singleton(sK6))),singleton(sK6))
| in(sK2(empty_set,singleton(sK6),powerset(singleton(sK6))),powerset(singleton(sK6))) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(13,plain,
( sK2(X0,X1,X2) != X1
| X2 = unordered_pair(X0,X1)
| sP1(X1,X0,X2) ),
inference(cnf,[status(esa)],[d2_tarski]) ).
cnf(l96,plain,
( sK2(empty_set,singleton(sK6),powerset(singleton(sK6))) != singleton(sK6)
| powerset(singleton(sK6)) = unordered_pair(empty_set,singleton(sK6))
| sP1(singleton(sK6),empty_set,powerset(singleton(sK6))) ),
inference(instantiation,[status(thm)],[13]) ).
cnf(l113,plain,
( ~ in(sK2(empty_set,singleton(sK6),powerset(singleton(sK6))),powerset(singleton(sK6)))
| ~ sP1(singleton(sK6),empty_set,powerset(singleton(sK6))) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(l45,plain,
( ~ in(sK2(empty_set,singleton(sK6),powerset(singleton(sK6))),powerset(singleton(sK6)))
| ~ sP1(singleton(sK6),empty_set,powerset(singleton(sK6))) ),
inference(instantiation,[status(thm)],[14]) ).
fof(reflexivity_r1_tarski,plain,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
cnf(22,plain,
subset(X0,X0),
inference(cnf,[status(esa)],[reflexivity_r1_tarski]) ).
cnf(l46,plain,
subset(singleton(sK6),singleton(sK6)),
inference(instantiation,[status(thm)],[22]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l59,l87,l105,l116,l58,l9,l218,l36,l96,l113,l45,l46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET889+1 : TPTP v9.0.0. Bugfixed v4.0.0.
% 0.03/0.14 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Jul 21 22:59:19 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % launching worker at depth: 1
% 0.14/0.36 % launching worker at depth: 2
% 0.14/0.36 % launching worker at depth: 4
% 0.14/0.36 % launching worker at depth: 3
% 0.14/0.36 % launching worker at depth: 5
% 0.14/0.36 % launching worker at depth: 6
% 0.14/0.36 % launching worker at depth: 7
% 0.14/0.36 % launching worker at depth: 8
% 0.14/0.36 % launching worker at depth: 9
% 0.14/0.36 % launching worker at depth: 10
% 0.20/0.44 % launching worker at depth: 11
% 114.40/14.74 % SZS status Theorem for theBenchmark
% 114.40/14.74 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------