%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SEU326+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/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 : Fri Jul 25 03:45:12 PM UTC 2025
% Result : Theorem 0.17s 0.41s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 3 unt; 0 def)
% Number of atoms : 56 ( 29 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 63 ( 31 ~; 20 |; 7 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t10_tops_2,plain,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( ~ ( B != empty_set
& complements_of_subsets(A,B) = empty_set )
& ~ ( complements_of_subsets(A,B) != empty_set
& B = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_tops_2) ).
fof(t10_tops_2_negated,plain,
~ ! [A,B] :
( element(B,powerset(powerset(A)))
=> ( ~ ( B != empty_set
& complements_of_subsets(A,B) = empty_set )
& ~ ( complements_of_subsets(A,B) != empty_set
& B = empty_set ) ) ),
inference(negate_conjecture,[status(cth)],[t10_tops_2]) ).
cnf(61,plain,
element(sK6,powerset(powerset(sK5))),
inference(cnf,[status(esa)],[t10_tops_2_negated]) ).
cnf(l0,plain,
element(sK6,powerset(powerset(sK5))),
inference(instantiation,[status(thm)],[61]) ).
fof(involutiveness_k7_setfam_1,plain,
! [A,B] :
( element(B,powerset(powerset(A)))
=> complements_of_subsets(A,complements_of_subsets(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
cnf(49,plain,
( ~ element(X0,powerset(powerset(X1)))
| complements_of_subsets(X1,complements_of_subsets(X1,X0)) = X0 ),
inference(cnf,[status(esa)],[involutiveness_k7_setfam_1]) ).
cnf(l1,plain,
( ~ element(sK6,powerset(powerset(sK5)))
| complements_of_subsets(sK5,complements_of_subsets(sK5,sK6)) = sK6 ),
inference(instantiation,[status(thm)],[49]) ).
cnf(64,plain,
( sK6 = empty_set
| ~ sP0 ),
inference(cnf,[status(esa)],[t10_tops_2_negated]) ).
cnf(l6,plain,
( sK6 = empty_set
| ~ sP0 ),
inference(instantiation,[status(thm)],[64]) ).
cnf(63,plain,
( complements_of_subsets(sK5,sK6) = empty_set
| sP0 ),
inference(cnf,[status(esa)],[t10_tops_2_negated]) ).
cnf(l13,plain,
( complements_of_subsets(sK5,sK6) = empty_set
| sP0 ),
inference(instantiation,[status(thm)],[63]) ).
fof(t46_setfam_1,plain,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( B != empty_set
& complements_of_subsets(A,B) = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).
cnf(70,plain,
( ~ element(X0,powerset(powerset(X1)))
| complements_of_subsets(X1,X0) != empty_set
| X0 = empty_set ),
inference(cnf,[status(esa)],[t46_setfam_1]) ).
cnf(l46,plain,
( ~ element(sK6,powerset(powerset(sK5)))
| complements_of_subsets(sK5,sK6) != empty_set
| sK6 = empty_set ),
inference(instantiation,[status(thm)],[70]) ).
cnf(l25,plain,
( ~ element(complements_of_subsets(sK5,sK6),powerset(powerset(sK5)))
| complements_of_subsets(sK5,complements_of_subsets(sK5,sK6)) != empty_set
| complements_of_subsets(sK5,sK6) = empty_set ),
inference(instantiation,[status(thm)],[70]) ).
fof(dt_k7_setfam_1,plain,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(complements_of_subsets(A,B),powerset(powerset(A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
cnf(40,plain,
( ~ element(X0,powerset(powerset(X1)))
| element(complements_of_subsets(X1,X0),powerset(powerset(X1))) ),
inference(cnf,[status(esa)],[dt_k7_setfam_1]) ).
cnf(l26,plain,
( ~ element(sK6,powerset(powerset(sK5)))
| element(complements_of_subsets(sK5,sK6),powerset(powerset(sK5))) ),
inference(instantiation,[status(thm)],[40]) ).
cnf(65,plain,
( complements_of_subsets(sK5,sK6) != empty_set
| ~ sP0 ),
inference(cnf,[status(esa)],[t10_tops_2_negated]) ).
cnf(l27,plain,
( complements_of_subsets(sK5,sK6) != empty_set
| ~ sP0 ),
inference(instantiation,[status(thm)],[65]) ).
cnf(62,plain,
( sK6 != empty_set
| sP0 ),
inference(cnf,[status(esa)],[t10_tops_2_negated]) ).
cnf(l43,plain,
( sK6 != empty_set
| sP0 ),
inference(instantiation,[status(thm)],[62]) ).
cnf(l44,plain,
( ~ element(sK6,powerset(powerset(sK5)))
| complements_of_subsets(sK5,sK6) != empty_set
| sK6 = empty_set ),
inference(instantiation,[status(thm)],[70]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l6,l13,l46,l25,l26,l27,l43,l44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU326+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.32 % Computer : n019.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Jul 22 00:50:34 EDT 2025
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % launching worker at depth: 5
% 0.13/0.33 % launching worker at depth: 7
% 0.13/0.33 % launching worker at depth: 1
% 0.13/0.33 % launching worker at depth: 2
% 0.13/0.33 % launching worker at depth: 3
% 0.13/0.33 % launching worker at depth: 6
% 0.13/0.33 % launching worker at depth: 4
% 0.13/0.33 % launching worker at depth: 8
% 0.13/0.33 % launching worker at depth: 9
% 0.13/0.34 % launching worker at depth: 10
% 0.17/0.39 % launching worker at depth: 11
% 0.17/0.41 % SZS status Theorem for theBenchmark
% 0.17/0.41 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------