%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SEU174+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 : n023.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 03:44:44 PM UTC 2025
% Result : Theorem 244.69s 31.16s
% Output : CNFRefutation 244.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 17 unt; 0 def)
% Number of atoms : 92 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 92 ( 42 ~; 33 |; 6 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 1 sgn 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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) ).
fof(t46_setfam_1_negated,plain,
~ ! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( B != empty_set
& complements_of_subsets(A,B) = empty_set ) ),
inference(negate_conjecture,[status(cth)],[t46_setfam_1]) ).
cnf(29,plain,
element(sK9,powerset(powerset(sK8))),
inference(cnf,[status(esa)],[t46_setfam_1_negated]) ).
cnf(l0,plain,
element(sK9,powerset(powerset(sK8))),
inference(instantiation,[status(thm)],[29]) ).
fof(t4_subset,plain,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
cnf(32,plain,
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| element(X0,X2) ),
inference(cnf,[status(esa)],[t4_subset]) ).
cnf(l1,plain,
( ~ in(sK3(sK9),sK9)
| ~ element(sK9,powerset(powerset(sK8)))
| element(sK3(sK9),powerset(sK8)) ),
inference(instantiation,[status(thm)],[32]) ).
fof(t2_subset,plain,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
cnf(26,plain,
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf,[status(esa)],[t2_subset]) ).
cnf(l3,plain,
( ~ element(sK3(sK9),sK9)
| in(sK3(sK9),sK9)
| empty(sK9) ),
inference(instantiation,[status(thm)],[26]) ).
fof(t8_boole,plain,
! [A,B] :
~ ( empty(A)
& A != B
& empty(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
cnf(36,plain,
( ~ empty(X0)
| ~ empty(X1)
| X0 = X1 ),
inference(cnf,[status(esa)],[t8_boole]) ).
cnf(l137,plain,
( ~ empty(empty_set)
| ~ empty(sK9)
| empty_set = sK9 ),
inference(instantiation,[status(thm)],[36]) ).
fof(fc1_xboole_0,plain,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
cnf(15,plain,
empty(empty_set),
inference(cnf,[status(esa)],[fc1_xboole_0]) ).
cnf(l147,plain,
empty(empty_set),
inference(instantiation,[status(thm)],[15]) ).
cnf(30,plain,
sK9 != empty_set,
inference(cnf,[status(esa)],[t46_setfam_1_negated]) ).
cnf(l434,plain,
sK9 != empty_set,
inference(instantiation,[status(thm)],[30]) ).
fof(existence_m1_subset_1,plain,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
cnf(13,plain,
element(sK3(X0),X0),
inference(cnf,[status(esa)],[existence_m1_subset_1]) ).
cnf(l120,plain,
element(sK3(sK9),sK9),
inference(instantiation,[status(thm)],[13]) ).
fof(d8_setfam_1,plain,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ! [C] :
( element(C,powerset(powerset(A)))
=> ( C = complements_of_subsets(A,B)
<=> ! [D] :
( element(D,powerset(A))
=> ( in(D,C)
<=> in(subset_complement(A,D),B) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).
cnf(4,plain,
( ~ in(X0,X1)
| ~ element(X2,powerset(powerset(X3)))
| ~ element(X1,powerset(powerset(X3)))
| ~ element(X0,powerset(X3))
| X1 != complements_of_subsets(X3,X2)
| in(subset_complement(X3,X0),X2) ),
inference(cnf,[status(esa)],[d8_setfam_1]) ).
cnf(l678,plain,
( ~ in(sK3(sK9),sK9)
| ~ element(complements_of_subsets(sK8,sK9),powerset(powerset(sK8)))
| ~ element(sK9,powerset(powerset(sK8)))
| ~ element(sK3(sK9),powerset(sK8))
| sK9 != complements_of_subsets(sK8,complements_of_subsets(sK8,sK9))
| in(subset_complement(sK8,sK3(sK9)),complements_of_subsets(sK8,sK9)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l733,plain,
( ~ element(sK3(sK9),sK9)
| in(sK3(sK9),sK9)
| empty(sK9) ),
inference(instantiation,[status(thm)],[26]) ).
cnf(l754,plain,
( ~ empty(sK9)
| ~ empty(empty_set)
| sK9 = empty_set ),
inference(instantiation,[status(thm)],[36]) ).
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(17,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(l776,plain,
( ~ element(sK9,powerset(powerset(sK8)))
| complements_of_subsets(sK8,complements_of_subsets(sK8,sK9)) = sK9 ),
inference(instantiation,[status(thm)],[17]) ).
cnf(l759,plain,
empty(empty_set),
inference(instantiation,[status(thm)],[15]) ).
cnf(l763,plain,
sK9 != empty_set,
inference(instantiation,[status(thm)],[30]) ).
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(12,plain,
( ~ element(X0,powerset(powerset(X1)))
| element(complements_of_subsets(X1,X0),powerset(powerset(X1))) ),
inference(cnf,[status(esa)],[dt_k7_setfam_1]) ).
cnf(l781,plain,
( ~ element(sK9,powerset(powerset(sK8)))
| element(complements_of_subsets(sK8,sK9),powerset(powerset(sK8))) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l741,plain,
element(sK3(sK9),sK9),
inference(instantiation,[status(thm)],[13]) ).
cnf(31,plain,
complements_of_subsets(sK8,sK9) = empty_set,
inference(cnf,[status(esa)],[t46_setfam_1_negated]) ).
cnf(l738,plain,
complements_of_subsets(sK8,sK9) = empty_set,
inference(instantiation,[status(thm)],[31]) ).
fof(t7_boole,plain,
! [A,B] :
~ ( in(A,B)
& empty(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
cnf(35,plain,
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf,[status(esa)],[t7_boole]) ).
cnf(l810,plain,
( ~ in(subset_complement(sK8,sK3(sK9)),empty_set)
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[35]) ).
cnf(l817,plain,
empty(empty_set),
inference(instantiation,[status(thm)],[15]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l137,l147,l434,l120,l678,l733,l754,l776,l759,l763,l781,l741,l738,l810,l817]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU174+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n023.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 23:43:19 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % launching worker at depth: 5
% 0.13/0.35 % launching worker at depth: 1
% 0.13/0.35 % launching worker at depth: 4
% 0.13/0.35 % launching worker at depth: 3
% 0.13/0.35 % launching worker at depth: 2
% 0.13/0.35 % launching worker at depth: 6
% 0.13/0.35 % launching worker at depth: 7
% 0.13/0.35 % launching worker at depth: 8
% 0.13/0.35 % launching worker at depth: 9
% 0.13/0.36 % launching worker at depth: 10
% 0.19/0.50 % launching worker at depth: 11
% 39.71/5.33 % launching worker at depth: 12
% 244.69/31.16 % SZS status Theorem for theBenchmark
% 244.69/31.16 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------