%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SEU113+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n024.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 03:44:29 PM UTC 2025
% Result : Theorem 0.19s 0.51s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 10 unt; 0 def)
% Number of atoms : 53 ( 3 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 47 ( 19 ~; 17 |; 4 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 27 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t26_finsub_1,plain,
! [A] : subset(finite_subsets(A),powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finsub_1) ).
fof(t26_finsub_1_negated,plain,
~ ! [A] : subset(finite_subsets(A),powerset(A)),
inference(negate_conjecture,[status(cth)],[t26_finsub_1]) ).
cnf(61,plain,
~ subset(finite_subsets(sK13),powerset(sK13)),
inference(cnf,[status(esa)],[t26_finsub_1_negated]) ).
cnf(l0,plain,
~ subset(finite_subsets(sK13),powerset(sK13)),
inference(instantiation,[status(thm)],[61]) ).
fof(d3_tarski,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
cnf(8,plain,
( in(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf,[status(esa)],[d3_tarski]) ).
cnf(l1,plain,
( in(sK1(finite_subsets(sK13),powerset(sK13)),finite_subsets(sK13))
| subset(finite_subsets(sK13),powerset(sK13)) ),
inference(instantiation,[status(thm)],[8]) ).
fof(d5_finsub_1,plain,
! [A,B] :
( preboolean(B)
=> ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( subset(C,A)
& finite(C) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_finsub_1) ).
cnf(10,plain,
( ~ in(X0,X1)
| ~ preboolean(X1)
| X1 != finite_subsets(X2)
| subset(X0,X2) ),
inference(cnf,[status(esa)],[d5_finsub_1]) ).
cnf(l2,plain,
( ~ in(sK1(finite_subsets(sK13),powerset(sK13)),finite_subsets(sK13))
| ~ preboolean(finite_subsets(sK13))
| finite_subsets(sK13) != finite_subsets(sK13)
| subset(sK1(finite_subsets(sK13),powerset(sK13)),sK13) ),
inference(instantiation,[status(thm)],[10]) ).
fof(fc2_finsub_1,plain,
! [A] :
( ~ empty(finite_subsets(A))
& cup_closed(finite_subsets(A))
& diff_closed(finite_subsets(A))
& preboolean(finite_subsets(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_finsub_1) ).
cnf(29,plain,
preboolean(finite_subsets(X0)),
inference(cnf,[status(esa)],[fc2_finsub_1]) ).
cnf(l3,plain,
preboolean(finite_subsets(sK13)),
inference(instantiation,[status(thm)],[29]) ).
fof(t3_subset,plain,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
cnf(64,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf,[status(esa)],[t3_subset]) ).
cnf(l4,plain,
( ~ subset(sK1(finite_subsets(sK13),powerset(sK13)),sK13)
| element(sK1(finite_subsets(sK13),powerset(sK13)),powerset(sK13)) ),
inference(instantiation,[status(thm)],[64]) ).
fof(t2_subset,plain,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
cnf(62,plain,
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf,[status(esa)],[t2_subset]) ).
cnf(l8,plain,
( ~ element(sK1(finite_subsets(sK13),powerset(sK13)),powerset(sK13))
| empty(powerset(sK13))
| in(sK1(finite_subsets(sK13),powerset(sK13)),powerset(sK13)) ),
inference(instantiation,[status(thm)],[62]) ).
fof(fc1_subset_1,plain,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
cnf(24,plain,
~ empty(powerset(X0)),
inference(cnf,[status(esa)],[fc1_subset_1]) ).
cnf(l21,plain,
~ empty(powerset(sK13)),
inference(instantiation,[status(thm)],[24]) ).
cnf(9,plain,
( ~ in(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf,[status(esa)],[d3_tarski]) ).
cnf(l29,plain,
( ~ in(sK1(finite_subsets(sK13),powerset(sK13)),powerset(sK13))
| subset(finite_subsets(sK13),powerset(sK13)) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l3,l4,l8,l21,l29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU113+1 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n024.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 23:30:04 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % launching worker at depth: 4
% 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: 3
% 0.13/0.34 % launching worker at depth: 1
% 0.13/0.34 % launching worker at depth: 6
% 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: 9
% 0.13/0.34 % launching worker at depth: 10
% 0.13/0.35 % launching worker at depth: 11
% 0.19/0.48 % launching worker at depth: 12
% 0.19/0.51 % SZS status Theorem for theBenchmark
% 0.19/0.51 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------