%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET908+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 : n031.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 03:32:57 PM UTC 2025
% Result : Theorem 2.59s 0.70s
% Output : CNFRefutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 9 unt; 0 def)
% Number of atoms : 42 ( 22 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 42 ( 20 ~; 17 |; 0 &)
% ( 5 <=>; 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; 3 con; 0-2 aty)
% Number of variables : 29 ( 3 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t49_zfmisc_1,plain,
! [A,B] : set_union2(singleton(A),B) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_zfmisc_1) ).
fof(t49_zfmisc_1_negated,plain,
~ ! [A,B] : set_union2(singleton(A),B) != empty_set,
inference(negate_conjecture,[status(cth)],[t49_zfmisc_1]) ).
cnf(24,plain,
set_union2(singleton(sK6),sK7) = empty_set,
inference(cnf,[status(esa)],[t49_zfmisc_1_negated]) ).
cnf(l0,plain,
set_union2(singleton(sK6),sK7) = empty_set,
inference(instantiation,[status(thm)],[24]) ).
fof(d1_xboole_0,plain,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
cnf(8,plain,
( X0 != empty_set
| ~ in(X1,X0) ),
inference(cnf,[status(esa)],[d1_xboole_0]) ).
cnf(l1,plain,
( set_union2(singleton(sK6),sK7) != empty_set
| ~ in(sK6,set_union2(singleton(sK6),sK7)) ),
inference(instantiation,[status(thm)],[8]) ).
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/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
cnf(11,plain,
( X0 != set_union2(X1,X2)
| ~ in(X3,X1)
| in(X3,X0) ),
inference(cnf,[status(esa)],[d2_xboole_0]) ).
cnf(l66,plain,
( set_union2(singleton(sK6),sK7) != set_union2(singleton(sK6),set_union2(sK7,sK7))
| ~ in(sK6,singleton(sK6))
| in(sK6,set_union2(singleton(sK6),sK7)) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(10,plain,
( X0 != set_union2(X1,X2)
| ~ in(X3,X0)
| in(X3,X1)
| in(X3,X2) ),
inference(cnf,[status(esa)],[d2_xboole_0]) ).
cnf(l87,plain,
( set_union2(singleton(sK6),singleton(sK6)) != set_union2(singleton(sK6),singleton(sK6))
| ~ in(sK6,set_union2(singleton(sK6),singleton(sK6)))
| in(sK6,singleton(sK6))
| in(sK6,singleton(sK6)) ),
inference(instantiation,[status(thm)],[10]) ).
fof(d1_tarski,plain,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
cnf(3,plain,
( X0 != singleton(X1)
| X2 != X1
| in(X2,X0) ),
inference(cnf,[status(esa)],[d1_tarski]) ).
cnf(l95,plain,
( set_union2(singleton(sK6),singleton(sK6)) != singleton(sK6)
| sK6 != sK6
| in(sK6,set_union2(singleton(sK6),singleton(sK6))) ),
inference(instantiation,[status(thm)],[3]) ).
fof(idempotence_k2_xboole_0,plain,
! [A,B] : set_union2(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
cnf(21,plain,
set_union2(X0,X0) = X0,
inference(cnf,[status(esa)],[idempotence_k2_xboole_0]) ).
cnf(l98,plain,
set_union2(singleton(sK6),singleton(sK6)) = singleton(sK6),
inference(instantiation,[status(thm)],[21]) ).
cnf(l86,plain,
set_union2(sK7,sK7) = sK7,
inference(instantiation,[status(thm)],[21]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l66,l87,l95,l98,l86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET908+1 : TPTP v9.0.0. Released v3.2.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n031.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 21 23:00:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % launching worker at depth: 3
% 0.12/0.33 % launching worker at depth: 2
% 0.12/0.33 % launching worker at depth: 7
% 0.12/0.33 % launching worker at depth: 4
% 0.12/0.33 % launching worker at depth: 5
% 0.12/0.33 % launching worker at depth: 6
% 0.12/0.33 % launching worker at depth: 8
% 0.12/0.33 % launching worker at depth: 1
% 0.12/0.33 % launching worker at depth: 9
% 0.19/0.34 % launching worker at depth: 10
% 2.59/0.70 % SZS status Theorem for theBenchmark
% 2.59/0.70 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------