%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET882+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 : n028.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 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 5 unt; 0 def)
% Number of atoms : 34 ( 22 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 37 ( 18 ~; 13 |; 1 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t23_zfmisc_1,plain,
! [A,B] :
( A != B
=> set_difference(unordered_pair(A,B),singleton(B)) = singleton(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_zfmisc_1) ).
fof(t23_zfmisc_1_negated,plain,
~ ! [A,B] :
( A != B
=> set_difference(unordered_pair(A,B),singleton(B)) = singleton(A) ),
inference(negate_conjecture,[status(cth)],[t23_zfmisc_1]) ).
cnf(15,plain,
set_difference(unordered_pair(sK4,sK5),singleton(sK5)) != singleton(sK4),
inference(cnf,[status(esa)],[t23_zfmisc_1_negated]) ).
cnf(l0,plain,
set_difference(unordered_pair(sK4,sK5),singleton(sK5)) != singleton(sK4),
inference(instantiation,[status(thm)],[15]) ).
fof(l39_zfmisc_1,plain,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ~ in(A,C)
& ( in(B,C)
| A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).
cnf(10,plain,
( ~ in(X0,X1)
| set_difference(unordered_pair(X2,X0),X1) = singleton(X2)
| in(X2,X1) ),
inference(cnf,[status(esa)],[l39_zfmisc_1]) ).
cnf(l1,plain,
( ~ in(sK5,singleton(sK5))
| set_difference(unordered_pair(sK4,sK5),singleton(sK5)) = singleton(sK4)
| in(sK4,singleton(sK5)) ),
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(l3,plain,
( singleton(sK5) != singleton(sK5)
| sK5 != sK5
| in(sK5,singleton(sK5)) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(2,plain,
( X0 != singleton(X1)
| ~ in(X2,X0)
| X2 = X1 ),
inference(cnf,[status(esa)],[d1_tarski]) ).
cnf(l2,plain,
( singleton(sK5) != singleton(sK5)
| ~ in(sK4,singleton(sK5))
| sK4 = sK5 ),
inference(instantiation,[status(thm)],[2]) ).
cnf(14,plain,
sK4 != sK5,
inference(cnf,[status(esa)],[t23_zfmisc_1_negated]) ).
cnf(l12,plain,
sK4 != sK5,
inference(instantiation,[status(thm)],[14]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l2,l12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET882+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n028.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 22:58:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % launching worker at depth: 6
% 0.12/0.33 % launching worker at depth: 1
% 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: 3
% 0.12/0.33 % launching worker at depth: 5
% 0.12/0.33 % launching worker at depth: 4
% 0.12/0.33 % launching worker at depth: 8
% 0.12/0.33 % launching worker at depth: 9
% 0.12/0.34 % launching worker at depth: 10
% 0.12/0.35 % SZS status Theorem for theBenchmark
% 0.12/0.35 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------