%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET918+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/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 03:32:59 PM UTC 2025
% Result : Theorem 285.59s 36.26s
% Output : CNFRefutation 285.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 16 unt; 0 def)
% Number of atoms : 59 ( 35 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 55 ( 25 ~; 19 |; 5 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 3 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t59_zfmisc_1,plain,
! [A,B,C] :
~ ( set_intersection2(unordered_pair(A,B),C) = singleton(A)
& in(B,C)
& A != B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t59_zfmisc_1) ).
fof(t59_zfmisc_1_negated,plain,
~ ! [A,B,C] :
~ ( set_intersection2(unordered_pair(A,B),C) = singleton(A)
& in(B,C)
& A != B ),
inference(negate_conjecture,[status(cth)],[t59_zfmisc_1]) ).
cnf(28,plain,
set_intersection2(unordered_pair(sK6,sK7),sK8) = singleton(sK6),
inference(cnf,[status(esa)],[t59_zfmisc_1_negated]) ).
cnf(l0,plain,
set_intersection2(unordered_pair(sK6,sK7),sK8) = singleton(sK6),
inference(instantiation,[status(thm)],[28]) ).
fof(d3_xboole_0,plain,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
cnf(17,plain,
( X0 != set_intersection2(X1,X2)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf,[status(esa)],[d3_xboole_0]) ).
cnf(l3,plain,
( set_intersection2(set_intersection2(unordered_pair(sK6,sK7),sK8),set_intersection2(unordered_pair(sK6,sK7),sK8)) != set_intersection2(singleton(sK6),singleton(sK6))
| ~ in(sK7,set_intersection2(set_intersection2(unordered_pair(sK6,sK7),sK8),set_intersection2(unordered_pair(sK6,sK7),sK8)))
| in(sK7,singleton(sK6)) ),
inference(instantiation,[status(thm)],[17]) ).
fof(d1_tarski,plain,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
cnf(3,plain,
( X0 != singleton(X1)
| ~ in(X2,X0)
| X2 = X1 ),
inference(cnf,[status(esa)],[d1_tarski]) ).
cnf(l7,plain,
( singleton(sK6) != singleton(sK6)
| ~ in(sK7,singleton(sK6))
| sK7 = sK6 ),
inference(instantiation,[status(thm)],[3]) ).
cnf(30,plain,
sK6 != sK7,
inference(cnf,[status(esa)],[t59_zfmisc_1_negated]) ).
cnf(l144,plain,
sK6 != sK7,
inference(instantiation,[status(thm)],[30]) ).
cnf(19,plain,
( X0 != set_intersection2(X1,X2)
| ~ in(X3,X1)
| ~ in(X3,X2)
| in(X3,X0) ),
inference(cnf,[status(esa)],[d3_xboole_0]) ).
cnf(l9,plain,
( set_intersection2(set_intersection2(unordered_pair(sK6,sK7),sK8),set_intersection2(unordered_pair(sK6,sK7),sK8)) != set_intersection2(sK8,unordered_pair(sK6,sK7))
| ~ in(sK7,sK8)
| ~ in(sK7,unordered_pair(sK6,sK7))
| in(sK7,set_intersection2(set_intersection2(unordered_pair(sK6,sK7),sK8),set_intersection2(unordered_pair(sK6,sK7),sK8))) ),
inference(instantiation,[status(thm)],[19]) ).
cnf(29,plain,
in(sK7,sK8),
inference(cnf,[status(esa)],[t59_zfmisc_1_negated]) ).
cnf(l13,plain,
in(sK7,sK8),
inference(instantiation,[status(thm)],[29]) ).
fof(commutativity_k3_xboole_0,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
cnf(2,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf,[status(esa)],[commutativity_k3_xboole_0]) ).
cnf(l121,plain,
set_intersection2(unordered_pair(sK6,sK7),sK8) = set_intersection2(sK8,unordered_pair(sK6,sK7)),
inference(instantiation,[status(thm)],[2]) ).
fof(d2_tarski,plain,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = A
| D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
cnf(10,plain,
( X0 != unordered_pair(X1,X2)
| X3 != X1
| in(X3,X0) ),
inference(cnf,[status(esa)],[d2_tarski]) ).
cnf(l23,plain,
( unordered_pair(sK6,sK7) != unordered_pair(sK7,sK6)
| sK7 != sK7
| in(sK7,unordered_pair(sK6,sK7)) ),
inference(instantiation,[status(thm)],[10]) ).
fof(idempotence_k3_xboole_0,plain,
! [A,B] : set_intersection2(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
cnf(25,plain,
set_intersection2(X0,X0) = X0,
inference(cnf,[status(esa)],[idempotence_k3_xboole_0]) ).
cnf(l126,plain,
set_intersection2(set_intersection2(unordered_pair(sK6,sK7),sK8),set_intersection2(unordered_pair(sK6,sK7),sK8)) = set_intersection2(unordered_pair(sK6,sK7),sK8),
inference(instantiation,[status(thm)],[25]) ).
fof(commutativity_k2_tarski,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
cnf(1,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf,[status(esa)],[commutativity_k2_tarski]) ).
cnf(l24,plain,
unordered_pair(sK6,sK7) = unordered_pair(sK7,sK6),
inference(instantiation,[status(thm)],[1]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l3,l7,l144,l9,l13,l121,l23,l126,l24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET918+1 : TPTP v9.0.0. Released v3.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Jul 21 23:01:34 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.35 % launching worker at depth: 9
% 0.12/0.36 % launching worker at depth: 10
% 10.21/1.67 % launching worker at depth: 11
% 285.59/36.26 % SZS status Theorem for theBenchmark
% 285.59/36.26 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------