%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SEU142+2 : 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 : 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 03:44:36 PM UTC 2025
% Result : Theorem 19.82s 2.82s
% Output : CNFRefutation 19.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 12 unt; 0 def)
% Number of atoms : 65 ( 38 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 59 ( 24 ~; 28 |; 1 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 3 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t69_enumset1,plain,
! [A] : unordered_pair(A,A) = singleton(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(t69_enumset1_negated,plain,
~ ! [A] : unordered_pair(A,A) = singleton(A),
inference(negate_conjecture,[status(cth)],[t69_enumset1]) ).
cnf(97,plain,
unordered_pair(sK13,sK13) != singleton(sK13),
inference(cnf,[status(esa)],[t69_enumset1_negated]) ).
cnf(l0,plain,
unordered_pair(sK13,sK13) != singleton(sK13),
inference(instantiation,[status(thm)],[97]) ).
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(11,plain,
( sK1(X0,X1) != X0
| X1 = singleton(X0)
| sP0(X1,X0) ),
inference(cnf,[status(esa)],[d1_tarski]) ).
cnf(l1,plain,
( sK1(sK13,unordered_pair(sK13,sK13)) != sK13
| unordered_pair(sK13,sK13) = singleton(sK13)
| sP0(unordered_pair(sK13,sK13),sK13) ),
inference(instantiation,[status(thm)],[11]) ).
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(16,plain,
( X0 != unordered_pair(X1,X2)
| ~ in(X3,X0)
| X3 = X1
| X3 = X2 ),
inference(cnf,[status(esa)],[d2_tarski]) ).
cnf(l124,plain,
( unordered_pair(sK13,sK13) != unordered_pair(sK13,sK13)
| ~ in(sK1(sK13,unordered_pair(sK13,sK13)),unordered_pair(sK13,sK13))
| sK1(sK13,unordered_pair(sK13,sK13)) = sK13
| sK1(sK13,unordered_pair(sK13,sK13)) = sK13 ),
inference(instantiation,[status(thm)],[16]) ).
cnf(10,plain,
( X0 = singleton(X1)
| in(sK1(X1,X0),X0)
| sP0(X0,X1) ),
inference(cnf,[status(esa)],[d1_tarski]) ).
cnf(l147,plain,
( unordered_pair(sK13,sK13) = singleton(sK13)
| in(sK1(sK13,unordered_pair(sK13,sK13)),unordered_pair(sK13,sK13))
| sP0(unordered_pair(sK13,sK13),sK13) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(13,plain,
( sK1(X0,X1) = X0
| ~ sP0(X1,X0) ),
inference(cnf,[status(esa)],[d1_tarski]) ).
cnf(l3,plain,
( sK1(sK13,unordered_pair(sK13,sK13)) = sK13
| ~ sP0(unordered_pair(sK13,sK13),sK13) ),
inference(instantiation,[status(thm)],[13]) ).
cnf(l148,plain,
( sK1(sK13,unordered_pair(sK13,sK13)) = sK13
| ~ sP0(unordered_pair(sK13,sK13),sK13) ),
inference(instantiation,[status(thm)],[13]) ).
cnf(17,plain,
( X0 != unordered_pair(X1,X2)
| X3 != X1
| in(X3,X0) ),
inference(cnf,[status(esa)],[d2_tarski]) ).
cnf(l7,plain,
( set_difference(set_intersection2(unordered_pair(sK13,sK13),unordered_pair(sK13,sK13)),empty_set) != unordered_pair(sK13,sK13)
| sK1(sK13,unordered_pair(sK13,sK13)) != sK13
| in(sK1(sK13,unordered_pair(sK13,sK13)),set_difference(set_intersection2(unordered_pair(sK13,sK13),unordered_pair(sK13,sK13)),empty_set)) ),
inference(instantiation,[status(thm)],[17]) ).
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(35,plain,
( X0 != set_intersection2(X1,X2)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf,[status(esa)],[d3_xboole_0]) ).
cnf(l8,plain,
( set_difference(set_intersection2(unordered_pair(sK13,sK13),unordered_pair(sK13,sK13)),empty_set) != set_intersection2(unordered_pair(sK13,sK13),unordered_pair(sK13,sK13))
| ~ in(sK1(sK13,unordered_pair(sK13,sK13)),set_difference(set_intersection2(unordered_pair(sK13,sK13),unordered_pair(sK13,sK13)),empty_set))
| in(sK1(sK13,unordered_pair(sK13,sK13)),unordered_pair(sK13,sK13)) ),
inference(instantiation,[status(thm)],[35]) ).
cnf(12,plain,
( ~ in(sK1(X0,X1),X1)
| ~ sP0(X1,X0) ),
inference(cnf,[status(esa)],[d1_tarski]) ).
cnf(l15,plain,
( ~ in(sK1(sK13,unordered_pair(sK13,sK13)),unordered_pair(sK13,sK13))
| ~ sP0(unordered_pair(sK13,sK13),sK13) ),
inference(instantiation,[status(thm)],[12]) ).
fof(t3_boole,plain,
! [A] : set_difference(A,empty_set) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
cnf(84,plain,
set_difference(X0,empty_set) = X0,
inference(cnf,[status(esa)],[t3_boole]) ).
cnf(l9,plain,
set_difference(set_intersection2(unordered_pair(sK13,sK13),unordered_pair(sK13,sK13)),empty_set) = set_intersection2(unordered_pair(sK13,sK13),unordered_pair(sK13,sK13)),
inference(instantiation,[status(thm)],[84]) ).
cnf(l21,plain,
set_difference(set_intersection2(unordered_pair(sK13,sK13),unordered_pair(sK13,sK13)),empty_set) = set_intersection2(unordered_pair(sK13,sK13),unordered_pair(sK13,sK13)),
inference(instantiation,[status(thm)],[84]) ).
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(60,plain,
set_intersection2(X0,X0) = X0,
inference(cnf,[status(esa)],[idempotence_k3_xboole_0]) ).
cnf(l23,plain,
set_intersection2(unordered_pair(sK13,sK13),unordered_pair(sK13,sK13)) = unordered_pair(sK13,sK13),
inference(instantiation,[status(thm)],[60]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l124,l147,l3,l148,l7,l8,l15,l9,l21,l23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU142+2 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34 % Computer : n024.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 23:35:34 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.35 % launching worker at depth: 10
% 2.39/0.67 % launching worker at depth: 11
% 19.82/2.82 % SZS status Theorem for theBenchmark
% 19.82/2.82 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------