%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET885+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 : n018.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 0.06s 0.27s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 40 ( 20 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 36 ( 15 ~; 13 |; 0 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 1 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t26_zfmisc_1,plain,
! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> A = C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_zfmisc_1) ).
fof(t26_zfmisc_1_negated,plain,
~ ! [A,B,C] :
( subset(unordered_pair(A,B),singleton(C))
=> A = C ),
inference(negate_conjecture,[status(cth)],[t26_zfmisc_1]) ).
cnf(22,plain,
subset(unordered_pair(sK6,sK7),singleton(sK8)),
inference(cnf,[status(esa)],[t26_zfmisc_1_negated]) ).
cnf(l0,plain,
subset(unordered_pair(sK6,sK7),singleton(sK8)),
inference(instantiation,[status(thm)],[22]) ).
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(16,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf,[status(esa)],[d3_tarski]) ).
cnf(l1,plain,
( ~ in(sK6,unordered_pair(sK6,sK7))
| ~ subset(unordered_pair(sK6,sK7),singleton(sK8))
| in(sK6,singleton(sK8)) ),
inference(instantiation,[status(thm)],[16]) ).
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(2,plain,
( X0 != singleton(X1)
| ~ in(X2,X0)
| X2 = X1 ),
inference(cnf,[status(esa)],[d1_tarski]) ).
cnf(l14,plain,
( singleton(sK8) != singleton(sK8)
| ~ in(sK6,singleton(sK8))
| sK6 = sK8 ),
inference(instantiation,[status(thm)],[2]) ).
cnf(23,plain,
sK6 != sK8,
inference(cnf,[status(esa)],[t26_zfmisc_1_negated]) ).
cnf(l19,plain,
sK6 != sK8,
inference(instantiation,[status(thm)],[23]) ).
fof(d2_tarski,plain,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = A
| D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
cnf(10,plain,
( X0 != unordered_pair(X1,X2)
| X3 != X2
| in(X3,X0) ),
inference(cnf,[status(esa)],[d2_tarski]) ).
cnf(l2,plain,
( unordered_pair(sK6,sK7) != unordered_pair(sK7,sK6)
| sK6 != sK6
| in(sK6,unordered_pair(sK6,sK7)) ),
inference(instantiation,[status(thm)],[10]) ).
fof(commutativity_k2_tarski,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox/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(l10,plain,
unordered_pair(sK6,sK7) = unordered_pair(sK7,sK6),
inference(instantiation,[status(thm)],[1]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l14,l19,l2,l10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.07 % Problem : SET885+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.07 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.26 % Computer : n018.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Mon Jul 21 22:58:49 EDT 2025
% 0.06/0.26 % CPUTime :
% 0.06/0.26 % launching worker at depth: 1
% 0.06/0.26 % launching worker at depth: 2
% 0.06/0.26 % launching worker at depth: 3
% 0.06/0.26 % launching worker at depth: 4
% 0.06/0.26 % launching worker at depth: 5
% 0.06/0.26 % launching worker at depth: 6
% 0.06/0.26 % launching worker at depth: 7
% 0.06/0.26 % launching worker at depth: 8
% 0.06/0.26 % launching worker at depth: 9
% 0.06/0.27 % launching worker at depth: 10
% 0.06/0.27 % SZS status Theorem for theBenchmark
% 0.06/0.27 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------