%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET909+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 : 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 03:32:57 PM UTC 2025
% Result : Theorem 0.20s 0.46s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 34 ( 20 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 33 ( 16 ~; 12 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 3 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t50_zfmisc_1,plain,
! [A,B,C] : set_union2(unordered_pair(A,B),C) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_zfmisc_1) ).
fof(t50_zfmisc_1_negated,plain,
~ ! [A,B,C] : set_union2(unordered_pair(A,B),C) != empty_set,
inference(negate_conjecture,[status(cth)],[t50_zfmisc_1]) ).
cnf(27,plain,
set_union2(unordered_pair(sK6,sK7),sK8) = empty_set,
inference(cnf,[status(esa)],[t50_zfmisc_1_negated]) ).
cnf(l0,plain,
set_union2(unordered_pair(sK6,sK7),sK8) = empty_set,
inference(instantiation,[status(thm)],[27]) ).
fof(d1_xboole_0,plain,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
cnf(3,plain,
( X0 != empty_set
| ~ in(X1,X0) ),
inference(cnf,[status(esa)],[d1_xboole_0]) ).
cnf(l1,plain,
( set_union2(unordered_pair(sK6,sK7),sK8) != empty_set
| ~ in(sK7,set_union2(unordered_pair(sK6,sK7),sK8)) ),
inference(instantiation,[status(thm)],[3]) ).
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/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
cnf(14,plain,
( X0 != set_union2(X1,X2)
| ~ in(X3,X1)
| in(X3,X0) ),
inference(cnf,[status(esa)],[d2_xboole_0]) ).
cnf(l2,plain,
( set_union2(unordered_pair(sK6,sK7),sK8) != set_union2(unordered_pair(sK7,sK6),sK8)
| ~ in(sK7,unordered_pair(sK7,sK6))
| in(sK7,set_union2(unordered_pair(sK6,sK7),sK8)) ),
inference(instantiation,[status(thm)],[14]) ).
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(6,plain,
( X0 != unordered_pair(X1,X2)
| X3 != X1
| in(X3,X0) ),
inference(cnf,[status(esa)],[d2_tarski]) ).
cnf(l6,plain,
( unordered_pair(sK7,sK6) != unordered_pair(sK7,sK6)
| sK7 != sK7
| in(sK7,unordered_pair(sK7,sK6)) ),
inference(instantiation,[status(thm)],[6]) ).
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(l5,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,l2,l6,l5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET909+1 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Jul 21 23:00:49 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % launching worker at depth: 2
% 0.13/0.34 % launching worker at depth: 4
% 0.13/0.34 % launching worker at depth: 1
% 0.13/0.34 % launching worker at depth: 3
% 0.13/0.34 % launching worker at depth: 6
% 0.13/0.34 % launching worker at depth: 5
% 0.13/0.34 % launching worker at depth: 7
% 0.13/0.34 % launching worker at depth: 8
% 0.13/0.34 % launching worker at depth: 9
% 0.13/0.35 % launching worker at depth: 10
% 0.20/0.46 % SZS status Theorem for theBenchmark
% 0.20/0.46 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------