%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET878+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 : n026.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 03:32:54 PM UTC 2025
% Result : Theorem 12.68s 1.95s
% Output : CNFRefutation 12.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 27 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 19 ( 9 ~; 7 |; 0 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 24 ( 1 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t19_zfmisc_1,plain,
! [A,B] : set_intersection2(singleton(A),unordered_pair(A,B)) = singleton(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_zfmisc_1) ).
fof(t19_zfmisc_1_negated,plain,
~ ! [A,B] : set_intersection2(singleton(A),unordered_pair(A,B)) = singleton(A),
inference(negate_conjecture,[status(cth)],[t19_zfmisc_1]) ).
cnf(15,plain,
set_intersection2(singleton(sK4),unordered_pair(sK4,sK5)) != singleton(sK4),
inference(cnf,[status(esa)],[t19_zfmisc_1_negated]) ).
cnf(l0,plain,
set_intersection2(singleton(sK4),unordered_pair(sK4,sK5)) != singleton(sK4),
inference(instantiation,[status(thm)],[15]) ).
fof(l32_zfmisc_1,plain,
! [A,B] :
( in(A,B)
=> set_intersection2(B,singleton(A)) = singleton(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_zfmisc_1) ).
cnf(12,plain,
( ~ in(X0,X1)
| set_intersection2(X1,singleton(X0)) = singleton(X0) ),
inference(cnf,[status(esa)],[l32_zfmisc_1]) ).
cnf(l3,plain,
( ~ in(sK4,unordered_pair(sK5,sK4))
| set_intersection2(unordered_pair(sK5,sK4),singleton(sK4)) = singleton(sK4) ),
inference(instantiation,[status(thm)],[12]) ).
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(5,plain,
( X0 != unordered_pair(X1,X2)
| X3 != X2
| in(X3,X0) ),
inference(cnf,[status(esa)],[d2_tarski]) ).
cnf(l7,plain,
( unordered_pair(sK5,sK4) != unordered_pair(sK5,sK4)
| sK4 != sK4
| in(sK4,unordered_pair(sK5,sK4)) ),
inference(instantiation,[status(thm)],[5]) ).
fof(commutativity_k3_xboole_0,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox/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(l18,plain,
set_intersection2(singleton(sK4),unordered_pair(sK4,sK5)) = set_intersection2(unordered_pair(sK4,sK5),singleton(sK4)),
inference(instantiation,[status(thm)],[2]) ).
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(l21,plain,
unordered_pair(sK4,sK5) = unordered_pair(sK5,sK4),
inference(instantiation,[status(thm)],[1]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l3,l7,l18,l21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET878+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n026.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 22:58:04 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % launching worker at depth: 1
% 0.13/0.35 % launching worker at depth: 5
% 0.13/0.35 % launching worker at depth: 6
% 0.13/0.35 % launching worker at depth: 7
% 0.13/0.35 % launching worker at depth: 2
% 0.13/0.35 % launching worker at depth: 3
% 0.13/0.35 % launching worker at depth: 4
% 0.13/0.35 % launching worker at depth: 8
% 0.13/0.35 % launching worker at depth: 9
% 0.20/0.35 % launching worker at depth: 10
% 0.20/0.54 % launching worker at depth: 11
% 12.68/1.95 % SZS status Theorem for theBenchmark
% 12.68/1.95 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------