%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET931+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 : n031.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 03:33:01 PM UTC 2025
% Result : Theorem 0.20s 0.53s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 1 unt; 0 def)
% Number of atoms : 92 ( 72 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 113 ( 57 ~; 43 |; 9 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 4 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t75_zfmisc_1,plain,
! [A,B,C] :
( set_difference(A,unordered_pair(B,C)) = empty_set
<=> ~ ( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t75_zfmisc_1) ).
fof(t75_zfmisc_1_negated,plain,
~ ! [A,B,C] :
( set_difference(A,unordered_pair(B,C)) = empty_set
<=> ~ ( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C) ) ),
inference(negate_conjecture,[status(cth)],[t75_zfmisc_1]) ).
cnf(12,plain,
( set_difference(sK3,unordered_pair(sK4,sK5)) = empty_set
| sK3 = unordered_pair(sK4,sK5)
| sK3 = empty_set
| sK3 = singleton(sK4)
| sK3 = singleton(sK5) ),
inference(cnf,[status(esa)],[t75_zfmisc_1_negated]) ).
cnf(l0,plain,
( set_difference(sK3,unordered_pair(sK4,sK5)) = empty_set
| sK3 = unordered_pair(sK4,sK5)
| sK3 = empty_set
| sK3 = singleton(sK4)
| sK3 = singleton(sK5) ),
inference(instantiation,[status(thm)],[12]) ).
fof(l46_zfmisc_1,plain,
! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ~ ( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l46_zfmisc_1) ).
cnf(3,plain,
( X0 != empty_set
| subset(X0,unordered_pair(X1,X2)) ),
inference(cnf,[status(esa)],[l46_zfmisc_1]) ).
cnf(l8,plain,
( sK3 != empty_set
| subset(sK3,unordered_pair(sK4,sK5)) ),
inference(instantiation,[status(thm)],[3]) ).
fof(t37_xboole_1,plain,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
cnf(11,plain,
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf,[status(esa)],[t37_xboole_1]) ).
cnf(l12,plain,
( ~ subset(sK3,unordered_pair(sK4,sK5))
| set_difference(sK3,unordered_pair(sK4,sK5)) = empty_set ),
inference(instantiation,[status(thm)],[11]) ).
cnf(16,plain,
( set_difference(sK3,unordered_pair(sK4,sK5)) != empty_set
| sK3 != unordered_pair(sK4,sK5) ),
inference(cnf,[status(esa)],[t75_zfmisc_1_negated]) ).
cnf(l3,plain,
( set_difference(sK3,unordered_pair(sK4,sK5)) != empty_set
| sK3 != unordered_pair(sK4,sK5) ),
inference(instantiation,[status(thm)],[16]) ).
cnf(2,plain,
( ~ subset(X0,unordered_pair(X1,X2))
| X0 = unordered_pair(X1,X2)
| X0 = empty_set
| X0 = singleton(X1)
| X0 = singleton(X2) ),
inference(cnf,[status(esa)],[l46_zfmisc_1]) ).
cnf(l18,plain,
( ~ subset(sK3,unordered_pair(sK4,sK5))
| sK3 = unordered_pair(sK4,sK5)
| sK3 = empty_set
| sK3 = singleton(sK4)
| sK3 = singleton(sK5) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(10,plain,
( set_difference(X0,X1) != empty_set
| subset(X0,X1) ),
inference(cnf,[status(esa)],[t37_xboole_1]) ).
cnf(l19,plain,
( set_difference(sK3,unordered_pair(sK4,sK5)) != empty_set
| subset(sK3,unordered_pair(sK4,sK5)) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(13,plain,
( set_difference(sK3,unordered_pair(sK4,sK5)) != empty_set
| sK3 != empty_set ),
inference(cnf,[status(esa)],[t75_zfmisc_1_negated]) ).
cnf(l89,plain,
( set_difference(sK3,unordered_pair(sK4,sK5)) != empty_set
| sK3 != empty_set ),
inference(instantiation,[status(thm)],[13]) ).
cnf(6,plain,
( X0 != unordered_pair(X1,X2)
| subset(X0,unordered_pair(X1,X2)) ),
inference(cnf,[status(esa)],[l46_zfmisc_1]) ).
cnf(l1,plain,
( sK3 != unordered_pair(sK4,sK5)
| subset(sK3,unordered_pair(sK4,sK5)) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(15,plain,
( set_difference(sK3,unordered_pair(sK4,sK5)) != empty_set
| sK3 != singleton(sK5) ),
inference(cnf,[status(esa)],[t75_zfmisc_1_negated]) ).
cnf(l2,plain,
( set_difference(sK3,unordered_pair(sK4,sK5)) != empty_set
| sK3 != singleton(sK5) ),
inference(instantiation,[status(thm)],[15]) ).
cnf(14,plain,
( set_difference(sK3,unordered_pair(sK4,sK5)) != empty_set
| sK3 != singleton(sK4) ),
inference(cnf,[status(esa)],[t75_zfmisc_1_negated]) ).
cnf(l5,plain,
( set_difference(sK3,unordered_pair(sK4,sK5)) != empty_set
| sK3 != singleton(sK4) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(l49,plain,
( set_difference(sK3,unordered_pair(sK4,sK5)) != empty_set
| sK3 != singleton(sK5) ),
inference(instantiation,[status(thm)],[15]) ).
cnf(l6,plain,
( ~ subset(sK3,unordered_pair(sK4,sK5))
| set_difference(sK3,unordered_pair(sK4,sK5)) = empty_set ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l17,plain,
( ~ subset(sK3,unordered_pair(sK4,sK5))
| set_difference(sK3,unordered_pair(sK4,sK5)) = empty_set ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l43,plain,
( set_difference(sK3,unordered_pair(sK4,sK5)) != empty_set
| sK3 != singleton(sK4) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(5,plain,
( X0 != singleton(X1)
| subset(X0,unordered_pair(X2,X1)) ),
inference(cnf,[status(esa)],[l46_zfmisc_1]) ).
cnf(l22,plain,
( sK3 != singleton(sK5)
| subset(sK3,unordered_pair(sK4,sK5)) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l78,plain,
( set_difference(sK3,unordered_pair(sK4,sK5)) != empty_set
| sK3 != empty_set ),
inference(instantiation,[status(thm)],[13]) ).
cnf(l25,plain,
( set_difference(sK3,unordered_pair(sK4,sK5)) != empty_set
| sK3 != unordered_pair(sK4,sK5) ),
inference(instantiation,[status(thm)],[16]) ).
cnf(l24,plain,
( ~ subset(sK3,unordered_pair(sK4,sK5))
| set_difference(sK3,unordered_pair(sK4,sK5)) = empty_set ),
inference(instantiation,[status(thm)],[11]) ).
cnf(4,plain,
( X0 != singleton(X1)
| subset(X0,unordered_pair(X1,X2)) ),
inference(cnf,[status(esa)],[l46_zfmisc_1]) ).
cnf(l28,plain,
( sK3 != singleton(sK4)
| subset(sK3,unordered_pair(sK4,sK5)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l8,l12,l3,l18,l19,l89,l1,l2,l5,l49,l6,l17,l43,l22,l78,l25,l24,l28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET931+1 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n031.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 23:02:49 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % launching worker at depth: 1
% 0.13/0.34 % launching worker at depth: 7
% 0.13/0.34 % launching worker at depth: 3
% 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: 8
% 0.13/0.34 % launching worker at depth: 5
% 0.13/0.34 % launching worker at depth: 6
% 0.13/0.35 % launching worker at depth: 9
% 0.13/0.38 % launching worker at depth: 10
% 0.20/0.53 % SZS status Theorem for theBenchmark
% 0.20/0.53 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------