%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET083+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/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 03:31:28 PM UTC 2025
% Result : Theorem 21.35s 3.06s
% Output : CNFRefutation 21.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 16 unt; 0 def)
% Number of atoms : 51 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 16 ~; 15 |; 5 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 19 ( 1 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(singleton_identified_by_element1,plain,
! [X,Y] :
( ( singleton(X) = singleton(Y)
& member(X,universal_class) )
=> X = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_identified_by_element1) ).
fof(singleton_identified_by_element1_negated,plain,
~ ! [X,Y] :
( ( singleton(X) = singleton(Y)
& member(X,universal_class) )
=> X = Y ),
inference(negate_conjecture,[status(cth)],[singleton_identified_by_element1]) ).
cnf(89,plain,
singleton(sK10) = singleton(sK11),
inference(cnf,[status(esa)],[singleton_identified_by_element1_negated]) ).
cnf(l0,plain,
singleton(sK10) = singleton(sK11),
inference(instantiation,[status(thm)],[89]) ).
fof(singleton_set_defn,plain,
! [X] : singleton(X) = unordered_pair(X,X),
file('Axioms/SET005+0.ax',singleton_set_defn) ).
cnf(12,plain,
singleton(X0) = unordered_pair(X0,X0),
inference(cnf,[status(esa)],[singleton_set_defn]) ).
cnf(l6,plain,
singleton(sK10) = unordered_pair(sK10,sK10),
inference(instantiation,[status(thm)],[12]) ).
fof(unordered_pair_defn,plain,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( member(U,universal_class)
& ( U = X
| U = Y ) ) ),
file('Axioms/SET005+0.ax',unordered_pair_defn) ).
cnf(9,plain,
( ~ member(X0,universal_class)
| X0 != X1
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf,[status(esa)],[unordered_pair_defn]) ).
cnf(l8,plain,
( ~ member(sK10,universal_class)
| sK10 != sK10
| member(sK10,unordered_pair(sK10,sK10)) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(90,plain,
member(sK10,universal_class),
inference(cnf,[status(esa)],[singleton_identified_by_element1_negated]) ).
cnf(l10,plain,
member(sK10,universal_class),
inference(instantiation,[status(thm)],[90]) ).
fof(first_second,plain,
! [X,Y] :
( ( member(X,universal_class)
& member(Y,universal_class) )
=> ( first(ordered_pair(X,Y)) = X
& second(ordered_pair(X,Y)) = Y ) ),
file('Axioms/SET005+0.ax',first_second) ).
cnf(17,plain,
( ~ member(X0,universal_class)
| ~ member(X1,universal_class)
| first(ordered_pair(X0,X1)) = X0 ),
inference(cnf,[status(esa)],[first_second]) ).
cnf(l23,plain,
( ~ member(sK10,universal_class)
| ~ member(sK10,universal_class)
| first(ordered_pair(sK10,sK10)) = sK10 ),
inference(instantiation,[status(thm)],[17]) ).
cnf(l25,plain,
member(sK10,universal_class),
inference(instantiation,[status(thm)],[90]) ).
cnf(l24,plain,
member(sK10,universal_class),
inference(instantiation,[status(thm)],[90]) ).
cnf(l53,plain,
singleton(sK11) = unordered_pair(sK11,sK11),
inference(instantiation,[status(thm)],[12]) ).
cnf(l62,plain,
( ~ member(sK10,universal_class)
| ~ member(sK10,universal_class)
| first(ordered_pair(sK10,sK10)) = sK10 ),
inference(instantiation,[status(thm)],[17]) ).
cnf(l63,plain,
member(sK10,universal_class),
inference(instantiation,[status(thm)],[90]) ).
cnf(l65,plain,
member(sK10,universal_class),
inference(instantiation,[status(thm)],[90]) ).
cnf(8,plain,
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(cnf,[status(esa)],[unordered_pair_defn]) ).
cnf(l49,plain,
( ~ member(sK10,unordered_pair(sK11,sK11))
| sK10 = sK11
| sK10 = sK11 ),
inference(instantiation,[status(thm)],[8]) ).
cnf(91,plain,
sK10 != sK11,
inference(cnf,[status(esa)],[singleton_identified_by_element1_negated]) ).
cnf(l66,plain,
sK10 != sK11,
inference(instantiation,[status(thm)],[91]) ).
cnf(l50,plain,
sK10 != sK11,
inference(instantiation,[status(thm)],[91]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l6,l8,l10,l23,l25,l24,l53,l62,l63,l65,l49,l66,l50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET083+1 : TPTP v9.0.0. Bugfixed v5.4.0.
% 0.06/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n031.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Jul 21 19:45:34 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % launching worker at depth: 2
% 0.13/0.34 % launching worker at depth: 1
% 0.13/0.34 % launching worker at depth: 4
% 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: 7
% 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: 9
% 0.13/0.37 % launching worker at depth: 10
% 3.91/0.82 % launching worker at depth: 11
% 21.35/3.06 % SZS status Theorem for theBenchmark
% 21.35/3.06 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------