%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET084-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 : Sat Jun 21 05:25:10 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 17
% Syntax : Number of formulae : 39 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 102 ( 34 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 113 ( 52 ~; 45 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 39 ( 36 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(singleton_type,type,
singleton: $i > $i ).
tff(x_type,type,
x: $i ).
tff(y_type,type,
y: $i ).
tff(universal_class_type,type,
universal_class: $i ).
tff(1,plain,
( ( singleton(x) = singleton(y) )
<=> ( singleton(x) = singleton(y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
singleton(x) = singleton(y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_identified_by_element2_1) ).
tff(3,plain,
singleton(x) = singleton(y),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( member(y,singleton(x))
<=> member(y,singleton(y)) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
( member(y,singleton(y))
<=> member(y,singleton(x)) ),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( member(y,universal_class)
<=> member(y,universal_class) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
member(y,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_identified_by_element2_2) ).
tff(8,plain,
member(y,universal_class),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
^ [X: $i] :
refl(( ( ~ member(X,universal_class)
| member(X,singleton(X)) )
<=> ( ~ member(X,universal_class)
| member(X,singleton(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) )
<=> ! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) )
<=> ! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_in_its_singleton) ).
tff(13,plain,
! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
( ( ~ ! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) )
| ~ member(y,universal_class)
| member(y,singleton(y)) )
<=> ( ~ ! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) )
| ~ member(y,universal_class)
| member(y,singleton(y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
( ~ ! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) )
| ~ member(y,universal_class)
| member(y,singleton(y)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) )
| ~ member(y,universal_class)
| member(y,singleton(y)) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
member(y,singleton(y)),
inference(unit_resolution,[status(thm)],[18,15,8]) ).
tff(20,plain,
member(y,singleton(x)),
inference(modus_ponens,[status(thm)],[19,5]) ).
tff(21,plain,
( ( y = x )
<=> ( x = y ) ),
inference(commutativity,[status(thm)],[]) ).
tff(22,plain,
( ( x = y )
<=> ( y = x ) ),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
( ( x != y )
<=> ( y != x ) ),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( ( x != y )
<=> ( x != y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
x != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_identified_by_element2_3) ).
tff(26,plain,
x != y,
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
y != x,
inference(modus_ponens,[status(thm)],[26,23]) ).
tff(28,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ member(Y,singleton(X))
| ( Y = X ) )
<=> ( ~ member(Y,singleton(X))
| ( Y = X ) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [Y: $i,X: $i] :
( ~ member(Y,singleton(X))
| ( Y = X ) )
<=> ! [Y: $i,X: $i] :
( ~ member(Y,singleton(X))
| ( Y = X ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [Y: $i,X: $i] :
( ~ member(Y,singleton(X))
| ( Y = X ) )
<=> ! [Y: $i,X: $i] :
( ~ member(Y,singleton(X))
| ( Y = X ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
! [Y: $i,X: $i] :
( ~ member(Y,singleton(X))
| ( Y = X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',only_member_in_singleton) ).
tff(32,plain,
! [Y: $i,X: $i] :
( ~ member(Y,singleton(X))
| ( Y = X ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [Y: $i,X: $i] :
( ~ member(Y,singleton(X))
| ( Y = X ) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [Y: $i,X: $i] :
( ~ member(Y,singleton(X))
| ( Y = X ) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ member(Y,singleton(X))
| ( Y = X ) )
| ~ member(y,singleton(x))
| ( y = x ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ member(Y,singleton(X))
| ( Y = X ) )
| ~ member(y,singleton(x))
| ( y = x ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(Y,singleton(X))
| ( Y = X ) )
| ~ member(y,singleton(x))
| ( y = x ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(Y,singleton(X))
| ( Y = X ) )
| ~ member(y,singleton(x))
| ( y = x ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ~ member(y,singleton(x))
| ( y = x ) ),
inference(unit_resolution,[status(thm)],[37,34]) ).
tff(39,plain,
$false,
inference(unit_resolution,[status(thm)],[38,27,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET084-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 04:14:09 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41 % SZS output start Proof
% See solution above
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------