%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET095-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:25:12 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 37 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 126 ( 13 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 162 ( 76 ~; 69 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 73 ( 66 !; 0 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
tff(subclass_type,type,
subclass: ( $i * $i ) > $o ).
tff(y_type,type,
y: $i ).
tff(unordered_pair_type,type,
unordered_pair: ( $i * $i ) > $i ).
tff(x_type,type,
x: $i ).
tff(singleton_type,type,
singleton: $i > $i ).
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(1,plain,
^ [X: $i] :
refl(( ( unordered_pair(X,X) = singleton(X) )
<=> ( unordered_pair(X,X) = singleton(X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( unordered_pair(X,X) = singleton(X) )
<=> ! [X: $i] : ( unordered_pair(X,X) = singleton(X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( unordered_pair(X,X) = singleton(X) )
<=> ! [X: $i] : ( unordered_pair(X,X) = singleton(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( unordered_pair(X,X) = singleton(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
tff(5,plain,
! [X: $i] : ( unordered_pair(X,X) = singleton(X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( unordered_pair(X,X) = singleton(X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( unordered_pair(X,X) = singleton(X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( unordered_pair(X,X) = singleton(X) )
| ( unordered_pair(x,x) = singleton(x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
unordered_pair(x,x) = singleton(x),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( subclass(unordered_pair(x,x),y)
<=> subclass(singleton(x),y) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( subclass(singleton(x),y)
<=> subclass(unordered_pair(x,x),y) ),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( ~ subclass(singleton(x),y)
<=> ~ subclass(unordered_pair(x,x),y) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( ~ subclass(singleton(x),y)
<=> ~ subclass(singleton(x),y) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
~ subclass(singleton(x),y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_of_singletons2_2) ).
tff(15,plain,
~ subclass(singleton(x),y),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
~ subclass(unordered_pair(x,x),y),
inference(modus_ponens,[status(thm)],[15,12]) ).
tff(17,plain,
( member(x,y)
<=> member(x,y) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
member(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_of_singletons2_1) ).
tff(19,plain,
member(x,y),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( subclass(unordered_pair(X,Y),Z)
| ~ member(Y,Z)
| ~ member(X,Z) )
<=> ( subclass(unordered_pair(X,Y),Z)
| ~ member(Y,Z)
| ~ member(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [Z: $i,Y: $i,X: $i] :
( subclass(unordered_pair(X,Y),Z)
| ~ member(Y,Z)
| ~ member(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( subclass(unordered_pair(X,Y),Z)
| ~ member(Y,Z)
| ~ member(X,Z) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [Z: $i,Y: $i,X: $i] :
( subclass(unordered_pair(X,Y),Z)
| ~ member(Y,Z)
| ~ member(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( subclass(unordered_pair(X,Y),Z)
| ~ member(Y,Z)
| ~ member(X,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(( ( ~ member(X,Z)
| ~ member(Y,Z)
| subclass(unordered_pair(X,Y),Z) )
<=> ( subclass(unordered_pair(X,Y),Z)
| ~ member(Y,Z)
| ~ member(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(X,Z)
| ~ member(Y,Z)
| subclass(unordered_pair(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( subclass(unordered_pair(X,Y),Z)
| ~ member(Y,Z)
| ~ member(X,Z) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ member(X,Z)
| ~ member(Y,Z)
| subclass(unordered_pair(X,Y),Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_is_subset) ).
tff(26,plain,
! [Z: $i,Y: $i,X: $i] :
( subclass(unordered_pair(X,Y),Z)
| ~ member(Y,Z)
| ~ member(X,Z) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [Z: $i,Y: $i,X: $i] :
( subclass(unordered_pair(X,Y),Z)
| ~ member(Y,Z)
| ~ member(X,Z) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
! [Z: $i,Y: $i,X: $i] :
( subclass(unordered_pair(X,Y),Z)
| ~ member(Y,Z)
| ~ member(X,Z) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [Z: $i,Y: $i,X: $i] :
( subclass(unordered_pair(X,Y),Z)
| ~ member(Y,Z)
| ~ member(X,Z) ),
inference(modus_ponens,[status(thm)],[28,21]) ).
tff(30,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( subclass(unordered_pair(X,Y),Z)
| ~ member(Y,Z)
| ~ member(X,Z) )
| ~ member(x,y)
| subclass(unordered_pair(x,x),y) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( subclass(unordered_pair(X,Y),Z)
| ~ member(Y,Z)
| ~ member(X,Z) )
| ~ member(x,y)
| subclass(unordered_pair(x,x),y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
( ( subclass(unordered_pair(x,x),y)
| ~ member(x,y)
| ~ member(x,y) )
<=> ( ~ member(x,y)
| subclass(unordered_pair(x,x),y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( subclass(unordered_pair(X,Y),Z)
| ~ member(Y,Z)
| ~ member(X,Z) )
| subclass(unordered_pair(x,x),y)
| ~ member(x,y)
| ~ member(x,y) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( subclass(unordered_pair(X,Y),Z)
| ~ member(Y,Z)
| ~ member(X,Z) )
| ~ member(x,y)
| subclass(unordered_pair(x,x),y) ) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( subclass(unordered_pair(X,Y),Z)
| ~ member(Y,Z)
| ~ member(X,Z) )
| subclass(unordered_pair(x,x),y)
| ~ member(x,y)
| ~ member(x,y) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( subclass(unordered_pair(X,Y),Z)
| ~ member(Y,Z)
| ~ member(X,Z) )
| ~ member(x,y)
| subclass(unordered_pair(x,x),y) ) ),
inference(transitivity,[status(thm)],[32,30]) ).
tff(34,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( subclass(unordered_pair(X,Y),Z)
| ~ member(Y,Z)
| ~ member(X,Z) )
| subclass(unordered_pair(x,x),y)
| ~ member(x,y)
| ~ member(x,y) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( subclass(unordered_pair(X,Y),Z)
| ~ member(Y,Z)
| ~ member(X,Z) )
| ~ member(x,y)
| subclass(unordered_pair(x,x),y) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
subclass(unordered_pair(x,x),y),
inference(unit_resolution,[status(thm)],[35,29,19]) ).
tff(37,plain,
$false,
inference(unit_resolution,[status(thm)],[36,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET095-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 04:18:01 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42 % SZS output start Proof
% See solution above
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------