%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET075-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:25:06 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 31 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 5 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 70 ( 36 ~; 23 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 62 ( 57 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(null_class_type,type,
null_class: $i ).
tff(y_type,type,
y: $i ).
tff(unordered_pair_type,type,
unordered_pair: ( $i * $i ) > $i ).
tff(x_type,type,
x: $i ).
tff(cross_product_type,type,
cross_product: ( $i * $i ) > $i ).
tff(v_type,type,
v: $i ).
tff(u_type,type,
u: $i ).
tff(ordered_pair_type,type,
ordered_pair: ( $i * $i ) > $i ).
tff(1,plain,
( ( unordered_pair(x,y) = null_class )
<=> ( unordered_pair(x,y) = null_class ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
unordered_pair(x,y) = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_2) ).
tff(3,plain,
unordered_pair(x,y) = null_class,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
null_class = unordered_pair(x,y),
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( member(y,null_class)
<=> member(y,unordered_pair(x,y)) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( member(y,unordered_pair(x,y))
<=> member(y,null_class) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( member(ordered_pair(x,y),cross_product(u,v))
<=> member(ordered_pair(x,y),cross_product(u,v)) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
member(ordered_pair(x,y),cross_product(u,v)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_1) ).
tff(9,plain,
member(ordered_pair(x,y),cross_product(u,v)),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
refl(( ( ~ member(ordered_pair(X,Y),cross_product(U,V))
| member(Y,unordered_pair(X,Y)) )
<=> ( ~ member(ordered_pair(X,Y),cross_product(U,V))
| member(Y,unordered_pair(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(X,Y),cross_product(U,V))
| member(Y,unordered_pair(X,Y)) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(X,Y),cross_product(U,V))
| member(Y,unordered_pair(X,Y)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(X,Y),cross_product(U,V))
| member(Y,unordered_pair(X,Y)) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(X,Y),cross_product(U,V))
| member(Y,unordered_pair(X,Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(X,Y),cross_product(U,V))
| member(Y,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_to_unordered_pair) ).
tff(14,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(X,Y),cross_product(U,V))
| member(Y,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(X,Y),cross_product(U,V))
| member(Y,unordered_pair(X,Y)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(X,Y),cross_product(U,V))
| member(Y,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(X,Y),cross_product(U,V))
| member(Y,unordered_pair(X,Y)) )
| ~ member(ordered_pair(x,y),cross_product(u,v))
| member(y,unordered_pair(x,y)) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(X,Y),cross_product(U,V))
| member(Y,unordered_pair(X,Y)) )
| ~ member(ordered_pair(x,y),cross_product(u,v))
| member(y,unordered_pair(x,y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(X,Y),cross_product(U,V))
| member(Y,unordered_pair(X,Y)) )
| ~ member(ordered_pair(x,y),cross_product(u,v))
| member(y,unordered_pair(x,y)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(X,Y),cross_product(U,V))
| member(Y,unordered_pair(X,Y)) )
| ~ member(ordered_pair(x,y),cross_product(u,v))
| member(y,unordered_pair(x,y)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
member(y,unordered_pair(x,y)),
inference(unit_resolution,[status(thm)],[19,16,9]) ).
tff(21,plain,
member(y,null_class),
inference(modus_ponens,[status(thm)],[20,6]) ).
tff(22,plain,
^ [Z: $i] :
refl(( ~ member(Z,null_class)
<=> ~ member(Z,null_class) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [Z: $i] : ~ member(Z,null_class)
<=> ! [Z: $i] : ~ member(Z,null_class) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [Z: $i] : ~ member(Z,null_class)
<=> ! [Z: $i] : ~ member(Z,null_class) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
! [Z: $i] : ~ member(Z,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).
tff(26,plain,
! [Z: $i] : ~ member(Z,null_class),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [Z: $i] : ~ member(Z,null_class),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [Z: $i] : ~ member(Z,null_class),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ ! [Z: $i] : ~ member(Z,null_class)
| ~ member(y,null_class) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
~ member(y,null_class),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
$false,
inference(unit_resolution,[status(thm)],[30,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET075-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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 04:14:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% See solution above
% 0.12/0.40 % E exiting
%------------------------------------------------------------------------------