%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET072-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 17
% Syntax : Number of formulae : 36 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 103 ( 72 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 120 ( 56 ~; 52 |; 0 &)
% ( 12 <=>; 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 73 ( 65 !; 0 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
tff(unordered_pair_type,type,
unordered_pair: ( $i * $i ) > $i ).
tff(y_type,type,
y: $i ).
tff(z_type,type,
z: $i ).
tff(x_type,type,
x: $i ).
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(cross_product_type,type,
cross_product: ( $i * $i ) > $i ).
tff(universal_class_type,type,
universal_class: $i ).
tff(ordered_pair_type,type,
ordered_pair: ( $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( unordered_pair(X,Y) = unordered_pair(Y,X) )
<=> ( unordered_pair(X,Y) = unordered_pair(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( unordered_pair(X,Y) = unordered_pair(Y,X) )
<=> ! [Y: $i,X: $i] : ( unordered_pair(X,Y) = unordered_pair(Y,X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( unordered_pair(X,Y) = unordered_pair(Y,X) )
<=> ! [Y: $i,X: $i] : ( unordered_pair(X,Y) = unordered_pair(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( unordered_pair(X,Y) = unordered_pair(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
tff(5,plain,
! [Y: $i,X: $i] : ( unordered_pair(X,Y) = unordered_pair(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( unordered_pair(X,Y) = unordered_pair(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( unordered_pair(X,Y) = unordered_pair(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( unordered_pair(X,Y) = unordered_pair(Y,X) )
| ( unordered_pair(z,y) = unordered_pair(y,z) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
unordered_pair(z,y) = unordered_pair(y,z),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
unordered_pair(y,z) = unordered_pair(z,y),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ( unordered_pair(x,z) = unordered_pair(y,z) )
<=> ( unordered_pair(x,z) = unordered_pair(y,z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
unordered_pair(x,z) = unordered_pair(y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_cancellation_1) ).
tff(13,plain,
unordered_pair(x,z) = unordered_pair(y,z),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ~ ! [Y: $i,X: $i] : ( unordered_pair(X,Y) = unordered_pair(Y,X) )
| ( unordered_pair(z,x) = unordered_pair(x,z) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(15,plain,
unordered_pair(z,x) = unordered_pair(x,z),
inference(unit_resolution,[status(thm)],[14,7]) ).
tff(16,plain,
unordered_pair(z,x) = unordered_pair(z,y),
inference(transitivity,[status(thm)],[15,13,10]) ).
tff(17,plain,
( ( x != y )
<=> ( x != y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
x != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_cancellation_3) ).
tff(19,plain,
x != y,
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( member(ordered_pair(x,y),cross_product(universal_class,universal_class))
<=> member(ordered_pair(x,y),cross_product(universal_class,universal_class)) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_cancellation_2) ).
tff(22,plain,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ( Y = Z )
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| ( unordered_pair(X,Y) != unordered_pair(X,Z) ) )
<=> ( ( Y = Z )
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| ( unordered_pair(X,Y) != unordered_pair(X,Z) ) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( Y = Z )
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| ( unordered_pair(X,Y) != unordered_pair(X,Z) ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( Y = Z )
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| ( unordered_pair(X,Y) != unordered_pair(X,Z) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( Y = Z )
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| ( unordered_pair(X,Y) != unordered_pair(X,Z) ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( Y = Z )
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| ( unordered_pair(X,Y) != unordered_pair(X,Z) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(( ( ( unordered_pair(X,Y) != unordered_pair(X,Z) )
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| ( unordered_pair(X,Y) != unordered_pair(X,Z) ) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ( unordered_pair(X,Y) != unordered_pair(X,Z) )
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| ( Y = Z ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ( Y = Z )
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| ( unordered_pair(X,Y) != unordered_pair(X,Z) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,axiom,
! [Z: $i,Y: $i,X: $i] :
( ( unordered_pair(X,Y) != unordered_pair(X,Z) )
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| ( Y = Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_cancellation) ).
tff(29,plain,
! [Z: $i,Y: $i,X: $i] :
( ( Y = Z )
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| ( unordered_pair(X,Y) != unordered_pair(X,Z) ) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [Z: $i,Y: $i,X: $i] :
( ( Y = Z )
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| ( unordered_pair(X,Y) != unordered_pair(X,Z) ) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
! [Z: $i,Y: $i,X: $i] :
( ( Y = Z )
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| ( unordered_pair(X,Y) != unordered_pair(X,Z) ) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [Z: $i,Y: $i,X: $i] :
( ( Y = Z )
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| ( unordered_pair(X,Y) != unordered_pair(X,Z) ) ),
inference(modus_ponens,[status(thm)],[31,24]) ).
tff(33,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( Y = Z )
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| ( unordered_pair(X,Y) != unordered_pair(X,Z) ) )
| ( x = y )
| ~ member(ordered_pair(x,y),cross_product(universal_class,universal_class))
| ( unordered_pair(z,x) != unordered_pair(z,y) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ( Y = Z )
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| ( unordered_pair(X,Y) != unordered_pair(X,Z) ) )
| ( x = y )
| ~ member(ordered_pair(x,y),cross_product(universal_class,universal_class))
| ( unordered_pair(z,x) != unordered_pair(z,y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( Y = Z )
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| ( unordered_pair(X,Y) != unordered_pair(X,Z) ) )
| ( x = y )
| ~ member(ordered_pair(x,y),cross_product(universal_class,universal_class))
| ( unordered_pair(z,x) != unordered_pair(z,y) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ( Y = Z )
| ~ member(ordered_pair(Y,Z),cross_product(universal_class,universal_class))
| ( unordered_pair(X,Y) != unordered_pair(X,Z) ) )
| ( x = y )
| ~ member(ordered_pair(x,y),cross_product(universal_class,universal_class))
| ( unordered_pair(z,x) != unordered_pair(z,y) ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
$false,
inference(unit_resolution,[status(thm)],[35,32,22,19,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET072-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n013.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 : Fri Jun 20 04:12:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41 % SZS output start Proof
% See solution above
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------