%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET018-7 : TPTP v9.0.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:24:50 AM UTC 2025
% Result : Unsatisfiable 0.22s 0.43s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 26 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 133 ( 84 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 189 ( 90 ~; 84 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 84 ( 76 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
tff(z_type,type,
z: $i ).
tff(x_type,type,
x: $i ).
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(universal_class_type,type,
universal_class: $i ).
tff(ordered_pair_type,type,
ordered_pair: ( $i * $i ) > $i ).
tff(y_type,type,
y: $i ).
tff(w_type,type,
w: $i ).
tff(1,plain,
( ( x != z )
<=> ( x != z ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
x != z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ordered_pair_determines_components2_3) ).
tff(3,plain,
x != z,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( member(x,universal_class)
<=> member(x,universal_class) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ordered_pair_determines_components2_2) ).
tff(6,plain,
member(x,universal_class),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( ( ordered_pair(w,x) = ordered_pair(y,z) )
<=> ( ordered_pair(w,x) = ordered_pair(y,z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
ordered_pair(w,x) = ordered_pair(y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ordered_pair_determines_components2_1) ).
tff(9,plain,
ordered_pair(w,x) = ordered_pair(y,z),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
refl(( ( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
<=> ( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( ( ordered_pair(W,X) != ordered_pair(Y,Z) )
| ~ member(X,universal_class) )
<=> ( ~ member(X,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ) )),
( ( ( ordered_pair(W,X) != ordered_pair(Y,Z) )
| ~ member(X,universal_class)
| ( X = Z ) )
<=> ( ~ member(X,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) )
| ( X = Z ) ) )),
rewrite(( ( ~ member(X,universal_class)
| ( ordered_pair(W,X) != ordered_pair(Y,Z) )
| ( X = Z ) )
<=> ( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ) )),
( ( ( ordered_pair(W,X) != ordered_pair(Y,Z) )
| ~ member(X,universal_class)
| ( X = Z ) )
<=> ( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ( ordered_pair(W,X) != ordered_pair(Y,Z) )
| ~ member(X,universal_class)
| ( X = Z ) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ( ordered_pair(W,X) != ordered_pair(Y,Z) )
| ~ member(X,universal_class)
| ( X = Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_determines_components2) ).
tff(16,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
| ( x = z )
| ~ member(x,universal_class)
| ( ordered_pair(w,x) != ordered_pair(y,z) ) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
| ( x = z )
| ~ member(x,universal_class)
| ( ordered_pair(w,x) != ordered_pair(y,z) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ( ~ member(x,universal_class)
| ( x = z )
| ( ordered_pair(w,x) != ordered_pair(y,z) ) )
<=> ( ( x = z )
| ~ member(x,universal_class)
| ( ordered_pair(w,x) != ordered_pair(y,z) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
| ~ member(x,universal_class)
| ( x = z )
| ( ordered_pair(w,x) != ordered_pair(y,z) ) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
| ( x = z )
| ~ member(x,universal_class)
| ( ordered_pair(w,x) != ordered_pair(y,z) ) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
| ~ member(x,universal_class)
| ( x = z )
| ( ordered_pair(w,x) != ordered_pair(y,z) ) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
| ( x = z )
| ~ member(x,universal_class)
| ( ordered_pair(w,x) != ordered_pair(y,z) ) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
| ~ member(x,universal_class)
| ( x = z )
| ( ordered_pair(w,x) != ordered_pair(y,z) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ member(X,universal_class)
| ( X = Z )
| ( ordered_pair(W,X) != ordered_pair(Y,Z) ) )
| ( x = z )
| ~ member(x,universal_class)
| ( ordered_pair(w,x) != ordered_pair(y,z) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
$false,
inference(unit_resolution,[status(thm)],[25,19,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET018-7 : TPTP v9.0.0. Bugfixed v7.3.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n004.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 04:02:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.43 % SZS status Unsatisfiable
% 0.22/0.43 % SZS output start Proof
% See solution above
% 0.22/0.44 % E exiting
%------------------------------------------------------------------------------