TSTP Solution File: SET017-7 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET017-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 : Tue Sep 20 05:04:49 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 44
% Syntax : Number of formulae : 102 ( 31 unt; 8 typ; 0 def)
% Number of atoms : 289 ( 107 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 319 ( 130 ~; 152 |; 0 &)
% ( 37 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 4 >; 4 *; 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 : 221 ( 203 !; 0 ?; 221 :)
% Comments :
%------------------------------------------------------------------------------
tff(x_type,type,
x: $i ).
tff(z_type,type,
z: $i ).
tff(y_type,type,
y: $i ).
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(unordered_pair_type,type,
unordered_pair: ( $i * $i ) > $i ).
tff(universal_class_type,type,
universal_class: $i ).
tff(cross_product_type,type,
cross_product: ( $i * $i ) > $i ).
tff(ordered_pair_type,type,
ordered_pair: ( $i * $i ) > $i ).
tff(1,plain,
( ( z = y )
<=> ( y = z ) ),
inference(commutativity,[status(thm)],]) ).
tff(2,plain,
( ( unordered_pair(x,y) = unordered_pair(x,z) )
<=> ( unordered_pair(x,y) = unordered_pair(x,z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
unordered_pair(x,y) = unordered_pair(x,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_cancellation_1) ).
tff(4,plain,
unordered_pair(x,y) = unordered_pair(x,z),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
unordered_pair(x,z) = unordered_pair(x,y),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( member(y,unordered_pair(x,z))
<=> member(y,unordered_pair(x,y)) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( member(y,unordered_pair(x,y))
<=> member(y,unordered_pair(x,z)) ),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( member(ordered_pair(y,z),cross_product(universal_class,universal_class))
<=> member(ordered_pair(y,z),cross_product(universal_class,universal_class)) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_cancellation_2) ).
tff(10,plain,
member(ordered_pair(y,z),cross_product(universal_class,universal_class)),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) )
<=> ( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_1_to_cartesian_product) ).
tff(15,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) )
| ~ member(ordered_pair(y,z),cross_product(universal_class,universal_class))
| member(y,universal_class) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) )
| ~ member(ordered_pair(y,z),cross_product(universal_class,universal_class))
| member(y,universal_class) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) )
| ~ member(ordered_pair(y,z),cross_product(universal_class,universal_class))
| member(y,universal_class) ),
inference(quant_inst,[status(thm)],]) ).
tff(20,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,universal_class) )
| ~ member(ordered_pair(y,z),cross_product(universal_class,universal_class))
| member(y,universal_class) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
member(y,universal_class),
inference(unit_resolution,[status(thm)],[20,17,10]) ).
tff(22,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) )
<=> ( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [Y: $i,X: $i] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) )
<=> ! [Y: $i,X: $i] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [Y: $i,X: $i] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) )
<=> ! [Y: $i,X: $i] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
! [Y: $i,X: $i] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
tff(26,plain,
! [Y: $i,X: $i] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [Y: $i,X: $i] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [Y: $i,X: $i] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) )
| ~ member(y,universal_class)
| member(y,unordered_pair(x,y)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) )
| ~ member(y,universal_class)
| member(y,unordered_pair(x,y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) )
| ~ member(y,universal_class)
| member(y,unordered_pair(x,y)) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) )
| ~ member(y,universal_class)
| member(y,unordered_pair(x,y)) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
member(y,unordered_pair(x,y)),
inference(unit_resolution,[status(thm)],[31,28,21]) ).
tff(33,plain,
member(y,unordered_pair(x,z)),
inference(modus_ponens,[status(thm)],[32,7]) ).
tff(34,plain,
( ( y != z )
<=> ( y != z ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
y != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_left_cancellation_3) ).
tff(36,plain,
y != z,
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
^ [Y: $i,U: $i,X: $i] :
refl(
( ( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
<=> ( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
<=> ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
<=> ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
^ [Y: $i,U: $i,X: $i] :
rewrite(
( ( ~ member(U,unordered_pair(X,Y))
| ( U = X )
| ( U = Y ) )
<=> ( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [Y: $i,U: $i,X: $i] :
( ~ member(U,unordered_pair(X,Y))
| ( U = X )
| ( U = Y ) )
<=> ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,axiom,
! [Y: $i,U: $i,X: $i] :
( ~ member(U,unordered_pair(X,Y))
| ( U = X )
| ( U = Y ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
tff(43,plain,
! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[45,38]) ).
tff(47,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( y = z )
| ( y = x )
| ~ member(y,unordered_pair(x,z)) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( y = z )
| ( y = x )
| ~ member(y,unordered_pair(x,z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( y = z )
| ( y = x )
| ~ member(y,unordered_pair(x,z)) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( y = z )
| ( y = x )
| ~ member(y,unordered_pair(x,z)) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
( ( y = x )
| ~ member(y,unordered_pair(x,z)) ),
inference(unit_resolution,[status(thm)],[49,46,36]) ).
tff(51,plain,
y = x,
inference(unit_resolution,[status(thm)],[50,33]) ).
tff(52,plain,
x = y,
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
( ( z = x )
<=> ( z = y ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ( z = x )
<=> ( y = z ) ),
inference(transitivity,[status(thm)],[53,1]) ).
tff(55,plain,
( ( y = z )
<=> ( z = x ) ),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( ( y != z )
<=> ( z != x ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
z != x,
inference(modus_ponens,[status(thm)],[36,56]) ).
tff(58,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(59,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)],[58]) ).
tff(60,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(61,axiom,
! [Y: $i,X: $i] : ( unordered_pair(X,Y) = unordered_pair(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
tff(62,plain,
! [Y: $i,X: $i] : ( unordered_pair(X,Y) = unordered_pair(Y,X) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [Y: $i,X: $i] : ( unordered_pair(X,Y) = unordered_pair(Y,X) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [Y: $i,X: $i] : ( unordered_pair(X,Y) = unordered_pair(Y,X) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
( ~ ! [Y: $i,X: $i] : ( unordered_pair(X,Y) = unordered_pair(Y,X) )
| ( unordered_pair(y,x) = unordered_pair(x,y) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
unordered_pair(y,x) = unordered_pair(x,y),
inference(unit_resolution,[status(thm)],[65,64]) ).
tff(67,plain,
unordered_pair(y,x) = unordered_pair(x,z),
inference(transitivity,[status(thm)],[66,4]) ).
tff(68,plain,
( member(z,unordered_pair(y,x))
<=> member(z,unordered_pair(x,z)) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( member(z,unordered_pair(x,z))
<=> member(z,unordered_pair(y,x)) ),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) )
<=> ( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) ) )),
inference(bind,[status(th)],]) ).
tff(71,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,axiom,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).
tff(74,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) ),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) )
| ~ member(ordered_pair(y,z),cross_product(universal_class,universal_class))
| member(z,universal_class) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) )
| ~ member(ordered_pair(y,z),cross_product(universal_class,universal_class))
| member(z,universal_class) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) )
| ~ member(ordered_pair(y,z),cross_product(universal_class,universal_class))
| member(z,universal_class) ),
inference(quant_inst,[status(thm)],]) ).
tff(79,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,universal_class) )
| ~ member(ordered_pair(y,z),cross_product(universal_class,universal_class))
| member(z,universal_class) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
member(z,universal_class),
inference(unit_resolution,[status(thm)],[79,76,10]) ).
tff(81,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) )
| ~ member(z,universal_class)
| member(z,unordered_pair(x,z)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) )
| ~ member(z,universal_class)
| member(z,unordered_pair(x,z)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) )
| ~ member(z,universal_class)
| member(z,unordered_pair(x,z)) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(Y,universal_class)
| member(Y,unordered_pair(X,Y)) )
| ~ member(z,universal_class)
| member(z,unordered_pair(x,z)) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
member(z,unordered_pair(x,z)),
inference(unit_resolution,[status(thm)],[83,28,80]) ).
tff(85,plain,
member(z,unordered_pair(y,x)),
inference(modus_ponens,[status(thm)],[84,69]) ).
tff(86,plain,
( ( y = z )
<=> ( z = y ) ),
inference(symmetry,[status(thm)],[1]) ).
tff(87,plain,
( ( y != z )
<=> ( z != y ) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
z != y,
inference(modus_ponens,[status(thm)],[36,87]) ).
tff(89,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( z = x )
| ( z = y )
| ~ member(z,unordered_pair(y,x)) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( z = x )
| ( z = y )
| ~ member(z,unordered_pair(y,x)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( z = x )
| ( z = y )
| ~ member(z,unordered_pair(y,x)) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( z = x )
| ( z = y )
| ~ member(z,unordered_pair(y,x)) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
( ( z = x )
| ( z = y )
| ~ member(z,unordered_pair(y,x)) ),
inference(unit_resolution,[status(thm)],[91,46]) ).
tff(93,plain,
z = x,
inference(unit_resolution,[status(thm)],[92,88,85]) ).
tff(94,plain,
$false,
inference(unit_resolution,[status(thm)],[93,57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET017-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n001.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 : Sat Sep 3 01:33:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------