%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET072-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 : 13
% Number of leaves : 33
% Syntax : Number of formulae : 88 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 306 ( 111 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 358 ( 145 ~; 177 |; 0 &)
% ( 36 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 5 ( 5 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 : 213 ( 197 !; 0 ?; 213 :)
% Comments :
%------------------------------------------------------------------------------
tff(z_type,type,
z: $i ).
tff(x_type,type,
x: $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,
( ( unordered_pair(x,z) = unordered_pair(y,z) )
<=> ( unordered_pair(x,z) = unordered_pair(y,z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
unordered_pair(x,z) = unordered_pair(y,z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_cancellation_1) ).
tff(3,plain,
unordered_pair(x,z) = unordered_pair(y,z),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( member(y,unordered_pair(x,z))
<=> member(y,unordered_pair(y,z)) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
( member(y,unordered_pair(y,z))
<=> member(y,unordered_pair(x,z)) ),
inference(symmetry,[status(thm)],[4]) ).
tff(6,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(7,axiom,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_cancellation_2) ).
tff(8,plain,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
refl(( ( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) )
<=> ( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).
tff(13,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) )
| ~ member(ordered_pair(x,y),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(V,Y) )
| ~ member(ordered_pair(x,y),cross_product(universal_class,universal_class))
| member(y,universal_class) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) )
| ~ member(ordered_pair(x,y),cross_product(universal_class,universal_class))
| member(y,universal_class) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(V,Y) )
| ~ member(ordered_pair(x,y),cross_product(universal_class,universal_class))
| member(y,universal_class) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
member(y,universal_class),
inference(unit_resolution,[status(thm)],[18,15,8]) ).
tff(20,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
<=> ( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
<=> ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
<=> ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
tff(24,plain,
! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
| ~ member(y,universal_class)
| member(y,unordered_pair(y,z)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
| ~ member(y,universal_class)
| member(y,unordered_pair(y,z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
| ~ member(y,universal_class)
| member(y,unordered_pair(y,z)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
| ~ member(y,universal_class)
| member(y,unordered_pair(y,z)) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ member(y,universal_class)
| member(y,unordered_pair(y,z)) ),
inference(unit_resolution,[status(thm)],[29,26]) ).
tff(31,plain,
member(y,unordered_pair(y,z)),
inference(unit_resolution,[status(thm)],[30,19]) ).
tff(32,plain,
member(y,unordered_pair(x,z)),
inference(modus_ponens,[status(thm)],[31,5]) ).
tff(33,plain,
( ( y = x )
<=> ( x = y ) ),
inference(commutativity,[status(thm)],[]) ).
tff(34,plain,
( ( x = y )
<=> ( y = x ) ),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
( ( x != y )
<=> ( y != x ) ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( x != y )
<=> ( x != y ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
x != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_right_cancellation_3) ).
tff(38,plain,
x != y,
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
y != x,
inference(modus_ponens,[status(thm)],[38,35]) ).
tff(40,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(41,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)],[40]) ).
tff(42,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(43,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(44,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)],[43]) ).
tff(45,axiom,
! [Y: $i,U: $i,X: $i] :
( ~ member(U,unordered_pair(X,Y))
| ( U = X )
| ( U = Y ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
tff(46,plain,
! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,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(51,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(52,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)],[51,50]) ).
tff(53,plain,
( ( y = z )
| ( y = x )
| ~ member(y,unordered_pair(x,z)) ),
inference(unit_resolution,[status(thm)],[52,49]) ).
tff(54,plain,
y = z,
inference(unit_resolution,[status(thm)],[53,39,32]) ).
tff(55,plain,
z = y,
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( ( x = z )
<=> ( x = y ) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( ( x = y )
<=> ( x = z ) ),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
( ( x != y )
<=> ( x != z ) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
x != z,
inference(modus_ponens,[status(thm)],[38,58]) ).
tff(60,plain,
unordered_pair(y,z) = unordered_pair(x,z),
inference(symmetry,[status(thm)],[3]) ).
tff(61,plain,
( member(x,unordered_pair(y,z))
<=> member(x,unordered_pair(x,z)) ),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
( member(x,unordered_pair(x,z))
<=> member(x,unordered_pair(y,z)) ),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
^ [V: $i,Y: $i,U: $i,X: $i] :
refl(( ( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) )
<=> ( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ) )),
inference(bind,[status(th)],[]) ).
tff(64,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) )
<=> ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,axiom,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product1) ).
tff(67,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
( ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) )
| ~ member(ordered_pair(x,y),cross_product(universal_class,universal_class))
| member(x,universal_class) )
<=> ( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) )
| ~ member(ordered_pair(x,y),cross_product(universal_class,universal_class))
| member(x,universal_class) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) )
| ~ member(ordered_pair(x,y),cross_product(universal_class,universal_class))
| member(x,universal_class) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [V: $i,Y: $i,U: $i,X: $i] :
( ~ member(ordered_pair(U,V),cross_product(X,Y))
| member(U,X) )
| ~ member(ordered_pair(x,y),cross_product(universal_class,universal_class))
| member(x,universal_class) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
member(x,universal_class),
inference(unit_resolution,[status(thm)],[72,69,8]) ).
tff(74,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
| ~ member(x,universal_class)
| member(x,unordered_pair(x,z)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
| ~ member(x,universal_class)
| member(x,unordered_pair(x,z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
| ~ member(x,universal_class)
| member(x,unordered_pair(x,z)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
| ~ member(x,universal_class)
| member(x,unordered_pair(x,z)) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
( ~ member(x,universal_class)
| member(x,unordered_pair(x,z)) ),
inference(unit_resolution,[status(thm)],[76,26]) ).
tff(78,plain,
member(x,unordered_pair(x,z)),
inference(unit_resolution,[status(thm)],[77,73]) ).
tff(79,plain,
member(x,unordered_pair(y,z)),
inference(modus_ponens,[status(thm)],[78,62]) ).
tff(80,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( x = y )
| ( x = z )
| ~ member(x,unordered_pair(y,z)) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( x = y )
| ( x = z )
| ~ member(x,unordered_pair(y,z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
( ( ( x = z )
| ( x = y )
| ~ member(x,unordered_pair(y,z)) )
<=> ( ( x = y )
| ( x = z )
| ~ member(x,unordered_pair(y,z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( x = z )
| ( x = y )
| ~ member(x,unordered_pair(y,z)) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( x = y )
| ( x = z )
| ~ member(x,unordered_pair(y,z)) ) ),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( x = z )
| ( x = y )
| ~ member(x,unordered_pair(y,z)) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( x = y )
| ( x = z )
| ~ member(x,unordered_pair(y,z)) ) ),
inference(transitivity,[status(thm)],[82,80]) ).
tff(84,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( x = z )
| ( x = y )
| ~ member(x,unordered_pair(y,z)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( x = y )
| ( x = z )
| ~ member(x,unordered_pair(y,z)) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
( ( x = z )
| ~ member(x,unordered_pair(y,z)) ),
inference(unit_resolution,[status(thm)],[85,49,38]) ).
tff(87,plain,
x = z,
inference(unit_resolution,[status(thm)],[86,79]) ).
tff(88,plain,
$false,
inference(unit_resolution,[status(thm)],[87,59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET072-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n011.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
% 0.13/0.35 % DateTime : Fri Jun 20 04:12:26 EDT 2025
% 0.13/0.35 % 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
%------------------------------------------------------------------------------