TSTP Solution File: SET084-6 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET084-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 05:05:30 EDT 2022
% Result : Unsatisfiable 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 30
% Syntax : Number of formulae : 64 ( 22 unt; 6 typ; 0 def)
% Number of atoms : 179 ( 94 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 190 ( 73 ~; 93 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 100 ( 91 !; 0 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
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(singleton_type,type,
singleton: $i > $i ).
tff(universal_class_type,type,
universal_class: $i ).
tff(1,plain,
( ( y = x )
<=> ( x = y ) ),
inference(commutativity,[status(thm)],]) ).
tff(2,plain,
( ( x = y )
<=> ( y = x ) ),
inference(symmetry,[status(thm)],[1]) ).
tff(3,plain,
( ( x != y )
<=> ( y != x ) ),
inference(monotonicity,[status(thm)],[2]) ).
tff(4,plain,
( ( x != y )
<=> ( x != y ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
x != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_identified_by_element2_3) ).
tff(6,plain,
x != y,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
y != x,
inference(modus_ponens,[status(thm)],[6,3]) ).
tff(8,plain,
^ [X: $i] :
refl(
( ( unordered_pair(X,X) = singleton(X) )
<=> ( unordered_pair(X,X) = singleton(X) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [X: $i] : ( unordered_pair(X,X) = singleton(X) )
<=> ! [X: $i] : ( unordered_pair(X,X) = singleton(X) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [X: $i] : ( unordered_pair(X,X) = singleton(X) )
<=> ! [X: $i] : ( unordered_pair(X,X) = singleton(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
! [X: $i] : ( unordered_pair(X,X) = singleton(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
tff(12,plain,
! [X: $i] : ( unordered_pair(X,X) = singleton(X) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [X: $i] : ( unordered_pair(X,X) = singleton(X) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [X: $i] : ( unordered_pair(X,X) = singleton(X) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( ~ ! [X: $i] : ( unordered_pair(X,X) = singleton(X) )
| ( unordered_pair(y,y) = singleton(y) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
unordered_pair(y,y) = singleton(y),
inference(unit_resolution,[status(thm)],[15,14]) ).
tff(17,plain,
singleton(y) = unordered_pair(y,y),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( ( singleton(x) = singleton(y) )
<=> ( singleton(x) = singleton(y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
singleton(x) = singleton(y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_identified_by_element2_1) ).
tff(20,plain,
singleton(x) = singleton(y),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( ~ ! [X: $i] : ( unordered_pair(X,X) = singleton(X) )
| ( unordered_pair(x,x) = singleton(x) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
unordered_pair(x,x) = singleton(x),
inference(unit_resolution,[status(thm)],[21,14]) ).
tff(23,plain,
unordered_pair(x,x) = unordered_pair(y,y),
inference(transitivity,[status(thm)],[22,20,17]) ).
tff(24,plain,
( member(y,unordered_pair(x,x))
<=> member(y,unordered_pair(y,y)) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( member(y,unordered_pair(y,y))
<=> member(y,unordered_pair(x,x)) ),
inference(symmetry,[status(thm)],[24]) ).
tff(26,plain,
( member(y,universal_class)
<=> member(y,universal_class) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
member(y,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_singleton_identified_by_element2_2) ).
tff(28,plain,
member(y,universal_class),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,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(30,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)],[29]) ).
tff(31,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(32,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(33,plain,
! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
| ~ member(y,universal_class)
| member(y,unordered_pair(y,y)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
| ~ member(y,universal_class)
| member(y,unordered_pair(y,y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
| ~ member(y,universal_class)
| member(y,unordered_pair(y,y)) ),
inference(quant_inst,[status(thm)],]) ).
tff(38,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(X,universal_class)
| member(X,unordered_pair(X,Y)) )
| ~ member(y,universal_class)
| member(y,unordered_pair(y,y)) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
member(y,unordered_pair(y,y)),
inference(unit_resolution,[status(thm)],[38,35,28]) ).
tff(40,plain,
member(y,unordered_pair(x,x)),
inference(modus_ponens,[status(thm)],[39,25]) ).
tff(41,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(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(quant_intro,[status(thm)],[41]) ).
tff(43,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(44,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(45,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)],[44]) ).
tff(46,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(47,plain,
! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( y = x )
| ~ member(y,unordered_pair(x,x)) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( y = x )
| ~ member(y,unordered_pair(x,x)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ( ( y = x )
| ( y = x )
| ~ member(y,unordered_pair(x,x)) )
<=> ( ( y = x )
| ~ member(y,unordered_pair(x,x)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( y = x )
| ( y = x )
| ~ member(y,unordered_pair(x,x)) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( y = x )
| ~ member(y,unordered_pair(x,x)) ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( y = x )
| ( y = x )
| ~ member(y,unordered_pair(x,x)) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( y = x )
| ~ member(y,unordered_pair(x,x)) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( y = x )
| ( y = x )
| ~ member(y,unordered_pair(x,x)) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( ( U = Y )
| ( U = X )
| ~ member(U,unordered_pair(X,Y)) )
| ( y = x )
| ~ member(y,unordered_pair(x,x)) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
( ( y = x )
| ~ member(y,unordered_pair(x,x)) ),
inference(unit_resolution,[status(thm)],[56,50]) ).
tff(58,plain,
$false,
inference(unit_resolution,[status(thm)],[57,40,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET084-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n029.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 : Sat Sep 3 02:18:45 EDT 2022
% 0.13/0.35 % 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.
% 0.21/0.43 % SZS status Unsatisfiable
% 0.21/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------