TSTP Solution File: SET024-3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET024-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 05:04:55 EDT 2022
% Result : Unsatisfiable 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of formulae : 49 ( 16 unt; 5 typ; 0 def)
% Number of atoms : 165 ( 49 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 207 ( 95 ~; 86 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 9 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 73 ( 66 !; 0 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(non_ordered_pair_type,type,
non_ordered_pair: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(singleton_set_type,type,
singleton_set: $i > $i ).
tff(little_set_type,type,
little_set: $i > $o ).
tff(1,plain,
^ [X: $i] :
refl(
( ( singleton_set(X) = non_ordered_pair(X,X) )
<=> ( singleton_set(X) = non_ordered_pair(X,X) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( singleton_set(X) = non_ordered_pair(X,X) )
<=> ! [X: $i] : ( singleton_set(X) = non_ordered_pair(X,X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( singleton_set(X) = non_ordered_pair(X,X) )
<=> ! [X: $i] : ( singleton_set(X) = non_ordered_pair(X,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( singleton_set(X) = non_ordered_pair(X,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',singleton_set) ).
tff(5,plain,
! [X: $i] : ( singleton_set(X) = non_ordered_pair(X,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( singleton_set(X) = non_ordered_pair(X,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( singleton_set(X) = non_ordered_pair(X,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( singleton_set(X) = non_ordered_pair(X,X) )
| ( singleton_set(a) = non_ordered_pair(a,a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
singleton_set(a) = non_ordered_pair(a,a),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
non_ordered_pair(a,a) = singleton_set(a),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( member(a,non_ordered_pair(a,a))
<=> member(a,singleton_set(a)) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( member(a,singleton_set(a))
<=> member(a,non_ordered_pair(a,a)) ),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( ~ member(a,singleton_set(a))
<=> ~ member(a,non_ordered_pair(a,a)) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ~ member(a,singleton_set(a))
<=> ~ member(a,singleton_set(a)) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
~ member(a,singleton_set(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_membership_of_singleton_set) ).
tff(16,plain,
~ member(a,singleton_set(a)),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ member(a,non_ordered_pair(a,a)),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
( little_set(a)
<=> little_set(a) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
little_set(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_little_set) ).
tff(20,plain,
little_set(a),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
^ [Y: $i,U: $i,X: $i] :
refl(
( ( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) )
<=> ( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [Y: $i,U: $i,X: $i] :
( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) )
<=> ! [Y: $i,U: $i,X: $i] :
( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Y: $i,U: $i,X: $i] :
( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) )
<=> ! [Y: $i,U: $i,X: $i] :
( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
^ [Y: $i,U: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( member(U,non_ordered_pair(X,Y))
| ~ little_set(U) )
<=> ( member(U,non_ordered_pair(X,Y))
| ~ little_set(U) ) )),
( ( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) )
<=> ( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) ) )),
rewrite(
( ( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) )
<=> ( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) ) )),
( ( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) )
<=> ( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [Y: $i,U: $i,X: $i] :
( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) )
<=> ! [Y: $i,U: $i,X: $i] :
( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [Y: $i,U: $i,X: $i] :
( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair3) ).
tff(27,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) )
| ~ little_set(a)
| member(a,non_ordered_pair(a,a)) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) )
| ~ little_set(a)
| member(a,non_ordered_pair(a,a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ( member(a,non_ordered_pair(a,a))
| ~ little_set(a)
| $false )
<=> ( ~ little_set(a)
| member(a,non_ordered_pair(a,a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ( a = a )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( a != a )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
( ( a != a )
<=> $false ),
inference(transitivity,[status(thm)],[35,33]) ).
tff(37,plain,
( ( member(a,non_ordered_pair(a,a))
| ~ little_set(a)
| ( a != a ) )
<=> ( member(a,non_ordered_pair(a,a))
| ~ little_set(a)
| $false ) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ( member(a,non_ordered_pair(a,a))
| ~ little_set(a)
| ( a != a ) )
<=> ( ~ little_set(a)
| member(a,non_ordered_pair(a,a)) ) ),
inference(transitivity,[status(thm)],[37,32]) ).
tff(39,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) )
| member(a,non_ordered_pair(a,a))
| ~ little_set(a)
| ( a != a ) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) )
| ~ little_set(a)
| member(a,non_ordered_pair(a,a)) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) )
| member(a,non_ordered_pair(a,a))
| ~ little_set(a)
| ( a != a ) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) )
| ~ little_set(a)
| member(a,non_ordered_pair(a,a)) ) ),
inference(transitivity,[status(thm)],[39,31]) ).
tff(41,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) )
| member(a,non_ordered_pair(a,a))
| ~ little_set(a)
| ( a != a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,non_ordered_pair(X,Y))
| ~ little_set(U)
| ( U != Y ) )
| ~ little_set(a)
| member(a,non_ordered_pair(a,a)) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
member(a,non_ordered_pair(a,a)),
inference(unit_resolution,[status(thm)],[42,30,20]) ).
tff(44,plain,
$false,
inference(unit_resolution,[status(thm)],[43,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET024-3 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 01:20:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------