TSTP Solution File: SET901+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET901+1 : TPTP v8.1.0. Released v3.2.0.
% 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 05:08:33 EDT 2022
% Result : Theorem 0.06s 0.28s
% Output : Proof 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of formulae : 12 ( 2 unt; 4 typ; 0 def)
% Number of atoms : 52 ( 40 equ)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 97 ( 54 ~; 0 |; 30 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 27 ( 24 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
tff(unordered_pair_type,type,
unordered_pair: ( $i * $i ) > $i ).
tff(singleton_type,type,
singleton: $i > $i ).
tff(empty_set_type,type,
empty_set: $i ).
tff(subset_type,type,
subset: ( $i * $i ) > $o ).
tff(1,plain,
^ [A: $i,B: $i,C: $i] :
rewrite(
( ( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) )
<=> ( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [A: $i,B: $i,C: $i] :
( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) )
<=> ! [A: $i,B: $i,C: $i] :
( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,axiom,
! [A: $i,B: $i,C: $i] :
( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l46_zfmisc_1) ).
tff(4,plain,
! [A: $i,B: $i,C: $i] :
( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
( ~ ! [A: $i,B: $i,C: $i] :
( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) )
<=> ~ ! [A: $i,B: $i,C: $i] :
( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
~ ! [A: $i,B: $i,C: $i] :
( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_zfmisc_1) ).
tff(7,plain,
~ ! [A: $i,B: $i,C: $i] :
( subset(A,unordered_pair(B,C))
<=> ~ ( ( A != empty_set )
& ( A != singleton(B) )
& ( A != singleton(C) )
& ( A != unordered_pair(B,C) ) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
$false,
inference(unit_resolution,[status(thm)],[7,4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SET901+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.07 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.06/0.26 % Computer : n012.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Sat Sep 3 08:28:48 EDT 2022
% 0.06/0.26 % CPUTime :
% 0.06/0.26 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.06/0.26 Usage: tptp [options] [-file:]file
% 0.06/0.26 -h, -? prints this message.
% 0.06/0.26 -smt2 print SMT-LIB2 benchmark.
% 0.06/0.26 -m, -model generate model.
% 0.06/0.26 -p, -proof generate proof.
% 0.06/0.26 -c, -core generate unsat core of named formulas.
% 0.06/0.26 -st, -statistics display statistics.
% 0.06/0.26 -t:timeout set timeout (in second).
% 0.06/0.26 -smt2status display status in smt2 format instead of SZS.
% 0.06/0.26 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.06/0.26 -<param>:<value> configuration parameter and value.
% 0.06/0.26 -o:<output-file> file to place output in.
% 0.06/0.28 % SZS status Theorem
% 0.06/0.28 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------