TSTP Solution File: NUM605+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM605+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 : Sun Sep 18 13:10:50 EDT 2022
% Result : Theorem 0.19s 0.49s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 29
% Syntax : Number of formulae : 55 ( 16 unt; 13 typ; 0 def)
% Number of atoms : 154 ( 89 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 159 ( 50 ~; 43 |; 10 &)
% ( 49 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 7 >; 3 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 29 ( 26 !; 0 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
tff(sz00_type,type,
sz00: $i ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(xk_type,type,
xk: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(slbdtrb0_type,type,
slbdtrb0: $i > $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(xQ_type,type,
xQ: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xO_type,type,
xO: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(xK_type,type,
xK: $i ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(1,plain,
( aSet0(xQ)
<=> aSet0(slbdtrb0(sz00)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( aSet0(xQ)
<=> aSet0(xQ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSubsetOf0(xQ,xO)
& ( sbrdtbr0(xQ) = xK )
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5078) ).
tff(4,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSubsetOf0(xQ,xO)
& ( sbrdtbr0(xQ) = xK ) ),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) )
& aSubsetOf0(xQ,xO) ),
inference(and_elim,[status(thm)],[4]) ).
tff(6,plain,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xO) ) ),
inference(and_elim,[status(thm)],[5]) ).
tff(7,plain,
aSet0(xQ),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
aSet0(xQ),
inference(modus_ponens,[status(thm)],[7,2]) ).
tff(9,plain,
aSet0(slbdtrb0(sz00)),
inference(modus_ponens,[status(thm)],[8,1]) ).
tff(10,plain,
^ [W0: $i] :
refl(
( ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) )
<=> ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
^ [W0: $i] :
rewrite(
( ( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,axiom,
! [W0: $i] :
( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardEmpty) ).
tff(18,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) ),
inference(modus_ponens,[status(thm)],[19,13]) ).
tff(21,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) ),
inference(modus_ponens,[status(thm)],[21,11]) ).
tff(23,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) )
| ~ aSet0(slbdtrb0(sz00))
| ( sbrdtbr0(slbdtrb0(sz00)) = sz00 ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) )
| ~ aSet0(slbdtrb0(sz00))
| ( sbrdtbr0(slbdtrb0(sz00)) = sz00 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( ~ aSet0(slbdtrb0(sz00))
| ( ( sbrdtbr0(slbdtrb0(sz00)) = sz00 )
<=> ( slbdtrb0(sz00) = slbdtrb0(sz00) ) ) )
<=> ( ~ aSet0(slbdtrb0(sz00))
| ( sbrdtbr0(slbdtrb0(sz00)) = sz00 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) )
| ~ aSet0(slbdtrb0(sz00))
| ( ( sbrdtbr0(slbdtrb0(sz00)) = sz00 )
<=> ( slbdtrb0(sz00) = slbdtrb0(sz00) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) )
| ~ aSet0(slbdtrb0(sz00))
| ( sbrdtbr0(slbdtrb0(sz00)) = sz00 ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) )
| ~ aSet0(slbdtrb0(sz00))
| ( ( sbrdtbr0(slbdtrb0(sz00)) = sz00 )
<=> ( slbdtrb0(sz00) = slbdtrb0(sz00) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) )
| ~ aSet0(slbdtrb0(sz00))
| ( sbrdtbr0(slbdtrb0(sz00)) = sz00 ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) )
| ~ aSet0(slbdtrb0(sz00))
| ( ( sbrdtbr0(slbdtrb0(sz00)) = sz00 )
<=> ( slbdtrb0(sz00) = slbdtrb0(sz00) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slbdtrb0(sz00) ) ) )
| ~ aSet0(slbdtrb0(sz00))
| ( sbrdtbr0(slbdtrb0(sz00)) = sz00 ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
sbrdtbr0(slbdtrb0(sz00)) = sz00,
inference(unit_resolution,[status(thm)],[28,22,9]) ).
tff(30,plain,
( ( sbrdtbr0(xQ) = xK )
<=> ( sbrdtbr0(slbdtrb0(sz00)) = szszuzczcdt0(xk) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( sbrdtbr0(xQ) = xK )
<=> ( sbrdtbr0(xQ) = xK ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
sbrdtbr0(xQ) = xK,
inference(and_elim,[status(thm)],[4]) ).
tff(33,plain,
sbrdtbr0(xQ) = xK,
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
sbrdtbr0(slbdtrb0(sz00)) = szszuzczcdt0(xk),
inference(modus_ponens,[status(thm)],[33,30]) ).
tff(35,plain,
szszuzczcdt0(xk) = sbrdtbr0(slbdtrb0(sz00)),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
szszuzczcdt0(xk) = sz00,
inference(transitivity,[status(thm)],[35,29]) ).
tff(37,plain,
( ( xK != sz00 )
<=> ( szszuzczcdt0(xk) != sz00 ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ( xK != sz00 )
<=> ( xK != sz00 ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
xK != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3462) ).
tff(40,plain,
xK != sz00,
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
szszuzczcdt0(xk) != sz00,
inference(modus_ponens,[status(thm)],[40,37]) ).
tff(42,plain,
$false,
inference(unit_resolution,[status(thm)],[41,36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM605+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 12:03:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------