TSTP Solution File: DAT093_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT093_1 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 : Fri Sep 16 14:36:42 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 22
% Syntax : Number of formulae : 49 ( 25 unt; 3 typ; 0 def)
% Number of atoms : 89 ( 75 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 57 ( 24 ~; 12 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number arithmetic : 304 ( 6 atm; 170 fun; 128 num; 0 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 9 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 3 usr; 5 con; 0-2 aty)
% Number of variables : 78 ( 71 !; 0 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
tff(length_type,type,
length: list > $int ).
tff(append_type,type,
append: ( list * list ) > list ).
tff(nil_type,type,
nil: list ).
tff(1,plain,
^ [L: list] :
refl(
( ( append(nil,L) = L )
<=> ( append(nil,L) = L ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [L: list] : ( append(nil,L) = L )
<=> ! [L: list] : ( append(nil,L) = L ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [L: list] : ( append(nil,L) = L )
<=> ! [L: list] : ( append(nil,L) = L ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [L: list] : ( append(nil,L) = L ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l_6) ).
tff(5,plain,
! [L: list] : ( append(nil,L) = L ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [L: list] : ( append(nil,L) = L ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [L: list] : ( append(nil,L) = L ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [L: list] : ( append(nil,L) = L )
| ( append(nil,nil) = nil ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
append(nil,nil) = nil,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
length(append(nil,nil)) = length(nil),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
length(nil) = length(append(nil,nil)),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( ( length(nil) != length(append(nil,nil)) )
| $greatereq($sum(length(nil),$product(-1,length(append(nil,nil)))),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(13,plain,
$greatereq($sum(length(nil),$product(-1,length(append(nil,nil)))),0),
inference(unit_resolution,[status(thm)],[12,11]) ).
tff(14,plain,
^ [K: list,L: list] :
refl(
( ( $sum(length(L),$sum(length(K),$product(-1,length(append(K,L))))) = -1 )
<=> ( $sum(length(L),$sum(length(K),$product(-1,length(append(K,L))))) = -1 ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [K: list,L: list] : ( $sum(length(L),$sum(length(K),$product(-1,length(append(K,L))))) = -1 )
<=> ! [K: list,L: list] : ( $sum(length(L),$sum(length(K),$product(-1,length(append(K,L))))) = -1 ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
^ [K: list,L: list] :
trans(
monotonicity(rewrite($sum(length(append(K,L)),$sum($product(-1,length(K)),$product(-1,length(L)))) = $sum($product(-1,length(L)),$sum($product(-1,length(K)),length(append(K,L))))),
( ( $sum(length(append(K,L)),$sum($product(-1,length(K)),$product(-1,length(L)))) = 1 )
<=> ( $sum($product(-1,length(L)),$sum($product(-1,length(K)),length(append(K,L)))) = 1 ) )),
rewrite(
( ( $sum($product(-1,length(L)),$sum($product(-1,length(K)),length(append(K,L)))) = 1 )
<=> ( $sum(length(L),$sum(length(K),$product(-1,length(append(K,L))))) = -1 ) )),
( ( $sum(length(append(K,L)),$sum($product(-1,length(K)),$product(-1,length(L)))) = 1 )
<=> ( $sum(length(L),$sum(length(K),$product(-1,length(append(K,L))))) = -1 ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [K: list,L: list] : ( $sum(length(append(K,L)),$sum($product(-1,length(K)),$product(-1,length(L)))) = 1 )
<=> ! [K: list,L: list] : ( $sum(length(L),$sum(length(K),$product(-1,length(append(K,L))))) = -1 ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
^ [K: list,L: list] :
rewrite(
( ( length(append(K,L)) = $sum(1,$sum(length(K),length(L))) )
<=> ( $sum(length(append(K,L)),$sum($product(-1,length(K)),$product(-1,length(L)))) = 1 ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [K: list,L: list] : ( length(append(K,L)) = $sum(1,$sum(length(K),length(L))) )
<=> ! [K: list,L: list] : ( $sum(length(append(K,L)),$sum($product(-1,length(K)),$product(-1,length(L)))) = 1 ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [K: list,L: list] : ( length(append(K,L)) = $sum(1,$sum(length(K),length(L))) )
<=> ! [K: list,L: list] : ( length(append(K,L)) = $sum(1,$sum(length(K),length(L))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ~ ~ ! [K: list,L: list] : ( length(append(K,L)) = $sum(1,$sum(length(K),length(L))) )
<=> ! [K: list,L: list] : ( length(append(K,L)) = $sum(1,$sum(length(K),length(L))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ~ ! [K: list,L: list] : ( length(append(K,L)) = $sum($sum(length(K),length(L)),1) )
<=> ~ ! [K: list,L: list] : ( length(append(K,L)) = $sum(1,$sum(length(K),length(L))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ~ ~ ! [K: list,L: list] : ( length(append(K,L)) = $sum($sum(length(K),length(L)),1) )
<=> ~ ~ ! [K: list,L: list] : ( length(append(K,L)) = $sum(1,$sum(length(K),length(L))) ) ),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
( ~ ~ ! [K: list,L: list] : ( length(append(K,L)) = $sum($sum(length(K),length(L)),1) )
<=> ! [K: list,L: list] : ( length(append(K,L)) = $sum(1,$sum(length(K),length(L))) ) ),
inference(transitivity,[status(thm)],[23,21]) ).
tff(25,axiom,
~ ~ ! [K: list,L: list] : ( length(append(K,L)) = $sum($sum(length(K),length(L)),1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).
tff(26,plain,
! [K: list,L: list] : ( length(append(K,L)) = $sum(1,$sum(length(K),length(L))) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [K: list,L: list] : ( length(append(K,L)) = $sum(1,$sum(length(K),length(L))) ),
inference(modus_ponens,[status(thm)],[26,20]) ).
tff(28,plain,
! [K: list,L: list] : ( $sum(length(append(K,L)),$sum($product(-1,length(K)),$product(-1,length(L)))) = 1 ),
inference(modus_ponens,[status(thm)],[27,19]) ).
tff(29,plain,
! [K: list,L: list] : ( $sum(length(L),$sum(length(K),$product(-1,length(append(K,L))))) = -1 ),
inference(modus_ponens,[status(thm)],[28,17]) ).
tff(30,plain,
! [K: list,L: list] : ( $sum(length(L),$sum(length(K),$product(-1,length(append(K,L))))) = -1 ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [K: list,L: list] : ( $sum(length(L),$sum(length(K),$product(-1,length(append(K,L))))) = -1 ),
inference(modus_ponens,[status(thm)],[30,15]) ).
tff(32,plain,
( ( ~ ! [K: list,L: list] : ( $sum(length(L),$sum(length(K),$product(-1,length(append(K,L))))) = -1 )
| ( $sum($product(2,length(nil)),$product(-1,length(append(nil,nil)))) = -1 ) )
<=> ( ~ ! [K: list,L: list] : ( $sum(length(L),$sum(length(K),$product(-1,length(append(K,L))))) = -1 )
| ( $sum($product(2,length(nil)),$product(-1,length(append(nil,nil)))) = -1 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ( $sum(length(nil),$sum(length(nil),$product(-1,length(append(nil,nil))))) = -1 )
<=> ( $sum($product(2,length(nil)),$product(-1,length(append(nil,nil)))) = -1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ( ~ ! [K: list,L: list] : ( $sum(length(L),$sum(length(K),$product(-1,length(append(K,L))))) = -1 )
| ( $sum(length(nil),$sum(length(nil),$product(-1,length(append(nil,nil))))) = -1 ) )
<=> ( ~ ! [K: list,L: list] : ( $sum(length(L),$sum(length(K),$product(-1,length(append(K,L))))) = -1 )
| ( $sum($product(2,length(nil)),$product(-1,length(append(nil,nil)))) = -1 ) ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ( ~ ! [K: list,L: list] : ( $sum(length(L),$sum(length(K),$product(-1,length(append(K,L))))) = -1 )
| ( $sum(length(nil),$sum(length(nil),$product(-1,length(append(nil,nil))))) = -1 ) )
<=> ( ~ ! [K: list,L: list] : ( $sum(length(L),$sum(length(K),$product(-1,length(append(K,L))))) = -1 )
| ( $sum($product(2,length(nil)),$product(-1,length(append(nil,nil)))) = -1 ) ) ),
inference(transitivity,[status(thm)],[34,32]) ).
tff(36,plain,
( ~ ! [K: list,L: list] : ( $sum(length(L),$sum(length(K),$product(-1,length(append(K,L))))) = -1 )
| ( $sum(length(nil),$sum(length(nil),$product(-1,length(append(nil,nil))))) = -1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
( ~ ! [K: list,L: list] : ( $sum(length(L),$sum(length(K),$product(-1,length(append(K,L))))) = -1 )
| ( $sum($product(2,length(nil)),$product(-1,length(append(nil,nil)))) = -1 ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
$sum($product(2,length(nil)),$product(-1,length(append(nil,nil)))) = -1,
inference(unit_resolution,[status(thm)],[37,31]) ).
tff(39,plain,
( ( $sum($product(2,length(nil)),$product(-1,length(append(nil,nil)))) != -1 )
| $lesseq($sum($product(2,length(nil)),$product(-1,length(append(nil,nil)))),-1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(40,plain,
$lesseq($sum($product(2,length(nil)),$product(-1,length(append(nil,nil)))),-1),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
( ( length(nil) = 0 )
<=> ( length(nil) = 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
length(nil) = 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
tff(43,plain,
length(nil) = 0,
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ( length(nil) != 0 )
| $greatereq(length(nil),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(45,plain,
$greatereq(length(nil),0),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
$false,
inference(theory_lemma,[status(thm)],[45,40,13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT093_1 : TPTP v8.1.0. Released v6.1.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n014.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 : Wed Aug 31 01:51:48 EDT 2022
% 0.13/0.33 % 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.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------