TSTP Solution File: DAT082_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT082_1 : TPTP v8.1.0. Released v6.1.0.
% 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 : Fri Sep 16 14:36:39 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 25
% Syntax : Number of formulae : 50 ( 23 unt; 3 typ; 0 def)
% Number of atoms : 86 ( 57 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 66 ( 29 ~; 24 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number arithmetic : 376 ( 26 atm; 112 fun; 216 num; 22 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 7 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 9 ( 3 usr; 5 con; 0-2 aty)
% Number of variables : 44 ( 40 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
tff(length_type,type,
length: list > $int ).
tff(cons_type,type,
cons: ( $int * list ) > list ).
tff(nil_type,type,
nil: list ).
tff(1,plain,
^ [H: $int,T: list] :
refl(
( ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 )
<=> ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 )
<=> ! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [H: $int,T: list] :
rewrite(
( ( length(cons(H,T)) = $sum(1,length(T)) )
<=> ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [H: $int,T: list] : ( length(cons(H,T)) = $sum(1,length(T)) )
<=> ! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [H: $int,T: list] : ( length(cons(H,T)) = $sum(1,length(T)) )
<=> ! [H: $int,T: list] : ( length(cons(H,T)) = $sum(1,length(T)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
! [H: $int,T: list] : ( length(cons(H,T)) = $sum(1,length(T)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l_1) ).
tff(7,plain,
! [H: $int,T: list] : ( length(cons(H,T)) = $sum(1,length(T)) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 ),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ( ~ ! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 )
| ( $sum(length(nil),$product(-1,length(cons(2,nil)))) = -1 ) )
<=> ( ~ ! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 )
| ( $sum(length(nil),$product(-1,length(cons(2,nil)))) = -1 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ( $sum($product(-1,length(nil)),length(cons(2,nil))) = 1 )
<=> ( $sum(length(nil),$product(-1,length(cons(2,nil)))) = -1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
$sum(length(cons(2,nil)),$product(-1,length(nil))) = $sum($product(-1,length(nil)),length(cons(2,nil))),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ( $sum(length(cons(2,nil)),$product(-1,length(nil))) = 1 )
<=> ( $sum($product(-1,length(nil)),length(cons(2,nil))) = 1 ) ),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
( ( $sum(length(cons(2,nil)),$product(-1,length(nil))) = 1 )
<=> ( $sum(length(nil),$product(-1,length(cons(2,nil)))) = -1 ) ),
inference(transitivity,[status(thm)],[14,12]) ).
tff(16,plain,
( ( ~ ! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 )
| ( $sum(length(cons(2,nil)),$product(-1,length(nil))) = 1 ) )
<=> ( ~ ! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 )
| ( $sum(length(nil),$product(-1,length(cons(2,nil)))) = -1 ) ) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( ( ~ ! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 )
| ( $sum(length(cons(2,nil)),$product(-1,length(nil))) = 1 ) )
<=> ( ~ ! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 )
| ( $sum(length(nil),$product(-1,length(cons(2,nil)))) = -1 ) ) ),
inference(transitivity,[status(thm)],[16,11]) ).
tff(18,plain,
( ~ ! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 )
| ( $sum(length(cons(2,nil)),$product(-1,length(nil))) = 1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 )
| ( $sum(length(nil),$product(-1,length(cons(2,nil)))) = -1 ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
$sum(length(nil),$product(-1,length(cons(2,nil)))) = -1,
inference(unit_resolution,[status(thm)],[19,10]) ).
tff(21,plain,
( ( $sum(length(nil),$product(-1,length(cons(2,nil)))) != -1 )
| $lesseq($sum(length(nil),$product(-1,length(cons(2,nil)))),-1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(22,plain,
$lesseq($sum(length(nil),$product(-1,length(cons(2,nil)))),-1),
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
( ( length(nil) = 0 )
<=> ( length(nil) = 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
length(nil) = 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
tff(25,plain,
length(nil) = 0,
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ( length(nil) != 0 )
| $greatereq(length(nil),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(27,plain,
$greatereq(length(nil),0),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ ! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 )
| ( $sum(length(cons(1,cons(2,nil))),$product(-1,length(cons(2,nil)))) = 1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
$sum(length(cons(1,cons(2,nil))),$product(-1,length(cons(2,nil)))) = 1,
inference(unit_resolution,[status(thm)],[28,10]) ).
tff(30,plain,
( ( $sum(length(cons(1,cons(2,nil))),$product(-1,length(cons(2,nil)))) != 1 )
| $greatereq($sum(length(cons(1,cons(2,nil))),$product(-1,length(cons(2,nil)))),1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(31,plain,
$greatereq($sum(length(cons(1,cons(2,nil))),$product(-1,length(cons(2,nil)))),1),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
( $greatereq(length(cons(1,cons(2,nil))),2)
| ~ $greatereq($sum(length(cons(1,cons(2,nil))),$product(-1,length(cons(2,nil)))),1)
| ~ $greatereq(length(nil),0)
| ~ $lesseq($sum(length(nil),$product(-1,length(cons(2,nil)))),-1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(33,plain,
$greatereq(length(cons(1,cons(2,nil))),2),
inference(unit_resolution,[status(thm)],[32,31,27,22]) ).
tff(34,plain,
( ( $sum(length(nil),$product(-1,length(cons(2,nil)))) != -1 )
| $greatereq($sum(length(nil),$product(-1,length(cons(2,nil)))),-1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(35,plain,
$greatereq($sum(length(nil),$product(-1,length(cons(2,nil)))),-1),
inference(unit_resolution,[status(thm)],[34,20]) ).
tff(36,plain,
( ( length(nil) != 0 )
| $lesseq(length(nil),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(37,plain,
$lesseq(length(nil),0),
inference(unit_resolution,[status(thm)],[36,25]) ).
tff(38,plain,
( ( $sum(length(cons(1,cons(2,nil))),$product(-1,length(cons(2,nil)))) != 1 )
| $lesseq($sum(length(cons(1,cons(2,nil))),$product(-1,length(cons(2,nil)))),1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(39,plain,
$lesseq($sum(length(cons(1,cons(2,nil))),$product(-1,length(cons(2,nil)))),1),
inference(unit_resolution,[status(thm)],[38,29]) ).
tff(40,plain,
( $lesseq(length(cons(1,cons(2,nil))),2)
| ~ $lesseq($sum(length(cons(1,cons(2,nil))),$product(-1,length(cons(2,nil)))),1)
| ~ $lesseq(length(nil),0)
| ~ $greatereq($sum(length(nil),$product(-1,length(cons(2,nil)))),-1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(41,plain,
$lesseq(length(cons(1,cons(2,nil))),2),
inference(unit_resolution,[status(thm)],[40,39,37,35]) ).
tff(42,plain,
( ( length(cons(1,cons(2,nil))) != 2 )
<=> ( length(cons(1,cons(2,nil))) != 2 ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,axiom,
length(cons(1,cons(2,nil))) != 2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).
tff(44,plain,
length(cons(1,cons(2,nil))) != 2,
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
( ( length(cons(1,cons(2,nil))) = 2 )
| ~ $lesseq(length(cons(1,cons(2,nil))),2)
| ~ $greatereq(length(cons(1,cons(2,nil))),2) ),
inference(theory_lemma,[status(thm)],]) ).
tff(46,plain,
( ~ $lesseq(length(cons(1,cons(2,nil))),2)
| ~ $greatereq(length(cons(1,cons(2,nil))),2) ),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
$false,
inference(unit_resolution,[status(thm)],[46,41,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT082_1 : TPTP v8.1.0. Released v6.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 01:58:27 EDT 2022
% 0.13/0.34 % 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.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------