TSTP Solution File: DAT092_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT092_1 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 59
% Syntax : Number of formulae : 141 ( 79 unt; 6 typ; 0 def)
% Number of atoms : 253 ( 213 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 147 ( 53 ~; 46 |; 0 &)
% ( 48 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number arithmetic : 673 ( 20 atm; 220 fun; 374 num; 59 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 7 ( 5 >; 2 *; 0 +; 0 <<)
% Number of predicates : 9 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 11 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 207 ( 184 !; 0 ?; 207 :)
% Comments :
%------------------------------------------------------------------------------
tff(length_type,type,
length: list > $int ).
tff(append_type,type,
append: ( list * list ) > list ).
tff(cons_type,type,
cons: ( $int * list ) > list ).
tff(nil_type,type,
nil: list ).
tff(head_type,type,
head: list > $int ).
tff(tail_type,type,
tail: list > list ).
tff(1,plain,
( ( 1 = 0 )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
^ [K: list,L: list] :
refl(
( ( $sum(length(K),$product(-1,length(append(K,L)))) = 0 )
<=> ( $sum(length(K),$product(-1,length(append(K,L)))) = 0 ) )),
inference(bind,[status(th)],]) ).
tff(3,plain,
( ! [K: list,L: list] : ( $sum(length(K),$product(-1,length(append(K,L)))) = 0 )
<=> ! [K: list,L: list] : ( $sum(length(K),$product(-1,length(append(K,L)))) = 0 ) ),
inference(quant_intro,[status(thm)],[2]) ).
tff(4,plain,
^ [K: list,L: list] :
trans(
monotonicity(rewrite($sum(length(append(K,L)),$product(-1,length(K))) = $sum($product(-1,length(K)),length(append(K,L)))),
( ( $sum(length(append(K,L)),$product(-1,length(K))) = 0 )
<=> ( $sum($product(-1,length(K)),length(append(K,L))) = 0 ) )),
rewrite(
( ( $sum($product(-1,length(K)),length(append(K,L))) = 0 )
<=> ( $sum(length(K),$product(-1,length(append(K,L)))) = 0 ) )),
( ( $sum(length(append(K,L)),$product(-1,length(K))) = 0 )
<=> ( $sum(length(K),$product(-1,length(append(K,L)))) = 0 ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [K: list,L: list] : ( $sum(length(append(K,L)),$product(-1,length(K))) = 0 )
<=> ! [K: list,L: list] : ( $sum(length(K),$product(-1,length(append(K,L)))) = 0 ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
^ [K: list,L: list] :
rewrite(
( ( length(append(K,L)) = length(K) )
<=> ( $sum(length(append(K,L)),$product(-1,length(K))) = 0 ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [K: list,L: list] : ( length(append(K,L)) = length(K) )
<=> ! [K: list,L: list] : ( $sum(length(append(K,L)),$product(-1,length(K))) = 0 ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [K: list,L: list] : ( length(append(K,L)) = length(K) )
<=> ! [K: list,L: list] : ( length(append(K,L)) = length(K) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
( ~ ~ ! [K: list,L: list] : ( length(append(K,L)) = length(K) )
<=> ! [K: list,L: list] : ( length(append(K,L)) = length(K) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
( ~ ! [K: list,L: list] : ( length(append(K,L)) = length(K) )
<=> ~ ! [K: list,L: list] : ( length(append(K,L)) = length(K) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
( ~ ~ ! [K: list,L: list] : ( length(append(K,L)) = length(K) )
<=> ~ ~ ! [K: list,L: list] : ( length(append(K,L)) = length(K) ) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ~ ~ ! [K: list,L: list] : ( length(append(K,L)) = length(K) )
<=> ! [K: list,L: list] : ( length(append(K,L)) = length(K) ) ),
inference(transitivity,[status(thm)],[11,9]) ).
tff(13,axiom,
~ ~ ! [K: list,L: list] : ( length(append(K,L)) = length(K) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(14,plain,
! [K: list,L: list] : ( length(append(K,L)) = length(K) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [K: list,L: list] : ( length(append(K,L)) = length(K) ),
inference(modus_ponens,[status(thm)],[14,8]) ).
tff(16,plain,
! [K: list,L: list] : ( $sum(length(append(K,L)),$product(-1,length(K))) = 0 ),
inference(modus_ponens,[status(thm)],[15,7]) ).
tff(17,plain,
! [K: list,L: list] : ( $sum(length(K),$product(-1,length(append(K,L)))) = 0 ),
inference(modus_ponens,[status(thm)],[16,5]) ).
tff(18,plain,
! [K: list,L: list] : ( $sum(length(K),$product(-1,length(append(K,L)))) = 0 ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [K: list,L: list] : ( $sum(length(K),$product(-1,length(append(K,L)))) = 0 ),
inference(modus_ponens,[status(thm)],[18,3]) ).
tff(20,plain,
( ~ ! [K: list,L: list] : ( $sum(length(K),$product(-1,length(append(K,L)))) = 0 )
| ( $sum(length(nil),$product(-1,length(append(nil,cons(0,append(nil,nil)))))) = 0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
$sum(length(nil),$product(-1,length(append(nil,cons(0,append(nil,nil)))))) = 0,
inference(unit_resolution,[status(thm)],[20,19]) ).
tff(22,plain,
( ( $sum(length(nil),$product(-1,length(append(nil,cons(0,append(nil,nil)))))) != 0 )
| $lesseq($sum(length(nil),$product(-1,length(append(nil,cons(0,append(nil,nil)))))),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(23,plain,
$lesseq($sum(length(nil),$product(-1,length(append(nil,cons(0,append(nil,nil)))))),0),
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
( ( $sum(length(nil),$product(-1,length(append(nil,cons(0,append(nil,nil)))))) != 0 )
| $greatereq($sum(length(nil),$product(-1,length(append(nil,cons(0,append(nil,nil)))))),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(25,plain,
$greatereq($sum(length(nil),$product(-1,length(append(nil,cons(0,append(nil,nil)))))),0),
inference(unit_resolution,[status(thm)],[24,21]) ).
tff(26,plain,
( ( length(nil) = 0 )
<=> ( length(nil) = 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
length(nil) = 0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
tff(28,plain,
length(nil) = 0,
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( ( length(nil) != 0 )
| $lesseq(length(nil),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(30,plain,
$lesseq(length(nil),0),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
( ( length(nil) != 0 )
| $greatereq(length(nil),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(32,plain,
$greatereq(length(nil),0),
inference(unit_resolution,[status(thm)],[31,28]) ).
tff(33,plain,
length(append(nil,cons(0,append(nil,nil)))) = 0,
inference(theory_lemma,[status(thm)],[32,30,25,23]) ).
tff(34,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(35,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)],[34]) ).
tff(36,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(37,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)],[36]) ).
tff(38,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(39,axiom,
! [H: $int,T: list] : ( length(cons(H,T)) = $sum(1,length(T)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_1) ).
tff(40,plain,
! [H: $int,T: list] : ( length(cons(H,T)) = $sum(1,length(T)) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 ),
inference(modus_ponens,[status(thm)],[40,37]) ).
tff(42,plain,
! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 ),
inference(modus_ponens,[status(thm)],[42,35]) ).
tff(44,plain,
( ( ~ ! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 )
| ( $sum(length(nil),$product(-1,length(cons(0,nil)))) = -1 ) )
<=> ( ~ ! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 )
| ( $sum(length(nil),$product(-1,length(cons(0,nil)))) = -1 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( $sum($product(-1,length(nil)),length(cons(0,nil))) = 1 )
<=> ( $sum(length(nil),$product(-1,length(cons(0,nil)))) = -1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
$sum(length(cons(0,nil)),$product(-1,length(nil))) = $sum($product(-1,length(nil)),length(cons(0,nil))),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ( $sum(length(cons(0,nil)),$product(-1,length(nil))) = 1 )
<=> ( $sum($product(-1,length(nil)),length(cons(0,nil))) = 1 ) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ( $sum(length(cons(0,nil)),$product(-1,length(nil))) = 1 )
<=> ( $sum(length(nil),$product(-1,length(cons(0,nil)))) = -1 ) ),
inference(transitivity,[status(thm)],[47,45]) ).
tff(49,plain,
( ( ~ ! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 )
| ( $sum(length(cons(0,nil)),$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(0,nil)))) = -1 ) ) ),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
( ( ~ ! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 )
| ( $sum(length(cons(0,nil)),$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(0,nil)))) = -1 ) ) ),
inference(transitivity,[status(thm)],[49,44]) ).
tff(51,plain,
( ~ ! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 )
| ( $sum(length(cons(0,nil)),$product(-1,length(nil))) = 1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [H: $int,T: list] : ( $sum(length(cons(H,T)),$product(-1,length(T))) = 1 )
| ( $sum(length(nil),$product(-1,length(cons(0,nil)))) = -1 ) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
$sum(length(nil),$product(-1,length(cons(0,nil)))) = -1,
inference(unit_resolution,[status(thm)],[52,43]) ).
tff(54,plain,
( ( $sum(length(nil),$product(-1,length(cons(0,nil)))) != -1 )
| $lesseq($sum(length(nil),$product(-1,length(cons(0,nil)))),-1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(55,plain,
$lesseq($sum(length(nil),$product(-1,length(cons(0,nil)))),-1),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
( ( $sum(length(nil),$product(-1,length(cons(0,nil)))) != -1 )
| $greatereq($sum(length(nil),$product(-1,length(cons(0,nil)))),-1) ),
inference(theory_lemma,[status(thm)],]) ).
tff(57,plain,
$greatereq($sum(length(nil),$product(-1,length(cons(0,nil)))),-1),
inference(unit_resolution,[status(thm)],[56,53]) ).
tff(58,plain,
^ [K: $int,L: list] :
refl(
( ( $sum(K,$product(-1,head(cons(K,L)))) = 0 )
<=> ( $sum(K,$product(-1,head(cons(K,L)))) = 0 ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 )
<=> ! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
^ [K: $int,L: list] :
trans(
monotonicity(rewrite($sum(head(cons(K,L)),$product(-1,K)) = $sum($product(-1,K),head(cons(K,L)))),
( ( $sum(head(cons(K,L)),$product(-1,K)) = 0 )
<=> ( $sum($product(-1,K),head(cons(K,L))) = 0 ) )),
rewrite(
( ( $sum($product(-1,K),head(cons(K,L))) = 0 )
<=> ( $sum(K,$product(-1,head(cons(K,L)))) = 0 ) )),
( ( $sum(head(cons(K,L)),$product(-1,K)) = 0 )
<=> ( $sum(K,$product(-1,head(cons(K,L)))) = 0 ) )),
inference(bind,[status(th)],]) ).
tff(61,plain,
( ! [K: $int,L: list] : ( $sum(head(cons(K,L)),$product(-1,K)) = 0 )
<=> ! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
^ [K: $int,L: list] :
rewrite(
( ( head(cons(K,L)) = K )
<=> ( $sum(head(cons(K,L)),$product(-1,K)) = 0 ) )),
inference(bind,[status(th)],]) ).
tff(63,plain,
( ! [K: $int,L: list] : ( head(cons(K,L)) = K )
<=> ! [K: $int,L: list] : ( $sum(head(cons(K,L)),$product(-1,K)) = 0 ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [K: $int,L: list] : ( head(cons(K,L)) = K )
<=> ! [K: $int,L: list] : ( head(cons(K,L)) = K ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,axiom,
! [K: $int,L: list] : ( head(cons(K,L)) = K ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
tff(66,plain,
! [K: $int,L: list] : ( head(cons(K,L)) = K ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [K: $int,L: list] : ( $sum(head(cons(K,L)),$product(-1,K)) = 0 ),
inference(modus_ponens,[status(thm)],[66,63]) ).
tff(68,plain,
! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 ),
inference(modus_ponens,[status(thm)],[67,61]) ).
tff(69,plain,
! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 ),
inference(modus_ponens,[status(thm)],[69,59]) ).
tff(71,plain,
( ~ ! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 )
| ( $sum(length(cons(0,nil)),$product(-1,head(cons(length(cons(0,nil)),nil)))) = 0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
$sum(length(cons(0,nil)),$product(-1,head(cons(length(cons(0,nil)),nil)))) = 0,
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
( ( $sum(length(cons(0,nil)),$product(-1,head(cons(length(cons(0,nil)),nil)))) != 0 )
| $lesseq($sum(length(cons(0,nil)),$product(-1,head(cons(length(cons(0,nil)),nil)))),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(74,plain,
$lesseq($sum(length(cons(0,nil)),$product(-1,head(cons(length(cons(0,nil)),nil)))),0),
inference(unit_resolution,[status(thm)],[73,72]) ).
tff(75,plain,
( ( $sum(length(cons(0,nil)),$product(-1,head(cons(length(cons(0,nil)),nil)))) != 0 )
| $greatereq($sum(length(cons(0,nil)),$product(-1,head(cons(length(cons(0,nil)),nil)))),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(76,plain,
$greatereq($sum(length(cons(0,nil)),$product(-1,head(cons(length(cons(0,nil)),nil)))),0),
inference(unit_resolution,[status(thm)],[75,72]) ).
tff(77,plain,
head(cons(length(cons(0,nil)),nil)) = 1,
inference(theory_lemma,[status(thm)],[76,74,32,30,57,55]) ).
tff(78,plain,
length(cons(0,nil)) = head(cons(length(cons(0,nil)),nil)),
inference(theory_lemma,[status(thm)],[76,74,32,30,57,55,32,30,57,55]) ).
tff(79,plain,
^ [K: $int,L: list] :
refl(
( ( cons(K,L) != nil )
<=> ( cons(K,L) != nil ) )),
inference(bind,[status(th)],]) ).
tff(80,plain,
( ! [K: $int,L: list] : ( cons(K,L) != nil )
<=> ! [K: $int,L: list] : ( cons(K,L) != nil ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
( ! [K: $int,L: list] : ( cons(K,L) != nil )
<=> ! [K: $int,L: list] : ( cons(K,L) != nil ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,axiom,
! [K: $int,L: list] : ( cons(K,L) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4) ).
tff(83,plain,
! [K: $int,L: list] : ( cons(K,L) != nil ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
! [K: $int,L: list] : ( cons(K,L) != nil ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [K: $int,L: list] : ( cons(K,L) != nil ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
( ~ ! [K: $int,L: list] : ( cons(K,L) != nil )
| ( cons(0,nil) != nil ) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
cons(0,nil) != nil,
inference(unit_resolution,[status(thm)],[86,85]) ).
tff(88,plain,
^ [L: list] :
refl(
( ( ( L = nil )
| ( L = cons(head(L),tail(L)) ) )
<=> ( ( L = nil )
| ( L = cons(head(L),tail(L)) ) ) )),
inference(bind,[status(th)],]) ).
tff(89,plain,
( ! [L: list] :
( ( L = nil )
| ( L = cons(head(L),tail(L)) ) )
<=> ! [L: list] :
( ( L = nil )
| ( L = cons(head(L),tail(L)) ) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [L: list] :
( ( L = nil )
| ( L = cons(head(L),tail(L)) ) )
<=> ! [L: list] :
( ( L = nil )
| ( L = cons(head(L),tail(L)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,axiom,
! [L: list] :
( ( L = nil )
| ( L = cons(head(L),tail(L)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3) ).
tff(92,plain,
! [L: list] :
( ( L = nil )
| ( L = cons(head(L),tail(L)) ) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [L: list] :
( ( L = nil )
| ( L = cons(head(L),tail(L)) ) ),
inference(skolemize,[status(sab)],[92]) ).
tff(94,plain,
! [L: list] :
( ( L = nil )
| ( L = cons(head(L),tail(L)) ) ),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
( ( ~ ! [L: list] :
( ( L = nil )
| ( L = cons(head(L),tail(L)) ) )
| ( cons(0,nil) = nil )
| ( cons(0,nil) = cons(head(cons(0,nil)),tail(cons(0,nil))) ) )
<=> ( ~ ! [L: list] :
( ( L = nil )
| ( L = cons(head(L),tail(L)) ) )
| ( cons(0,nil) = nil )
| ( cons(0,nil) = cons(head(cons(0,nil)),tail(cons(0,nil))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
( ~ ! [L: list] :
( ( L = nil )
| ( L = cons(head(L),tail(L)) ) )
| ( cons(0,nil) = nil )
| ( cons(0,nil) = cons(head(cons(0,nil)),tail(cons(0,nil))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
( ~ ! [L: list] :
( ( L = nil )
| ( L = cons(head(L),tail(L)) ) )
| ( cons(0,nil) = nil )
| ( cons(0,nil) = cons(head(cons(0,nil)),tail(cons(0,nil))) ) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
cons(0,nil) = cons(head(cons(0,nil)),tail(cons(0,nil))),
inference(unit_resolution,[status(thm)],[97,94,87]) ).
tff(99,plain,
cons(head(cons(0,nil)),tail(cons(0,nil))) = cons(0,nil),
inference(symmetry,[status(thm)],[98]) ).
tff(100,plain,
length(cons(head(cons(0,nil)),tail(cons(0,nil)))) = length(cons(0,nil)),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
( ~ ! [K: list,L: list] : ( $sum(length(K),$product(-1,length(append(K,L)))) = 0 )
| ( $sum(length(cons(head(cons(0,nil)),tail(cons(0,nil)))),$product(-1,length(append(cons(head(cons(0,nil)),tail(cons(0,nil))),nil)))) = 0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,plain,
$sum(length(cons(head(cons(0,nil)),tail(cons(0,nil)))),$product(-1,length(append(cons(head(cons(0,nil)),tail(cons(0,nil))),nil)))) = 0,
inference(unit_resolution,[status(thm)],[101,19]) ).
tff(103,plain,
( ( $sum(length(cons(head(cons(0,nil)),tail(cons(0,nil)))),$product(-1,length(append(cons(head(cons(0,nil)),tail(cons(0,nil))),nil)))) != 0 )
| $lesseq($sum(length(cons(head(cons(0,nil)),tail(cons(0,nil)))),$product(-1,length(append(cons(head(cons(0,nil)),tail(cons(0,nil))),nil)))),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(104,plain,
$lesseq($sum(length(cons(head(cons(0,nil)),tail(cons(0,nil)))),$product(-1,length(append(cons(head(cons(0,nil)),tail(cons(0,nil))),nil)))),0),
inference(unit_resolution,[status(thm)],[103,102]) ).
tff(105,plain,
( ( $sum(length(cons(head(cons(0,nil)),tail(cons(0,nil)))),$product(-1,length(append(cons(head(cons(0,nil)),tail(cons(0,nil))),nil)))) != 0 )
| $greatereq($sum(length(cons(head(cons(0,nil)),tail(cons(0,nil)))),$product(-1,length(append(cons(head(cons(0,nil)),tail(cons(0,nil))),nil)))),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(106,plain,
$greatereq($sum(length(cons(head(cons(0,nil)),tail(cons(0,nil)))),$product(-1,length(append(cons(head(cons(0,nil)),tail(cons(0,nil))),nil)))),0),
inference(unit_resolution,[status(thm)],[105,102]) ).
tff(107,plain,
length(cons(head(cons(0,nil)),tail(cons(0,nil)))) = length(append(cons(head(cons(0,nil)),tail(cons(0,nil))),nil)),
inference(theory_lemma,[status(thm)],[106,104]) ).
tff(108,plain,
length(append(cons(head(cons(0,nil)),tail(cons(0,nil))),nil)) = length(cons(head(cons(0,nil)),tail(cons(0,nil)))),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
append(cons(head(cons(0,nil)),tail(cons(0,nil))),nil) = append(cons(0,nil),nil),
inference(monotonicity,[status(thm)],[99]) ).
tff(110,plain,
append(cons(0,nil),nil) = append(cons(head(cons(0,nil)),tail(cons(0,nil))),nil),
inference(symmetry,[status(thm)],[109]) ).
tff(111,plain,
^ [I: $int,K: list,L: list] :
refl(
( ( append(cons(I,K),L) = cons(I,append(K,L)) )
<=> ( append(cons(I,K),L) = cons(I,append(K,L)) ) )),
inference(bind,[status(th)],]) ).
tff(112,plain,
( ! [I: $int,K: list,L: list] : ( append(cons(I,K),L) = cons(I,append(K,L)) )
<=> ! [I: $int,K: list,L: list] : ( append(cons(I,K),L) = cons(I,append(K,L)) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,plain,
( ! [I: $int,K: list,L: list] : ( append(cons(I,K),L) = cons(I,append(K,L)) )
<=> ! [I: $int,K: list,L: list] : ( append(cons(I,K),L) = cons(I,append(K,L)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,axiom,
! [I: $int,K: list,L: list] : ( append(cons(I,K),L) = cons(I,append(K,L)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_7) ).
tff(115,plain,
! [I: $int,K: list,L: list] : ( append(cons(I,K),L) = cons(I,append(K,L)) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
! [I: $int,K: list,L: list] : ( append(cons(I,K),L) = cons(I,append(K,L)) ),
inference(skolemize,[status(sab)],[115]) ).
tff(117,plain,
! [I: $int,K: list,L: list] : ( append(cons(I,K),L) = cons(I,append(K,L)) ),
inference(modus_ponens,[status(thm)],[116,112]) ).
tff(118,plain,
( ~ ! [I: $int,K: list,L: list] : ( append(cons(I,K),L) = cons(I,append(K,L)) )
| ( append(cons(0,nil),nil) = cons(0,append(nil,nil)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(119,plain,
append(cons(0,nil),nil) = cons(0,append(nil,nil)),
inference(unit_resolution,[status(thm)],[118,117]) ).
tff(120,plain,
cons(0,append(nil,nil)) = append(cons(0,nil),nil),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
^ [L: list] :
refl(
( ( append(nil,L) = L )
<=> ( append(nil,L) = L ) )),
inference(bind,[status(th)],]) ).
tff(122,plain,
( ! [L: list] : ( append(nil,L) = L )
<=> ! [L: list] : ( append(nil,L) = L ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,plain,
( ! [L: list] : ( append(nil,L) = L )
<=> ! [L: list] : ( append(nil,L) = L ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,axiom,
! [L: list] : ( append(nil,L) = L ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_6) ).
tff(125,plain,
! [L: list] : ( append(nil,L) = L ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
! [L: list] : ( append(nil,L) = L ),
inference(skolemize,[status(sab)],[125]) ).
tff(127,plain,
! [L: list] : ( append(nil,L) = L ),
inference(modus_ponens,[status(thm)],[126,122]) ).
tff(128,plain,
( ~ ! [L: list] : ( append(nil,L) = L )
| ( append(nil,cons(0,append(nil,nil))) = cons(0,append(nil,nil)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
append(nil,cons(0,append(nil,nil))) = cons(0,append(nil,nil)),
inference(unit_resolution,[status(thm)],[128,127]) ).
tff(130,plain,
append(nil,cons(0,append(nil,nil))) = append(cons(head(cons(0,nil)),tail(cons(0,nil))),nil),
inference(transitivity,[status(thm)],[129,120,110]) ).
tff(131,plain,
length(append(nil,cons(0,append(nil,nil)))) = length(append(cons(head(cons(0,nil)),tail(cons(0,nil))),nil)),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
length(append(nil,cons(0,append(nil,nil)))) = 1,
inference(transitivity,[status(thm)],[131,108,100,78,77]) ).
tff(133,plain,
1 = length(append(nil,cons(0,append(nil,nil)))),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
1 = 0,
inference(transitivity,[status(thm)],[133,33]) ).
tff(135,plain,
$false,
inference(modus_ponens,[status(thm)],[134,1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT092_1 : TPTP v8.1.0. Released v6.1.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n009.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 01:46:50 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.
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------