TSTP Solution File: DAT080_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT080_1 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 14:36:38 EDT 2022
% Result : Theorem 0.14s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 44
% Syntax : Number of formulae : 106 ( 34 unt; 4 typ; 0 def)
% Number of atoms : 284 ( 205 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 236 ( 61 ~; 103 |; 0 &)
% ( 68 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number arithmetic : 1265 ( 31 atm; 321 fun; 785 num; 128 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 8 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 14 ( 3 usr; 10 con; 0-2 aty)
% Number of variables : 191 ( 173 !; 0 ?; 191 :)
% Comments :
%------------------------------------------------------------------------------
tff(count_type,type,
count: ( $int * list ) > $int ).
tff(nil_type,type,
nil: list ).
tff(cons_type,type,
cons: ( $int * list ) > list ).
tff(in_type,type,
in: ( $int * list ) > $o ).
tff(1,plain,
^ [K: $int] :
refl(
( ( count(K,nil) = 0 )
<=> ( count(K,nil) = 0 ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [K: $int] : ( count(K,nil) = 0 )
<=> ! [K: $int] : ( count(K,nil) = 0 ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [K: $int] : ( count(K,nil) = 0 )
<=> ! [K: $int] : ( count(K,nil) = 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [K: $int] : ( count(K,nil) = 0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a) ).
tff(5,plain,
! [K: $int] : ( count(K,nil) = 0 ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [K: $int] : ( count(K,nil) = 0 ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [K: $int] : ( count(K,nil) = 0 ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [K: $int] : ( count(K,nil) = 0 )
| ( count(4,nil) = 0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
count(4,nil) = 0,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ( count(4,nil) != 0 )
| $lesseq(count(4,nil),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(11,plain,
$lesseq(count(4,nil),0),
inference(unit_resolution,[status(thm)],[10,9]) ).
tff(12,plain,
^ [K: $int,H: $int,T: list] :
refl(
( ( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
<=> ( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
<=> ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
^ [K: $int,H: $int,T: list] :
rewrite(
( ( ( $sum(K,$product(-1,H)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
<=> ( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [K: $int,H: $int,T: list] :
( ( $sum(K,$product(-1,H)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
<=> ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
^ [K: $int,H: $int,T: list] :
rewrite(
( ( ( K = H )
| ( count(K,cons(H,T)) = count(K,T) ) )
<=> ( ( $sum(K,$product(-1,H)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [K: $int,H: $int,T: list] :
( ( K = H )
| ( count(K,cons(H,T)) = count(K,T) ) )
<=> ! [K: $int,H: $int,T: list] :
( ( $sum(K,$product(-1,H)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [K: $int,H: $int,T: list] :
( ( K = H )
| ( count(K,cons(H,T)) = count(K,T) ) )
<=> ! [K: $int,H: $int,T: list] :
( ( K = H )
| ( count(K,cons(H,T)) = count(K,T) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ! [K: $int,H: $int,T: list,N: $int] :
( ( K = H )
| ( count(K,cons(H,T)) = count(K,T) ) )
<=> ! [K: $int,H: $int,T: list] :
( ( K = H )
| ( count(K,cons(H,T)) = count(K,T) ) ) ),
inference(elim_unused_vars,[status(thm)],]) ).
tff(20,plain,
^ [K: $int,H: $int,T: list,N: $int] :
rewrite(
( ( ( K != H )
=> ( count(K,cons(H,T)) = count(K,T) ) )
<=> ( ( K = H )
| ( count(K,cons(H,T)) = count(K,T) ) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [K: $int,H: $int,T: list,N: $int] :
( ( K != H )
=> ( count(K,cons(H,T)) = count(K,T) ) )
<=> ! [K: $int,H: $int,T: list,N: $int] :
( ( K = H )
| ( count(K,cons(H,T)) = count(K,T) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [K: $int,H: $int,T: list,N: $int] :
( ( K != H )
=> ( count(K,cons(H,T)) = count(K,T) ) )
<=> ! [K: $int,H: $int,T: list] :
( ( K = H )
| ( count(K,cons(H,T)) = count(K,T) ) ) ),
inference(transitivity,[status(thm)],[21,19]) ).
tff(23,axiom,
! [K: $int,H: $int,T: list,N: $int] :
( ( K != H )
=> ( count(K,cons(H,T)) = count(K,T) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_3) ).
tff(24,plain,
! [K: $int,H: $int,T: list] :
( ( K = H )
| ( count(K,cons(H,T)) = count(K,T) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [K: $int,H: $int,T: list] :
( ( K = H )
| ( count(K,cons(H,T)) = count(K,T) ) ),
inference(modus_ponens,[status(thm)],[24,18]) ).
tff(26,plain,
! [K: $int,H: $int,T: list] :
( ( $sum(K,$product(-1,H)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) ),
inference(modus_ponens,[status(thm)],[25,17]) ).
tff(27,plain,
! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) ),
inference(modus_ponens,[status(thm)],[26,15]) ).
tff(28,plain,
! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) ),
inference(modus_ponens,[status(thm)],[28,13]) ).
tff(30,plain,
( ( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(count(4,cons(1,cons(2,cons(3,nil)))),$product(-1,count(4,cons(2,cons(3,nil))))) = 0 ) )
<=> ( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(count(4,cons(1,cons(2,cons(3,nil)))),$product(-1,count(4,cons(2,cons(3,nil))))) = 0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( $false
| ( $sum(count(4,cons(1,cons(2,cons(3,nil)))),$product(-1,count(4,cons(2,cons(3,nil))))) = 0 ) )
<=> ( $sum(count(4,cons(1,cons(2,cons(3,nil)))),$product(-1,count(4,cons(2,cons(3,nil))))) = 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ( -3 = 0 )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
$sum(1,-4) = -3,
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
$product(-1,4) = -4,
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
$sum(1,$product(-1,4)) = $sum(1,-4),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
$sum(1,$product(-1,4)) = -3,
inference(transitivity,[status(thm)],[35,33]) ).
tff(37,plain,
( ( $sum(1,$product(-1,4)) = 0 )
<=> ( -3 = 0 ) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ( $sum(1,$product(-1,4)) = 0 )
<=> $false ),
inference(transitivity,[status(thm)],[37,32]) ).
tff(39,plain,
( ( ( $sum(1,$product(-1,4)) = 0 )
| ( $sum(count(4,cons(1,cons(2,cons(3,nil)))),$product(-1,count(4,cons(2,cons(3,nil))))) = 0 ) )
<=> ( $false
| ( $sum(count(4,cons(1,cons(2,cons(3,nil)))),$product(-1,count(4,cons(2,cons(3,nil))))) = 0 ) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( ( $sum(1,$product(-1,4)) = 0 )
| ( $sum(count(4,cons(1,cons(2,cons(3,nil)))),$product(-1,count(4,cons(2,cons(3,nil))))) = 0 ) )
<=> ( $sum(count(4,cons(1,cons(2,cons(3,nil)))),$product(-1,count(4,cons(2,cons(3,nil))))) = 0 ) ),
inference(transitivity,[status(thm)],[39,31]) ).
tff(41,plain,
( ( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(1,$product(-1,4)) = 0 )
| ( $sum(count(4,cons(1,cons(2,cons(3,nil)))),$product(-1,count(4,cons(2,cons(3,nil))))) = 0 ) )
<=> ( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(count(4,cons(1,cons(2,cons(3,nil)))),$product(-1,count(4,cons(2,cons(3,nil))))) = 0 ) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(1,$product(-1,4)) = 0 )
| ( $sum(count(4,cons(1,cons(2,cons(3,nil)))),$product(-1,count(4,cons(2,cons(3,nil))))) = 0 ) )
<=> ( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(count(4,cons(1,cons(2,cons(3,nil)))),$product(-1,count(4,cons(2,cons(3,nil))))) = 0 ) ) ),
inference(transitivity,[status(thm)],[41,30]) ).
tff(43,plain,
( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(1,$product(-1,4)) = 0 )
| ( $sum(count(4,cons(1,cons(2,cons(3,nil)))),$product(-1,count(4,cons(2,cons(3,nil))))) = 0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(count(4,cons(1,cons(2,cons(3,nil)))),$product(-1,count(4,cons(2,cons(3,nil))))) = 0 ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
$sum(count(4,cons(1,cons(2,cons(3,nil)))),$product(-1,count(4,cons(2,cons(3,nil))))) = 0,
inference(unit_resolution,[status(thm)],[44,29]) ).
tff(46,plain,
( ( $sum(count(4,cons(1,cons(2,cons(3,nil)))),$product(-1,count(4,cons(2,cons(3,nil))))) != 0 )
| $lesseq($sum(count(4,cons(1,cons(2,cons(3,nil)))),$product(-1,count(4,cons(2,cons(3,nil))))),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(47,plain,
$lesseq($sum(count(4,cons(1,cons(2,cons(3,nil)))),$product(-1,count(4,cons(2,cons(3,nil))))),0),
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
^ [N: $int,L: list] :
refl(
( ( in(N,L)
<=> ~ $lesseq(count(N,L),0) )
<=> ( in(N,L)
<=> ~ $lesseq(count(N,L),0) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [N: $int,L: list] :
( in(N,L)
<=> ~ $lesseq(count(N,L),0) )
<=> ! [N: $int,L: list] :
( in(N,L)
<=> ~ $lesseq(count(N,L),0) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [N: $int,L: list] :
( in(N,L)
<=> ~ $lesseq(count(N,L),0) )
<=> ! [N: $int,L: list] :
( in(N,L)
<=> ~ $lesseq(count(N,L),0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
^ [N: $int,L: list] :
rewrite(
( ( in(N,L)
<=> $greater(count(N,L),0) )
<=> ( in(N,L)
<=> ~ $lesseq(count(N,L),0) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [N: $int,L: list] :
( in(N,L)
<=> $greater(count(N,L),0) )
<=> ! [N: $int,L: list] :
( in(N,L)
<=> ~ $lesseq(count(N,L),0) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,axiom,
! [N: $int,L: list] :
( in(N,L)
<=> $greater(count(N,L),0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_8) ).
tff(54,plain,
! [N: $int,L: list] :
( in(N,L)
<=> ~ $lesseq(count(N,L),0) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [N: $int,L: list] :
( in(N,L)
<=> ~ $lesseq(count(N,L),0) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
! [N: $int,L: list] :
( in(N,L)
<=> ~ $lesseq(count(N,L),0) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [N: $int,L: list] :
( in(N,L)
<=> ~ $lesseq(count(N,L),0) ),
inference(modus_ponens,[status(thm)],[56,49]) ).
tff(58,plain,
( ~ ! [N: $int,L: list] :
( in(N,L)
<=> ~ $lesseq(count(N,L),0) )
| ( in(4,cons(1,cons(2,cons(3,nil))))
<=> ~ $lesseq(count(4,cons(1,cons(2,cons(3,nil)))),0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
( in(4,cons(1,cons(2,cons(3,nil))))
<=> ~ $lesseq(count(4,cons(1,cons(2,cons(3,nil)))),0) ),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
( in(4,cons(1,cons(2,cons(3,nil))))
<=> in(4,cons(1,cons(2,cons(3,nil)))) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ~ ~ in(4,cons(1,cons(2,cons(3,nil))))
<=> in(4,cons(1,cons(2,cons(3,nil)))) ),
inference(rewrite,[status(thm)],]) ).
tff(62,axiom,
~ ~ in(4,cons(1,cons(2,cons(3,nil)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).
tff(63,plain,
in(4,cons(1,cons(2,cons(3,nil)))),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
in(4,cons(1,cons(2,cons(3,nil)))),
inference(modus_ponens,[status(thm)],[63,60]) ).
tff(65,plain,
( ~ ( in(4,cons(1,cons(2,cons(3,nil))))
<=> ~ $lesseq(count(4,cons(1,cons(2,cons(3,nil)))),0) )
| ~ in(4,cons(1,cons(2,cons(3,nil))))
| ~ $lesseq(count(4,cons(1,cons(2,cons(3,nil)))),0) ),
inference(tautology,[status(thm)],]) ).
tff(66,plain,
( ~ ( in(4,cons(1,cons(2,cons(3,nil))))
<=> ~ $lesseq(count(4,cons(1,cons(2,cons(3,nil)))),0) )
| ~ $lesseq(count(4,cons(1,cons(2,cons(3,nil)))),0) ),
inference(unit_resolution,[status(thm)],[65,64]) ).
tff(67,plain,
~ $lesseq(count(4,cons(1,cons(2,cons(3,nil)))),0),
inference(unit_resolution,[status(thm)],[66,59]) ).
tff(68,plain,
( ( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(count(4,cons(2,cons(3,nil))),$product(-1,count(4,cons(3,nil)))) = 0 ) )
<=> ( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(count(4,cons(2,cons(3,nil))),$product(-1,count(4,cons(3,nil)))) = 0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ( $false
| ( $sum(count(4,cons(2,cons(3,nil))),$product(-1,count(4,cons(3,nil)))) = 0 ) )
<=> ( $sum(count(4,cons(2,cons(3,nil))),$product(-1,count(4,cons(3,nil)))) = 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ( -2 = 0 )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
$sum(2,-4) = -2,
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
$sum(2,$product(-1,4)) = $sum(2,-4),
inference(monotonicity,[status(thm)],[34]) ).
tff(73,plain,
$sum(2,$product(-1,4)) = -2,
inference(transitivity,[status(thm)],[72,71]) ).
tff(74,plain,
( ( $sum(2,$product(-1,4)) = 0 )
<=> ( -2 = 0 ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ( $sum(2,$product(-1,4)) = 0 )
<=> $false ),
inference(transitivity,[status(thm)],[74,70]) ).
tff(76,plain,
( ( ( $sum(2,$product(-1,4)) = 0 )
| ( $sum(count(4,cons(2,cons(3,nil))),$product(-1,count(4,cons(3,nil)))) = 0 ) )
<=> ( $false
| ( $sum(count(4,cons(2,cons(3,nil))),$product(-1,count(4,cons(3,nil)))) = 0 ) ) ),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
( ( ( $sum(2,$product(-1,4)) = 0 )
| ( $sum(count(4,cons(2,cons(3,nil))),$product(-1,count(4,cons(3,nil)))) = 0 ) )
<=> ( $sum(count(4,cons(2,cons(3,nil))),$product(-1,count(4,cons(3,nil)))) = 0 ) ),
inference(transitivity,[status(thm)],[76,69]) ).
tff(78,plain,
( ( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(2,$product(-1,4)) = 0 )
| ( $sum(count(4,cons(2,cons(3,nil))),$product(-1,count(4,cons(3,nil)))) = 0 ) )
<=> ( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(count(4,cons(2,cons(3,nil))),$product(-1,count(4,cons(3,nil)))) = 0 ) ) ),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
( ( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(2,$product(-1,4)) = 0 )
| ( $sum(count(4,cons(2,cons(3,nil))),$product(-1,count(4,cons(3,nil)))) = 0 ) )
<=> ( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(count(4,cons(2,cons(3,nil))),$product(-1,count(4,cons(3,nil)))) = 0 ) ) ),
inference(transitivity,[status(thm)],[78,68]) ).
tff(80,plain,
( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(2,$product(-1,4)) = 0 )
| ( $sum(count(4,cons(2,cons(3,nil))),$product(-1,count(4,cons(3,nil)))) = 0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(count(4,cons(2,cons(3,nil))),$product(-1,count(4,cons(3,nil)))) = 0 ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
$sum(count(4,cons(2,cons(3,nil))),$product(-1,count(4,cons(3,nil)))) = 0,
inference(unit_resolution,[status(thm)],[81,29]) ).
tff(83,plain,
( ( $sum(count(4,cons(2,cons(3,nil))),$product(-1,count(4,cons(3,nil)))) != 0 )
| $lesseq($sum(count(4,cons(2,cons(3,nil))),$product(-1,count(4,cons(3,nil)))),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(84,plain,
$lesseq($sum(count(4,cons(2,cons(3,nil))),$product(-1,count(4,cons(3,nil)))),0),
inference(unit_resolution,[status(thm)],[83,82]) ).
tff(85,plain,
( ( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(count(4,cons(3,nil)),$product(-1,count(4,nil))) = 0 ) )
<=> ( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(count(4,cons(3,nil)),$product(-1,count(4,nil))) = 0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
( ( $false
| ( $sum(count(4,cons(3,nil)),$product(-1,count(4,nil))) = 0 ) )
<=> ( $sum(count(4,cons(3,nil)),$product(-1,count(4,nil))) = 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ( -1 = 0 )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
$sum(3,-4) = -1,
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
$sum(3,$product(-1,4)) = $sum(3,-4),
inference(monotonicity,[status(thm)],[34]) ).
tff(90,plain,
$sum(3,$product(-1,4)) = -1,
inference(transitivity,[status(thm)],[89,88]) ).
tff(91,plain,
( ( $sum(3,$product(-1,4)) = 0 )
<=> ( -1 = 0 ) ),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
( ( $sum(3,$product(-1,4)) = 0 )
<=> $false ),
inference(transitivity,[status(thm)],[91,87]) ).
tff(93,plain,
( ( ( $sum(3,$product(-1,4)) = 0 )
| ( $sum(count(4,cons(3,nil)),$product(-1,count(4,nil))) = 0 ) )
<=> ( $false
| ( $sum(count(4,cons(3,nil)),$product(-1,count(4,nil))) = 0 ) ) ),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
( ( ( $sum(3,$product(-1,4)) = 0 )
| ( $sum(count(4,cons(3,nil)),$product(-1,count(4,nil))) = 0 ) )
<=> ( $sum(count(4,cons(3,nil)),$product(-1,count(4,nil))) = 0 ) ),
inference(transitivity,[status(thm)],[93,86]) ).
tff(95,plain,
( ( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(3,$product(-1,4)) = 0 )
| ( $sum(count(4,cons(3,nil)),$product(-1,count(4,nil))) = 0 ) )
<=> ( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(count(4,cons(3,nil)),$product(-1,count(4,nil))) = 0 ) ) ),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(3,$product(-1,4)) = 0 )
| ( $sum(count(4,cons(3,nil)),$product(-1,count(4,nil))) = 0 ) )
<=> ( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(count(4,cons(3,nil)),$product(-1,count(4,nil))) = 0 ) ) ),
inference(transitivity,[status(thm)],[95,85]) ).
tff(97,plain,
( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(3,$product(-1,4)) = 0 )
| ( $sum(count(4,cons(3,nil)),$product(-1,count(4,nil))) = 0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(98,plain,
( ~ ! [K: $int,H: $int,T: list] :
( ( $sum(H,$product(-1,K)) = 0 )
| ( $sum(count(K,cons(H,T)),$product(-1,count(K,T))) = 0 ) )
| ( $sum(count(4,cons(3,nil)),$product(-1,count(4,nil))) = 0 ) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
$sum(count(4,cons(3,nil)),$product(-1,count(4,nil))) = 0,
inference(unit_resolution,[status(thm)],[98,29]) ).
tff(100,plain,
( ( $sum(count(4,cons(3,nil)),$product(-1,count(4,nil))) != 0 )
| $lesseq($sum(count(4,cons(3,nil)),$product(-1,count(4,nil))),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(101,plain,
$lesseq($sum(count(4,cons(3,nil)),$product(-1,count(4,nil))),0),
inference(unit_resolution,[status(thm)],[100,99]) ).
tff(102,plain,
$false,
inference(theory_lemma,[status(thm)],[101,84,67,47,11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT080_1 : TPTP v8.1.0. Released v6.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 01:49:08 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------