TSTP Solution File: DAT091_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT091_1 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 14:36:41 EDT 2022
% Result : Theorem 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 35
% Syntax : Number of formulae : 83 ( 23 unt; 3 typ; 0 def)
% Number of atoms : 254 ( 238 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 267 ( 104 ~; 107 |; 0 &)
% ( 48 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number arithmetic : 727 ( 0 atm; 241 fun; 352 num; 134 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 273 ( 244 !; 0 ?; 273 :)
% Comments :
%------------------------------------------------------------------------------
tff(nil_type,type,
nil: list ).
tff(cons_type,type,
cons: ( $int * list ) > list ).
tff(count_type,type,
count: ( $int * list ) > $int ).
tff(1,plain,
^ [K: $int,L: list] :
refl(
( ( cons(K,L) != nil )
<=> ( cons(K,L) != nil ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [K: $int,L: list] : ( cons(K,L) != nil )
<=> ! [K: $int,L: list] : ( cons(K,L) != nil ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [K: $int,L: list] : ( cons(K,L) != nil )
<=> ! [K: $int,L: list] : ( cons(K,L) != nil ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [K: $int,L: list] : ( cons(K,L) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4) ).
tff(5,plain,
! [K: $int,L: list] : ( cons(K,L) != nil ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [K: $int,L: list] : ( cons(K,L) != nil ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [K: $int,L: list] : ( cons(K,L) != nil ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [K: $int,L: list] : ( cons(K,L) != nil )
| ( cons(-1,nil) != nil ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
cons(-1,nil) != nil,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,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)],[12]) ).
tff(14,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(15,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)],[14]) ).
tff(16,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(17,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(18,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(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,N: $int] :
( ( K = H )
| ( count(K,cons(H,T)) = count(K,T) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,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)],[19,17]) ).
tff(21,axiom,
! [K: $int,H: $int,T: list,N: $int] :
( ( K != H )
=> ( count(K,cons(H,T)) = count(K,T) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_3) ).
tff(22,plain,
! [K: $int,H: $int,T: list] :
( ( K = H )
| ( count(K,cons(H,T)) = count(K,T) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [K: $int,H: $int,T: list] :
( ( K = H )
| ( count(K,cons(H,T)) = count(K,T) ) ),
inference(modus_ponens,[status(thm)],[22,16]) ).
tff(24,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)],[23,15]) ).
tff(25,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)],[24,13]) ).
tff(26,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)],[25]) ).
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)],[26,11]) ).
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 ) )
| ( $sum(count(0,nil),$product(-1,count(0,cons(-1,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 ) )
| ( $sum(count(0,nil),$product(-1,count(0,cons(-1,nil)))) = 0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ( $false
| ( $sum(count(0,nil),$product(-1,count(0,cons(-1,nil)))) = 0 ) )
<=> ( $sum(count(0,nil),$product(-1,count(0,cons(-1,nil)))) = 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( $sum($product(-1,count(0,nil)),count(0,cons(-1,nil))) = 0 )
<=> ( $sum(count(0,nil),$product(-1,count(0,cons(-1,nil)))) = 0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
$sum(count(0,cons(-1,nil)),$product(-1,count(0,nil))) = $sum($product(-1,count(0,nil)),count(0,cons(-1,nil))),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ( $sum(count(0,cons(-1,nil)),$product(-1,count(0,nil))) = 0 )
<=> ( $sum($product(-1,count(0,nil)),count(0,cons(-1,nil))) = 0 ) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ( $sum(count(0,cons(-1,nil)),$product(-1,count(0,nil))) = 0 )
<=> ( $sum(count(0,nil),$product(-1,count(0,cons(-1,nil)))) = 0 ) ),
inference(transitivity,[status(thm)],[32,30]) ).
tff(34,plain,
( ( -1 = 0 )
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
$sum(-1,0) = -1,
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
$product(-1,0) = 0,
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
$sum(-1,$product(-1,0)) = $sum(-1,0),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
$sum(-1,$product(-1,0)) = -1,
inference(transitivity,[status(thm)],[37,35]) ).
tff(39,plain,
( ( $sum(-1,$product(-1,0)) = 0 )
<=> ( -1 = 0 ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( $sum(-1,$product(-1,0)) = 0 )
<=> $false ),
inference(transitivity,[status(thm)],[39,34]) ).
tff(41,plain,
( ( ( $sum(-1,$product(-1,0)) = 0 )
| ( $sum(count(0,cons(-1,nil)),$product(-1,count(0,nil))) = 0 ) )
<=> ( $false
| ( $sum(count(0,nil),$product(-1,count(0,cons(-1,nil)))) = 0 ) ) ),
inference(monotonicity,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ( $sum(-1,$product(-1,0)) = 0 )
| ( $sum(count(0,cons(-1,nil)),$product(-1,count(0,nil))) = 0 ) )
<=> ( $sum(count(0,nil),$product(-1,count(0,cons(-1,nil)))) = 0 ) ),
inference(transitivity,[status(thm)],[41,29]) ).
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(-1,0)) = 0 )
| ( $sum(count(0,cons(-1,nil)),$product(-1,count(0,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 ) )
| ( $sum(count(0,nil),$product(-1,count(0,cons(-1,nil)))) = 0 ) ) ),
inference(monotonicity,[status(thm)],[42]) ).
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 ) )
| ( $sum(-1,$product(-1,0)) = 0 )
| ( $sum(count(0,cons(-1,nil)),$product(-1,count(0,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 ) )
| ( $sum(count(0,nil),$product(-1,count(0,cons(-1,nil)))) = 0 ) ) ),
inference(transitivity,[status(thm)],[43,28]) ).
tff(45,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(-1,0)) = 0 )
| ( $sum(count(0,cons(-1,nil)),$product(-1,count(0,nil))) = 0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,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 ) )
| ( $sum(count(0,nil),$product(-1,count(0,cons(-1,nil)))) = 0 ) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
$sum(count(0,nil),$product(-1,count(0,cons(-1,nil)))) = 0,
inference(unit_resolution,[status(thm)],[46,27]) ).
tff(48,plain,
^ [L1: list,L2: list,N: $int] :
rewrite(
( ( ( L1 = L2 )
| ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) )
<=> ( ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 )
| ( L1 = L2 ) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [L1: list,L2: list,N: $int] :
( ( L1 = L2 )
| ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) )
<=> ! [L1: list,L2: list,N: $int] :
( ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 )
| ( L1 = L2 ) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
^ [L1: list,L2: list,N: $int] :
refl(
( ( ( L1 = L2 )
| ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) )
<=> ( ( L1 = L2 )
| ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [L1: list,L2: list,N: $int] :
( ( L1 = L2 )
| ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) )
<=> ! [L1: list,L2: list,N: $int] :
( ( L1 = L2 )
| ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [L1: list,L2: list,N: $int] :
( ( L1 = L2 )
| ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) )
<=> ! [L1: list,L2: list,N: $int] :
( ( L1 = L2 )
| ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) ) ),
inference(pull_quant,[status(thm)],]) ).
tff(53,plain,
^ [L1: list,L2: list] :
pull_quant(
( ( ( L1 = L2 )
| ! [N: $int] : ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) )
<=> ! [N: $int] :
( ( L1 = L2 )
| ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) )
<=> ! [L1: list,L2: list,N: $int] :
( ( L1 = L2 )
| ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) )
<=> ! [L1: list,L2: list,N: $int] :
( ( L1 = L2 )
| ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) ) ),
inference(transitivity,[status(thm)],[54,52]) ).
tff(56,plain,
( ! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) )
<=> ! [L1: list,L2: list,N: $int] :
( ( L1 = L2 )
| ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) ) ),
inference(transitivity,[status(thm)],[55,51]) ).
tff(57,plain,
^ [L1: list,L2: list] :
rewrite(
( ( ( L1 = L2 )
| ! [N: $int] : ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) )
<=> ( ( L1 = L2 )
| ! [N: $int] : ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) )
<=> ! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) )
<=> ! [L1: list,L2: list,N: $int] :
( ( L1 = L2 )
| ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) ) ),
inference(transitivity,[status(thm)],[58,56]) ).
tff(60,plain,
^ [L1: list,L2: list] :
rewrite(
( ( ( L1 = L2 )
| ! [N: $int] : ( $sum(count(N,L1),$product(-1,count(N,L2))) != 0 ) )
<=> ( ( L1 = L2 )
| ! [N: $int] : ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) ) )),
inference(bind,[status(th)],]) ).
tff(61,plain,
( ! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( $sum(count(N,L1),$product(-1,count(N,L2))) != 0 ) )
<=> ! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
^ [L1: list,L2: list] :
rewrite(
( ( ( L1 = L2 )
| ! [N: $int] : ( count(N,L1) != count(N,L2) ) )
<=> ( ( L1 = L2 )
| ! [N: $int] : ( $sum(count(N,L1),$product(-1,count(N,L2))) != 0 ) ) )),
inference(bind,[status(th)],]) ).
tff(63,plain,
( ! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( count(N,L1) != count(N,L2) ) )
<=> ! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( $sum(count(N,L1),$product(-1,count(N,L2))) != 0 ) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( count(N,L1) != count(N,L2) ) )
<=> ! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( count(N,L1) != count(N,L2) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ~ ~ ! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( count(N,L1) != count(N,L2) ) )
<=> ! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( count(N,L1) != count(N,L2) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ~ ! [L1: list,L2: list] :
( ( L1 != L2 )
=> ! [N: $int] : ( count(N,L1) != count(N,L2) ) )
<=> ~ ! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( count(N,L1) != count(N,L2) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ~ ~ ! [L1: list,L2: list] :
( ( L1 != L2 )
=> ! [N: $int] : ( count(N,L1) != count(N,L2) ) )
<=> ~ ~ ! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( count(N,L1) != count(N,L2) ) ) ),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
( ~ ~ ! [L1: list,L2: list] :
( ( L1 != L2 )
=> ! [N: $int] : ( count(N,L1) != count(N,L2) ) )
<=> ! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( count(N,L1) != count(N,L2) ) ) ),
inference(transitivity,[status(thm)],[67,65]) ).
tff(69,axiom,
~ ~ ! [L1: list,L2: list] :
( ( L1 != L2 )
=> ! [N: $int] : ( count(N,L1) != count(N,L2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).
tff(70,plain,
! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( count(N,L1) != count(N,L2) ) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( count(N,L1) != count(N,L2) ) ),
inference(modus_ponens,[status(thm)],[70,64]) ).
tff(72,plain,
! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( $sum(count(N,L1),$product(-1,count(N,L2))) != 0 ) ),
inference(modus_ponens,[status(thm)],[71,63]) ).
tff(73,plain,
! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) ),
inference(modus_ponens,[status(thm)],[72,61]) ).
tff(74,plain,
! [L1: list,L2: list] :
( ( L1 = L2 )
| ! [N: $int] : ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [L1: list,L2: list,N: $int] :
( ( L1 = L2 )
| ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 ) ),
inference(modus_ponens,[status(thm)],[74,59]) ).
tff(76,plain,
! [L1: list,L2: list,N: $int] :
( ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 )
| ( L1 = L2 ) ),
inference(modus_ponens,[status(thm)],[75,49]) ).
tff(77,plain,
( ( ~ ! [L1: list,L2: list,N: $int] :
( ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 )
| ( L1 = L2 ) )
| ( $sum(count(0,nil),$product(-1,count(0,cons(-1,nil)))) != 0 )
| ( cons(-1,nil) = nil ) )
<=> ( ~ ! [L1: list,L2: list,N: $int] :
( ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 )
| ( L1 = L2 ) )
| ( $sum(count(0,nil),$product(-1,count(0,cons(-1,nil)))) != 0 )
| ( cons(-1,nil) = nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
( ~ ! [L1: list,L2: list,N: $int] :
( ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 )
| ( L1 = L2 ) )
| ( $sum(count(0,nil),$product(-1,count(0,cons(-1,nil)))) != 0 )
| ( cons(-1,nil) = nil ) ),
inference(quant_inst,[status(thm)],]) ).
tff(79,plain,
( ~ ! [L1: list,L2: list,N: $int] :
( ( $sum(count(N,L2),$product(-1,count(N,L1))) != 0 )
| ( L1 = L2 ) )
| ( $sum(count(0,nil),$product(-1,count(0,cons(-1,nil)))) != 0 )
| ( cons(-1,nil) = nil ) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
$false,
inference(unit_resolution,[status(thm)],[79,76,47,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT091_1 : TPTP v8.1.0. Released v6.1.0.
% 0.10/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Aug 31 01:46:19 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.11/0.36 % SZS status Theorem
% 0.11/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------